Finite Group Databasebeta

← #35570360

Subgroups — #35570360

Order 21248.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910620C211yesmaximal, characteristic, complemented
2#24910620C211yesmaximal, characteristic, complemented
3#24910611C211yesmaximal, characteristic, complemented
4#24910587C211yesmaximal, characteristic, complemented
5#24910587C211yesmaximal, characteristic, complemented
6#24910528C211yesmaximal, characteristic, complemented
7#24910515C211yesmaximal, characteristic, complemented
8#24910515C211yesmaximal, characteristic, complemented
9#24910505C211yesmaximal, characteristic, complemented
10#24910505C211yesmaximal, characteristic, complemented
11#24910459C211yesmaximal, characteristic, complemented
12#24910459C211yesmaximal, characteristic, complemented
13#24910447C211yesmaximal, characteristic, complemented
14#24910447C211yesmaximal, characteristic, complemented
15#24910447C211yesmaximal, characteristic, complemented
16#24910257C211yesmaximal, characteristic, complemented
17#24910257C211yesmaximal, characteristic, complemented
18#24910242C211yesmaximal, characteristic, complemented
19#24910242C211yesmaximal, characteristic, complemented
20#24910189C211yesmaximal, characteristic, complemented
21#24910168C211yesmaximal, characteristic, complemented
22#24910168C211yesmaximal, characteristic, complemented
23#24910158C211yesmaximal, characteristic, complemented
24#24910158C211yesmaximal, characteristic, complemented
25#24910124C211yesmaximal, characteristic, complemented
26#24910124C211yesmaximal, characteristic, complemented
27#24910124C211yesmaximal, characteristic, complemented
28#123×Dic83C211yesmaximal, characteristic, complemented
29#121×Dic83C211yesmaximal, characteristic, complemented
30#121×Dic83C211yesmaximal, characteristic, complemented
31C2×#560×C83C211yesmaximal, characteristic
32C2×D4×Dic83C2211yescharacteristic
33C2×D4×Dic83C2211yescharacteristic
34C2×D4×Dic83C2211yescharacteristic
35C2×D4×Dic83C2211yescharacteristic
36C2×D4×Dic83C2211yescharacteristic
37C2×D4×Dic83C2211yescharacteristic
38C2×D4×Dic83C2211yescharacteristic
39C2×D4×Dic83C2211yescharacteristic
40C2×D4×Dic83C2211yescharacteristic
41C2×D4×Dic83C2211yescharacteristic, complemented
42C2×D4×Dic83C2211yescharacteristic, complemented
43C2×D4×Dic83C2211yescharacteristic, complemented
44C2×#14581751C2211yescharacteristic, complemented
45C2×#14581751C2211yescharacteristic, complemented
46C22×C22⋊Dic83C2211yescharacteristic
47C22×C22⋊Dic83C2211yescharacteristic
48C22×C22⋊Dic83C2211yescharacteristic
49C22×C4×Dic83C2211yescharacteristic, complemented
50#19127604C2211yescharacteristic
51#19127604C2211yescharacteristic
52#19127604C2211yescharacteristic
53#19127604C2211yescharacteristic
54#19127604C2211yescharacteristic
55#19127604C2211yescharacteristic
56#19127604C2211yescharacteristic
57#19127604C2211yescharacteristic
58#19127604C2211yescharacteristic
59#19127604C2211yescharacteristic, complemented
60#19127604C2211yescharacteristic, complemented
61#19127604C2211yescharacteristic, complemented
62#19127600C2211yescharacteristic, complemented
63#19127600C2211yescharacteristic, complemented
64#19127600C2211yescharacteristic, complemented
65#19127600C2211yescharacteristic, complemented
66#19127600C2211yescharacteristic, complemented
67#19127600C2211yescharacteristic, complemented
68#19127594C2211yescharacteristic
69#19127594C2211yescharacteristic
70#19127594C2211yescharacteristic
71#19127594C2211yescharacteristic
72#19127594C2211yescharacteristic
73#19127594C2211yescharacteristic
74#19127594C2211yescharacteristic
75#19127594C2211yescharacteristic
76#19127594C2211yescharacteristic
77#19127594C2211yescharacteristic
78#19127594C2211yescharacteristic
79#19127594C2211yescharacteristic
80#19127594C2211yescharacteristic
81#19127594C2211yescharacteristic
82#19127594C2211yescharacteristic
83#19127594C2211yescharacteristic
84#19127594C2211yescharacteristic
85#19127594C2211yescharacteristic
86#19127594C2211yescharacteristic, complemented
87#19127594C2211yescharacteristic, complemented
88#19127594C2211yescharacteristic, complemented
89#19127594C2211yescharacteristic, complemented
90#19127594C2211yescharacteristic, complemented
91#19127594C2211yescharacteristic, complemented
92#19127587C2211yescharacteristic, complemented
93#19127587C2211yescharacteristic, complemented
94#19127587C2211yescharacteristic, complemented
95#19127587C2211yescharacteristic, complemented
96#19127587C2211yescharacteristic, complemented
97#19127587C2211yescharacteristic, complemented
98#19127587C2211yescharacteristic, complemented
99#19127587C2211yescharacteristic, complemented
100#19127587C2211yescharacteristic, complemented
101#19127587C2211yescharacteristic, complemented
102#19127587C2211yescharacteristic, complemented
103#19127587C2211yescharacteristic, complemented
104#19127581C2211yescharacteristic
105#19127581C2211yescharacteristic
106#19127581C2211yescharacteristic
107#19127581C2211yescharacteristic
108#19127581C2211yescharacteristic
109#19127581C2211yescharacteristic
110#19127581C2211yescharacteristic
111#19127581C2211yescharacteristic
112#19127581C2211yescharacteristic
113#19127581C2211yescharacteristic
114#19127581C2211yescharacteristic
115#19127581C2211yescharacteristic
116#19127581C2211yescharacteristic
117#19127581C2211yescharacteristic
118#19127581C2211yescharacteristic
119#19127581C2211yescharacteristic
120#19127581C2211yescharacteristic
121#19127581C2211yescharacteristic
122#19127581C2211yescharacteristic, complemented
123#19127581C2211yescharacteristic, complemented
124#19127581C2211yescharacteristic, complemented
125#19127581C2211yescharacteristic, complemented
126#19127581C2211yescharacteristic, complemented
127#19127581C2211yescharacteristic, complemented
128#19127576C2211yescharacteristic
129#19127576C2211yescharacteristic
130#19127576C2211yescharacteristic
131#19127576C2211yescharacteristic
132#19127576C2211yescharacteristic
133#19127576C2211yescharacteristic
134#19127576C2211yescharacteristic
135#19127576C2211yescharacteristic
136#19127576C2211yescharacteristic
137#19127576C2211yescharacteristic, complemented
138#19127576C2211yescharacteristic, complemented
139#19127576C2211yescharacteristic, complemented
140#19127567C2211yescharacteristic, complemented
141#19127564C2211yescharacteristic, complemented
142#19127561C2211yescharacteristic, complemented
143#19127561C2211yescharacteristic, complemented
144#19127561C2211yescharacteristic, complemented
145#19127561C2211yescharacteristic, complemented
146#19127557C2211yescharacteristic
147C4⋊C4×Dic83C2211yescharacteristic, complemented
148C4⋊C4×Dic83C2211yescharacteristic, complemented
149C4⋊C4×Dic83C2211yescharacteristic, complemented
150C4⋊C4×Dic83C2211yescharacteristic, complemented
151C4⋊C4×Dic83C2211yescharacteristic, complemented
152C4⋊C4×Dic83C2211yescharacteristic, complemented
153C4×C4⋊Dic83C2211yescharacteristic, complemented
154C4×C4⋊Dic83C2211yescharacteristic, complemented
155C22⋊C4×Dic83C2211yescharacteristic
156C22⋊C4×Dic83C2211yescharacteristic
157C22⋊C4×Dic83C2211yescharacteristic
158C22⋊C4×Dic83C2211yescharacteristic
159C22⋊C4×Dic83C2211yescharacteristic
160C22⋊C4×Dic83C2211yescharacteristic
161C22⋊C4×Dic83C2211yescharacteristic
162C22⋊C4×Dic83C2211yescharacteristic
163C22⋊C4×Dic83C2211yescharacteristic
164C22⋊C4×Dic83C2211yescharacteristic, complemented
165C22⋊C4×Dic83C2211yescharacteristic, complemented
166C22⋊C4×Dic83C2211yescharacteristic, complemented
167C4×C22⋊Dic83C2211yescharacteristic, complemented
168C4×C22⋊Dic83C2211yescharacteristic, complemented
169#19127547C2211yescharacteristic, complemented
170C2×C83⋊#95C2211yescharacteristic, complemented
171C2×C83⋊#95C2211yescharacteristic, complemented
172#560×C83C4116yescomplemented
173C2×#127×C83C2211yescharacteristic
174C2×#126×C83C2211yescharacteristic
175C2×#126×C83C2211yescharacteristic
176C2×#123×C83C2211yescharacteristic
177C2×#123×C83C2211yescharacteristic
178C2×#123×C83C2211yescharacteristic
179C2×#121×C83C2211yescharacteristic
180C2×#121×C83C2211yescharacteristic
181C2×#121×C83C2211yescharacteristic
182C2×#121×C83C2211yescharacteristic
183C2×#121×C83C2211yescharacteristic
184C2×#121×C83C2211yescharacteristic
185C2×#120×C83C2211yescharacteristic
186C2×#120×C83C2211yescharacteristic
187C2×#120×C83C2211yescharacteristic
188C23×Dic83C2311yescharacteristic
189C23×Dic83C2311yescharacteristic
190C23×Dic83C2311yescharacteristic
191C23×Dic83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197C23×Dic83C2311yescharacteristic
198C23×Dic83C2311yescharacteristic
199C23×Dic83C2311yescharacteristic
200D4×Dic83—42no—
201D4×Dic83—42no—
202D4×Dic83—42no—
203D4×Dic83—42no—
204D4×Dic83—42no—
205D4×Dic83—42no—
206D4×Dic83—42no—
207D4×Dic83—42no—
208D4×Dic83—42no—
209D4×Dic83—42no—
210D4×Dic83—42no—
211D4×Dic83—42no—
212#14581751—42no—
213#14581751—42no—
214C2×C4⋊Dic83C2311yescharacteristic
215C2×C4⋊Dic83C2311yescharacteristic
216C2×C4⋊Dic83C2311yescharacteristic
217C2×C4⋊Dic83C2311yescharacteristic
218C2×C4⋊Dic83C2311yescharacteristic
219C2×C4⋊Dic83C2311yescharacteristic
220C2×C4⋊Dic83C2311yescharacteristic
221C2×C4⋊Dic83C2311yescharacteristic
222C2×C4⋊Dic83C2311yescharacteristic
223C2×C4⋊Dic83C2311yescharacteristic
224C2×C4⋊Dic83C2311yescharacteristic
225C2×C4⋊Dic83C2311yescharacteristic
226C2×C4⋊Dic83C2311yescharacteristic
227C2×C4⋊Dic83C2311yescharacteristic
228C2×C4⋊Dic83C2311yescharacteristic
229C2×C4⋊Dic83C2311yescharacteristic
230C2×C4⋊Dic83C2311yescharacteristic
231C2×C4⋊Dic83C2311yescharacteristic
232C2×C22⋊Dic83—42no—
233C2×C22⋊Dic83—42no—
234C2×C22⋊Dic83—42no—
235C2×C22⋊Dic83C2311yescharacteristic
236C2×C22⋊Dic83C2311yescharacteristic
237C2×C22⋊Dic83C2311yescharacteristic
238C2×C22⋊Dic83C2311yescharacteristic
239C2×C22⋊Dic83C2311yescharacteristic
240C2×C22⋊Dic83C2311yescharacteristic
241C2×C22⋊Dic83C2311yescharacteristic
242C2×C22⋊Dic83C2311yescharacteristic
243C2×C22⋊Dic83C2311yescharacteristic
244C2×C22⋊Dic83C2311yescharacteristic
245C2×C22⋊Dic83C2311yescharacteristic
246C2×C22⋊Dic83C2311yescharacteristic
247C2×C22⋊Dic83C2311yescharacteristic
248C2×C22⋊Dic83C2311yescharacteristic
249C2×C22⋊Dic83C2311yescharacteristic
250C2×C22⋊Dic83C2311yescharacteristic
251C2×C22⋊Dic83C2311yescharacteristic
252C2×C22⋊Dic83C2311yescharacteristic
253C2×C22⋊Dic83C2311yescharacteristic
254C2×C22⋊Dic83C2311yescharacteristic
255C2×C22⋊Dic83C2311yescharacteristic
256C2×C22⋊Dic83C2311yescharacteristic
257C2×C22⋊Dic83C2311yescharacteristic
258C2×C22⋊Dic83C2311yescharacteristic
259C2×C22⋊Dic83C2311yescharacteristic
260C2×C22⋊Dic83C2311yescharacteristic
261C2×C22⋊Dic83C2311yescharacteristic
262C2×C22⋊Dic83C2311yescharacteristic
263C2×C22⋊Dic83C2311yescharacteristic
264C2×C22⋊Dic83C2311yescharacteristic
265C2×C22⋊Dic83C2311yescharacteristic
266C2×C22⋊Dic83C2311yescharacteristic
267C2×C22⋊Dic83C2311yescharacteristic
268C2×C22⋊Dic83C2311yescharacteristic
269C2×C22⋊Dic83C2311yescharacteristic
270C2×C22⋊Dic83C2311yescharacteristic
271C2×C4×Dic83—42no—
272C2×C4×Dic83C2311yescharacteristic
273C2×C4×Dic83C2311yescharacteristic
274C2×C4×Dic83C2311yescharacteristic
275C2×C4×Dic83C2311yescharacteristic
276C2×C4×Dic83C2311yescharacteristic
277C2×C4×Dic83C2311yescharacteristic
278C2×C4×Dic83C2311yescharacteristic
279C2×C4×Dic83C2311yescharacteristic
280C2×C4×Dic83C2311yescharacteristic
281C2×C4×Dic83C2311yescharacteristic
282C2×C4×Dic83C2311yescharacteristic
283C2×C4×Dic83C2311yescharacteristic
284C2×C4×Dic83C2311yescharacteristic
285C2×C4×Dic83C2311yescharacteristic
286C2×C4×Dic83C2311yescharacteristic
287C2×C4×Dic83C2311yescharacteristic
288C2×C4×Dic83C2311yescharacteristic
289C2×C4×Dic83C2311yescharacteristic
290C83⋊#95C2311yescharacteristic
291C83⋊#95C2311yescharacteristic
292C83⋊#95C2311yescharacteristic
293C83⋊#95C2311yescharacteristic
294C83⋊#95C2311yescharacteristic
295C83⋊#95C2311yescharacteristic
296C83⋊#95C2311yescharacteristic
297C83⋊#95C2311yescharacteristic
298C83⋊#95C2311yescharacteristic
299C83⋊#95C2311yescharacteristic
300C83⋊#95C2311yescharacteristic
301C83⋊#95C2311yescharacteristic
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C25×C83C2311yescharacteristic
327C22×D4×C83C2311yescharacteristic
328C22×D4×C83C2311yescharacteristic
329C22×D4×C83C2311yescharacteristic
330C22×D4×C83C2311yescharacteristic
331C22×D4×C83C2311yescharacteristic
332C22×D4×C83C2311yescharacteristic
333C22×D4×C83C2311yescharacteristic
334C22×D4×C83C2311yescharacteristic
335C22×D4×C83C2311yescharacteristic
336C22×D4×C83C2311yescharacteristic
337C22×D4×C83C2311yescharacteristic
338C22×D4×C83C2311yescharacteristic
339C23×C4×C83C2311yescharacteristic
340C23×C4×C83C2311yescharacteristic
341C23×C4×C83C2311yescharacteristic
342#127×C83C2×C418yescomplemented
343#126×C83C2×C418yescomplemented
344#126×C83C2×C418yescomplemented
345#123×C83C2×C418yescomplemented
346#123×C83C2×C418yescomplemented
347#123×C83C2×C418yescomplemented
348#121×C83C2×C418yescomplemented
349#121×C83C2×C418yescomplemented
350#121×C83C2×C418yescomplemented
351#121×C83C2×C418yescomplemented
352#121×C83C2×C418yescomplemented
353#121×C83C2×C418yescomplemented
354#120×C83C2×C418yescomplemented
355#120×C83C2×C418yescomplemented
356#120×C83C2×C418yescomplemented
357C2×C4⋊C4×C83C2311yescharacteristic
358C2×C4⋊C4×C83C2311yescharacteristic
359C2×C4⋊C4×C83C2311yescharacteristic
360C2×C4⋊C4×C83C2311yescharacteristic
361C2×C4⋊C4×C83C2311yescharacteristic
362C2×C4⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C22⋊C4×C83C2311yescharacteristic
365C2×C22⋊C4×C83C2311yescharacteristic
366C2×C22⋊C4×C83C2311yescharacteristic
367C2×C22⋊C4×C83C2311yescharacteristic
368C2×C22⋊C4×C83C2311yescharacteristic
369C2×C22⋊C4×C83C2311yescharacteristic
370C2×C22⋊C4×C83C2311yescharacteristic
371C2×C22⋊C4×C83C2311yescharacteristic
372C2×C22⋊C4×C83C2311yescharacteristic
373C2×C22⋊C4×C83C2311yescharacteristic
374C2×C22⋊C4×C83C2311yescharacteristic
375C2×C42×C83C2311yescharacteristic
376C22×Dic83—22no—
377C22×Dic83—22no—
378C22×Dic83—22no—
379C22×Dic83—22no—
380C22×Dic83—22no—
381C22×Dic83—22no—
382C22×Dic83—22no—
383C22×Dic83—22no—
384C22×Dic83—41no—
385C22×Dic83—41no—
386C22×Dic83—41no—
387C22×Dic83—41no—
388C22×Dic83—41no—
389C22×Dic83—41no—
390C22×Dic83—41no—
391C22×Dic83—41no—
392C22×Dic83—41no—
393C22×Dic83—41no—
394C22×Dic83—41no—
395C22×Dic83—41no—
396C22×Dic83—41no—
397C22×Dic83—41no—
398C22×Dic83—41no—
399C22×Dic83—41no—
400C22×Dic83—41no—
401C22×Dic83—41no—
402C22×Dic83—41no—
403C22×Dic83—41no—
404C22×Dic83—41no—
405C22×Dic83—41no—
406C22×Dic83—41no—
407C22×Dic83—41no—
408C22×Dic83—41no—
409C22×Dic83—41no—
410C22×Dic83—41no—
411C22×Dic83—41no—
412C22×Dic83C2411yescharacteristic
413C22×Dic83C2411yescharacteristic
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C22×Dic83C2411yescharacteristic
418C22×Dic83C2411yescharacteristic
419C22×Dic83C2411yescharacteristic
420C22×Dic83C2411yescharacteristic
421C22×Dic83C2411yescharacteristic
422C22×Dic83C2411yescharacteristic
423C22×Dic83C2411yescharacteristic
424C22×Dic83C2411yescharacteristic
425C22×Dic83C2411yescharacteristic
426C22×Dic83C2411yescharacteristic
427C22×Dic83C2411yescharacteristic
428C4⋊Dic83—22no—
429C4⋊Dic83—22no—
430C4⋊Dic83—22no—
431C4⋊Dic83—22no—
432C4⋊Dic83—41no—
433C4⋊Dic83—41no—
434C4⋊Dic83—41no—
435C4⋊Dic83—41no—
436C4⋊Dic83—41no—
437C4⋊Dic83—41no—
438C4⋊Dic83—41no—
439C4⋊Dic83—41no—
440C4⋊Dic83—41no—
441C4⋊Dic83—41no—
442C4⋊Dic83—41no—
443C4⋊Dic83—41no—
444C4⋊Dic83—41no—
445C4⋊Dic83—41no—
446C22⋊Dic83—22no—
447C22⋊Dic83—22no—
448C22⋊Dic83—22no—
449C22⋊Dic83—22no—
450C22⋊Dic83—22no—
451C22⋊Dic83—22no—
452C22⋊Dic83—22no—
453C22⋊Dic83—22no—
454C22⋊Dic83—22no—
455C22⋊Dic83—22no—
456C22⋊Dic83—41no—
457C22⋊Dic83—41no—
458C22⋊Dic83—41no—
459C22⋊Dic83—41no—
460C22⋊Dic83—41no—
461C22⋊Dic83—41no—
462C22⋊Dic83—41no—
463C22⋊Dic83—41no—
464C22⋊Dic83—41no—
465C22⋊Dic83—41no—
466C22⋊Dic83—41no—
467C22⋊Dic83—41no—
468C22⋊Dic83—41no—
469C22⋊Dic83—41no—
470C22⋊Dic83—41no—
471C22⋊Dic83—41no—
472C22⋊Dic83—41no—
473C22⋊Dic83—41no—
474C22⋊Dic83—41no—
475C22⋊Dic83—41no—
476C22⋊Dic83—41no—
477C22⋊Dic83—41no—
478C22⋊Dic83—41no—
479C22⋊Dic83—41no—
480C22⋊Dic83—41no—
481C22⋊Dic83—41no—
482C4×Dic83—22no—
483C4×Dic83—22no—
484C4×Dic83—22no—
485C4×Dic83—22no—
486C4×Dic83—22no—
487C4×Dic83—41no—
488C4×Dic83—41no—
489C4×Dic83—41no—
490C4×Dic83—41no—
491C4×Dic83—41no—
492C4×Dic83—41no—
493C4×Dic83—41no—
494C4×Dic83—41no—
495C4×Dic83—41no—
496C4×Dic83—41no—
497C4×Dic83—41no—
498C4×Dic83—41no—
499C4×Dic83—41no—
500C24×C83—41no—
501C24×C83—41no—
502C24×C83—41no—
503C24×C83—41no—
504C24×C83—41no—
505C24×C83—41no—
506C24×C83C22×C414yes—
507C24×C83C2411yescharacteristic
508C24×C83C2411yescharacteristic
509C24×C83C2411yescharacteristic
510C24×C83C2411yescharacteristic
511C24×C83C2411yescharacteristic
512C24×C83C2411yescharacteristic
513C2×D4×C83—41no—
514C2×D4×C83—41no—
515C2×D4×C83—41no—
516C2×D4×C83—41no—
517C2×D4×C83—41no—
518C2×D4×C83—41no—
519C2×D4×C83—41no—
520C2×D4×C83—41no—
521C2×D4×C83—41no—
522C2×D4×C83—41no—
523C2×D4×C83—41no—
524C2×D4×C83—41no—
525C2×D4×C83—41no—
526C2×D4×C83—41no—
527C2×D4×C83—41no—
528C2×D4×C83—41no—
529C2×D4×C83—41no—
530C2×D4×C83—41no—
531C2×D4×C83—41no—
532C2×D4×C83—41no—
533C2×D4×C83—41no—
534C2×D4×C83—41no—
535C2×D4×C83—41no—
536C2×D4×C83—41no—
537C2×D4×C83C22×C414yes—
538C2×D4×C83C22×C414yes—
539C2×D4×C83C22×C414yes—
540C2×D4×C83C22×C414yes—
541C2×D4×C83C22×C414yes—
542C2×D4×C83C22×C414yes—
543C2×D4×C83C22×C414yes—
544C2×D4×C83C22×C414yes—
545C2×D4×C83C22×C414yes—
546C2×D4×C83C22×C414yes—
547C2×D4×C83C22×C414yes—
548C2×D4×C83C22×C414yes—
549C22×C4×C83—41no—
550C22×C4×C83—41no—
551C22×C4×C83—41no—
552C22×C4×C83—41no—
553C22×C4×C83—41no—
554C22×C4×C83—41no—
555C22×C4×C83C22×C414yes—
556C22×C4×C83C22×C414yes—
557C22×C4×C83C22×C414yes—
558C22×C4×C83C2411yescharacteristic
559C22×C4×C83C2411yescharacteristic
560C22×C4×C83C2411yescharacteristic
561C22×C4×C83C2411yescharacteristic
562C22×C4×C83C2411yescharacteristic
563C22×C4×C83C2411yescharacteristic
564C22×C4×C83C2411yescharacteristic
565C22×C4×C83C2411yescharacteristic
566C22×C4×C83C2411yescharacteristic
567C4⋊C4×C83C22×C414yes—
568C4⋊C4×C83C22×C414yes—
569C4⋊C4×C83C22×C414yes—
570C4⋊C4×C83C22×C414yes—
571C4⋊C4×C83C22×C414yes—
572C4⋊C4×C83C22×C414yes—
573C22⋊C4×C83C22×C414yes—
574C22⋊C4×C83C22×C414yes—
575C22⋊C4×C83C22×C414yes—
576C22⋊C4×C83C22×C414yes—
577C22⋊C4×C83C22×C414yes—
578C22⋊C4×C83C22×C414yes—
579C22⋊C4×C83C22×C414yes—
580C22⋊C4×C83C22×C414yes—
581C22⋊C4×C83C22×C414yes—
582C22⋊C4×C83C22×C414yes—
583C22⋊C4×C83C22×C414yes—
584C22⋊C4×C83C22×C414yes—
585C42×C83C22×C414yes—
586C23×C83—21no—
587C23×C83—21no—
588C23×C83—21no—
589C23×C83—21no—
590C23×C83—21no—
591C23×C83—21no—
592C23×C83—21no—
593C23×C83—21no—
594C23×C83—21no—
595C23×C83—21no—
596C23×C83—21no—
597C23×C83—21no—
598C23×C83—21no—
599C23×C83—21no—
600C23×C83—21no—
601C23×C83—21no—
602C23×C83—21no—
603C23×C83—21no—
604C23×C83—21no—
605C23×C83—21no—
606C23×C83—21no—
607C23×C83—21no—
608C23×C83—21no—
609C23×C83—21no—
610C23×C83—21no—
611C23×C83—21no—
612C23×C83—21no—
613C23×C83—21no—
614C23×C83—21no—
615C23×C83—21no—
616C23×C83—21no—
617C23×C83—21no—
618C23×C83—21no—
619C23×C83—21no—
620C23×C83—21no—
621C23×C83—21no—
622C23×C83—44no—
623C23×C83—44no—
624C23×C83—44no—
625C23×C83—82no—
626C23×C83—82no—
627C23×C83—82no—
628C23×C83—82no—
629C23×C83C23×C412yes—
630C23×C83C23×C412yes—
631C23×C83C23×C412yes—
632C23×C83C23×C412yes—
633C23×C83C23×C412yes—
634C23×C83C23×C412yes—
635C23×C83C2511yescharacteristic
636D4×C83—44no—
637D4×C83—44no—
638D4×C83—44no—
639D4×C83—44no—
640D4×C83—44no—
641D4×C83—44no—
642D4×C83—44no—
643D4×C83—44no—
644D4×C83—44no—
645D4×C83—44no—
646D4×C83—44no—
647D4×C83—44no—
648C2×C4×C83—21no—
649C2×C4×C83—21no—
650C2×C4×C83—21no—
651C2×C4×C83—21no—
652C2×C4×C83—21no—
653C2×C4×C83—21no—
654C2×C4×C83—21no—
655C2×C4×C83—21no—
656C2×C4×C83—21no—
657C2×C4×C83—21no—
658C2×C4×C83—21no—
659C2×C4×C83—21no—
660C2×C4×C83—21no—
661C2×C4×C83—21no—
662C2×C4×C83—21no—
663C2×C4×C83—21no—
664C2×C4×C83—21no—
665C2×C4×C83—21no—
666C2×C4×C83—44no—
667C2×C4×C83—44no—
668C2×C4×C83—44no—
669C2×C4×C83C23×C412yes—
670C2×C4×C83C23×C412yes—
671C2×C4×C83C23×C412yes—
672C2×C4×C83C23×C412yes—
673C2×C4×C83C23×C412yes—
674C2×C4×C83C23×C412yes—
675C2×C4×C83C23×C412yes—
676C2×C4×C83C23×C412yes—
677C2×C4×C83C23×C412yes—
678C2×Dic83—21no—
679C2×Dic83—21no—
680C2×Dic83—21no—
681C2×Dic83—21no—
682C2×Dic83—21no—
683C2×Dic83—21no—
684C2×Dic83—21no—
685C2×Dic83—21no—
686C2×Dic83—21no—
687C2×Dic83—21no—
688C2×Dic83—21no—
689C2×Dic83—21no—
690C2×Dic83—21no—
691C2×Dic83—21no—
692C2×Dic83—21no—
693C2×Dic83—21no—
694C2×Dic83—21no—
695C2×Dic83—21no—
696C2×Dic83—21no—
697C2×Dic83—21no—
698C2×Dic83—21no—
699C2×Dic83—21no—
700C2×Dic83—21no—
701C2×Dic83—21no—
702C2×Dic83—21no—
703C2×Dic83—21no—
704C2×Dic83—21no—
705C2×Dic83—21no—
706C2×Dic83—21no—
707C2×Dic83—21no—
708C2×Dic83—21no—
709C2×Dic83—21no—
710C2×Dic83—21no—
711C2×Dic83—21no—
712C2×Dic83—21no—
713C2×Dic83—21no—
714C2×Dic83—21no—
715C2×Dic83—21no—
716C2×Dic83—21no—
717C2×Dic83—21no—
718C2×Dic83—21no—
719C2×Dic83—21no—
720C2×Dic83—21no—
721C2×Dic83—21no—
722C2×Dic83—21no—
723C2×Dic83—44no—
724C2×Dic83—44no—
725C2×Dic83—82no—
726C2×Dic83—82no—
727C2×Dic83—82no—
728C2×Dic83—82no—
729C2×Dic83—82no—
730C2×Dic83—82no—
731C2×Dic83—82no—
732C2×Dic83—82no—
733C2×Dic83—82no—
734C2×Dic83—82no—
735C2×Dic83H(5,𝔽2)12yes—
736C2×Dic83H(5,𝔽2)12yes—
737C2×Dic83H(5,𝔽2)12yes—
738C22×C83—22no—
739C22×C83—22no—
740C22×C83—22no—
741C22×C83—22no—
742C22×C83—22no—
743C22×C83—22no—
744C22×C83—22no—
745C22×C83—22no—
746C22×C83—22no—
747C22×C83—22no—
748C22×C83—22no—
749C22×C83—22no—
750C22×C83—22no—
751C22×C83—22no—
752C22×C83—22no—
753C22×C83—22no—
754C22×C83—22no—
755C22×C83—22no—
756C22×C83—41no—
757C22×C83—41no—
758C22×C83—41no—
759C22×C83—41no—
760C22×C83—41no—
761C22×C83—41no—
762C22×C83—41no—
763C22×C83—41no—
764C22×C83—41no—
765C22×C83—41no—
766C22×C83—41no—
767C22×C83—41no—
768C22×C83—41no—
769C22×C83—41no—
770C22×C83—41no—
771C22×C83—41no—
772C22×C83—41no—
773C22×C83—41no—
774C22×C83—41no—
775C22×C83—41no—
776C22×C83—41no—
777C22×C83—41no—
778C22×C83—41no—
779C22×C83—41no—
780C22×C83—88no—
781C22×C83C24×C411yescharacteristic
782C22×C83C2×H(5,𝔽2)11yescharacteristic
783C22×C83C2×H(5,𝔽2)11yescharacteristic
784C22×C83C2×H(5,𝔽2)11yescharacteristic
785C22×C83#58511yescharacteristic
786C22×C83#58511yescharacteristic
787C22×C83#58511yescharacteristic
788C4×C83—22no—
789C4×C83—22no—
790C4×C83—22no—
791C4×C83—22no—
792C4×C83—22no—
793C4×C83—22no—
794C4×C83—22no—
795C4×C83—22no—
796C4×C83—22no—
797Dic83—22no—
798Dic83—22no—
799Dic83—22no—
800Dic83—41no—
801Dic83—41no—
802Dic83—41no—
803Dic83—41no—
804Dic83—41no—
805Dic83—41no—
806Dic83—41no—
807Dic83—41no—
808Dic83—41no—
809Dic83—41no—
810Dic83—41no—
811Dic83—41no—
812Dic83—41no—
813#34517—831nomaximal, Sylow
814C2×C83—42no—
815C2×C83—42no—
816C2×C83—42no—
817C2×C83—42no—
818C2×C83—42no—
819C2×C83—42no—
820C2×C83C4×H(5,𝔽2)11yescharacteristic
821C2×C83C4×H(5,𝔽2)11yescharacteristic
822C2×C83C4×H(5,𝔽2)11yescharacteristic
823C2×C83#353411yescharacteristic
824C2×C83#354211yescharacteristic
825C2×C83#354611yescharacteristic
826C2×C83#356611yescharacteristic
827C2×#560D8311yescharacteristic
828#2377—831no—
829#2377—831no—
830#2376—831no—
831#2373—831no—
832#2373—831no—
833#2366—831no—
834#2364—831no—
835#2364—831no—
836#2363—831no—
837#2363—831no—
838#2359—831no—
839#2359—831no—
840#2358—831no—
841#2358—831no—
842#2358—831no—
843#2335—831no—
844#2335—831no—
845#2334—831no—
846#2334—831no—
847#2328—831no—
848#2325—831no—
849#2325—831no—
850#2324—831no—
851#2324—831no—
852#2321—831no—
853#2321—831no—
854#2321—831no—
855C4×#123—831no—
856C4×#121—831no—
857C4×#121—831no—
858C83#3451711yescharacteristic, complemented, Sylow
859#560Dic83116yescomplemented
860C2×#127C2×D8311yescharacteristic
861C2×#126C2×D8311yescharacteristic
862C2×#126C2×D8311yescharacteristic
863C2×#123C2×D8311yescharacteristic
864C2×#123C2×D8311yescharacteristic
865C2×#123C2×D8311yescharacteristic
866C2×#121C2×D8311yescharacteristic
867C2×#121C2×D8311yescharacteristic
868C2×#121C2×D8311yescharacteristic
869C2×#121C2×D8311yescharacteristic
870C2×#121C2×D8311yescharacteristic
871C2×#121C2×D8311yescharacteristic
872C2×#120C2×D8311yescharacteristic
873C2×#120C2×D8311yescharacteristic
874C2×#120C2×D8311yescharacteristic
875C2×C4×D4—831no—
876C2×C4×D4—831no—
877C2×C4×D4—831no—
878C2×C4×D4—831no—
879C2×C4×D4—831no—
880C2×C4×D4—831no—
881C2×C4×D4—831no—
882C2×C4×D4—831no—
883C2×C4×D4—831no—
884C2×C4×D4—831no—
885C2×C4×D4—831no—
886C2×C4×D4—831no—
887C2×#117—831no—
888C2×#117—831no—
889C22×C22⋊C4—831no—
890C22×C22⋊C4—831no—
891C22×C22⋊C4—831no—
892C22×C42—831no—
893#390—831no—
894#390—831no—
895#390—831no—
896#390—831no—
897#390—831no—
898#390—831no—
899#390—831no—
900#390—831no—
901#390—831no—
902#390—831no—
903#390—831no—
904#390—831no—
905#389—831no—
906#389—831no—
907#389—831no—
908#389—831no—
909#389—831no—
910#389—831no—
911#388—831no—
912#388—831no—
913#388—831no—
914#388—831no—
915#388—831no—
916#388—831no—
917#388—831no—
918#388—831no—
919#388—831no—
920#388—831no—
921#388—831no—
922#388—831no—
923#388—831no—
924#388—831no—
925#388—831no—
926#388—831no—
927#388—831no—
928#388—831no—
929#388—831no—
930#388—831no—
931#388—831no—
932#388—831no—
933#388—831no—
934#388—831no—
935#387—831no—
936#387—831no—
937#387—831no—
938#387—831no—
939#387—831no—
940#387—831no—
941#387—831no—
942#387—831no—
943#387—831no—
944#387—831no—
945#387—831no—
946#387—831no—
947#386—831no—
948#386—831no—
949#386—831no—
950#386—831no—
951#386—831no—
952#386—831no—
953#386—831no—
954#386—831no—
955#386—831no—
956#386—831no—
957#386—831no—
958#386—831no—
959#386—831no—
960#386—831no—
961#386—831no—
962#386—831no—
963#386—831no—
964#386—831no—
965#386—831no—
966#386—831no—
967#386—831no—
968#386—831no—
969#386—831no—
970#386—831no—
971#385—831no—
972#385—831no—
973#385—831no—
974#385—831no—
975#385—831no—
976#385—831no—
977#385—831no—
978#385—831no—
979#385—831no—
980#385—831no—
981#385—831no—
982#385—831no—
983#382—831no—
984#381—831no—
985#380—831no—
986#380—831no—
987#380—831no—
988#380—831no—
989#379—831no—
990C4×C4⋊C4—831no—
991C4×C4⋊C4—831no—
992C4×C4⋊C4—831no—
993C4×C4⋊C4—831no—
994C4×C4⋊C4—831no—
995C4×C4⋊C4—831no—
996C4×C4⋊C4—831no—
997C4×C4⋊C4—831no—
998C4×C22⋊C4—831no—
999C4×C22⋊C4—831no—
1000C4×C22⋊C4—831no—
1001C4×C22⋊C4—831no—
1002C4×C22⋊C4—831no—
1003C4×C22⋊C4—831no—
1004C4×C22⋊C4—831no—
1005C4×C22⋊C4—831no—
1006C4×C22⋊C4—831no—
1007C4×C22⋊C4—831no—
1008C4×C22⋊C4—831no—
1009C4×C22⋊C4—831no—
1010C4×C22⋊C4—831no—
1011C4×C22⋊C4—831no—
1012#376—831no—
1013C2×#95—831no—
1014C2×#95—831no—
1015C25C22×D8311yescharacteristic
1016C22×D4C22×D8311yescharacteristic
1017C22×D4C22×D8311yescharacteristic
1018C22×D4C22×D8311yescharacteristic
1019C22×D4C22×D8311yescharacteristic
1020C22×D4C22×D8311yescharacteristic
1021C22×D4C22×D8311yescharacteristic
1022C22×D4C22×D8311yescharacteristic
1023C22×D4C22×D8311yescharacteristic
1024C22×D4C22×D8311yescharacteristic
1025C22×D4C22×D8311yescharacteristic
1026C22×D4C22×D8311yescharacteristic
1027C22×D4C22×D8311yescharacteristic
1028C23×C4—831no—
1029C23×C4—831no—
1030C23×C4—831no—
1031C23×C4—831no—
1032C23×C4—831no—
1033C23×C4—831no—
1034C23×C4—831no—
1035C23×C4—831no—
1036C23×C4—831no—
1037C23×C4—831no—
1038C23×C4—831no—
1039C23×C4—831no—
1040C23×C4C22×D8311yescharacteristic
1041C23×C4C22×D8311yescharacteristic
1042C23×C4C22×D8311yescharacteristic
1043#127C2×Dic8318yescomplemented
1044#126C2×Dic8318yescomplemented
1045#126C2×Dic8318yescomplemented
1046#123C2×Dic8318yescomplemented
1047#123C2×Dic8318yescomplemented
1048#123C2×Dic8318yescomplemented
1049#121C2×Dic8318yescomplemented
1050#121C2×Dic8318yescomplemented
1051#121C2×Dic8318yescomplemented
1052#121C2×Dic8318yescomplemented
1053#121C2×Dic8318yescomplemented
1054#121C2×Dic8318yescomplemented
1055#120C2×Dic8318yescomplemented
1056#120C2×Dic8318yescomplemented
1057#120C2×Dic8318yescomplemented
1058C4×D4—3322no—
1059C4×D4—3322no—
1060C4×D4—3322no—
1061C4×D4—3322no—
1062C4×D4—3322no—
1063C4×D4—3322no—
1064C4×D4—3322no—
1065C4×D4—3322no—
1066C4×D4—3322no—
1067C4×D4—3322no—
1068C4×D4—3322no—
1069C4×D4—3322no—
1070#117—3322no—
1071#117—3322no—
1072C2×C4⋊C4—831no—
1073C2×C4⋊C4—831no—
1074C2×C4⋊C4—831no—
1075C2×C4⋊C4—831no—
1076C2×C4⋊C4—831no—
1077C2×C4⋊C4—831no—
1078C2×C4⋊C4—831no—
1079C2×C4⋊C4—831no—
1080C2×C4⋊C4—831no—
1081C2×C4⋊C4—831no—
1082C2×C4⋊C4—831no—
1083C2×C4⋊C4—831no—
1084C2×C4⋊C4—831no—
1085C2×C4⋊C4—831no—
1086C2×C4⋊C4—831no—
1087C2×C4⋊C4—831no—
1088C2×C4⋊C4—831no—
1089C2×C4⋊C4—831no—
1090C2×C4⋊C4C22×D8311yescharacteristic
1091C2×C4⋊C4C22×D8311yescharacteristic
1092C2×C4⋊C4C22×D8311yescharacteristic
1093C2×C4⋊C4C22×D8311yescharacteristic
1094C2×C4⋊C4C22×D8311yescharacteristic
1095C2×C4⋊C4C22×D8311yescharacteristic
1096C2×C22⋊C4—3322no—
1097C2×C22⋊C4—3322no—
1098C2×C22⋊C4—3322no—
1099C2×C22⋊C4—831no—
1100C2×C22⋊C4—831no—
1101C2×C22⋊C4—831no—
1102C2×C22⋊C4—831no—
1103C2×C22⋊C4—831no—
1104C2×C22⋊C4—831no—
1105C2×C22⋊C4—831no—
1106C2×C22⋊C4—831no—
1107C2×C22⋊C4—831no—
1108C2×C22⋊C4—831no—
1109C2×C22⋊C4—831no—
1110C2×C22⋊C4—831no—
1111C2×C22⋊C4—831no—
1112C2×C22⋊C4—831no—
1113C2×C22⋊C4—831no—
1114C2×C22⋊C4—831no—
1115C2×C22⋊C4—831no—
1116C2×C22⋊C4—831no—
1117C2×C22⋊C4—831no—
1118C2×C22⋊C4—831no—
1119C2×C22⋊C4—831no—
1120C2×C22⋊C4—831no—
1121C2×C22⋊C4—831no—
1122C2×C22⋊C4—831no—
1123C2×C22⋊C4—831no—
1124C2×C22⋊C4—831no—
1125C2×C22⋊C4—831no—
1126C2×C22⋊C4—831no—
1127C2×C22⋊C4—831no—
1128C2×C22⋊C4—831no—
1129C2×C22⋊C4—831no—
1130C2×C22⋊C4—831no—
1131C2×C22⋊C4—831no—
1132C2×C22⋊C4—831no—
1133C2×C22⋊C4—831no—
1134C2×C22⋊C4—831no—
1135C2×C22⋊C4C22×D8311yescharacteristic
1136C2×C22⋊C4C22×D8311yescharacteristic
1137C2×C22⋊C4C22×D8311yescharacteristic
1138C2×C22⋊C4C22×D8311yescharacteristic
1139C2×C22⋊C4C22×D8311yescharacteristic
1140C2×C22⋊C4C22×D8311yescharacteristic
1141C2×C22⋊C4C22×D8311yescharacteristic
1142C2×C22⋊C4C22×D8311yescharacteristic
1143C2×C22⋊C4C22×D8311yescharacteristic
1144C2×C22⋊C4C22×D8311yescharacteristic
1145C2×C22⋊C4C22×D8311yescharacteristic
1146C2×C22⋊C4C22×D8311yescharacteristic
1147C2×C42—3322no—
1148C2×C42—831no—
1149C2×C42—831no—
1150C2×C42—831no—
1151C2×C42—831no—
1152C2×C42—831no—
1153C2×C42—831no—
1154C2×C42—831no—
1155C2×C42—831no—
1156C2×C42—831no—
1157C2×C42—831no—
1158C2×C42—831no—
1159C2×C42—831no—
1160C2×C42—831no—
1161C2×C42—831no—
1162C2×C42—831no—
1163C2×C42—831no—
1164C2×C42—831no—
1165C2×C42—831no—
1166C2×C42C22×D8311yescharacteristic
1167#95—831no—
1168#95—831no—
1169#95—831no—
1170#95—831no—
1171#95—831no—
1172#95—831no—
1173#95—831no—
1174#95—831no—
1175#95—831no—
1176#95—831no—
1177#95—831no—
1178#95—831no—
1179#95—831no—
1180#95—831no—
1181#95—831no—
1182#95—831no—
1183#95—831no—
1184#95—831no—
1185#95—831no—
1186#95—831no—
1187#95—831no—
1188#95—831no—
1189#95—831no—
1190#95—831no—
1191#95—831no—
1192#95—831no—
1193#95—831no—
1194#95—831no—
1195#95—831no—
1196#95—831no—
1197#95—831no—
1198#95—831no—
1199#95—831no—
1200#95—831no—
1201#95—831no—
1202#95—831no—
1203C24—41no—
1204C24—41no—
1205C24—41no—
1206C24—41no—
1207C24—41no—
1208C24—41no—
1209C24C22×Dic8314yes—
1210C24C23×D8311yescharacteristic
1211C24C23×D8311yescharacteristic
1212C24C23×D8311yescharacteristic
1213C24C23×D8311yescharacteristic
1214C24C23×D8311yescharacteristic
1215C24C23×D8311yescharacteristic
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—41no—
1224C2×D4—41no—
1225C2×D4—41no—
1226C2×D4—41no—
1227C2×D4—41no—
1228C2×D4—41no—
1229C2×D4—41no—
1230C2×D4—41no—
1231C2×D4—41no—
1232C2×D4—41no—
1233C2×D4—41no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4C22×Dic8314yes—
1241C2×D4C22×Dic8314yes—
1242C2×D4C22×Dic8314yes—
1243C2×D4C22×Dic8314yes—
1244C2×D4C22×Dic8314yes—
1245C2×D4C22×Dic8314yes—
1246C2×D4C22×Dic8314yes—
1247C2×D4C22×Dic8314yes—
1248C2×D4C22×Dic8314yes—
1249C2×D4C22×Dic8314yes—
1250C2×D4C22×Dic8314yes—
1251C2×D4C22×Dic8314yes—
1252C22×C4—41no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—3321no—
1259C22×C4—3321no—
1260C22×C4—3321no—
1261C22×C4—3321no—
1262C22×C4—3321no—
1263C22×C4—3321no—
1264C22×C4—3321no—
1265C22×C4—3321no—
1266C22×C4—3321no—
1267C22×C4—3321no—
1268C22×C4—3321no—
1269C22×C4—3321no—
1270C22×C4—3321no—
1271C22×C4—3321no—
1272C22×C4—3321no—
1273C22×C4—3321no—
1274C22×C4—3321no—
1275C22×C4—3321no—
1276C22×C4—3321no—
1277C22×C4—3321no—
1278C22×C4—3321no—
1279C22×C4—3321no—
1280C22×C4—3321no—
1281C22×C4—3321no—
1282C22×C4—3321no—
1283C22×C4—3321no—
1284C22×C4—3321no—
1285C22×C4—3321no—
1286C22×C4—831no—
1287C22×C4—831no—
1288C22×C4—831no—
1289C22×C4—831no—
1290C22×C4—831no—
1291C22×C4—831no—
1292C22×C4—831no—
1293C22×C4—831no—
1294C22×C4—831no—
1295C22×C4—831no—
1296C22×C4—831no—
1297C22×C4—831no—
1298C22×C4—831no—
1299C22×C4—831no—
1300C22×C4—831no—
1301C22×C4—831no—
1302C22×C4—1662no—
1303C22×C4—1662no—
1304C22×C4—1662no—
1305C22×C4—1662no—
1306C22×C4—1662no—
1307C22×C4—1662no—
1308C22×C4—1662no—
1309C22×C4—1662no—
1310C22×C4C22×Dic8314yes—
1311C22×C4C22×Dic8314yes—
1312C22×C4C22×Dic8314yes—
1313C22×C4C23×D8311yescharacteristic
1314C22×C4C23×D8311yescharacteristic
1315C22×C4C23×D8311yescharacteristic
1316C22×C4C23×D8311yescharacteristic
1317C22×C4C23×D8311yescharacteristic
1318C22×C4C23×D8311yescharacteristic
1319C22×C4C23×D8311yescharacteristic
1320C22×C4C23×D8311yescharacteristic
1321C22×C4C23×D8311yescharacteristic
1322C4⋊C4—3321no—
1323C4⋊C4—3321no—
1324C4⋊C4—3321no—
1325C4⋊C4—3321no—
1326C4⋊C4—3321no—
1327C4⋊C4—3321no—
1328C4⋊C4—3321no—
1329C4⋊C4—3321no—
1330C4⋊C4—3321no—
1331C4⋊C4—3321no—
1332C4⋊C4—3321no—
1333C4⋊C4—3321no—
1334C4⋊C4—3321no—
1335C4⋊C4—3321no—
1336C4⋊C4—1662no—
1337C4⋊C4—1662no—
1338C4⋊C4—1662no—
1339C4⋊C4—1662no—
1340C4⋊C4C22×Dic8314yes—
1341C4⋊C4C22×Dic8314yes—
1342C4⋊C4C22×Dic8314yes—
1343C4⋊C4C22×Dic8314yes—
1344C4⋊C4C22×Dic8314yes—
1345C4⋊C4C22×Dic8314yes—
1346C22⋊C4—3321no—
1347C22⋊C4—3321no—
1348C22⋊C4—3321no—
1349C22⋊C4—3321no—
1350C22⋊C4—3321no—
1351C22⋊C4—3321no—
1352C22⋊C4—3321no—
1353C22⋊C4—3321no—
1354C22⋊C4—3321no—
1355C22⋊C4—3321no—
1356C22⋊C4—3321no—
1357C22⋊C4—3321no—
1358C22⋊C4—3321no—
1359C22⋊C4—3321no—
1360C22⋊C4—3321no—
1361C22⋊C4—3321no—
1362C22⋊C4—3321no—
1363C22⋊C4—3321no—
1364C22⋊C4—3321no—
1365C22⋊C4—3321no—
1366C22⋊C4—3321no—
1367C22⋊C4—3321no—
1368C22⋊C4—3321no—
1369C22⋊C4—3321no—
1370C22⋊C4—3321no—
1371C22⋊C4—3321no—
1372C22⋊C4—1662no—
1373C22⋊C4—1662no—
1374C22⋊C4—1662no—
1375C22⋊C4—1662no—
1376C22⋊C4—1662no—
1377C22⋊C4—1662no—
1378C22⋊C4—1662no—
1379C22⋊C4—1662no—
1380C22⋊C4—1662no—
1381C22⋊C4—1662no—
1382C22⋊C4C22×Dic8314yes—
1383C22⋊C4C22×Dic8314yes—
1384C22⋊C4C22×Dic8314yes—
1385C22⋊C4C22×Dic8314yes—
1386C22⋊C4C22×Dic8314yes—
1387C22⋊C4C22×Dic8314yes—
1388C22⋊C4C22×Dic8314yes—
1389C22⋊C4C22×Dic8314yes—
1390C22⋊C4C22×Dic8314yes—
1391C22⋊C4C22×Dic8314yes—
1392C22⋊C4C22×Dic8314yes—
1393C22⋊C4C22×Dic8314yes—
1394C42—3321no—
1395C42—3321no—
1396C42—3321no—
1397C42—3321no—
1398C42—3321no—
1399C42—3321no—
1400C42—3321no—
1401C42—3321no—
1402C42—3321no—
1403C42—3321no—
1404C42—3321no—
1405C42—3321no—
1406C42—3321no—
1407C42—1662no—
1408C42—1662no—
1409C42—1662no—
1410C42—1662no—
1411C42—1662no—
1412C42C22×Dic8314yes—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—44no—
1450C23—44no—
1451C23—44no—
1452C23—82no—
1453C23—82no—
1454C23—82no—
1455C23—82no—
1456C23C23×Dic8312yes—
1457C23C23×Dic8312yes—
1458C23C23×Dic8312yes—
1459C23C23×Dic8312yes—
1460C23C23×Dic8312yes—
1461C23C23×Dic8312yes—
1462C23C24×D8311yescharacteristic
1463D4—44no—
1464D4—44no—
1465D4—44no—
1466D4—44no—
1467D4—44no—
1468D4—44no—
1469D4—44no—
1470D4—44no—
1471D4—44no—
1472D4—44no—
1473D4—44no—
1474D4—44no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—44no—
1494C2×C4—44no—
1495C2×C4—44no—
1496C2×C4—3324no—
1497C2×C4—3324no—
1498C2×C4—832no—
1499C2×C4—832no—
1500C2×C4—832no—
1501C2×C4—6642no—
1502C2×C4—6642no—
1503C2×C4—6642no—
1504C2×C4—6642no—
1505C2×C4—6642no—
1506C2×C4—6642no—
1507C2×C4—6642no—
1508C2×C4—6642no—
1509C2×C4—6642no—
1510C2×C4—6642no—
1511C2×C4—1661no—
1512C2×C4—1661no—
1513C2×C4—1661no—
1514C2×C4—1661no—
1515C2×C4—1661no—
1516C2×C4—1661no—
1517C2×C4—1661no—
1518C2×C4—1661no—
1519C2×C4—1661no—
1520C2×C4—1661no—
1521C2×C4—1661no—
1522C2×C4—1661no—
1523C2×C4—1661no—
1524C2×C4—1661no—
1525C2×C4—1661no—
1526C2×C4—1661no—
1527C2×C4—1661no—
1528C2×C4—1661no—
1529C2×C4—1661no—
1530C2×C4—1661no—
1531C2×C4—1661no—
1532C2×C4—1661no—
1533C2×C4—1661no—
1534C2×C4—1661no—
1535C2×C4—1661no—
1536C2×C4—1661no—
1537C2×C4—1661no—
1538C2×C4—1661no—
1539C2×C4—1661no—
1540C2×C4—1661no—
1541C2×C4—1661no—
1542C2×C4—1661no—
1543C2×C4—1661no—
1544C2×C4—1661no—
1545C2×C4—1661no—
1546C2×C4—1661no—
1547C2×C4—1661no—
1548C2×C4—1661no—
1549C2×C4—1661no—
1550C2×C4—1661no—
1551C2×C4—1661no—
1552C2×C4—1661no—
1553C2×C4—1661no—
1554C2×C4—1661no—
1555C2×C4—1661no—
1556C2×C4C23×Dic8312yes—
1557C2×C4C23×Dic8312yes—
1558C2×C4C23×Dic8312yes—
1559C2×C4C23×Dic8312yes—
1560C2×C4C23×Dic8312yes—
1561C2×C4C23×Dic8312yes—
1562C2×C4C23×Dic8312yes—
1563C2×C4C23×Dic8312yes—
1564C2×C4C23×Dic8312yes—
1565C22—22no—
1566C22—22no—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—22no—
1571C22—22no—
1572C22—22no—
1573C22—22no—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—88no—
1608C22C24×Dic8311yescharacteristic
1609C22H(5,𝔽2)×D8311yescharacteristic
1610C22H(5,𝔽2)×D8311yescharacteristic
1611C22H(5,𝔽2)×D8311yescharacteristic
1612C22#1912853611yescharacteristic
1613C22#1912853611yescharacteristic
1614C22#1912853611yescharacteristic
1615C4—22no—
1616C4—22no—
1617C4—22no—
1618C4—22no—
1619C4—22no—
1620C4—22no—
1621C4—22no—
1622C4—22no—
1623C4—22no—
1624C4—3321no—
1625C4—3321no—
1626C4—3321no—
1627C4—3321no—
1628C4—3321no—
1629C4—3321no—
1630C4—3321no—
1631C4—3321no—
1632C4—3321no—
1633C4—3321no—
1634C4—3321no—
1635C4—3321no—
1636C4—3321no—
1637C4—1662no—
1638C4—1662no—
1639C4—1662no—
1640C2—42no—
1641C2—42no—
1642C2—42no—
1643C2—42no—
1644C2—42no—
1645C2—42no—
1646C2H(5,𝔽2)×Dic8311yescharacteristic
1647C2H(5,𝔽2)×Dic8311yescharacteristic
1648C2H(5,𝔽2)×Dic8311yescharacteristic
1649C2#2492164411yescharacteristic
1650C2#2492176811yescharacteristic
1651C2#2492182611yescharacteristic
1652C2#2492212011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
Fitting, prime radicalC2×#560×C83C2
socle, cosocleC23×C83C25
hypercenterC2×#560D83
hypocenterC83#34517
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#560

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #24910620C2semidirect
2. #24910620C2semidirect
3. #24910611C2semidirect
4. #24910587C2semidirect
5. #24910587C2semidirect
6. #24910528C2semidirect
7. #24910515C2semidirect
8. #24910515C2semidirect
9. #24910505C2semidirect
10. #24910505C2semidirect
11. #24910459C2semidirect
12. #24910459C2semidirect
13. #24910447C2semidirect
14. #24910447C2semidirect
15. #24910447C2semidirect
16. #24910257C2semidirect
17. #24910257C2semidirect
18. #24910242C2semidirect
19. #24910242C2semidirect
20. #24910189C2semidirect
21. #24910168C2semidirect
22. #24910168C2semidirect
23. #24910158C2semidirect
24. #24910158C2semidirect
25. #24910124C2semidirect
26. #24910124C2semidirect
27. #24910124C2semidirect
28. #123×Dic83C2semidirect
29. #121×Dic83C2semidirect
30. #121×Dic83C2semidirect
41. C2×D4×Dic83C22semidirect
42. C2×D4×Dic83C22semidirect
43. C2×D4×Dic83C22semidirect
44. C2×#14581751C22semidirect
45. C2×#14581751C22semidirect
49. C22×C4×Dic83C22semidirect
59. #19127604C22semidirect
60. #19127604C22semidirect
61. #19127604C22semidirect
62. #19127600C22semidirect
63. #19127600C22semidirect
64. #19127600C22semidirect
65. #19127600C22semidirect
66. #19127600C22semidirect
67. #19127600C22semidirect
86. #19127594C22semidirect
87. #19127594C22semidirect
88. #19127594C22semidirect
89. #19127594C22semidirect
90. #19127594C22semidirect
91. #19127594C22semidirect
92. #19127587C22semidirect
93. #19127587C22semidirect
94. #19127587C22semidirect
95. #19127587C22semidirect
96. #19127587C22semidirect
97. #19127587C22semidirect
98. #19127587C22semidirect
99. #19127587C22semidirect
100. #19127587C22semidirect
101. #19127587C22semidirect
102. #19127587C22semidirect
103. #19127587C22semidirect
122. #19127581C22semidirect
123. #19127581C22semidirect
124. #19127581C22semidirect
125. #19127581C22semidirect
126. #19127581C22semidirect
127. #19127581C22semidirect
137. #19127576C22semidirect
138. #19127576C22semidirect
139. #19127576C22semidirect
140. #19127567C22semidirect
141. #19127564C22semidirect
142. #19127561C22semidirect
143. #19127561C22semidirect
144. #19127561C22semidirect
145. #19127561C22semidirect
147. C4⋊C4×Dic83C22semidirect
148. C4⋊C4×Dic83C22semidirect
149. C4⋊C4×Dic83C22semidirect
150. C4⋊C4×Dic83C22semidirect
151. C4⋊C4×Dic83C22semidirect
152. C4⋊C4×Dic83C22semidirect
153. C4×C4⋊Dic83C22semidirect
154. C4×C4⋊Dic83C22semidirect
164. C22⋊C4×Dic83C22semidirect
165. C22⋊C4×Dic83C22semidirect
166. C22⋊C4×Dic83C22semidirect
167. C4×C22⋊Dic83C22semidirect
168. C4×C22⋊Dic83C22semidirect
169. #19127547C22semidirect
170. C2×C83⋊#95C22semidirect
171. C2×C83⋊#95C22semidirect
172. #560×C83C4semidirect
342. #127×C83C2×C4semidirect
343. #126×C83C2×C4semidirect
344. #126×C83C2×C4semidirect
345. #123×C83C2×C4semidirect
346. #123×C83C2×C4semidirect
347. #123×C83C2×C4semidirect
348. #121×C83C2×C4semidirect
349. #121×C83C2×C4semidirect
350. #121×C83C2×C4semidirect
351. #121×C83C2×C4semidirect
352. #121×C83C2×C4semidirect
353. #121×C83C2×C4semidirect
354. #120×C83C2×C4semidirect
355. #120×C83C2×C4semidirect
356. #120×C83C2×C4semidirect
858. C83#34517semidirect
859. #560Dic83semidirect
1043. #127C2×Dic83semidirect
1044. #126C2×Dic83semidirect
1045. #126C2×Dic83semidirect
1046. #123C2×Dic83semidirect
1047. #123C2×Dic83semidirect
1048. #123C2×Dic83semidirect
1049. #121C2×Dic83semidirect
1050. #121C2×Dic83semidirect
1051. #121C2×Dic83semidirect
1052. #121C2×Dic83semidirect
1053. #121C2×Dic83semidirect
1054. #121C2×Dic83semidirect
1055. #120C2×Dic83semidirect
1056. #120C2×Dic83semidirect
1057. #120C2×Dic83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249106202
#249106112
#249105872
#249105282
#249105152
#249105052
#249104592
#249104472
#249102572
#249102422
#249101892
#249101682
#249101582
#249101242
#123×Dic832
#121×Dic832
C2×#560×C832
#3451783