Finite Group Databasebeta

← #35570024

Subgroups — #35570024

Order 21248.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910655C211yesmaximal, characteristic, complemented
2#24910629C211yesmaximal, characteristic, complemented
3#24910611C211yesmaximal, characteristic, complemented
4#24910604C211yesmaximal, characteristic
5#24910599C211yesmaximal, characteristic, complemented
6#24910587C211yesmaximal, characteristic, complemented
7#24910538C211yesmaximal, characteristic, complemented
8#24910494C211yesmaximal, characteristic, complemented
9#24910459C211yesmaximal, characteristic, complemented
10#24910412C211yesmaximal, characteristic, complemented
11#24910403C211yesmaximal, characteristic, complemented
12#24910356C211yesmaximal, characteristic, complemented
13#24910356C211yesmaximal, characteristic, complemented
14#24910312C211yesmaximal, characteristic, complemented
15#24910312C211yesmaximal, characteristic, complemented
16#24910278C211yesmaximal, characteristic, complemented
17#24910257C211yesmaximal, characteristic, complemented
18#24910257C211yesmaximal, characteristic, complemented
19#24910257C211yesmaximal, characteristic, complemented
20#24910242C211yesmaximal, characteristic, complemented
21#24910221C211yesmaximal, characteristic, complemented
22#24910147C211yesmaximal, characteristic, complemented
23#24910124C211yesmaximal, characteristic
24#24910096C211yesmaximal, characteristic, complemented
25#24910072C211yesmaximal, characteristic, complemented
26#24910061C211yesmaximal, characteristic, complemented
27#24910061C211yesmaximal, characteristic, complemented
28#126×Dic83C211yesmaximal, characteristic, complemented
29#24909961C211yesmaximal, characteristic, complemented
30#24909928C211yesmaximal, characteristic, complemented
31C2×#551×C83C211yesmaximal, characteristic
32C2×Q8×Dic83C2211yescharacteristic, complemented
33C2×D4×Dic83C2211yescharacteristic
34C2×#14581751C2211yescharacteristic
35C2×#14581751C2211yescharacteristic
36C2×#14581751C2211yescharacteristic, complemented
37C22×C22⋊Dic83C2211yescharacteristic
38#19127608C2211yescharacteristic, complemented
39#19127608C2211yescharacteristic, complemented
40#19127608C2211yescharacteristic, complemented
41#19127604C2211yescharacteristic
42#19127604C2211yescharacteristic
43#19127604C2211yescharacteristic
44#19127604C2211yescharacteristic
45#19127604C2211yescharacteristic
46#19127600C2211yescharacteristic, complemented
47#19127600C2211yescharacteristic, complemented
48#19127600C2211yescharacteristic, complemented
49#19127600C2211yescharacteristic, complemented
50#19127600C2211yescharacteristic, complemented
51#19127600C2211yescharacteristic, complemented
52#19127600C2211yescharacteristic, complemented
53#19127600C2211yescharacteristic, complemented
54#19127594C2211yescharacteristic
55#19127594C2211yescharacteristic
56#19127594C2211yescharacteristic
57#19127594C2211yescharacteristic
58#19127594C2211yescharacteristic
59#19127594C2211yescharacteristic
60#19127594C2211yescharacteristic
61#19127594C2211yescharacteristic
62#19127594C2211yescharacteristic
63#19127594C2211yescharacteristic
64#19127594C2211yescharacteristic
65#19127594C2211yescharacteristic
66#19127594C2211yescharacteristic
67#19127594C2211yescharacteristic
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
87#19127594C2211yescharacteristic
88#19127594C2211yescharacteristic, complemented
89#19127594C2211yescharacteristic, complemented
90#19127594C2211yescharacteristic, complemented
91#19127594C2211yescharacteristic, complemented
92#19127594C2211yescharacteristic, complemented
93#19127594C2211yescharacteristic, 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#19127587C2211yescharacteristic, complemented
105#19127587C2211yescharacteristic, complemented
106#19127587C2211yescharacteristic, complemented
107#19127587C2211yescharacteristic, complemented
108#19127587C2211yescharacteristic, complemented
109#19127587C2211yescharacteristic, complemented
110#19127581C2211yescharacteristic
111#19127581C2211yescharacteristic
112#19127581C2211yescharacteristic
113#19127581C2211yescharacteristic
114#19127581C2211yescharacteristic
115#19127581C2211yescharacteristic
116#19127576C2211yescharacteristic
117#19127576C2211yescharacteristic
118#19127576C2211yescharacteristic
119#19127576C2211yescharacteristic
120#19127576C2211yescharacteristic
121#19127576C2211yescharacteristic, complemented
122#19127576C2211yescharacteristic, complemented
123#19127576C2211yescharacteristic, complemented
124#19127571C2211yescharacteristic, complemented
125#19127569C2211yescharacteristic, complemented
126#19127569C2211yescharacteristic, complemented
127#19127569C2211yescharacteristic, complemented
128#19127567C2211yescharacteristic, complemented
129#19127564C2211yescharacteristic
130#19127564C2211yescharacteristic
131#19127561C2211yescharacteristic
132#19127561C2211yescharacteristic
133#19127561C2211yescharacteristic
134#19127561C2211yescharacteristic
135#19127561C2211yescharacteristic
136#19127561C2211yescharacteristic
137#19127561C2211yescharacteristic, complemented
138#19127557C2211yescharacteristic
139#19127557C2211yescharacteristic
140#19127557C2211yescharacteristic
141C4⋊C4×Dic83C2211yescharacteristic, complemented
142C4⋊C4×Dic83C2211yescharacteristic, complemented
143C4⋊C4×Dic83C2211yescharacteristic, complemented
144C4⋊C4×Dic83C2211yescharacteristic, complemented
145C4⋊C4×Dic83C2211yescharacteristic, complemented
146C4⋊C4×Dic83C2211yescharacteristic, complemented
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
154C22⋊C4×Dic83C2211yescharacteristic
155C22⋊C4×Dic83C2211yescharacteristic
156C22⋊C4×Dic83C2211yescharacteristic
157C22⋊C4×Dic83C2211yescharacteristic
158C22⋊C4×Dic83C2211yescharacteristic
159C22⋊C4×Dic83C2211yescharacteristic, complemented
160C22⋊C4×Dic83C2211yescharacteristic, complemented
161C22⋊C4×Dic83C2211yescharacteristic, complemented
162C4×C22⋊Dic83C2211yescharacteristic
163C4×C22⋊Dic83C2211yescharacteristic
164C4×C22⋊Dic83C2211yescharacteristic
165C4×C22⋊Dic83C2211yescharacteristic
166C4×C22⋊Dic83C2211yescharacteristic
167C4×C22⋊Dic83C2211yescharacteristic
168C4×C22⋊Dic83C2211yescharacteristic, complemented
169#19127547C2211yescharacteristic, complemented
170C2×C83⋊#95C2211yescharacteristic, complemented
171C42×Dic83C2211yescharacteristic, complemented
172#551×C83C4116yescomplemented
173C2×#126×C83C2211yescharacteristic
174C2×#126×C83C2211yescharacteristic
175C2×#124×C83C2211yescharacteristic
176C2×#123×C83C2211yescharacteristic
177C2×#123×C83C2211yescharacteristic
178C2×#123×C83C2211yescharacteristic
179C2×C22⋊Q8×C83C2211yescharacteristic
180C2×C22⋊Q8×C83C2211yescharacteristic
181C2×#120×C83C2211yescharacteristic
182C2×C4×D4×C83C2211yescharacteristic
183C2×C4×D4×C83C2211yescharacteristic
184C2×#117×C83C2211yescharacteristic
185C2×#117×C83C2211yescharacteristic
186C22×C22⋊C4×C83C2211yescharacteristic
187C22×C22⋊C4×C83C2211yescharacteristic
188C23×Dic83C2311yescharacteristic
189C23×Dic83C2311yescharacteristic
190C23×Dic83C2311yescharacteristic
191C23×Dic83C2311yescharacteristic
192Q8×Dic83—42no—
193D4×Dic83—42no—
194#14581751—42no—
195#14581751—42no—
196#14581751—42no—
197C2×C4⋊Dic83C2311yescharacteristic
198C2×C4⋊Dic83C2311yescharacteristic
199C2×C4⋊Dic83C2311yescharacteristic
200C2×C4⋊Dic83C2311yescharacteristic
201C2×C4⋊Dic83C2311yescharacteristic
202C2×C4⋊Dic83C2311yescharacteristic
203C2×C4⋊Dic83C2311yescharacteristic
204C2×C4⋊Dic83C2311yescharacteristic
205C2×C4⋊Dic83C2311yescharacteristic
206C2×C4⋊Dic83C2311yescharacteristic
207C2×C4⋊Dic83C2311yescharacteristic
208C2×C4⋊Dic83C2311yescharacteristic
209C2×C4⋊Dic83C2311yescharacteristic
210C2×C4⋊Dic83C2311yescharacteristic
211C2×C4⋊Dic83C2311yescharacteristic
212C2×C4⋊Dic83C2311yescharacteristic
213C2×C4⋊Dic83C2311yescharacteristic
214C2×C4⋊Dic83C2311yescharacteristic
215C2×C4⋊Dic83C2311yescharacteristic
216C2×C4⋊Dic83C2311yescharacteristic
217C2×C4⋊Dic83C2311yescharacteristic
218C2×C4⋊Dic83C2311yescharacteristic
219C2×C22⋊Dic83—42no—
220C2×C22⋊Dic83C2311yescharacteristic
221C2×C22⋊Dic83C2311yescharacteristic
222C2×C22⋊Dic83C2311yescharacteristic
223C2×C22⋊Dic83C2311yescharacteristic
224C2×C22⋊Dic83C2311yescharacteristic
225C2×C22⋊Dic83C2311yescharacteristic
226C2×C22⋊Dic83C2311yescharacteristic
227C2×C22⋊Dic83C2311yescharacteristic
228C2×C22⋊Dic83C2311yescharacteristic
229C2×C22⋊Dic83C2311yescharacteristic
230C2×C22⋊Dic83C2311yescharacteristic
231C2×C22⋊Dic83C2311yescharacteristic
232C2×C22⋊Dic83C2311yescharacteristic
233C2×C22⋊Dic83C2311yescharacteristic
234C2×C22⋊Dic83C2311yescharacteristic
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×C4×Dic83C2311yescharacteristic
249C2×C4×Dic83C2311yescharacteristic
250C2×C4×Dic83C2311yescharacteristic
251C2×C4×Dic83C2311yescharacteristic
252C2×C4×Dic83C2311yescharacteristic
253C2×C4×Dic83C2311yescharacteristic
254C2×C4×Dic83C2311yescharacteristic
255C2×C4×Dic83C2311yescharacteristic
256C2×C4×Dic83C2311yescharacteristic
257C2×C4×Dic83C2311yescharacteristic
258C2×C4×Dic83C2311yescharacteristic
259C2×C4×Dic83C2311yescharacteristic
260C2×C4×Dic83C2311yescharacteristic
261C2×C4×Dic83C2311yescharacteristic
262C2×C4×Dic83C2311yescharacteristic
263C2×C4×Dic83C2311yescharacteristic
264C2×C4×Dic83C2311yescharacteristic
265C2×C4×Dic83C2311yescharacteristic
266C2×C4×Dic83C2311yescharacteristic
267C2×C4×Dic83C2311yescharacteristic
268C2×C4×Dic83C2311yescharacteristic
269C2×C4×Dic83C2311yescharacteristic
270C83⋊#95C2311yescharacteristic
271C83⋊#95C2311yescharacteristic
272C83⋊#95C2311yescharacteristic
273C83⋊#95C2311yescharacteristic
274C83⋊#95C2311yescharacteristic
275C83⋊#95C2311yescharacteristic
276C83⋊#95C2311yescharacteristic
277C83⋊#95C2311yescharacteristic
278C83⋊#95C2311yescharacteristic
279C83⋊#95C2311yescharacteristic
280C83⋊#95C2311yescharacteristic
281C83⋊#95C2311yescharacteristic
282C83⋊#95C2311yescharacteristic
283C83⋊#95C2311yescharacteristic
284C83⋊#95C2311yescharacteristic
285C83⋊#95C2311yescharacteristic
286C83⋊#95C2311yescharacteristic
287C83⋊#95C2311yescharacteristic
288C83⋊#95C2311yescharacteristic
289C83⋊#95C2311yescharacteristic
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
314C25×C83C2311yescharacteristic
315C22×Q8×C83C2311yescharacteristic
316C22×D4×C83C2311yescharacteristic
317C22×D4×C83C2311yescharacteristic
318C22×D4×C83C2311yescharacteristic
319C23×C4×C83C2311yescharacteristic
320C23×C4×C83C2311yescharacteristic
321C23×C4×C83C2311yescharacteristic
322C23×C4×C83C2311yescharacteristic
323C23×C4×C83C2311yescharacteristic
324#126×C83C2×C418yescomplemented
325#126×C83C2×C418yescomplemented
326#124×C83C2×C418yes—
327#123×C83C2×C418yes—
328#123×C83C2×C418yescomplemented
329#123×C83C2×C418yescomplemented
330C22⋊Q8×C83C2×C418yescomplemented
331C22⋊Q8×C83C2×C418yescomplemented
332#120×C83C2×C418yes—
333C4×D4×C83C2×C418yescomplemented
334C4×D4×C83C2×C418yescomplemented
335#117×C83C2×C418yescomplemented
336#117×C83C2×C418yescomplemented
337C2×C4⋊C4×C83C2311yescharacteristic
338C2×C4⋊C4×C83C2311yescharacteristic
339C2×C4⋊C4×C83C2311yescharacteristic
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C22⋊C4×C83C2×C418yescomplemented
346C2×C22⋊C4×C83C2×C418yescomplemented
347C2×C22⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C22⋊C4×C83C2311yescharacteristic
358C2×C22⋊C4×C83C2311yescharacteristic
359C2×C22⋊C4×C83C2311yescharacteristic
360C2×C22⋊C4×C83C2311yescharacteristic
361C2×C42×C83C2311yescharacteristic
362C2×C42×C83C2311yescharacteristic
363C2×C42×C83C2311yescharacteristic
364C22×Dic83—22no—
365C22×Dic83—41no—
366C22×Dic83—41no—
367C22×Dic83—41no—
368C22×Dic83—41no—
369C22×Dic83—41no—
370C22×Dic83—41no—
371C22×Dic83—41no—
372C22×Dic83—41no—
373C22×Dic83—41no—
374C22×Dic83—41no—
375C22×Dic83—41no—
376C22×Dic83C2411yescharacteristic
377C22×Dic83C2411yescharacteristic
378C22×Dic83C2411yescharacteristic
379C22×Dic83C2411yescharacteristic
380C22×Dic83C2411yescharacteristic
381C22×Dic83C2411yescharacteristic
382C22×Dic83C2411yescharacteristic
383C22×Dic83C2411yescharacteristic
384C22×Dic83C2411yescharacteristic
385C22×Dic83C2411yescharacteristic
386C22×Dic83C2411yescharacteristic
387C22×Dic83C2411yescharacteristic
388C22×Dic83C2411yescharacteristic
389C22×Dic83C2411yescharacteristic
390C22×Dic83C2411yescharacteristic
391C22×Dic83C2411yescharacteristic
392C4⋊Dic83—22no—
393C4⋊Dic83—22no—
394C4⋊Dic83—22no—
395C4⋊Dic83—41no—
396C4⋊Dic83—41no—
397C4⋊Dic83—41no—
398C4⋊Dic83—41no—
399C4⋊Dic83—41no—
400C4⋊Dic83—41no—
401C4⋊Dic83—41no—
402C4⋊Dic83—41no—
403C4⋊Dic83—41no—
404C4⋊Dic83—41no—
405C4⋊Dic83—41no—
406C4⋊Dic83—41no—
407C4⋊Dic83—41no—
408C4⋊Dic83—41no—
409C4⋊Dic83—41no—
410C4⋊Dic83—41no—
411C4⋊Dic83—41no—
412C4⋊Dic83—41no—
413C4⋊Dic83—41no—
414C22⋊Dic83—22no—
415C22⋊Dic83—22no—
416C22⋊Dic83—22no—
417C22⋊Dic83—41no—
418C22⋊Dic83—41no—
419C22⋊Dic83—41no—
420C22⋊Dic83—41no—
421C22⋊Dic83—41no—
422C22⋊Dic83—41no—
423C22⋊Dic83—41no—
424C22⋊Dic83—41no—
425C22⋊Dic83—41no—
426C22⋊Dic83—41no—
427C22⋊Dic83—41no—
428C22⋊Dic83—41no—
429C22⋊Dic83—41no—
430C22⋊Dic83—41no—
431C22⋊Dic83—41no—
432C22⋊Dic83—41no—
433C22⋊Dic83—41no—
434C22⋊Dic83—41no—
435C22⋊Dic83—41no—
436C22⋊Dic83—41no—
437C22⋊Dic83—41no—
438C22⋊Dic83—41no—
439C22⋊Dic83—41no—
440C22⋊Dic83—41no—
441C22⋊Dic83—41no—
442C4×Dic83—22no—
443C4×Dic83—22no—
444C4×Dic83—41no—
445C4×Dic83—41no—
446C4×Dic83—41no—
447C4×Dic83—41no—
448C4×Dic83—41no—
449C4×Dic83—41no—
450C4×Dic83—41no—
451C4×Dic83—41no—
452C4×Dic83—41no—
453C4×Dic83—41no—
454C4×Dic83—41no—
455C4×Dic83—41no—
456C4×Dic83—41no—
457C4×Dic83—41no—
458C4×Dic83—41no—
459C4×Dic83—41no—
460C4×Dic83—41no—
461C4×Dic83—41no—
462C4×Dic83—41no—
463C4×Dic83—41no—
464C24×C83—41no—
465C24×C83—41no—
466C24×C83—41no—
467C24×C83—41no—
468C24×C83—41no—
469C24×C83—41no—
470C24×C83C22×C414yes—
471C24×C83C2411yescharacteristic
472C24×C83C2411yescharacteristic
473C24×C83C2411yescharacteristic
474C24×C83C2411yescharacteristic
475C2×Q8×C83—41no—
476C2×Q8×C83—41no—
477C2×Q8×C83C22×C414yes—
478C2×D4×C83—41no—
479C2×D4×C83—41no—
480C2×D4×C83—41no—
481C2×D4×C83—41no—
482C2×D4×C83—41no—
483C2×D4×C83—41no—
484C2×D4×C83C22×C414yes—
485C2×D4×C83C22×C414yes—
486C2×D4×C83C22×C414yes—
487C22×C4×C83—41no—
488C22×C4×C83—41no—
489C22×C4×C83—41no—
490C22×C4×C83—41no—
491C22×C4×C83—41no—
492C22×C4×C83—41no—
493C22×C4×C83—41no—
494C22×C4×C83—41no—
495C22×C4×C83—41no—
496C22×C4×C83—41no—
497C22×C4×C83C22×C414yes—
498C22×C4×C83C22×C414yes—
499C22×C4×C83C22×C414yes—
500C22×C4×C83C22×C414yes—
501C22×C4×C83C22×C414yes—
502C22×C4×C83C2411yescharacteristic
503C22×C4×C83C2411yescharacteristic
504C22×C4×C83C2411yescharacteristic
505C22×C4×C83C2411yescharacteristic
506C22×C4×C83C2411yescharacteristic
507C22×C4×C83C2411yescharacteristic
508C22×C4×C83C2411yescharacteristic
509C22×C4×C83C2411yescharacteristic
510C22×C4×C83C2411yescharacteristic
511C22×C4×C83C2411yescharacteristic
512C22×C4×C83C2411yescharacteristic
513C4⋊C4×C83C22×C414yes—
514C4⋊C4×C83C22×C414yes—
515C4⋊C4×C83C22×C414yes—
516C4⋊C4×C83C22×C414yes—
517C4⋊C4×C83C22×C414yes—
518C4⋊C4×C83C22×C414yes—
519C4⋊C4×C83C22×C414yes—
520C4⋊C4×C83C22×C414yes—
521C22⋊C4×C83C22×C414yes—
522C22⋊C4×C83C22×C414yes—
523C22⋊C4×C83C22×C414yes—
524C22⋊C4×C83C22×C414yes—
525C22⋊C4×C83C22×C414yes—
526C22⋊C4×C83C22×C414yes—
527C22⋊C4×C83C22×C414yes—
528C22⋊C4×C83C22×C414yes—
529C22⋊C4×C83C22×C414yes—
530C22⋊C4×C83C22×C414yes—
531C22⋊C4×C83C22×C414yes—
532C22⋊C4×C83C22×C414yes—
533C22⋊C4×C83C22×C414yes—
534C22⋊C4×C83C22×C414yes—
535C42×C83C22×C414yes—
536C42×C83C22×C414yes—
537C42×C83C22×C414yes—
538C23×C83—21no—
539C23×C83—21no—
540C23×C83—21no—
541C23×C83—21no—
542C23×C83—21no—
543C23×C83—21no—
544C23×C83—21no—
545C23×C83—21no—
546C23×C83—21no—
547C23×C83—21no—
548C23×C83—21no—
549C23×C83—21no—
550C23×C83—21no—
551C23×C83—21no—
552C23×C83—21no—
553C23×C83—21no—
554C23×C83—21no—
555C23×C83—21no—
556C23×C83—21no—
557C23×C83—21no—
558C23×C83—21no—
559C23×C83—21no—
560C23×C83—21no—
561C23×C83—21no—
562C23×C83—44no—
563C23×C83—44no—
564C23×C83—44no—
565C23×C83—82no—
566C23×C83—82no—
567C23×C83—82no—
568C23×C83—82no—
569C23×C83C23×C412yes—
570C23×C83C23×C412yes—
571C23×C83C23×C412yes—
572C23×C83C23×C412yes—
573C23×C83C2511yescharacteristic
574Q8×C83—44no—
575D4×C83—44no—
576D4×C83—44no—
577D4×C83—44no—
578C2×C4×C83—21no—
579C2×C4×C83—21no—
580C2×C4×C83—21no—
581C2×C4×C83—21no—
582C2×C4×C83—21no—
583C2×C4×C83—21no—
584C2×C4×C83—21no—
585C2×C4×C83—21no—
586C2×C4×C83—21no—
587C2×C4×C83—21no—
588C2×C4×C83—21no—
589C2×C4×C83—21no—
590C2×C4×C83—21no—
591C2×C4×C83—21no—
592C2×C4×C83—21no—
593C2×C4×C83—21no—
594C2×C4×C83—21no—
595C2×C4×C83—21no—
596C2×C4×C83—21no—
597C2×C4×C83—21no—
598C2×C4×C83—21no—
599C2×C4×C83—21no—
600C2×C4×C83—44no—
601C2×C4×C83—44no—
602C2×C4×C83—44no—
603C2×C4×C83—44no—
604C2×C4×C83—44no—
605C2×C4×C83C23×C412yes—
606C2×C4×C83C23×C412yes—
607C2×C4×C83C23×C412yes—
608C2×C4×C83C23×C412yes—
609C2×C4×C83C23×C412yes—
610C2×C4×C83C23×C412yes—
611C2×C4×C83C23×C412yes—
612C2×C4×C83C23×C412yes—
613C2×C4×C83C23×C412yes—
614C2×C4×C83C23×C412yes—
615C2×C4×C83C23×C412yes—
616C2×Dic83—21no—
617C2×Dic83—21no—
618C2×Dic83—21no—
619C2×Dic83—21no—
620C2×Dic83—21no—
621C2×Dic83—21no—
622C2×Dic83—21no—
623C2×Dic83—21no—
624C2×Dic83—21no—
625C2×Dic83—21no—
626C2×Dic83—21no—
627C2×Dic83—21no—
628C2×Dic83—21no—
629C2×Dic83—21no—
630C2×Dic83—21no—
631C2×Dic83—21no—
632C2×Dic83—21no—
633C2×Dic83—21no—
634C2×Dic83—21no—
635C2×Dic83—21no—
636C2×Dic83—21no—
637C2×Dic83—21no—
638C2×Dic83—21no—
639C2×Dic83—21no—
640C2×Dic83—21no—
641C2×Dic83—21no—
642C2×Dic83—21no—
643C2×Dic83—21no—
644C2×Dic83—21no—
645C2×Dic83—21no—
646C2×Dic83—21no—
647C2×Dic83—21no—
648C2×Dic83—21no—
649C2×Dic83—21no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—21no—
656C2×Dic83—21no—
657C2×Dic83—21no—
658C2×Dic83—21no—
659C2×Dic83—21no—
660C2×Dic83—21no—
661C2×Dic83—21no—
662C2×Dic83—21no—
663C2×Dic83—82no—
664C2×Dic83—82no—
665C2×Dic83—82no—
666C2×Dic83—82no—
667C2×Dic83H(5,𝔽2)12yes—
668C22×C83—22no—
669C22×C83—22no—
670C22×C83—22no—
671C22×C83—22no—
672C22×C83—22no—
673C22×C83—22no—
674C22×C83—22no—
675C22×C83—22no—
676C22×C83—22no—
677C22×C83—22no—
678C22×C83—22no—
679C22×C83—22no—
680C22×C83—41no—
681C22×C83—41no—
682C22×C83—41no—
683C22×C83—41no—
684C22×C83—41no—
685C22×C83—41no—
686C22×C83—41no—
687C22×C83—41no—
688C22×C83—41no—
689C22×C83—41no—
690C22×C83—41no—
691C22×C83—41no—
692C22×C83—41no—
693C22×C83—41no—
694C22×C83—41no—
695C22×C83—41no—
696C22×C83—88no—
697C22×C83C24×C411yescharacteristic
698C22×C83C2×H(5,𝔽2)11yescharacteristic
699C22×C83#58511yescharacteristic
700C22×C83#58511yescharacteristic
701C22×C83#58511yescharacteristic
702C22×C83#58511yescharacteristic
703C22×C83#58511yescharacteristic
704C4×C83—22no—
705C4×C83—22no—
706C4×C83—22no—
707C4×C83—22no—
708C4×C83—22no—
709C4×C83—22no—
710C4×C83—22no—
711C4×C83—22no—
712C4×C83—22no—
713C4×C83—22no—
714C4×C83—22no—
715Dic83—22no—
716Dic83—41no—
717Dic83—41no—
718Dic83—41no—
719Dic83—41no—
720Dic83—41no—
721Dic83—41no—
722Dic83—41no—
723Dic83—41no—
724Dic83—41no—
725Dic83—41no—
726Dic83—41no—
727Dic83—41no—
728Dic83—41no—
729Dic83—41no—
730Dic83—41no—
731#34504—831nomaximal, Sylow
732C2×C83—42no—
733C2×C83—42no—
734C2×C83—42no—
735C2×C83—42no—
736C2×C83#342811yescharacteristic
737C2×C83#342811yescharacteristic
738C2×C83C4×H(5,𝔽2)11yescharacteristic
739C2×C83#356011yescharacteristic
740C2×C83#356211yescharacteristic
741C2×C83#356611yescharacteristic
742C2×C83#356811yescharacteristic
743C2×#551D8311yescharacteristic
744#2383—831no—
745#2378—831no—
746#2376—831no—
747#2375—831no—
748#2374—831no—
749#2373—831no—
750#2367—831no—
751#2362—831no—
752#2359—831no—
753#2354—831no—
754#2353—831no—
755#2347—831no—
756#2347—831no—
757#2342—831no—
758#2342—831no—
759#2337—831no—
760#2335—831no—
761#2335—831no—
762#2335—831no—
763#2334—831no—
764#2332—831no—
765#2323—831no—
766#2321—831no—
767#2318—831no—
768#2314—831no—
769#2312—831no—
770#2312—831no—
771C4×#126—831no—
772#2298—831no—
773#2293—831no—
774C83#3450411yescharacteristic, complemented, Sylow
775#551Dic83116yescomplemented
776C2×#126C2×D8311yescharacteristic
777C2×#126C2×D8311yescharacteristic
778C2×#124C2×D8311yescharacteristic
779C2×#123C2×D8311yescharacteristic
780C2×#123C2×D8311yescharacteristic
781C2×#123C2×D8311yescharacteristic
782C2×C22⋊Q8C2×D8311yescharacteristic
783C2×C22⋊Q8C2×D8311yescharacteristic
784C2×#120C2×D8311yescharacteristic
785C2×C4×Q8—831no—
786C2×C4×D4—831no—
787C2×C4×D4C2×D8311yescharacteristic
788C2×C4×D4C2×D8311yescharacteristic
789C2×#117—831no—
790C2×#117—831no—
791C2×#117—831no—
792C2×#117C2×D8311yescharacteristic
793C2×#117C2×D8311yescharacteristic
794C22×C22⋊C4—831no—
795C22×C22⋊C4C2×D8311yescharacteristic
796C22×C22⋊C4C2×D8311yescharacteristic
797#391—831no—
798#391—831no—
799#391—831no—
800#390—831no—
801#390—831no—
802#390—831no—
803#390—831no—
804#390—831no—
805#389—831no—
806#389—831no—
807#389—831no—
808#389—831no—
809#389—831no—
810#389—831no—
811#389—831no—
812#389—831no—
813#388—831no—
814#388—831no—
815#388—831no—
816#388—831no—
817#388—831no—
818#388—831no—
819#388—831no—
820#388—831no—
821#388—831no—
822#388—831no—
823#388—831no—
824#388—831no—
825#388—831no—
826#388—831no—
827#388—831no—
828#388—831no—
829#388—831no—
830#388—831no—
831#388—831no—
832#388—831no—
833#388—831no—
834#388—831no—
835#388—831no—
836#388—831no—
837#388—831no—
838#388—831no—
839#388—831no—
840#388—831no—
841#388—831no—
842#388—831no—
843#388—831no—
844#388—831no—
845#388—831no—
846#388—831no—
847#388—831no—
848#388—831no—
849#388—831no—
850#388—831no—
851#388—831no—
852#388—831no—
853#387—831no—
854#387—831no—
855#387—831no—
856#387—831no—
857#387—831no—
858#387—831no—
859#387—831no—
860#387—831no—
861#387—831no—
862#387—831no—
863#387—831no—
864#387—831no—
865#387—831no—
866#387—831no—
867#387—831no—
868#387—831no—
869#386—831no—
870#386—831no—
871#386—831no—
872#386—831no—
873#386—831no—
874#386—831no—
875#385—831no—
876#385—831no—
877#385—831no—
878#385—831no—
879#385—831no—
880#385—831no—
881#385—831no—
882#385—831no—
883#384—831no—
884#383—831no—
885#383—831no—
886#383—831no—
887#382—831no—
888#381—831no—
889#381—831no—
890#380—831no—
891#380—831no—
892#380—831no—
893#380—831no—
894#380—831no—
895#380—831no—
896#380—831no—
897#379—831no—
898#379—831no—
899#379—831no—
900C4×C4⋊C4—831no—
901C4×C4⋊C4—831no—
902C4×C4⋊C4—831no—
903C4×C4⋊C4—831no—
904C4×C4⋊C4—831no—
905C4×C4⋊C4—831no—
906C4×C4⋊C4—831no—
907C4×C4⋊C4—831no—
908C4×C4⋊C4—831no—
909C4×C4⋊C4—831no—
910C4×C4⋊C4—831no—
911C4×C4⋊C4—831no—
912C4×C4⋊C4—831no—
913C4×C22⋊C4—831no—
914C4×C22⋊C4—831no—
915C4×C22⋊C4—831no—
916C4×C22⋊C4—831no—
917C4×C22⋊C4—831no—
918C4×C22⋊C4—831no—
919C4×C22⋊C4—831no—
920C4×C22⋊C4—831no—
921C4×C22⋊C4—831no—
922C4×C22⋊C4—831no—
923C4×C22⋊C4—831no—
924C4×C22⋊C4—831no—
925C4×C22⋊C4—831no—
926C4×C22⋊C4—831no—
927C4×C22⋊C4—831no—
928#376—831no—
929C2×#95—831no—
930C43—831no—
931C25C22×D8311yescharacteristic
932C22×Q8C22×D8311yescharacteristic
933C22×D4C22×D8311yescharacteristic
934C22×D4C22×D8311yescharacteristic
935C22×D4C22×D8311yescharacteristic
936C23×C4—831no—
937C23×C4—831no—
938C23×C4—831no—
939C23×C4—831no—
940C23×C4C22×D8311yescharacteristic
941C23×C4C22×D8311yescharacteristic
942C23×C4C22×D8311yescharacteristic
943C23×C4C22×D8311yescharacteristic
944C23×C4C22×D8311yescharacteristic
945#126C2×Dic8318yescomplemented
946#126C2×Dic8318yescomplemented
947#124C2×Dic8318yes—
948#123C2×Dic8318yes—
949#123C2×Dic8318yescomplemented
950#123C2×Dic8318yescomplemented
951C22⋊Q8C2×Dic8318yescomplemented
952C22⋊Q8C2×Dic8318yescomplemented
953#120C2×Dic8318yes—
954C4×Q8—3322no—
955C4×D4—3322no—
956C4×D4C2×Dic8318yescomplemented
957C4×D4C2×Dic8318yescomplemented
958#117—3322no—
959#117—3322no—
960#117—3322no—
961#117C2×Dic8318yescomplemented
962#117C2×Dic8318yescomplemented
963C2×C4⋊C4—831no—
964C2×C4⋊C4—831no—
965C2×C4⋊C4—831no—
966C2×C4⋊C4—831no—
967C2×C4⋊C4—831no—
968C2×C4⋊C4—831no—
969C2×C4⋊C4—831no—
970C2×C4⋊C4—831no—
971C2×C4⋊C4—831no—
972C2×C4⋊C4—831no—
973C2×C4⋊C4—831no—
974C2×C4⋊C4—831no—
975C2×C4⋊C4—831no—
976C2×C4⋊C4—831no—
977C2×C4⋊C4—831no—
978C2×C4⋊C4—831no—
979C2×C4⋊C4—831no—
980C2×C4⋊C4—831no—
981C2×C4⋊C4—831no—
982C2×C4⋊C4—831no—
983C2×C4⋊C4—831no—
984C2×C4⋊C4—831no—
985C2×C4⋊C4C22×D8311yescharacteristic
986C2×C4⋊C4C22×D8311yescharacteristic
987C2×C4⋊C4C22×D8311yescharacteristic
988C2×C4⋊C4C22×D8311yescharacteristic
989C2×C4⋊C4C22×D8311yescharacteristic
990C2×C4⋊C4C22×D8311yescharacteristic
991C2×C4⋊C4C22×D8311yescharacteristic
992C2×C4⋊C4C22×D8311yescharacteristic
993C2×C22⋊C4—3322no—
994C2×C22⋊C4—831no—
995C2×C22⋊C4—831no—
996C2×C22⋊C4—831no—
997C2×C22⋊C4—831no—
998C2×C22⋊C4—831no—
999C2×C22⋊C4—831no—
1000C2×C22⋊C4—831no—
1001C2×C22⋊C4—831no—
1002C2×C22⋊C4—831no—
1003C2×C22⋊C4—831no—
1004C2×C22⋊C4—831no—
1005C2×C22⋊C4—831no—
1006C2×C22⋊C4—831no—
1007C2×C22⋊C4—831no—
1008C2×C22⋊C4—831no—
1009C2×C22⋊C4—831no—
1010C2×C22⋊C4—831no—
1011C2×C22⋊C4—831no—
1012C2×C22⋊C4—831no—
1013C2×C22⋊C4—831no—
1014C2×C22⋊C4—831no—
1015C2×C22⋊C4—831no—
1016C2×C22⋊C4—831no—
1017C2×C22⋊C4—831no—
1018C2×C22⋊C4—831no—
1019C2×C22⋊C4—831no—
1020C2×C22⋊C4—831no—
1021C2×C22⋊C4—831no—
1022C2×C22⋊C4C2×Dic8318yescomplemented
1023C2×C22⋊C4C2×Dic8318yescomplemented
1024C2×C22⋊C4C22×D8311yescharacteristic
1025C2×C22⋊C4C22×D8311yescharacteristic
1026C2×C22⋊C4C22×D8311yescharacteristic
1027C2×C22⋊C4C22×D8311yescharacteristic
1028C2×C22⋊C4C22×D8311yescharacteristic
1029C2×C22⋊C4C22×D8311yescharacteristic
1030C2×C22⋊C4C22×D8311yescharacteristic
1031C2×C22⋊C4C22×D8311yescharacteristic
1032C2×C22⋊C4C22×D8311yescharacteristic
1033C2×C22⋊C4C22×D8311yescharacteristic
1034C2×C22⋊C4C22×D8311yescharacteristic
1035C2×C22⋊C4C22×D8311yescharacteristic
1036C2×C22⋊C4C22×D8311yescharacteristic
1037C2×C22⋊C4C22×D8311yescharacteristic
1038C2×C42—831no—
1039C2×C42—831no—
1040C2×C42—831no—
1041C2×C42—831no—
1042C2×C42—831no—
1043C2×C42—831no—
1044C2×C42—831no—
1045C2×C42—831no—
1046C2×C42—831no—
1047C2×C42—831no—
1048C2×C42—831no—
1049C2×C42—831no—
1050C2×C42—831no—
1051C2×C42—831no—
1052C2×C42—831no—
1053C2×C42—831no—
1054C2×C42—831no—
1055C2×C42—831no—
1056C2×C42—831no—
1057C2×C42—831no—
1058C2×C42—831no—
1059C2×C42—831no—
1060C2×C42C22×D8311yescharacteristic
1061C2×C42C22×D8311yescharacteristic
1062C2×C42C22×D8311yescharacteristic
1063#95—831no—
1064#95—831no—
1065#95—831no—
1066#95—831no—
1067#95—831no—
1068#95—831no—
1069#95—831no—
1070#95—831no—
1071#95—831no—
1072#95—831no—
1073#95—831no—
1074#95—831no—
1075#95—831no—
1076#95—831no—
1077#95—831no—
1078#95—831no—
1079#95—831no—
1080#95—831no—
1081#95—831no—
1082#95—831no—
1083#95—831no—
1084#95—831no—
1085#95—831no—
1086#95—831no—
1087#95—831no—
1088#95—831no—
1089#95—831no—
1090#95—831no—
1091#95—831no—
1092#95—831no—
1093#95—831no—
1094#95—831no—
1095#95—831no—
1096#95—831no—
1097#95—831no—
1098#95—831no—
1099#95—831no—
1100#95—831no—
1101#95—831no—
1102#95—831no—
1103#95—831no—
1104#95—831no—
1105#95—831no—
1106#95—831no—
1107C24—41no—
1108C24—41no—
1109C24—41no—
1110C24—41no—
1111C24—41no—
1112C24—41no—
1113C24C22×Dic8314yes—
1114C24C23×D8311yescharacteristic
1115C24C23×D8311yescharacteristic
1116C24C23×D8311yescharacteristic
1117C24C23×D8311yescharacteristic
1118C2×Q8—41no—
1119C2×Q8—41no—
1120C2×Q8C22×Dic8314yes—
1121C2×D4—41no—
1122C2×D4—41no—
1123C2×D4—41no—
1124C2×D4—41no—
1125C2×D4—41no—
1126C2×D4—41no—
1127C2×D4C22×Dic8314yes—
1128C2×D4C22×Dic8314yes—
1129C2×D4C22×Dic8314yes—
1130C22×C4—41no—
1131C22×C4—41no—
1132C22×C4—41no—
1133C22×C4—41no—
1134C22×C4—41no—
1135C22×C4—41no—
1136C22×C4—41no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4—41no—
1140C22×C4—3321no—
1141C22×C4—3321no—
1142C22×C4—3321no—
1143C22×C4—3321no—
1144C22×C4—3321no—
1145C22×C4—3321no—
1146C22×C4—3321no—
1147C22×C4—3321no—
1148C22×C4—3321no—
1149C22×C4—3321no—
1150C22×C4—3321no—
1151C22×C4—831no—
1152C22×C4—831no—
1153C22×C4—831no—
1154C22×C4—831no—
1155C22×C4—831no—
1156C22×C4—831no—
1157C22×C4—831no—
1158C22×C4—831no—
1159C22×C4—831no—
1160C22×C4—831no—
1161C22×C4—831no—
1162C22×C4—831no—
1163C22×C4—831no—
1164C22×C4—831no—
1165C22×C4—831no—
1166C22×C4—831no—
1167C22×C4—1662no—
1168C22×C4C22×Dic8314yes—
1169C22×C4C22×Dic8314yes—
1170C22×C4C22×Dic8314yes—
1171C22×C4C22×Dic8314yes—
1172C22×C4C22×Dic8314yes—
1173C22×C4C23×D8311yescharacteristic
1174C22×C4C23×D8311yescharacteristic
1175C22×C4C23×D8311yescharacteristic
1176C22×C4C23×D8311yescharacteristic
1177C22×C4C23×D8311yescharacteristic
1178C22×C4C23×D8311yescharacteristic
1179C22×C4C23×D8311yescharacteristic
1180C22×C4C23×D8311yescharacteristic
1181C22×C4C23×D8311yescharacteristic
1182C22×C4C23×D8311yescharacteristic
1183C22×C4C23×D8311yescharacteristic
1184C4⋊C4—3321no—
1185C4⋊C4—3321no—
1186C4⋊C4—3321no—
1187C4⋊C4—3321no—
1188C4⋊C4—3321no—
1189C4⋊C4—3321no—
1190C4⋊C4—3321no—
1191C4⋊C4—3321no—
1192C4⋊C4—3321no—
1193C4⋊C4—3321no—
1194C4⋊C4—3321no—
1195C4⋊C4—3321no—
1196C4⋊C4—3321no—
1197C4⋊C4—3321no—
1198C4⋊C4—3321no—
1199C4⋊C4—3321no—
1200C4⋊C4—3321no—
1201C4⋊C4—3321no—
1202C4⋊C4—3321no—
1203C4⋊C4—1662no—
1204C4⋊C4—1662no—
1205C4⋊C4—1662no—
1206C4⋊C4C22×Dic8314yes—
1207C4⋊C4C22×Dic8314yes—
1208C4⋊C4C22×Dic8314yes—
1209C4⋊C4C22×Dic8314yes—
1210C4⋊C4C22×Dic8314yes—
1211C4⋊C4C22×Dic8314yes—
1212C4⋊C4C22×Dic8314yes—
1213C4⋊C4C22×Dic8314yes—
1214C22⋊C4—3321no—
1215C22⋊C4—3321no—
1216C22⋊C4—3321no—
1217C22⋊C4—3321no—
1218C22⋊C4—3321no—
1219C22⋊C4—3321no—
1220C22⋊C4—3321no—
1221C22⋊C4—3321no—
1222C22⋊C4—3321no—
1223C22⋊C4—3321no—
1224C22⋊C4—3321no—
1225C22⋊C4—3321no—
1226C22⋊C4—3321no—
1227C22⋊C4—3321no—
1228C22⋊C4—3321no—
1229C22⋊C4—3321no—
1230C22⋊C4—3321no—
1231C22⋊C4—3321no—
1232C22⋊C4—3321no—
1233C22⋊C4—3321no—
1234C22⋊C4—3321no—
1235C22⋊C4—3321no—
1236C22⋊C4—3321no—
1237C22⋊C4—3321no—
1238C22⋊C4—3321no—
1239C22⋊C4—1662no—
1240C22⋊C4—1662no—
1241C22⋊C4—1662no—
1242C22⋊C4C22×Dic8314yes—
1243C22⋊C4C22×Dic8314yes—
1244C22⋊C4C22×Dic8314yes—
1245C22⋊C4C22×Dic8314yes—
1246C22⋊C4C22×Dic8314yes—
1247C22⋊C4C22×Dic8314yes—
1248C22⋊C4C22×Dic8314yes—
1249C22⋊C4C22×Dic8314yes—
1250C22⋊C4C22×Dic8314yes—
1251C22⋊C4C22×Dic8314yes—
1252C22⋊C4C22×Dic8314yes—
1253C22⋊C4C22×Dic8314yes—
1254C22⋊C4C22×Dic8314yes—
1255C22⋊C4C22×Dic8314yes—
1256C42—3321no—
1257C42—3321no—
1258C42—3321no—
1259C42—3321no—
1260C42—3321no—
1261C42—3321no—
1262C42—3321no—
1263C42—3321no—
1264C42—3321no—
1265C42—3321no—
1266C42—3321no—
1267C42—3321no—
1268C42—3321no—
1269C42—3321no—
1270C42—3321no—
1271C42—3321no—
1272C42—3321no—
1273C42—3321no—
1274C42—3321no—
1275C42—3321no—
1276C42—1662no—
1277C42—1662no—
1278C42C22×Dic8314yes—
1279C42C22×Dic8314yes—
1280C42C22×Dic8314yes—
1281C23—21no—
1282C23—21no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—44no—
1306C23—44no—
1307C23—44no—
1308C23—82no—
1309C23—82no—
1310C23—82no—
1311C23—82no—
1312C23C23×Dic8312yes—
1313C23C23×Dic8312yes—
1314C23C23×Dic8312yes—
1315C23C23×Dic8312yes—
1316C23C24×D8311yescharacteristic
1317Q8—44no—
1318D4—44no—
1319D4—44no—
1320D4—44no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—44no—
1344C2×C4—44no—
1345C2×C4—44no—
1346C2×C4—44no—
1347C2×C4—44no—
1348C2×C4—832no—
1349C2×C4—6642no—
1350C2×C4—6642no—
1351C2×C4—6642no—
1352C2×C4—6642no—
1353C2×C4—1661no—
1354C2×C4—1661no—
1355C2×C4—1661no—
1356C2×C4—1661no—
1357C2×C4—1661no—
1358C2×C4—1661no—
1359C2×C4—1661no—
1360C2×C4—1661no—
1361C2×C4—1661no—
1362C2×C4—1661no—
1363C2×C4—1661no—
1364C2×C4—1661no—
1365C2×C4—1661no—
1366C2×C4—1661no—
1367C2×C4—1661no—
1368C2×C4—1661no—
1369C2×C4—1661no—
1370C2×C4—1661no—
1371C2×C4—1661no—
1372C2×C4—1661no—
1373C2×C4—1661no—
1374C2×C4—1661no—
1375C2×C4—1661no—
1376C2×C4—1661no—
1377C2×C4—1661no—
1378C2×C4—1661no—
1379C2×C4—1661no—
1380C2×C4—1661no—
1381C2×C4—1661no—
1382C2×C4—1661no—
1383C2×C4—1661no—
1384C2×C4—1661no—
1385C2×C4—1661no—
1386C2×C4—1661no—
1387C2×C4—1661no—
1388C2×C4—1661no—
1389C2×C4—1661no—
1390C2×C4—1661no—
1391C2×C4—1661no—
1392C2×C4—1661no—
1393C2×C4—1661no—
1394C2×C4—1661no—
1395C2×C4—1661no—
1396C2×C4—1661no—
1397C2×C4—1661no—
1398C2×C4—1661no—
1399C2×C4—1661no—
1400C2×C4C23×Dic8312yes—
1401C2×C4C23×Dic8312yes—
1402C2×C4C23×Dic8312yes—
1403C2×C4C23×Dic8312yes—
1404C2×C4C23×Dic8312yes—
1405C2×C4C23×Dic8312yes—
1406C2×C4C23×Dic8312yes—
1407C2×C4C23×Dic8312yes—
1408C2×C4C23×Dic8312yes—
1409C2×C4C23×Dic8312yes—
1410C2×C4C23×Dic8312yes—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—22no—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—41no—
1439C22—88no—
1440C22C24×Dic8311yescharacteristic
1441C22H(5,𝔽2)×D8311yescharacteristic
1442C22#1912853611yescharacteristic
1443C22#1912853711yescharacteristic
1444C22#1912853711yescharacteristic
1445C22#1912853711yescharacteristic
1446C22#1912853711yescharacteristic
1447C4—22no—
1448C4—22no—
1449C4—22no—
1450C4—22no—
1451C4—22no—
1452C4—22no—
1453C4—22no—
1454C4—22no—
1455C4—22no—
1456C4—22no—
1457C4—22no—
1458C4—3321no—
1459C4—3321no—
1460C4—3321no—
1461C4—3321no—
1462C4—3321no—
1463C4—3321no—
1464C4—3321no—
1465C4—3321no—
1466C4—3321no—
1467C4—3321no—
1468C4—3321no—
1469C4—3321no—
1470C4—3321no—
1471C4—3321no—
1472C4—3321no—
1473C4—1662no—
1474C2—42no—
1475C2—42no—
1476C2—42no—
1477C2—42no—
1478C2#2492066611yescharacteristic
1479C2#2492066611yescharacteristic
1480C2H(5,𝔽2)×Dic8311yescharacteristic
1481C2#2492201011yescharacteristic
1482C2#2492204411yescharacteristic
1483C2#2492212111yescharacteristic
1484C2#2492215411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC2×#551×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#120×C83C22
hypercenterC2×#551D83
hypocenterC83#34504
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #24910655C2semidirect
2. #24910629C2semidirect
3. #24910611C2semidirect
5. #24910599C2semidirect
6. #24910587C2semidirect
7. #24910538C2semidirect
8. #24910494C2semidirect
9. #24910459C2semidirect
10. #24910412C2semidirect
11. #24910403C2semidirect
12. #24910356C2semidirect
13. #24910356C2semidirect
14. #24910312C2semidirect
15. #24910312C2semidirect
16. #24910278C2semidirect
17. #24910257C2semidirect
18. #24910257C2semidirect
19. #24910257C2semidirect
20. #24910242C2semidirect
21. #24910221C2semidirect
22. #24910147C2semidirect
24. #24910096C2semidirect
25. #24910072C2semidirect
26. #24910061C2semidirect
27. #24910061C2semidirect
28. #126×Dic83C2semidirect
29. #24909961C2semidirect
30. #24909928C2semidirect
32. C2×Q8×Dic83C22semidirect
36. C2×#14581751C22semidirect
38. #19127608C22semidirect
39. #19127608C22semidirect
40. #19127608C22semidirect
46. #19127600C22semidirect
47. #19127600C22semidirect
48. #19127600C22semidirect
49. #19127600C22semidirect
50. #19127600C22semidirect
51. #19127600C22semidirect
52. #19127600C22semidirect
53. #19127600C22semidirect
88. #19127594C22semidirect
89. #19127594C22semidirect
90. #19127594C22semidirect
91. #19127594C22semidirect
92. #19127594C22semidirect
93. #19127594C22semidirect
94. #19127587C22semidirect
95. #19127587C22semidirect
96. #19127587C22semidirect
97. #19127587C22semidirect
98. #19127587C22semidirect
99. #19127587C22semidirect
100. #19127587C22semidirect
101. #19127587C22semidirect
102. #19127587C22semidirect
103. #19127587C22semidirect
104. #19127587C22semidirect
105. #19127587C22semidirect
106. #19127587C22semidirect
107. #19127587C22semidirect
108. #19127587C22semidirect
109. #19127587C22semidirect
121. #19127576C22semidirect
122. #19127576C22semidirect
123. #19127576C22semidirect
124. #19127571C22semidirect
125. #19127569C22semidirect
126. #19127569C22semidirect
127. #19127569C22semidirect
128. #19127567C22semidirect
137. #19127561C22semidirect
141. C4⋊C4×Dic83C22semidirect
142. C4⋊C4×Dic83C22semidirect
143. C4⋊C4×Dic83C22semidirect
144. C4⋊C4×Dic83C22semidirect
145. C4⋊C4×Dic83C22semidirect
146. C4⋊C4×Dic83C22semidirect
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
159. C22⋊C4×Dic83C22semidirect
160. C22⋊C4×Dic83C22semidirect
161. C22⋊C4×Dic83C22semidirect
168. C4×C22⋊Dic83C22semidirect
169. #19127547C22semidirect
170. C2×C83⋊#95C22semidirect
171. C42×Dic83C22semidirect
172. #551×C83C4semidirect
324. #126×C83C2×C4semidirect
325. #126×C83C2×C4semidirect
328. #123×C83C2×C4semidirect
329. #123×C83C2×C4semidirect
330. C22⋊Q8×C83C2×C4semidirect
331. C22⋊Q8×C83C2×C4semidirect
333. C4×D4×C83C2×C4semidirect
334. C4×D4×C83C2×C4semidirect
335. #117×C83C2×C4semidirect
336. #117×C83C2×C4semidirect
345. C2×C22⋊C4×C83C2×C4semidirect
346. C2×C22⋊C4×C83C2×C4semidirect
774. C83#34504semidirect
775. #551Dic83semidirect
945. #126C2×Dic83semidirect
946. #126C2×Dic83semidirect
949. #123C2×Dic83semidirect
950. #123C2×Dic83semidirect
951. C22⋊Q8C2×Dic83semidirect
952. C22⋊Q8C2×Dic83semidirect
956. C4×D4C2×Dic83semidirect
957. C4×D4C2×Dic83semidirect
961. #117C2×Dic83semidirect
962. #117C2×Dic83semidirect
1022. C2×C22⋊C4C2×Dic83semidirect
1023. C2×C22⋊C4C2×Dic83semidirect

Maximal subgroups

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

subgroupindex
#249106552
#249106292
#249106112
#249106042
#249105992
#249105872
#249105382
#249104942
#249104592
#249104122
#249104032
#249103562
#249103122
#249102782
#249102572
#249102422
#249102212
#249101472
#249101242
#249100962
#249100722
#249100612
#126×Dic832
#249099612
#249099282
C2×#551×C832
#3450483