Finite Group Databasebeta

← #35566537

Subgroups — #35566537

Order 21248.

2396 conjugacy classes of subgroups.

The subgroup lattice has 1522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128382C211yesmaximal, characteristic
2#24910596C211yesmaximal, characteristic, complemented
3#24910596C211yesmaximal, characteristic, complemented
4#24910585C211yesmaximal, characteristic, complemented
5#24910578C211yesmaximal, characteristic, complemented
6#24910541C211yesmaximal, characteristic, complemented
7#24910536C211yesmaximal, characteristic, complemented
8#24910487C211yesmaximal, characteristic, complemented
9#24910449C211yesmaximal, characteristic, complemented
10#24910435C211yesmaximal, characteristic, complemented
11#24910401C211yesmaximal, characteristic, complemented
12#24910353C211yesmaximal, characteristic, complemented
13#24910321C211yesmaximal, characteristic, complemented
14#24910308C211yesmaximal, characteristic, complemented
15#24910308C211yesmaximal, characteristic, complemented
16#24910272C211yesmaximal, characteristic, complemented
17#24910250C211yesmaximal, characteristic, complemented
18#24910233C211yesmaximal, characteristic, complemented
19#24910213C211yesmaximal, characteristic, complemented
20#24910137C211yesmaximal, characteristic, complemented
21#24910124C211yesmaximal, characteristic
22C4×#14581785C211yesmaximal, characteristic, complemented
23#24909995C211yesmaximal, characteristic, complemented
24C4×#14581773C211yesmaximal, characteristic, complemented
25#24909957C211yesmaximal, characteristic, complemented
26#24909903C211yesmaximal, characteristic, complemented
27C2×#19127589C211yesmaximal, characteristic, complemented
28#24909818C211yesmaximal, characteristic, complemented
29#24909816C211yesmaximal, characteristic, complemented
30C4×D4×Dic83C211yesmaximal, characteristic, complemented
31C83×#2358C211yesmaximal, characteristic
32#19128382C4116yescomplemented
33C2×#14581785C2211yescharacteristic
34C2×#14581785C2211yescharacteristic
35C2×#14581779C2211yescharacteristic
36C2×#14581773C2211yescharacteristic
37C2×#14581773C2211yescharacteristic
38C2×#14581773C2211yescharacteristic
39C2×#14581769C2211yescharacteristic
40C2×#14581769C2211yescharacteristic
41C2×#14581757C2211yescharacteristic, complemented
42C2×D4×Dic83C2211yescharacteristic
43C2×D4×Dic83C2211yescharacteristic
44C2×D4×Dic83C2211yescharacteristic
45C2×#14581748C2211yescharacteristic
46C2×#14581748C2211yescharacteristic
47C2×#14581748C2211yescharacteristic
48C2×#14581748C2211yescharacteristic
49C22×Dic83⋊C4C2211yescharacteristic
50C22×C22⋊Dic83C2211yescharacteristic
51C22×C22⋊Dic83C2211yescharacteristic
52C22×C22⋊Dic83C2211yescharacteristic
53C22×C4×Dic83C2211yescharacteristic
54C22×C4×Dic83C2211yescharacteristic, complemented
55#19127607C2211yescharacteristic, complemented
56#19127605C2211yescharacteristic, complemented
57#19127605C2211yescharacteristic, complemented
58#19127604C2211yescharacteristic
59#19127604C2211yescharacteristic
60#19127598C2211yescharacteristic, complemented
61#19127598C2211yescharacteristic, complemented
62#19127596C2211yescharacteristic, complemented
63#19127596C2211yescharacteristic, complemented
64#19127595C2211yescharacteristic
65#19127595C2211yescharacteristic
66#19127595C2211yescharacteristic
67#19127595C2211yescharacteristic
68#19127595C2211yescharacteristic, complemented
69#19127595C2211yescharacteristic, complemented
70#19127594C2211yescharacteristic
71#19127594C2211yescharacteristic
72#19127594C2211yescharacteristic
73#19127594C2211yescharacteristic
74#19127589C2211yescharacteristic
75#19127589C2211yescharacteristic
76#19127589C2211yescharacteristic
77#19127589C2211yescharacteristic
78#19127589C2211yescharacteristic
79#19127589C2211yescharacteristic
80#19127589C2211yescharacteristic
81#19127589C2211yescharacteristic
82#19127589C2211yescharacteristic
83#19127589C2211yescharacteristic
84#19127589C2211yescharacteristic
85#19127589C2211yescharacteristic
86#19127589C2211yescharacteristic, complemented
87#19127589C2211yescharacteristic, complemented
88#19127589C2211yescharacteristic, complemented
89#19127589C2211yescharacteristic, complemented
90#19127588C2211yescharacteristic, complemented
91#19127588C2211yescharacteristic, complemented
92#19127588C2211yescharacteristic, complemented
93#19127588C2211yescharacteristic, complemented
94#19127586C2211yescharacteristic, complemented
95#19127586C2211yescharacteristic, complemented
96#19127585C2211yescharacteristic, complemented
97#19127585C2211yescharacteristic, complemented
98#19127584C2211yescharacteristic, complemented
99#19127584C2211yescharacteristic, complemented
100#19127583C2211yescharacteristic, complemented
101#19127583C2211yescharacteristic, complemented
102#19127582C2211yescharacteristic, complemented
103#19127582C2211yescharacteristic, complemented
104#19127582C2211yescharacteristic, complemented
105#19127582C2211yescharacteristic, complemented
106#19127581C2211yescharacteristic
107#19127581C2211yescharacteristic
108#19127581C2211yescharacteristic
109#19127576C2211yescharacteristic
110#19127574C2211yescharacteristic
111#19127574C2211yescharacteristic
112#19127574C2211yescharacteristic
113#19127574C2211yescharacteristic
114#19127574C2211yescharacteristic, complemented
115#19127573C2211yescharacteristic, complemented
116#19127573C2211yescharacteristic, complemented
117#19127568C2211yescharacteristic, complemented
118#19127568C2211yescharacteristic, complemented
119#19127566C2211yescharacteristic, complemented
120#19127562C2211yescharacteristic
121#19127562C2211yescharacteristic
122#19127562C2211yescharacteristic, complemented
123#19127559C2211yescharacteristic
124#19127559C2211yescharacteristic
125#19127557C2211yescharacteristic
126C4⋊C4×Dic83C2211yescharacteristic, complemented
127C4⋊C4×Dic83C2211yescharacteristic, complemented
128C4⋊C4×Dic83C2211yescharacteristic, complemented
129C4⋊C4×Dic83C2211yescharacteristic, complemented
130C4×Dic83⋊C4C2211yescharacteristic, complemented
131C4×Dic83⋊C4C2211yescharacteristic, complemented
132C4×Dic83⋊C4C2211yescharacteristic, complemented
133C4×Dic83⋊C4C2211yescharacteristic, complemented
134C4×Dic83⋊C4C2211yescharacteristic, complemented
135C4×Dic83⋊C4C2211yescharacteristic, complemented
136C4×C4⋊Dic83C2211yescharacteristic, complemented
137C4×C4⋊Dic83C2211yescharacteristic, complemented
138#19127552C2211yescharacteristic, complemented
139#19127552C2211yescharacteristic, complemented
140#19127552C2211yescharacteristic, complemented
141#19127552C2211yescharacteristic, complemented
142#19127552C2211yescharacteristic, complemented
143#19127552C2211yescharacteristic, complemented
144C22⋊C4×Dic83C2211yescharacteristic
145C22⋊C4×Dic83C2211yescharacteristic
146C22⋊C4×Dic83C2211yescharacteristic
147C22⋊C4×Dic83C2211yescharacteristic
148C22⋊C4×Dic83C2211yescharacteristic
149C22⋊C4×Dic83C2211yescharacteristic
150C22⋊C4×Dic83C2211yescharacteristic
151C22⋊C4×Dic83C2211yescharacteristic
152C22⋊C4×Dic83C2211yescharacteristic
153C22⋊C4×Dic83C2211yescharacteristic
154C22⋊C4×Dic83C2211yescharacteristic
155C22⋊C4×Dic83C2211yescharacteristic, complemented
156C22⋊C4×Dic83C2211yescharacteristic, complemented
157C22⋊C4×Dic83C2211yescharacteristic, complemented
158C4×C22⋊Dic83C2211yescharacteristic
159C4×C22⋊Dic83C2211yescharacteristic
160C4×C22⋊Dic83C2211yescharacteristic
161C4×C22⋊Dic83C2211yescharacteristic
162C4×C22⋊Dic83C2211yescharacteristic
163C4×C22⋊Dic83C2211yescharacteristic
164C4×C22⋊Dic83C2211yescharacteristic
165C4×C22⋊Dic83C2211yescharacteristic
166C4×C22⋊Dic83C2211yescharacteristic, complemented
167C4×C22⋊Dic83C2211yescharacteristic, complemented
168#19127546C2211yescharacteristic, complemented
169#19127546C2211yescharacteristic, complemented
170C2×C83⋊#95C2211yescharacteristic
171C2×C83⋊#95C2211yescharacteristic
172C42×Dic83C2211yescharacteristic, complemented
173C2×#120×C83C2211yescharacteristic
174C2×C4×D4×C83C2211yescharacteristic
175C2×C4×D4×C83C2211yescharacteristic
176C22×C22⋊C4×C83C2211yescharacteristic
177C22×C22⋊C4×C83C2211yescharacteristic
178#390×C83C2211yescharacteristic
179#388×C83C2211yescharacteristic
180#388×C83C2211yescharacteristic
181#386×C83C2211yescharacteristic
182#386×C83C2211yescharacteristic
183#386×C83C2211yescharacteristic
184#385×C83C2211yescharacteristic
185#385×C83C2211yescharacteristic
186C4×C22⋊C4×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic
188C22×Dic166C2311yescharacteristic
189C23×Dic83C2311yescharacteristic
190C23×Dic83C2311yescharacteristic
191C23×Dic83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C23×Dic83C2311yescharacteristic
194C23×Dic83C2311yescharacteristic
195C23×Dic83C2311yescharacteristic
196C23×Dic83C2311yescharacteristic
197#14581785C2×C418yescomplemented
198#14581785C2×C418yescomplemented
199#14581779C2×C418yescomplemented
200#14581773C2×C418yescomplemented
201#14581773C2×C418yescomplemented
202#14581773C2×C418yescomplemented
203#14581769C2×C418yescomplemented
204#14581769C2×C418yescomplemented
205#14581757—42no—
206D4×Dic83—24no—
207D4×Dic83C2×C418yescomplemented
208D4×Dic83C2×C418yescomplemented
209#14581748—24no—
210#14581748—42no—
211#14581748C2×C418yescomplemented
212#14581748C2×C418yescomplemented
213C2×C4⋊Dic83C2311yescharacteristic
214C2×C4⋊Dic83C2311yescharacteristic
215C2×C4⋊Dic83C2311yescharacteristic
216C2×C4⋊Dic83C2311yescharacteristic
217C2×C4⋊Dic83C2311yescharacteristic
218C2×Dic83⋊C4—24no—
219C2×Dic83⋊C4C2311yescharacteristic
220C2×Dic83⋊C4C2311yescharacteristic
221C2×Dic83⋊C4C2311yescharacteristic
222C2×Dic83⋊C4C2311yescharacteristic
223C2×Dic83⋊C4C2311yescharacteristic
224C2×Dic83⋊C4C2311yescharacteristic
225C2×Dic83⋊C4C2311yescharacteristic
226C2×Dic83⋊C4C2311yescharacteristic
227C2×Dic83⋊C4C2311yescharacteristic
228C2×Dic83⋊C4C2311yescharacteristic
229C2×Dic83⋊C4C2311yescharacteristic
230C2×Dic83⋊C4C2311yescharacteristic
231C2×Dic83⋊C4C2311yescharacteristic
232C2×Dic83⋊C4C2311yescharacteristic
233C2×Dic83⋊C4C2311yescharacteristic
234C2×Dic83⋊C4C2311yescharacteristic
235C2×Dic83⋊C4C2311yescharacteristic
236C2×Dic83⋊C4C2311yescharacteristic
237C2×C22⋊Dic83—24no—
238C2×C22⋊Dic83C2×C418yescomplemented
239C2×C22⋊Dic83C2×C418yescomplemented
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×C4×Dic83—42no—
265C2×C4×Dic83—42no—
266C2×C4×Dic83C2311yescharacteristic
267C2×C4×Dic83C2311yescharacteristic
268C2×C4×Dic83C2311yescharacteristic
269C2×C4×Dic83C2311yescharacteristic
270C2×C4×Dic83C2311yescharacteristic
271C2×C4×Dic83C2311yescharacteristic
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
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
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
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C25×C83C2311yescharacteristic
331C22×D4×C83C2311yescharacteristic
332C22×D4×C83C2311yescharacteristic
333C22×D4×C83C2311yescharacteristic
334C23×C4×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336C23×C4×C83C2311yescharacteristic
337C23×C4×C83C2311yescharacteristic
338C23×C4×C83C2311yescharacteristic
339#120×C83C2×C418yes—
340C4×D4×C83—24no—
341C4×D4×C83—42no—
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C22⋊C4×C83—24no—
346C2×C22⋊C4×C83—42no—
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
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370C2×Dic166—41no—
371C2×Dic166—41no—
372C2×Dic166C22×C414yes—
373C22×Dic83—22no—
374C22×Dic83—22no—
375C22×Dic83—22no—
376C22×Dic83—22no—
377C22×Dic83—41no—
378C22×Dic83—41no—
379C22×Dic83—41no—
380C22×Dic83—41no—
381C22×Dic83—41no—
382C22×Dic83—41no—
383C22×Dic83—41no—
384C22×Dic83—41no—
385C22×Dic83—41no—
386C22×Dic83—41no—
387C22×Dic83—41no—
388C22×Dic83—41no—
389C22×Dic83—41no—
390C22×Dic83—41no—
391C22×Dic83C22×C414yes—
392C22×Dic83C22×C414yes—
393C22×Dic83C22×C414yes—
394C22×Dic83C22×C414yes—
395C22×Dic83C22×C414yes—
396C22×Dic83#4114yes—
397C22×Dic83C2411yescharacteristic
398C22×Dic83C2411yescharacteristic
399C22×Dic83C2411yescharacteristic
400C22×Dic83C2411yescharacteristic
401C22×Dic83C2411yescharacteristic
402C22×Dic83C2411yescharacteristic
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2411yescharacteristic
405C22×Dic83C2411yescharacteristic
406C22×Dic83C2411yescharacteristic
407C22×Dic83C2411yescharacteristic
408C22×Dic83C2411yescharacteristic
409C22×Dic83C2411yescharacteristic
410C22×Dic83C2411yescharacteristic
411C22×Dic83C2411yescharacteristic
412C22×Dic83C2411yescharacteristic
413C4⋊Dic83—22no—
414C4⋊Dic83—41no—
415C4⋊Dic83—41no—
416C4⋊Dic83C22×C414yes—
417C4⋊Dic83C22×C414yes—
418Dic83⋊C4—22no—
419Dic83⋊C4—22no—
420Dic83⋊C4—22no—
421Dic83⋊C4—22no—
422Dic83⋊C4—22no—
423Dic83⋊C4—22no—
424Dic83⋊C4—22no—
425Dic83⋊C4—41no—
426Dic83⋊C4—41no—
427Dic83⋊C4—41no—
428Dic83⋊C4—41no—
429Dic83⋊C4—41no—
430Dic83⋊C4C22×C414yes—
431Dic83⋊C4C22×C414yes—
432Dic83⋊C4C22×C414yes—
433Dic83⋊C4C22×C414yes—
434Dic83⋊C4C22×C414yes—
435Dic83⋊C4C22×C414yes—
436C22⋊Dic83—22no—
437C22⋊Dic83—22no—
438C22⋊Dic83—22no—
439C22⋊Dic83—22no—
440C22⋊Dic83—22no—
441C22⋊Dic83—22no—
442C22⋊Dic83—22no—
443C22⋊Dic83—41no—
444C22⋊Dic83—41no—
445C22⋊Dic83—41no—
446C22⋊Dic83—41no—
447C22⋊Dic83—41no—
448C22⋊Dic83—41no—
449C22⋊Dic83C22×C414yes—
450C22⋊Dic83C22×C414yes—
451C22⋊Dic83C22×C414yes—
452C22⋊Dic83C22×C414yes—
453C22⋊Dic83C22×C414yes—
454C22⋊Dic83C22×C414yes—
455C22⋊Dic83C22×C414yes—
456C22⋊Dic83C22×C414yes—
457C22⋊Dic83C22×C414yes—
458C22⋊Dic83C22×C414yes—
459C22⋊Dic83C22×C414yes—
460C4×Dic83—22no—
461C4×Dic83—22no—
462C4×Dic83—22no—
463C4×Dic83—22no—
464C4×Dic83—22no—
465C4×Dic83—22no—
466C4×Dic83—41no—
467C4×Dic83—41no—
468C4×Dic83—41no—
469C4×Dic83—41no—
470C4×Dic83—41no—
471C4×Dic83—41no—
472C4×Dic83—41no—
473C4×Dic83—41no—
474C4×Dic83—41no—
475C4×Dic83—41no—
476C4×Dic83—41no—
477C4×Dic83—41no—
478C4×Dic83—41no—
479C4×Dic83—41no—
480C4×Dic83—41no—
481C4×Dic83—41no—
482C4×Dic83—41no—
483C4×Dic83C22×C414yes—
484C4×Dic83C22×C414yes—
485C4×Dic83C22×C414yes—
486C24×C83—22no—
487C24×C83—22no—
488C24×C83—41no—
489C24×C83—41no—
490C24×C83—41no—
491C24×C83—41no—
492C24×C83C22×C414yes—
493C24×C83C2411yescharacteristic
494C24×C83C2411yescharacteristic
495C24×C83C2411yescharacteristic
496C24×C83C2411yescharacteristic
497C2×D4×C83—22no—
498C2×D4×C83—22no—
499C2×D4×C83—41no—
500C2×D4×C83—41no—
501C2×D4×C83—41no—
502C2×D4×C83—41no—
503C2×D4×C83C22×C414yes—
504C2×D4×C83C22×C414yes—
505C2×D4×C83C22×C414yes—
506C22×C4×C83—22no—
507C22×C4×C83—22no—
508C22×C4×C83—22no—
509C22×C4×C83—22no—
510C22×C4×C83—22no—
511C22×C4×C83—22no—
512C22×C4×C83—22no—
513C22×C4×C83—41no—
514C22×C4×C83—41no—
515C22×C4×C83—41no—
516C22×C4×C83—41no—
517C22×C4×C83—41no—
518C22×C4×C83—41no—
519C22×C4×C83—41no—
520C22×C4×C83—41no—
521C22×C4×C83C2411yescharacteristic
522C22×C4×C83C2411yescharacteristic
523C22×C4×C83C2411yescharacteristic
524C22×C4×C83C2411yescharacteristic
525C22×C4×C83C2411yescharacteristic
526C22×C4×C83C2411yescharacteristic
527C22×C4×C83C2411yescharacteristic
528C22×C4×C83C2411yescharacteristic
529C22×C4×C83C2411yescharacteristic
530C22×C4×C83C2411yescharacteristic
531C22×C4×C83C2411yescharacteristic
532C4⋊C4×C83—22no—
533C4⋊C4×C83—22no—
534C4⋊C4×C83—41no—
535C22⋊C4×C83—22no—
536C22⋊C4×C83—22no—
537C22⋊C4×C83—22no—
538C22⋊C4×C83—22no—
539C22⋊C4×C83—22no—
540C22⋊C4×C83—22no—
541C22⋊C4×C83—41no—
542C22⋊C4×C83—41no—
543C22⋊C4×C83—41no—
544C22⋊C4×C83—41no—
545C22⋊C4×C83C22×C414yes—
546C22⋊C4×C83C22×C414yes—
547C22⋊C4×C83C22×C414yes—
548C22⋊C4×C83#4114yes—
549C42×C83—22no—
550C42×C83—41no—
551C42×C83—41no—
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—21no—
563C23×C83—21no—
564C23×C83—21no—
565C23×C83—21no—
566C23×C83—21no—
567C23×C83—21no—
568C23×C83—21no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83—21no—
574C23×C83—28no—
575C23×C83—44no—
576C23×C83—44no—
577C23×C83—82no—
578C23×C83—82no—
579C23×C83—82no—
580C23×C83—82no—
581C23×C83C23×C412yes—
582C23×C83C23×C412yes—
583C23×C83C23×C412yes—
584C23×C83C23×C412yes—
585C23×C83C2×#4112yes—
586C23×C83C2×#4112yes—
587C23×C83C2511yescharacteristic
588D4×C83—28no—
589D4×C83—44no—
590D4×C83—44no—
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—21no—
601C2×C4×C83—21no—
602C2×C4×C83—21no—
603C2×C4×C83—21no—
604C2×C4×C83—21no—
605C2×C4×C83—21no—
606C2×C4×C83—21no—
607C2×C4×C83—21no—
608C2×C4×C83—21no—
609C2×C4×C83—21no—
610C2×C4×C83—21no—
611C2×C4×C83—21no—
612C2×C4×C83—21no—
613C2×C4×C83—21no—
614C2×C4×C83—21no—
615C2×C4×C83—21no—
616C2×C4×C83—21no—
617C2×C4×C83—21no—
618C2×C4×C83—44no—
619C2×C4×C83—44no—
620C2×C4×C83—82no—
621C2×C4×C83—82no—
622C2×C4×C83—82no—
623C2×C4×C83C23×C412yes—
624C2×C4×C83C23×C412yes—
625C2×C4×C83C23×C412yes—
626C2×C4×C83C2×#4112yes—
627C2×C4×C83C2×#4112yes—
628C2×C4×C83H(5,𝔽2)12yes—
629C2×Dic83—28no—
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—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—21no—
668C2×Dic83—44no—
669C2×Dic83—44no—
670C2×Dic83—44no—
671C2×Dic83—44no—
672C2×Dic83—44no—
673C2×Dic83—44no—
674C2×Dic83—82no—
675C2×Dic83C23×C412yes—
676C2×Dic83C23×C412yes—
677C2×Dic83C23×C412yes—
678C2×Dic83C23×C412yes—
679C2×Dic83C23×C412yes—
680C2×Dic83C23×C412yes—
681C2×Dic83C23×C412yes—
682C2×Dic83C23×C412yes—
683C2×Dic83C2×#4112yes—
684C2×Dic83C2×#4112yes—
685Dic166—44no—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—22no—
690C22×C83—22no—
691C22×C83—22no—
692C22×C83—22no—
693C22×C83—22no—
694C22×C83—22no—
695C22×C83—22no—
696C22×C83—22no—
697C22×C83—22no—
698C22×C83—22no—
699C22×C83—22no—
700C22×C83—22no—
701C22×C83—41no—
702C22×C83—41no—
703C22×C83—41no—
704C22×C83—41no—
705C22×C83—41no—
706C22×C83—41no—
707C22×C83—41no—
708C22×C83—41no—
709C22×C83—41no—
710C22×C83—41no—
711C22×C83—41no—
712C22×C83—41no—
713C22×C83—88no—
714C22×C83C4×#4114yes—
715C22×C83C24×C411yescharacteristic
716C22×C83C22×#4111yescharacteristic
717C22×C83C22×#4111yescharacteristic
718C22×C83C2×H(5,𝔽2)11yescharacteristic
719C22×C83#58511yescharacteristic
720C22×C83#58511yescharacteristic
721C22×C83#58511yescharacteristic
722C4×C83—22no—
723C4×C83—22no—
724C4×C83—22no—
725C4×C83—22no—
726C4×C83—22no—
727C4×C83—22no—
728C4×C83—41no—
729C4×C83—41no—
730C4×C83—41no—
731C4×C83—41no—
732C4×C83—41no—
733Dic83—22no—
734Dic83—22no—
735Dic83—22no—
736Dic83—22no—
737Dic83—22no—
738Dic83—22no—
739Dic83—22no—
740Dic83—22no—
741Dic83—22no—
742Dic83—22no—
743Dic83—41no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34315—831nomaximal, Sylow
750C2×C83—24no—
751C2×C83—42no—
752C2×C83—42no—
753C2×C83—42no—
754C2×C83C2×C4×#4111yescharacteristic
755C2×C83#342811yescharacteristic
756C2×C83C4×H(5,𝔽2)11yescharacteristic
757C2×C83#350511yescharacteristic
758C2×C83#351011yescharacteristic
759C2×C83#351311yescharacteristic
760C2×C83#352111yescharacteristic
761C2×#551—831no—
762#2374—831no—
763#2374—831no—
764#2373—831no—
765#2373—831no—
766#2368—831no—
767#2367—831no—
768#2362—831no—
769#2359—831no—
770#2358D8311yescharacteristic
771#2357—831no—
772#2353—831no—
773#2347—831no—
774#2343—831no—
775#2342—831no—
776#2342—831no—
777#2337—831no—
778#2335—831no—
779#2334—831no—
780#2332—831no—
781#2322—831no—
782#2321—831no—
783C4×#126—831no—
784C4×C22⋊Q8—831no—
785C4×#123—831no—
786#2298—831no—
787#2290—831no—
788C2×#388—831no—
789#2274—831no—
790#2273—831no—
791C42×D4—831no—
792C83#3431511yescharacteristic, complemented, Sylow
793#551—8316no—
794C2×#126—831no—
795C2×#126—831no—
796C2×#124—831no—
797C2×#123—831no—
798C2×#123—831no—
799C2×#123—831no—
800C2×C22⋊Q8—831no—
801C2×C22⋊Q8—831no—
802C2×#120C2×D8311yescharacteristic
803C2×C4×Q8—831no—
804C2×C4×D4—831no—
805C2×C4×D4—831no—
806C2×C4×D4—831no—
807C2×C4×D4C2×D8311yescharacteristic
808C2×C4×D4C2×D8311yescharacteristic
809C2×#117—831no—
810C2×#117—831no—
811C2×#117—831no—
812C2×#117—831no—
813C22×C4⋊C4—831no—
814C22×C22⋊C4—831no—
815C22×C22⋊C4—831no—
816C22×C22⋊C4—831no—
817C22×C22⋊C4C2×D8311yescharacteristic
818C22×C22⋊C4C2×D8311yescharacteristic
819C22×C42—831no—
820C22×C42—831no—
821#391—831no—
822#391—831no—
823#391—831no—
824#390—831no—
825#390—831no—
826#390C2×D8311yescharacteristic
827#389—831no—
828#389—831no—
829#389—831no—
830#389—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#388—831no—
854#388—831no—
855#388—831no—
856#388—831no—
857#388C2×D8311yescharacteristic
858#388C2×D8311yescharacteristic
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#387—831no—
870#387—831no—
871#387—831no—
872#387—831no—
873#387—831no—
874#387—831no—
875#386—831no—
876#386—831no—
877#386—831no—
878#386C2×D8311yescharacteristic
879#386C2×D8311yescharacteristic
880#386C2×D8311yescharacteristic
881#385—831no—
882#385—831no—
883#385—831no—
884#385—831no—
885#385—831no—
886#385—831no—
887#385—831no—
888#385—831no—
889#385C2×D8311yescharacteristic
890#385C2×D8311yescharacteristic
891#383—831no—
892#383—831no—
893#382—831no—
894#381—831no—
895#381—831no—
896#381—831no—
897#380—831no—
898#380—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×C4⋊C4—831no—
914C4×C4⋊C4—831no—
915C4×C4⋊C4—831no—
916C4×C4⋊C4—831no—
917C4×C4⋊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—
928C4×C22⋊C4—831no—
929C4×C22⋊C4—831no—
930C4×C22⋊C4—831no—
931C4×C22⋊C4—831no—
932C4×C22⋊C4—831no—
933C4×C22⋊C4—831no—
934C4×C22⋊C4—831no—
935C4×C22⋊C4—831no—
936C4×C22⋊C4—831no—
937C4×C22⋊C4—831no—
938C4×C22⋊C4—831no—
939C4×C22⋊C4—831no—
940C4×C22⋊C4—831no—
941C4×C22⋊C4—831no—
942C4×C22⋊C4C2×D8311yescharacteristic
943C4×C22⋊C4C2×D8311yescharacteristic
944#376—831no—
945#376—831no—
946C2×#95—831no—
947C2×#95—831no—
948C43—831no—
949C25C22×D8311yescharacteristic
950C22×Q8—831no—
951C22×D4C22×D8311yescharacteristic
952C22×D4C22×D8311yescharacteristic
953C22×D4C22×D8311yescharacteristic
954C23×C4—831no—
955C23×C4—831no—
956C23×C4—831no—
957C23×C4—831no—
958C23×C4—831no—
959C23×C4—831no—
960C23×C4—831no—
961C23×C4—831no—
962C23×C4C22×D8311yescharacteristic
963C23×C4C22×D8311yescharacteristic
964C23×C4C22×D8311yescharacteristic
965C23×C4C22×D8311yescharacteristic
966C23×C4C22×D8311yescharacteristic
967#126—838no—
968#126—838no—
969#124—838no—
970#123—838no—
971#123—838no—
972#123—838no—
973C22⋊Q8—838no—
974C22⋊Q8—838no—
975#120C4×D8318yes—
976C4×Q8—3322no—
977C4×D4—24no—
978C4×D4—42no—
979C4×D4—838no—
980C4×D4—838no—
981C4×D4—1664no—
982#117—3322no—
983#117—838no—
984#117—838no—
985#117—1664no—
986C2×C4⋊C4—831no—
987C2×C4⋊C4—831no—
988C2×C4⋊C4—831no—
989C2×C4⋊C4—831no—
990C2×C4⋊C4—831no—
991C2×C4⋊C4—831no—
992C2×C4⋊C4—831no—
993C2×C4⋊C4—831no—
994C2×C4⋊C4—831no—
995C2×C4⋊C4—831no—
996C2×C4⋊C4—831no—
997C2×C4⋊C4—831no—
998C2×C4⋊C4—831no—
999C2×C4⋊C4—831no—
1000C2×C4⋊C4—831no—
1001C2×C4⋊C4—831no—
1002C2×C4⋊C4—831no—
1003C2×C4⋊C4—831no—
1004C2×C4⋊C4—831no—
1005C2×C4⋊C4—831no—
1006C2×C4⋊C4—831no—
1007C2×C4⋊C4—831no—
1008C2×C4⋊C4—831no—
1009C2×C4⋊C4—1664no—
1010C2×C4⋊C4C22×D8311yescharacteristic
1011C2×C4⋊C4C22×D8311yescharacteristic
1012C2×C4⋊C4C22×D8311yescharacteristic
1013C2×C22⋊C4—24no—
1014C2×C22⋊C4—42no—
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—838no—
1022C2×C22⋊C4—838no—
1023C2×C22⋊C4—831no—
1024C2×C22⋊C4—831no—
1025C2×C22⋊C4—831no—
1026C2×C22⋊C4—831no—
1027C2×C22⋊C4—831no—
1028C2×C22⋊C4—831no—
1029C2×C22⋊C4—831no—
1030C2×C22⋊C4—831no—
1031C2×C22⋊C4—831no—
1032C2×C22⋊C4—831no—
1033C2×C22⋊C4—831no—
1034C2×C22⋊C4—831no—
1035C2×C22⋊C4—831no—
1036C2×C22⋊C4—831no—
1037C2×C22⋊C4—831no—
1038C2×C22⋊C4—831no—
1039C2×C22⋊C4—831no—
1040C2×C22⋊C4—831no—
1041C2×C22⋊C4—1664no—
1042C2×C22⋊C4C22×D8311yescharacteristic
1043C2×C22⋊C4C22×D8311yescharacteristic
1044C2×C22⋊C4C22×D8311yescharacteristic
1045C2×C22⋊C4C22×D8311yescharacteristic
1046C2×C22⋊C4C22×D8311yescharacteristic
1047C2×C22⋊C4C22×D8311yescharacteristic
1048C2×C22⋊C4C22×D8311yescharacteristic
1049C2×C22⋊C4C22×D8311yescharacteristic
1050C2×C22⋊C4C22×D8311yescharacteristic
1051C2×C22⋊C4C22×D8311yescharacteristic
1052C2×C22⋊C4C22×D8311yescharacteristic
1053C2×C22⋊C4C22×D8311yescharacteristic
1054C2×C22⋊C4C22×D8311yescharacteristic
1055C2×C22⋊C4C22×D8311yescharacteristic
1056C2×C42—3322no—
1057C2×C42—3322no—
1058C2×C42—831no—
1059C2×C42—831no—
1060C2×C42—831no—
1061C2×C42—831no—
1062C2×C42—831no—
1063C2×C42—831no—
1064C2×C42—831no—
1065C2×C42—831no—
1066C2×C42—831no—
1067C2×C42—831no—
1068C2×C42—831no—
1069C2×C42—831no—
1070C2×C42—831no—
1071C2×C42—831no—
1072C2×C42—831no—
1073C2×C42—831no—
1074C2×C42—831no—
1075C2×C42—831no—
1076C2×C42—831no—
1077C2×C42—831no—
1078C2×C42—831no—
1079C2×C42—831no—
1080C2×C42—831no—
1081C2×C42—831no—
1082C2×C42—831no—
1083C2×C42—831no—
1084C2×C42C22×D8311yescharacteristic
1085C2×C42C22×D8311yescharacteristic
1086C2×C42C22×D8311yescharacteristic
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—
1107#95—831no—
1108#95—831no—
1109#95—831no—
1110#95—831no—
1111#95—831no—
1112#95—831no—
1113#95—831no—
1114#95—831no—
1115#95—831no—
1116#95—831no—
1117#95—831no—
1118#95—831no—
1119#95—831no—
1120#95—831no—
1121#95—831no—
1122#95—831no—
1123#95—831no—
1124#95—831no—
1125#95C22×D8311yescharacteristic
1126#95C22×D8311yescharacteristic
1127#95C22×D8311yescharacteristic
1128#95C22×D8311yescharacteristic
1129#95C22×D8311yescharacteristic
1130#95C22×D8311yescharacteristic
1131C24—22no—
1132C24—22no—
1133C24—41no—
1134C24—41no—
1135C24—41no—
1136C24—41no—
1137C24C2×C4×D8314yes—
1138C24C23×D8311yescharacteristic
1139C24C23×D8311yescharacteristic
1140C24C23×D8311yescharacteristic
1141C24C23×D8311yescharacteristic
1142C2×Q8—3321no—
1143C2×Q8—3321no—
1144C2×Q8—834no—
1145C2×D4—22no—
1146C2×D4—22no—
1147C2×D4—41no—
1148C2×D4—41no—
1149C2×D4—41no—
1150C2×D4—41no—
1151C2×D4C2×C4×D8314yes—
1152C2×D4C2×C4×D8314yes—
1153C2×D4C2×C4×D8314yes—
1154C22×C4—22no—
1155C22×C4—22no—
1156C22×C4—22no—
1157C22×C4—22no—
1158C22×C4—22no—
1159C22×C4—22no—
1160C22×C4—22no—
1161C22×C4—41no—
1162C22×C4—41no—
1163C22×C4—41no—
1164C22×C4—41no—
1165C22×C4—41no—
1166C22×C4—41no—
1167C22×C4—41no—
1168C22×C4—41no—
1169C22×C4—3321no—
1170C22×C4—3321no—
1171C22×C4—3321no—
1172C22×C4—3321no—
1173C22×C4—3321no—
1174C22×C4—3321no—
1175C22×C4—3321no—
1176C22×C4—3321no—
1177C22×C4—3321no—
1178C22×C4—3321no—
1179C22×C4—3321no—
1180C22×C4—3321no—
1181C22×C4—3321no—
1182C22×C4—3321no—
1183C22×C4—834no—
1184C22×C4—834no—
1185C22×C4—834no—
1186C22×C4—834no—
1187C22×C4—834no—
1188C22×C4—834no—
1189C22×C4—831no—
1190C22×C4—831no—
1191C22×C4—831no—
1192C22×C4—831no—
1193C22×C4—831no—
1194C22×C4—831no—
1195C22×C4—831no—
1196C22×C4—831no—
1197C22×C4—831no—
1198C22×C4—831no—
1199C22×C4—831no—
1200C22×C4—831no—
1201C22×C4—831no—
1202C22×C4—831no—
1203C22×C4—831no—
1204C22×C4—831no—
1205C22×C4—1662no—
1206C22×C4—1662no—
1207C22×C4—1662no—
1208C22×C4—1662no—
1209C22×C4C23×D8311yescharacteristic
1210C22×C4C23×D8311yescharacteristic
1211C22×C4C23×D8311yescharacteristic
1212C22×C4C23×D8311yescharacteristic
1213C22×C4C23×D8311yescharacteristic
1214C22×C4C23×D8311yescharacteristic
1215C22×C4C23×D8311yescharacteristic
1216C22×C4C23×D8311yescharacteristic
1217C22×C4C23×D8311yescharacteristic
1218C22×C4C23×D8311yescharacteristic
1219C22×C4C23×D8311yescharacteristic
1220C4⋊C4—22no—
1221C4⋊C4—22no—
1222C4⋊C4—41no—
1223C4⋊C4—3321no—
1224C4⋊C4—3321no—
1225C4⋊C4—3321no—
1226C4⋊C4—3321no—
1227C4⋊C4—3321no—
1228C4⋊C4—3321no—
1229C4⋊C4—3321no—
1230C4⋊C4—834no—
1231C4⋊C4—834no—
1232C4⋊C4—834no—
1233C4⋊C4—834no—
1234C4⋊C4—834no—
1235C4⋊C4—834no—
1236C4⋊C4—834no—
1237C4⋊C4—834no—
1238C4⋊C4—1662no—
1239C4⋊C4—1662no—
1240C4⋊C4—1662no—
1241C4⋊C4—1662no—
1242C4⋊C4—1662no—
1243C4⋊C4—1662no—
1244C4⋊C4—1662no—
1245C4⋊C4—1662no—
1246C22⋊C4—22no—
1247C22⋊C4—22no—
1248C22⋊C4—22no—
1249C22⋊C4—22no—
1250C22⋊C4—22no—
1251C22⋊C4—22no—
1252C22⋊C4—41no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—3321no—
1257C22⋊C4—3321no—
1258C22⋊C4—3321no—
1259C22⋊C4—3321no—
1260C22⋊C4—3321no—
1261C22⋊C4—3321no—
1262C22⋊C4—834no—
1263C22⋊C4—834no—
1264C22⋊C4—834no—
1265C22⋊C4—834no—
1266C22⋊C4—834no—
1267C22⋊C4—834no—
1268C22⋊C4—834no—
1269C22⋊C4—834no—
1270C22⋊C4—834no—
1271C22⋊C4—834no—
1272C22⋊C4—834no—
1273C22⋊C4—1662no—
1274C22⋊C4—1662no—
1275C22⋊C4—1662no—
1276C22⋊C4—1662no—
1277C22⋊C4—1662no—
1278C22⋊C4—1662no—
1279C22⋊C4—1662no—
1280C22⋊C4C2×C4×D8314yes—
1281C22⋊C4C2×C4×D8314yes—
1282C22⋊C4C2×C4×D8314yes—
1283C22⋊C4#1305058914yes—
1284C42—22no—
1285C42—41no—
1286C42—41no—
1287C42—3321no—
1288C42—3321no—
1289C42—3321no—
1290C42—3321no—
1291C42—3321no—
1292C42—3321no—
1293C42—3321no—
1294C42—3321no—
1295C42—3321no—
1296C42—3321no—
1297C42—3321no—
1298C42—3321no—
1299C42—3321no—
1300C42—3321no—
1301C42—3321no—
1302C42—3321no—
1303C42—3321no—
1304C42—834no—
1305C42—834no—
1306C42—834no—
1307C42—1662no—
1308C42—1662no—
1309C42—1662no—
1310C42—1662no—
1311C42—1662no—
1312C42—1662no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23—21no—
1333C23—21no—
1334C23—21no—
1335C23—28no—
1336C23—44no—
1337C23—44no—
1338C23—82no—
1339C23—82no—
1340C23—82no—
1341C23—82no—
1342C23C22×C4×D8312yes—
1343C23C22×C4×D8312yes—
1344C23C22×C4×D8312yes—
1345C23C22×C4×D8312yes—
1346C23#41×D8312yes—
1347C23C2×#1305058912yes—
1348C23C24×D8311yescharacteristic
1349Q8—3324no—
1350D4—28no—
1351D4—44no—
1352D4—44no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—44no—
1381C2×C4—44no—
1382C2×C4—82no—
1383C2×C4—82no—
1384C2×C4—82no—
1385C2×C4—3324no—
1386C2×C4—3324no—
1387C2×C4—3324no—
1388C2×C4—3324no—
1389C2×C4—3324no—
1390C2×C4—3324no—
1391C2×C4—832no—
1392C2×C4—832no—
1393C2×C4—832no—
1394C2×C4—832no—
1395C2×C4—832no—
1396C2×C4—832no—
1397C2×C4—832no—
1398C2×C4—832no—
1399C2×C4—832no—
1400C2×C4—832no—
1401C2×C4—6642no—
1402C2×C4—1661no—
1403C2×C4—1661no—
1404C2×C4—1661no—
1405C2×C4—1661no—
1406C2×C4—1661no—
1407C2×C4—1661no—
1408C2×C4—1661no—
1409C2×C4—1661no—
1410C2×C4—1661no—
1411C2×C4—1661no—
1412C2×C4—1661no—
1413C2×C4—1661no—
1414C2×C4—1661no—
1415C2×C4—1661no—
1416C2×C4—1661no—
1417C2×C4—1661no—
1418C2×C4—1661no—
1419C2×C4—1661no—
1420C2×C4—1668no—
1421C2×C4—1661no—
1422C2×C4—1661no—
1423C2×C4—1661no—
1424C2×C4—1661no—
1425C2×C4—1661no—
1426C2×C4—1661no—
1427C2×C4—1661no—
1428C2×C4—1661no—
1429C2×C4—1661no—
1430C2×C4—1661no—
1431C2×C4—1661no—
1432C2×C4—1661no—
1433C2×C4—1661no—
1434C2×C4—1661no—
1435C2×C4—1661no—
1436C2×C4—1661no—
1437C2×C4—1661no—
1438C2×C4—1661no—
1439C2×C4—1661no—
1440C2×C4—1661no—
1441C2×C4C22×C4×D8312yes—
1442C2×C4C22×C4×D8312yes—
1443C2×C4C22×C4×D8312yes—
1444C2×C4C2×#1305058912yes—
1445C2×C4C2×#1305058912yes—
1446C2×C4#1458183712yes—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—22no—
1456C22—22no—
1457C22—22no—
1458C22—22no—
1459C22—22no—
1460C22—22no—
1461C22—22no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—88no—
1475C22C4×#1305058914yes—
1476C22C23×C4×D8311yescharacteristic
1477C22C2×#41×D8311yescharacteristic
1478C22C22×#1305058911yescharacteristic
1479C22C2×#1458183711yescharacteristic
1480C22#1912853611yescharacteristic
1481C22#1912853611yescharacteristic
1482C22#1912853711yescharacteristic
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—41no—
1490C4—41no—
1491C4—41no—
1492C4—41no—
1493C4—41no—
1494C4—3321no—
1495C4—3321no—
1496C4—3321no—
1497C4—3321no—
1498C4—3321no—
1499C4—3321no—
1500C4—1662no—
1501C4—1662no—
1502C4—1662no—
1503C4—1662no—
1504C4—1662no—
1505C4—1662no—
1506C4—1662no—
1507C4—1662no—
1508C4—1662no—
1509C4—1662no—
1510C2—24no—
1511C2—42no—
1512C2—42no—
1513C2—42no—
1514C2C2×C4×#1305058911yescharacteristic
1515C2#2492066111yescharacteristic
1516C2C4×#1458183711yescharacteristic
1517C2#2492129011yescharacteristic
1518C2#2492135111yescharacteristic
1519C2#2492138811yescharacteristic
1520C2#2492151611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2358C2
socle, cosocleC23×C83C25
prime radicalC2×#120×C83C22
hypercenter#2358D83
hypocenterC83#34315
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2358

Complements

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

NH ≅ G/Ntype
2. #24910596C2semidirect
3. #24910596C2semidirect
4. #24910585C2semidirect
5. #24910578C2semidirect
6. #24910541C2semidirect
7. #24910536C2semidirect
8. #24910487C2semidirect
9. #24910449C2semidirect
10. #24910435C2semidirect
11. #24910401C2semidirect
12. #24910353C2semidirect
13. #24910321C2semidirect
14. #24910308C2semidirect
15. #24910308C2semidirect
16. #24910272C2semidirect
17. #24910250C2semidirect
18. #24910233C2semidirect
19. #24910213C2semidirect
20. #24910137C2semidirect
22. C4×#14581785C2semidirect
23. #24909995C2semidirect
24. C4×#14581773C2semidirect
25. #24909957C2semidirect
26. #24909903C2semidirect
27. C2×#19127589C2semidirect
28. #24909818C2semidirect
29. #24909816C2semidirect
30. C4×D4×Dic83C2semidirect
32. #19128382C4semidirect
41. C2×#14581757C22semidirect
54. C22×C4×Dic83C22semidirect
55. #19127607C22semidirect
56. #19127605C22semidirect
57. #19127605C22semidirect
60. #19127598C22semidirect
61. #19127598C22semidirect
62. #19127596C22semidirect
63. #19127596C22semidirect
68. #19127595C22semidirect
69. #19127595C22semidirect
86. #19127589C22semidirect
87. #19127589C22semidirect
88. #19127589C22semidirect
89. #19127589C22semidirect
90. #19127588C22semidirect
91. #19127588C22semidirect
92. #19127588C22semidirect
93. #19127588C22semidirect
94. #19127586C22semidirect
95. #19127586C22semidirect
96. #19127585C22semidirect
97. #19127585C22semidirect
98. #19127584C22semidirect
99. #19127584C22semidirect
100. #19127583C22semidirect
101. #19127583C22semidirect
102. #19127582C22semidirect
103. #19127582C22semidirect
104. #19127582C22semidirect
105. #19127582C22semidirect
114. #19127574C22semidirect
115. #19127573C22semidirect
116. #19127573C22semidirect
117. #19127568C22semidirect
118. #19127568C22semidirect
119. #19127566C22semidirect
122. #19127562C22semidirect
126. C4⋊C4×Dic83C22semidirect
127. C4⋊C4×Dic83C22semidirect
128. C4⋊C4×Dic83C22semidirect
129. C4⋊C4×Dic83C22semidirect
130. C4×Dic83⋊C4C22semidirect
131. C4×Dic83⋊C4C22semidirect
132. C4×Dic83⋊C4C22semidirect
133. C4×Dic83⋊C4C22semidirect
134. C4×Dic83⋊C4C22semidirect
135. C4×Dic83⋊C4C22semidirect
136. C4×C4⋊Dic83C22semidirect
137. C4×C4⋊Dic83C22semidirect
138. #19127552C22semidirect
139. #19127552C22semidirect
140. #19127552C22semidirect
141. #19127552C22semidirect
142. #19127552C22semidirect
143. #19127552C22semidirect
155. C22⋊C4×Dic83C22semidirect
156. C22⋊C4×Dic83C22semidirect
157. C22⋊C4×Dic83C22semidirect
166. C4×C22⋊Dic83C22semidirect
167. C4×C22⋊Dic83C22semidirect
168. #19127546C22semidirect
169. #19127546C22semidirect
172. C42×Dic83C22semidirect
197. #14581785C2×C4semidirect
198. #14581785C2×C4semidirect
199. #14581779C2×C4semidirect
200. #14581773C2×C4semidirect
201. #14581773C2×C4semidirect
202. #14581773C2×C4semidirect
203. #14581769C2×C4semidirect
204. #14581769C2×C4semidirect
207. D4×Dic83C2×C4semidirect
208. D4×Dic83C2×C4semidirect
211. #14581748C2×C4semidirect
212. #14581748C2×C4semidirect
238. C2×C22⋊Dic83C2×C4semidirect
239. C2×C22⋊Dic83C2×C4semidirect
792. C83#34315semidirect

Maximal subgroups

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

subgroupindex
C2×#191283822
#249105962
#249105852
#249105782
#249105412
#249105362
#249104872
#249104492
#249104352
#249104012
#249103532
#249103212
#249103082
#249102722
#249102502
#249102332
#249102132
#249101372
#249101242
C4×#145817852
#249099952
C4×#145817732
#249099572
#249099032
C2×#191275892
#249098182
#249098162
C4×D4×Dic832
C83×#23582
#3431583