Finite Group Databasebeta

← #57166

Subgroups — #57166

Order 256.

957 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2829C211yesmaximal, characteristic, complemented
2#2820C211yesmaximal, characteristic, complemented
3#2814C211yesmaximal, characteristic, complemented
4#2797C211yesmaximal, characteristic, complemented
5#2756C211yesmaximal, characteristic, complemented
6#2737C211yesmaximal, characteristic, complemented
7#2706C211yesmaximal, characteristic, complemented
8#2705C211yesmaximal, characteristic, complemented
9#2701C211yesmaximal, characteristic, complemented
10#2697C211yesmaximal, characteristic, complemented
11#2697C211yesmaximal, characteristic, complemented
12#2694C211yesmaximal, characteristic, complemented
13#2685C211yesmaximal, characteristic, complemented
14#2679C211yesmaximal, characteristic, complemented
15#2678C211yesmaximal, characteristic, complemented
16#2678C211yesmaximal, characteristic, complemented
17#2672C211yesmaximal, characteristic, complemented
18#2670C211yesmaximal, characteristic, complemented
19#2668C211yesmaximal, characteristic, complemented
20#2651C211yesmaximal, characteristic, complemented
21#2644C211yesmaximal, characteristic, complemented
22#2617C211yesmaximal, characteristic, complemented
23#2610C211yesmaximal, characteristic, complemented
24#2539C211yesmaximal, characteristic, complemented
25#2531C211yesmaximal, characteristic, complemented
26#2518C211yesmaximal, characteristic, complemented
27#2490C211yesmaximal, characteristic, complemented
28#2479C211yesmaximal, characteristic, complemented
29#2472C211yesmaximal, characteristic, complemented
30#2412C211yesmaximal, characteristic, complemented
31#2411C211yesmaximal, characteristic, complemented
32C2×#126C2211yescharacteristic, complemented
33C2×#125C2211yescharacteristic, complemented
34C2×#124C2211yescharacteristic
35C2×#124C2211yescharacteristic, complemented
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic
39C2×#123C2211yescharacteristic, complemented
40C2×#123C2211yescharacteristic, complemented
41C2×C22⋊Q8C2211yescharacteristic, complemented
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#120C2211yescharacteristic
46C2×#120C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×#120C2211yescharacteristic
51C2×#120C2211yescharacteristic, complemented
52C2×#120C2211yescharacteristic, complemented
53C2×#117C2211yescharacteristic, complemented
54C22×C22⋊C4C2211yescharacteristic, complemented
55C22×C22⋊C4C2211yescharacteristic, complemented
56#399C2211yescharacteristic, complemented
57#399C2211yescharacteristic, complemented
58#399C2211yescharacteristic, complemented
59#399C2211yescharacteristic, complemented
60#399C2211yescharacteristic, complemented
61#398C2211yescharacteristic, complemented
62#398C2211yescharacteristic, complemented
63#398C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#397C2211yescharacteristic, complemented
66#397C2211yescharacteristic, complemented
67#397C2211yescharacteristic, complemented
68#397C2211yescharacteristic, complemented
69#397C2211yescharacteristic, complemented
70#397C2211yescharacteristic, complemented
71#397C2211yescharacteristic, complemented
72#397C2211yescharacteristic, complemented
73#397C2211yescharacteristic, complemented
74#397C2211yescharacteristic, complemented
75#397C2211yescharacteristic, complemented
76#397C2211yescharacteristic, complemented
77#397C2211yescharacteristic, complemented
78#397C2211yescharacteristic, complemented
79#396C2211yescharacteristic, complemented
80#396C2211yescharacteristic, complemented
81#396C2211yescharacteristic, complemented
82#396C2211yescharacteristic, complemented
83#396C2211yescharacteristic, complemented
84#396C2211yescharacteristic, complemented
85#396C2211yescharacteristic, complemented
86#396C2211yescharacteristic, complemented
87#396C2211yescharacteristic, complemented
88#395C2211yescharacteristic, complemented
89#395C2211yescharacteristic, complemented
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic
101#394C2211yescharacteristic
102#394C2211yescharacteristic
103#394C2211yescharacteristic
104#394C2211yescharacteristic
105#394C2211yescharacteristic
106#394C2211yescharacteristic, complemented
107#394C2211yescharacteristic, complemented
108#394C2211yescharacteristic, complemented
109#394C2211yescharacteristic, complemented
110#394C2211yescharacteristic, complemented
111#394C2211yescharacteristic, complemented
112#393C2211yescharacteristic, complemented
113#393C2211yescharacteristic, complemented
114#392C2211yescharacteristic
115#392C2211yescharacteristic
116#392C2211yescharacteristic
117#392C2211yescharacteristic
118#392C2211yescharacteristic
119#392C2211yescharacteristic
120#390C2211yescharacteristic
121#390C2211yescharacteristic
122#390C2211yescharacteristic
123#390C2211yescharacteristic
124#390C2211yescharacteristic
125#390C2211yescharacteristic
126#390C2211yescharacteristic
127#390C2211yescharacteristic
128#390C2211yescharacteristic
129#390C2211yescharacteristic, complemented
130#390C2211yescharacteristic, complemented
131#390C2211yescharacteristic, complemented
132#390C2211yescharacteristic, complemented
133#390C2211yescharacteristic, complemented
134#389C2211yescharacteristic, complemented
135#389C2211yescharacteristic, complemented
136#389C2211yescharacteristic, complemented
137#388C2211yescharacteristic, complemented
138#388C2211yescharacteristic, complemented
139#388C2211yescharacteristic, complemented
140#388C2211yescharacteristic, complemented
141#388C2211yescharacteristic, complemented
142#388C2211yescharacteristic, complemented
143#388C2211yescharacteristic, complemented
144#388C2211yescharacteristic, complemented
145#388C2211yescharacteristic, complemented
146#388C2211yescharacteristic, complemented
147#388C2211yescharacteristic, complemented
148#388C2211yescharacteristic, complemented
149#388C2211yescharacteristic, complemented
150#388C2211yescharacteristic, complemented
151#388C2211yescharacteristic, complemented
152#388C2211yescharacteristic, complemented
153#388C2211yescharacteristic, complemented
154#387C2211yescharacteristic, complemented
155#387C2211yescharacteristic, complemented
156#387C2211yescharacteristic, complemented
157#387C2211yescharacteristic, complemented
158#386C2211yescharacteristic
159#386C2211yescharacteristic
160#386C2211yescharacteristic
161#386C2211yescharacteristic
162#386C2211yescharacteristic
163#386C2211yescharacteristic
164#386C2211yescharacteristic
165#386C2211yescharacteristic, complemented
166#386C2211yescharacteristic, complemented
167#386C2211yescharacteristic, complemented
168#386C2211yescharacteristic, complemented
169#385C2211yescharacteristic, complemented
170#385C2211yescharacteristic, complemented
171#385C2211yescharacteristic, complemented
172#383C2211yescharacteristic, complemented
173#382C2211yescharacteristic, complemented
174#381C2211yescharacteristic, complemented
175#380C2211yescharacteristic, complemented
176#380C2211yescharacteristic, complemented
177#380C2211yescharacteristic, complemented
178#380C2211yescharacteristic, complemented
179#379C2211yescharacteristic, complemented
180#379C2211yescharacteristic, complemented
181#379C2211yescharacteristic, complemented
182#379C2211yescharacteristic, complemented
183C4×C4⋊C4C2211yescharacteristic, complemented
184C4×C22⋊C4C2211yescharacteristic, complemented
185C4×C22⋊C4C2211yescharacteristic, complemented
186#376C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C25C2311yescharacteristic
189C22×Q8C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C22×D4C2311yescharacteristic
202C22×D4C2311yescharacteristic
203C22×D4C2311yescharacteristic
204C22×D4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210#126—42no—
211#125—42no—
212#124—42no—
213#124—42no—
214#123—42no—
215#123—42no—
216#123—42no—
217#123—42no—
218#123—42no—
219C22⋊Q8—42no—
220#121—42no—
221#121—42no—
222#121—42no—
223#120—42no—
224#120—42no—
225#120—42no—
226#120—42no—
227#120—42no—
228#120—42no—
229#120—42no—
230#120—42no—
231#117—42no—
232C2×C4⋊C4C2311yescharacteristic
233C2×C4⋊C4C2311yescharacteristic
234C2×C4⋊C4C2311yescharacteristic
235C2×C4⋊C4C2311yescharacteristic
236C2×C4⋊C4C2311yescharacteristic
237C2×C4⋊C4C2311yescharacteristic
238C2×C4⋊C4C2311yescharacteristic
239C2×C4⋊C4C2311yescharacteristic
240C2×C4⋊C4C2311yescharacteristic
241C2×C4⋊C4C2311yescharacteristic
242C2×C4⋊C4C2311yescharacteristic
243C2×C4⋊C4C2311yescharacteristic
244C2×C4⋊C4C2311yescharacteristic
245C2×C4⋊C4C2311yescharacteristic
246C2×C4⋊C4C2311yescharacteristic
247C2×C4⋊C4C2311yescharacteristic
248C2×C4⋊C4C2311yescharacteristic
249C2×C4⋊C4C2311yescharacteristic
250C2×C4⋊C4C2311yescharacteristic
251C2×C4⋊C4C2311yescharacteristic
252C2×C4⋊C4C2311yescharacteristic
253C2×C4⋊C4C2311yescharacteristic
254C2×C4⋊C4C2311yescharacteristic
255C2×C4⋊C4C2311yescharacteristic
256C2×C4⋊C4C2311yescharacteristic
257C2×C4⋊C4C2311yescharacteristic
258C2×C4⋊C4C2311yescharacteristic
259C2×C4⋊C4C2311yescharacteristic
260C2×C22⋊C4—42no—
261C2×C22⋊C4—42no—
262C2×C22⋊C4C2311yescharacteristic
263C2×C22⋊C4C2311yescharacteristic
264C2×C22⋊C4C2311yescharacteristic
265C2×C22⋊C4C2311yescharacteristic
266C2×C22⋊C4C2311yescharacteristic
267C2×C22⋊C4C2311yescharacteristic
268C2×C22⋊C4C2311yescharacteristic
269C2×C22⋊C4C2311yescharacteristic
270C2×C22⋊C4C2311yescharacteristic
271C2×C22⋊C4C2311yescharacteristic
272C2×C22⋊C4C2311yescharacteristic
273C2×C22⋊C4C2311yescharacteristic
274C2×C22⋊C4C2311yescharacteristic
275C2×C22⋊C4C2311yescharacteristic
276C2×C22⋊C4C2311yescharacteristic
277C2×C22⋊C4C2311yescharacteristic
278C2×C22⋊C4C2311yescharacteristic
279C2×C22⋊C4C2311yescharacteristic
280C2×C22⋊C4C2311yescharacteristic
281C2×C22⋊C4C2311yescharacteristic
282C2×C22⋊C4C2311yescharacteristic
283C2×C22⋊C4C2311yescharacteristic
284C2×C22⋊C4C2311yescharacteristic
285C2×C22⋊C4C2311yescharacteristic
286C2×C22⋊C4C2311yescharacteristic
287C2×C22⋊C4C2311yescharacteristic
288C2×C22⋊C4C2311yescharacteristic
289C2×C22⋊C4C2311yescharacteristic
290C2×C22⋊C4C2311yescharacteristic
291C2×C22⋊C4C2311yescharacteristic
292C2×C22⋊C4C2311yescharacteristic
293C2×C22⋊C4C2311yescharacteristic
294C2×C22⋊C4C2311yescharacteristic
295C2×C22⋊C4C2311yescharacteristic
296C2×C22⋊C4C2311yescharacteristic
297C2×C22⋊C4C2311yescharacteristic
298C2×C22⋊C4C2311yescharacteristic
299C2×C22⋊C4C2311yescharacteristic
300C2×C22⋊C4C2311yescharacteristic
301C2×C22⋊C4C2311yescharacteristic
302C2×C22⋊C4C2311yescharacteristic
303C2×C22⋊C4C2311yescharacteristic
304C2×C22⋊C4C2311yescharacteristic
305C2×C22⋊C4C2311yescharacteristic
306C2×C22⋊C4C2311yescharacteristic
307C2×C22⋊C4C2311yescharacteristic
308C2×C22⋊C4C2311yescharacteristic
309C2×C22⋊C4C2311yescharacteristic
310C2×C22⋊C4C2311yescharacteristic
311C2×C22⋊C4C2311yescharacteristic
312C2×C22⋊C4C2311yescharacteristic
313C2×C22⋊C4C2311yescharacteristic
314C2×C22⋊C4C2311yescharacteristic
315C2×C22⋊C4C2311yescharacteristic
316C2×C22⋊C4C2311yescharacteristic
317C2×C22⋊C4C2311yescharacteristic
318C2×C22⋊C4C2311yescharacteristic
319C2×C22⋊C4C2311yescharacteristic
320C2×C22⋊C4C2311yescharacteristic
321C2×C22⋊C4C2311yescharacteristic
322C2×C22⋊C4C2311yescharacteristic
323C2×C22⋊C4C2311yescharacteristic
324C2×C22⋊C4C2311yescharacteristic
325C2×C22⋊C4C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328C2×C42C2311yescharacteristic
329C2×C42C2311yescharacteristic
330C2×C42C2311yescharacteristic
331C2×C42C2311yescharacteristic
332C2×C42C2311yescharacteristic
333C2×C42C2311yescharacteristic
334#95C2311yescharacteristic
335#95C2311yescharacteristic
336#95C2311yescharacteristic
337#95C2311yescharacteristic
338#95C2311yescharacteristic
339#95C2311yescharacteristic
340#95C2311yescharacteristic
341#95C2311yescharacteristic
342#95C2311yescharacteristic
343#95C2311yescharacteristic
344#95C2311yescharacteristic
345#95C2311yescharacteristic
346#95C2311yescharacteristic
347#95C2311yescharacteristic
348#95C2311yescharacteristic
349#95C2311yescharacteristic
350#95C2311yescharacteristic
351#95C2311yescharacteristic
352#95C2311yescharacteristic
353#95C2311yescharacteristic
354#95C2311yescharacteristic
355#95C2311yescharacteristic
356#95C2311yescharacteristic
357#95C2311yescharacteristic
358#95C2311yescharacteristic
359#95C2311yescharacteristic
360#95C2311yescharacteristic
361#95C2311yescharacteristic
362#95C2311yescharacteristic
363#95C2311yescharacteristic
364#95C2311yescharacteristic
365#95C2311yescharacteristic
366C24—22no—
367C24—22no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24C2411yescharacteristic
381C24C2411yescharacteristic
382C24C2411yescharacteristic
383C24C2411yescharacteristic
384C24C2411yescharacteristic
385C24C2411yescharacteristic
386C24C2411yescharacteristic
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4—41no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4C2411yescharacteristic
451C22×C4C2411yescharacteristic
452C22×C4C2411yescharacteristic
453C22×C4C2411yescharacteristic
454C22×C4C2411yescharacteristic
455C22×C4C2411yescharacteristic
456C22×C4C2411yescharacteristic
457C22×C4C2411yescharacteristic
458C22×C4C2411yescharacteristic
459C22×C4C2411yescharacteristic
460C22×C4C2411yescharacteristic
461C22×C4C2411yescharacteristic
462C22×C4C2411yescharacteristic
463C22×C4C2411yescharacteristic
464C22×C4C2411yescharacteristic
465C22×C4C2411yescharacteristic
466C22×C4C2411yescharacteristic
467C22×C4C2411yescharacteristic
468C22×C4C2411yescharacteristic
469C22×C4C2411yescharacteristic
470C22×C4C2411yescharacteristic
471C22×C4C2411yescharacteristic
472C22×C4C2411yescharacteristic
473C22×C4C2411yescharacteristic
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—41no—
530C22⋊C4—41no—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C22⋊C4—41no—
544C22⋊C4—41no—
545C22⋊C4—41no—
546C22⋊C4—41no—
547C22⋊C4—41no—
548C22⋊C4—41no—
549C22⋊C4—41no—
550C22⋊C4—41no—
551C22⋊C4—41no—
552C22⋊C4—41no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C22⋊C4—41no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C42—22no—
567C42—22no—
568C42—41no—
569C42—41no—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—41no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—44no—
622C23—44no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23—82no—
628C23—82no—
629C23—82no—
630C23—82no—
631C23—82no—
632C23—82no—
633C23—82no—
634C23—82no—
635C23H(5,𝔽2)12yes—
636C23H(5,𝔽2)12yes—
637C23C2511yescharacteristic
638Q8—82no—
639D4—82no—
640D4—82no—
641D4—82no—
642D4—82no—
643D4—82no—
644D4—82no—
645D4—82no—
646D4—82no—
647D4—82no—
648D4—82no—
649D4—82no—
650D4—82no—
651D4—82no—
652D4—82no—
653D4—82no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—44no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4H(5,𝔽2)12yes—
730C2×C4H(5,𝔽2)12yes—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—88no—
781C22—88no—
782C22C2×H(5,𝔽2)11yescharacteristic
783C22C2×H(5,𝔽2)11yescharacteristic
784C22C2×H(5,𝔽2)11yescharacteristic
785C22C2×H(5,𝔽2)11yescharacteristic
786C22#58511yescharacteristic
787C22#58511yescharacteristic
788C22#58511yescharacteristic
789C4—22no—
790C4—22no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C2—42no—
814C2—42no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2—81no—
819C2—81no—
820C2#353411yescharacteristic
821C2#354211yescharacteristic
822C2#354211yescharacteristic
823C2#354311yescharacteristic
824C2#354511yescharacteristic
825C2#354511yescharacteristic
826C2#356011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2829C2semidirect
2. #2820C2semidirect
3. #2814C2semidirect
4. #2797C2semidirect
5. #2756C2semidirect
6. #2737C2semidirect
7. #2706C2semidirect
8. #2705C2semidirect
9. #2701C2semidirect
10. #2697C2semidirect
11. #2697C2semidirect
12. #2694C2semidirect
13. #2685C2semidirect
14. #2679C2semidirect
15. #2678C2semidirect
16. #2678C2semidirect
17. #2672C2semidirect
18. #2670C2semidirect
19. #2668C2semidirect
20. #2651C2semidirect
21. #2644C2semidirect
22. #2617C2semidirect
23. #2610C2semidirect
24. #2539C2semidirect
25. #2531C2semidirect
26. #2518C2semidirect
27. #2490C2semidirect
28. #2479C2semidirect
29. #2472C2semidirect
30. #2412C2semidirect
31. #2411C2semidirect
32. C2×#126C22semidirect
33. C2×#125C22semidirect
35. C2×#124C22semidirect
39. C2×#123C22semidirect
40. C2×#123C22semidirect
41. C2×C22⋊Q8C22semidirect
51. C2×#120C22semidirect
52. C2×#120C22semidirect
53. C2×#117C22semidirect
54. C22×C22⋊C4C22semidirect
55. C22×C22⋊C4C22semidirect
56. #399C22semidirect
57. #399C22semidirect
58. #399C22semidirect
59. #399C22semidirect
60. #399C22semidirect
61. #398C22semidirect
62. #398C22semidirect
63. #398C22semidirect
64. #398C22semidirect
65. #397C22semidirect
66. #397C22semidirect
67. #397C22semidirect
68. #397C22semidirect
69. #397C22semidirect
70. #397C22semidirect
71. #397C22semidirect
72. #397C22semidirect
73. #397C22semidirect
74. #397C22semidirect
75. #397C22semidirect
76. #397C22semidirect
77. #397C22semidirect
78. #397C22semidirect
79. #396C22semidirect
80. #396C22semidirect
81. #396C22semidirect
82. #396C22semidirect
83. #396C22semidirect
84. #396C22semidirect
85. #396C22semidirect
86. #396C22semidirect
87. #396C22semidirect
88. #395C22semidirect
89. #395C22semidirect
106. #394C22semidirect
107. #394C22semidirect
108. #394C22semidirect
109. #394C22semidirect
110. #394C22semidirect
111. #394C22semidirect
112. #393C22semidirect
113. #393C22semidirect
129. #390C22semidirect
130. #390C22semidirect
131. #390C22semidirect
132. #390C22semidirect
133. #390C22semidirect
134. #389C22semidirect
135. #389C22semidirect
136. #389C22semidirect
137. #388C22semidirect
138. #388C22semidirect
139. #388C22semidirect
140. #388C22semidirect
141. #388C22semidirect
142. #388C22semidirect
143. #388C22semidirect
144. #388C22semidirect
145. #388C22semidirect
146. #388C22semidirect
147. #388C22semidirect
148. #388C22semidirect
149. #388C22semidirect
150. #388C22semidirect
151. #388C22semidirect
152. #388C22semidirect
153. #388C22semidirect
154. #387C22semidirect
155. #387C22semidirect
156. #387C22semidirect
157. #387C22semidirect
165. #386C22semidirect
166. #386C22semidirect
167. #386C22semidirect
168. #386C22semidirect
169. #385C22semidirect
170. #385C22semidirect
171. #385C22semidirect
172. #383C22semidirect
173. #382C22semidirect
174. #381C22semidirect
175. #380C22semidirect
176. #380C22semidirect
177. #380C22semidirect
178. #380C22semidirect
179. #379C22semidirect
180. #379C22semidirect
181. #379C22semidirect
182. #379C22semidirect
183. C4×C4⋊C4C22semidirect
184. C4×C22⋊C4C22semidirect
185. C4×C22⋊C4C22semidirect
186. #376C22semidirect

Maximal subgroups

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

subgroupindex
#28292
#28202
#28142
#27972
#27562
#27372
#27062
#27052
#27012
#26972
#26942
#26852
#26792
#26782
#26722
#26702
#26682
#26512
#26442
#26172
#26102
#25392
#25312
#25182
#24902
#24792
#24722
#24122
#24112