Finite Group Databasebeta

← #47000

Subgroups — #47000

Order 256.

1057 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2841C211yesmaximal, characteristic, complemented
2#2784C211yesmaximal, characteristic, complemented
3#2764C211yesmaximal, characteristic, complemented
4#2763C211yesmaximal, characteristic, complemented
5#2750C211yesmaximal, characteristic, complemented
6#2749C211yesmaximal, characteristic, complemented
7#2743C211yesmaximal, characteristic, complemented
8#2737C211yesmaximal, characteristic, complemented
9#2708C211yesmaximal, characteristic, complemented
10#2708C211yesmaximal, characteristic, complemented
11#2706C211yesmaximal, characteristic, complemented
12#2706C211yesmaximal, characteristic, complemented
13#2693C211yesmaximal, characteristic, complemented
14#2609C211yesmaximal, characteristic, complemented
15#2598C211yesmaximal, characteristic, complemented
16#2579C211yesmaximal, characteristic, complemented
17#2534C211yesmaximal, characteristic, complemented
18#2477C211yesmaximal, characteristic, complemented
19#2464C211yesmaximal, characteristic, complemented
20#2450C211yesmaximal, characteristic, complemented
21#2430C211yesmaximal, characteristic, complemented
22#2424C211yesmaximal, characteristic, complemented
23#2418C211yesmaximal, characteristic, complemented
24#2411C211yesmaximal, characteristic, complemented
25#2407C211yesmaximal, characteristic, complemented
26#2406C211yesmaximal, characteristic, complemented
27#2404C211yesmaximal, characteristic, complemented
28#2404C211yesmaximal, characteristic, complemented
29#2318C211yesmaximal, characteristic, complemented
30#2315C211yesmaximal, characteristic, complemented
31#2311C211yesmaximal, characteristic, complemented
32C22×#41C2211yescharacteristic
33C22×#41C2211yescharacteristic
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic, complemented
38C2×#123C2211yescharacteristic, complemented
39C2×C22⋊Q8C2211yescharacteristic, complemented
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic, complemented
43C2×#120C2211yescharacteristic
44C2×#120C2211yescharacteristic
45C2×#120C2211yescharacteristic
46C2×C4×D4C2211yescharacteristic
47C2×C4×D4C2211yescharacteristic
48C2×C4×D4C2211yescharacteristic
49C2×#117C2211yescharacteristic
50C2×#117C2211yescharacteristic, complemented
51C22×C4⋊C4C2211yescharacteristic, complemented
52C22×C22⋊C4C2211yescharacteristic
53C22×C22⋊C4C2211yescharacteristic
54C22×C22⋊C4C2211yescharacteristic
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#400C2211yescharacteristic, complemented
62#399C2211yescharacteristic
63#399C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#398C2211yescharacteristic, complemented
66#398C2211yescharacteristic, complemented
67#398C2211yescharacteristic, complemented
68#398C2211yescharacteristic, complemented
69#397C2211yescharacteristic
70#397C2211yescharacteristic, complemented
71#397C2211yescharacteristic, complemented
72#397C2211yescharacteristic, complemented
73#397C2211yescharacteristic, complemented
74#396C2211yescharacteristic
75#396C2211yescharacteristic
76#396C2211yescharacteristic
77#396C2211yescharacteristic
78#396C2211yescharacteristic
79#396C2211yescharacteristic, complemented
80#396C2211yescharacteristic, complemented
81#395C2211yescharacteristic, complemented
82#395C2211yescharacteristic, complemented
83#395C2211yescharacteristic, complemented
84#394C2211yescharacteristic
85#394C2211yescharacteristic
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic, complemented
93#393C2211yescharacteristic
94#393C2211yescharacteristic
95#393C2211yescharacteristic
96#393C2211yescharacteristic
97#393C2211yescharacteristic, complemented
98#392C2211yescharacteristic
99#392C2211yescharacteristic
100#392C2211yescharacteristic
101#392C2211yescharacteristic
102#392C2211yescharacteristic
103#391C2211yescharacteristic, complemented
104#391C2211yescharacteristic, complemented
105#391C2211yescharacteristic, complemented
106#390C2211yescharacteristic
107#390C2211yescharacteristic
108#390C2211yescharacteristic
109#390C2211yescharacteristic, complemented
110#388C2211yescharacteristic
111#388C2211yescharacteristic
112#388C2211yescharacteristic
113#388C2211yescharacteristic
114#388C2211yescharacteristic
115#388C2211yescharacteristic
116#388C2211yescharacteristic
117#388C2211yescharacteristic, complemented
118#388C2211yescharacteristic, complemented
119#388C2211yescharacteristic, complemented
120#387C2211yescharacteristic, complemented
121#387C2211yescharacteristic, complemented
122#387C2211yescharacteristic, complemented
123#387C2211yescharacteristic, complemented
124#387C2211yescharacteristic, complemented
125#386C2211yescharacteristic
126#386C2211yescharacteristic
127#386C2211yescharacteristic
128#386C2211yescharacteristic
129#386C2211yescharacteristic
130#386C2211yescharacteristic
131#386C2211yescharacteristic
132#386C2211yescharacteristic
133#386C2211yescharacteristic
134#386C2211yescharacteristic
135#386C2211yescharacteristic
136#386C2211yescharacteristic
137#386C2211yescharacteristic
138#386C2211yescharacteristic
139#386C2211yescharacteristic
140#386C2211yescharacteristic
141#386C2211yescharacteristic
142#386C2211yescharacteristic
143#386C2211yescharacteristic
144#386C2211yescharacteristic, complemented
145#386C2211yescharacteristic, complemented
146#386C2211yescharacteristic, complemented
147#386C2211yescharacteristic, complemented
148#386C2211yescharacteristic, complemented
149#385C2211yescharacteristic
150#385C2211yescharacteristic
151#385C2211yescharacteristic
152#385C2211yescharacteristic
153#385C2211yescharacteristic
154#385C2211yescharacteristic
155#385C2211yescharacteristic
156#385C2211yescharacteristic
157#385C2211yescharacteristic
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic, complemented
161#385C2211yescharacteristic, complemented
162#385C2211yescharacteristic, complemented
163#385C2211yescharacteristic, complemented
164#385C2211yescharacteristic, complemented
165#385C2211yescharacteristic, complemented
166#385C2211yescharacteristic, complemented
167#383C2211yescharacteristic, complemented
168#383C2211yescharacteristic, complemented
169#382C2211yescharacteristic, complemented
170#382C2211yescharacteristic, complemented
171#381C2211yescharacteristic
172#381C2211yescharacteristic
173#381C2211yescharacteristic
174#381C2211yescharacteristic, complemented
175#380C2211yescharacteristic
176#380C2211yescharacteristic
177#380C2211yescharacteristic
178#380C2211yescharacteristic
179#380C2211yescharacteristic
180#380C2211yescharacteristic
181#380C2211yescharacteristic, complemented
182#380C2211yescharacteristic, complemented
183#380C2211yescharacteristic, complemented
184#379C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C2×#41—24no—
189C2×#41—42no—
190C2×#41—42no—
191C2×#41—42no—
192C2×#41—42no—
193C2×#41—42no—
194C22×Q8C2311yescharacteristic
195C22×Q8C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C22×D4C2311yescharacteristic
202C22×D4C2311yescharacteristic
203C22×D4C2311yescharacteristic
204C22×D4C2311yescharacteristic
205C22×D4C2311yescharacteristic
206C22×D4C2311yescharacteristic
207C22×D4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216C23×C4C2311yescharacteristic
217C23×C4C2311yescharacteristic
218C23×C4C2311yescharacteristic
219C23×C4C2311yescharacteristic
220C23×C4C2311yescharacteristic
221#123—42no—
222#123—42no—
223#123—42no—
224#123—42no—
225#123—42no—
226C22⋊Q8—42no—
227#121—42no—
228#121—42no—
229#121—42no—
230#120—42no—
231#120—42no—
232#120—42no—
233C4×D4—24no—
234C4×D4—42no—
235C4×D4—42no—
236#117—42no—
237#117—42no—
238C2×C4⋊C4—42no—
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×C4⋊C4C2311yescharacteristic
261C2×C4⋊C4C2311yescharacteristic
262C2×C4⋊C4C2311yescharacteristic
263C2×C4⋊C4C2311yescharacteristic
264C2×C4⋊C4C2311yescharacteristic
265C2×C4⋊C4C2311yescharacteristic
266C2×C4⋊C4C2311yescharacteristic
267C2×C22⋊C4—24no—
268C2×C22⋊C4—42no—
269C2×C22⋊C4—42no—
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×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325#95C2311yescharacteristic
326#95C2311yescharacteristic
327#95C2311yescharacteristic
328#95C2311yescharacteristic
329#95C2311yescharacteristic
330#95C2311yescharacteristic
331#95C2311yescharacteristic
332#95C2311yescharacteristic
333#95C2311yescharacteristic
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
366#95C2311yescharacteristic
367#95C2311yescharacteristic
368#95C2311yescharacteristic
369C24—22no—
370C24—22no—
371C24—22no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C24C2411yescharacteristic
380C24C2411yescharacteristic
381C24C2411yescharacteristic
382#41—416no—
383#41—416no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—41no—
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—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
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—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—41no—
438C22×C4—41no—
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×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4#4114yescomplemented
465C22×C4C2411yescharacteristic
466C22×C4C2411yescharacteristic
467C22×C4C2411yescharacteristic
468C22×C4C2411yescharacteristic
469C22×C4C2411yescharacteristic
470C22×C4C2411yescharacteristic
471C22×C4C2411yescharacteristic
472C22×C4C2411yescharacteristic
473C22×C4C2411yescharacteristic
474C22×C4C2411yescharacteristic
475C22×C4C2411yescharacteristic
476C22×C4C2411yescharacteristic
477C22×C4C2411yescharacteristic
478C22×C4C2411yescharacteristic
479C22×C4C2411yescharacteristic
480C22×C4C2411yescharacteristic
481C22×C4C2411yescharacteristic
482C22×C4C2411yescharacteristic
483C22×C4C2411yescharacteristic
484C22×C4C2411yescharacteristic
485C22×C4C2411yescharacteristic
486C22×C4C2411yescharacteristic
487C22×C4C2411yescharacteristic
488C22×C4C2411yescharacteristic
489C22×C4C2411yescharacteristic
490C4⋊C4—22no—
491C4⋊C4—22no—
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—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
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—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C42—22no—
569C42—22no—
570C42—22no—
571C42—41no—
572C42—41no—
573C23—28no—
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—82no—
612C23—82no—
613C23—82no—
614C23—82no—
615C23—82no—
616C23—82no—
617C23C2×#4112yes—
618C23H(5,𝔽2)12yes—
619C23H(5,𝔽2)12yes—
620C23H(5,𝔽2)12yes—
621C232−1+412yes—
622C23C2511yescharacteristic
623Q8—44no—
624Q8—44no—
625D4—44no—
626D4—44no—
627D4—44no—
628D4—44no—
629D4—44no—
630D4—44no—
631D4—44no—
632D4—44no—
633D4—44no—
634D4—82no—
635D4—82no—
636D4—82no—
637C2×C4—28no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4C2×#4112yes—
723C2×C4C2×#4112yes—
724C2×C4H(5,𝔽2)12yes—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
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—88no—
768C22C22×#4111yescharacteristic
769C22C2×H(5,𝔽2)11yescharacteristic
770C22C2×H(5,𝔽2)11yescharacteristic
771C22C2×H(5,𝔽2)11yescharacteristic
772C22C2×H(5,𝔽2)11yescharacteristic
773C22C2×2−1+411yescharacteristic
774C22#58511yescharacteristic
775C4—22no—
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C2—42no—
801C2—42no—
802C2—42no—
803C2—42no—
804C2—42no—
805C2—81no—
806C2#349011yescharacteristic
807C2#349211yescharacteristic
808C2#349411yescharacteristic
809C2#353211yescharacteristic
810C2#353511yescharacteristic
811C2#353611yescharacteristic
812C2#354211yescharacteristic
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. #2841C2semidirect
2. #2784C2semidirect
3. #2764C2semidirect
4. #2763C2semidirect
5. #2750C2semidirect
6. #2749C2semidirect
7. #2743C2semidirect
8. #2737C2semidirect
9. #2708C2semidirect
10. #2708C2semidirect
11. #2706C2semidirect
12. #2706C2semidirect
13. #2693C2semidirect
14. #2609C2semidirect
15. #2598C2semidirect
16. #2579C2semidirect
17. #2534C2semidirect
18. #2477C2semidirect
19. #2464C2semidirect
20. #2450C2semidirect
21. #2430C2semidirect
22. #2424C2semidirect
23. #2418C2semidirect
24. #2411C2semidirect
25. #2407C2semidirect
26. #2406C2semidirect
27. #2404C2semidirect
28. #2404C2semidirect
29. #2318C2semidirect
30. #2315C2semidirect
31. #2311C2semidirect
37. C2×#123C22semidirect
38. C2×#123C22semidirect
39. C2×C22⋊Q8C22semidirect
42. C2×#121C22semidirect
50. C2×#117C22semidirect
51. C22×C4⋊C4C22semidirect
55. #400C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #400C22semidirect
63. #399C22semidirect
64. #398C22semidirect
65. #398C22semidirect
66. #398C22semidirect
67. #398C22semidirect
68. #398C22semidirect
70. #397C22semidirect
71. #397C22semidirect
72. #397C22semidirect
73. #397C22semidirect
79. #396C22semidirect
80. #396C22semidirect
81. #395C22semidirect
82. #395C22semidirect
83. #395C22semidirect
92. #394C22semidirect
97. #393C22semidirect
103. #391C22semidirect
104. #391C22semidirect
105. #391C22semidirect
109. #390C22semidirect
117. #388C22semidirect
118. #388C22semidirect
119. #388C22semidirect
120. #387C22semidirect
121. #387C22semidirect
122. #387C22semidirect
123. #387C22semidirect
124. #387C22semidirect
144. #386C22semidirect
145. #386C22semidirect
146. #386C22semidirect
147. #386C22semidirect
148. #386C22semidirect
160. #385C22semidirect
161. #385C22semidirect
162. #385C22semidirect
163. #385C22semidirect
164. #385C22semidirect
165. #385C22semidirect
166. #385C22semidirect
167. #383C22semidirect
168. #383C22semidirect
169. #382C22semidirect
170. #382C22semidirect
174. #381C22semidirect
181. #380C22semidirect
182. #380C22semidirect
183. #380C22semidirect
185. C4×C22⋊C4C22semidirect
186. C2×#95C22semidirect
464. C22×C4#41semidirect

Maximal subgroups

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

subgroupindex
#28412
#27842
#27642
#27632
#27502
#27492
#27432
#27372
#27082
#27062
#26932
#26092
#25982
#25792
#25342
#24772
#24642
#24502
#24302
#24242
#24182
#24112
#24072
#24062
#24042
#23182
#23152
#23112