Finite Group Databasebeta

← #45462

Subgroups — #45462

Order 256.

1041 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2849C211yesmaximal, characteristic, complemented
2#2847C211yesmaximal, characteristic, complemented
3#2841C211yesmaximal, characteristic, complemented
4#2813C211yesmaximal, characteristic, complemented
5#2781C211yesmaximal, characteristic, complemented
6#2779C211yesmaximal, characteristic, complemented
7#2747C211yesmaximal, characteristic, complemented
8#2743C211yesmaximal, characteristic, complemented
9#2741C211yesmaximal, characteristic, complemented
10#2740C211yesmaximal, characteristic, complemented
11#2708C211yesmaximal, characteristic, complemented
12#2706C211yesmaximal, characteristic, complemented
13#2696C211yesmaximal, characteristic, complemented
14#2686C211yesmaximal, characteristic, complemented
15#2672C211yesmaximal, characteristic, complemented
16#2671C211yesmaximal, characteristic, complemented
17#2591C211yesmaximal, characteristic, complemented
18#2579C211yesmaximal, characteristic, complemented
19#2564C211yesmaximal, characteristic, complemented
20#2543C211yesmaximal, characteristic, complemented
21#2505C211yesmaximal, characteristic, complemented
22#2472C211yesmaximal, characteristic, complemented
23#2449C211yesmaximal, characteristic, complemented
24#2444C211yesmaximal, characteristic, complemented
25#2443C211yesmaximal, characteristic, complemented
26#2424C211yesmaximal, characteristic, complemented
27#2424C211yesmaximal, characteristic, complemented
28#2418C211yesmaximal, characteristic, complemented
29#2377C211yesmaximal, characteristic, complemented
30#2376C211yesmaximal, characteristic, complemented
31C2×#380C211yesmaximal, characteristic, complemented
32C24×C4C2211yescharacteristic
33C2×#124C2211yescharacteristic
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic, complemented
38C2×C22⋊Q8C2211yescharacteristic
39C2×C22⋊Q8C2211yescharacteristic, complemented
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#121C2211yescharacteristic
46C2×#121C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic
52C2×C4×D4C2211yescharacteristic
53C22×C4⋊C4C2211yescharacteristic
54C22×C4⋊C4C2211yescharacteristic
55C22×C22⋊C4C2211yescharacteristic
56C22×C22⋊C4C2211yescharacteristic
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#400C2211yescharacteristic, complemented
62#400C2211yescharacteristic, complemented
63#400C2211yescharacteristic, complemented
64#399C2211yescharacteristic
65#399C2211yescharacteristic, complemented
66#399C2211yescharacteristic, complemented
67#399C2211yescharacteristic, complemented
68#398C2211yescharacteristic, complemented
69#398C2211yescharacteristic, complemented
70#398C2211yescharacteristic, complemented
71#398C2211yescharacteristic, complemented
72#398C2211yescharacteristic, complemented
73#398C2211yescharacteristic, complemented
74#397C2211yescharacteristic
75#397C2211yescharacteristic
76#397C2211yescharacteristic, complemented
77#397C2211yescharacteristic, complemented
78#397C2211yescharacteristic, complemented
79#397C2211yescharacteristic, complemented
80#396C2211yescharacteristic
81#396C2211yescharacteristic
82#396C2211yescharacteristic, complemented
83#396C2211yescharacteristic, complemented
84#396C2211yescharacteristic, complemented
85#395C2211yescharacteristic, complemented
86#395C2211yescharacteristic, complemented
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic, complemented
96#394C2211yescharacteristic, complemented
97#394C2211yescharacteristic, complemented
98#394C2211yescharacteristic, complemented
99#394C2211yescharacteristic, complemented
100#393C2211yescharacteristic
101#393C2211yescharacteristic, complemented
102#392C2211yescharacteristic
103#392C2211yescharacteristic
104#392C2211yescharacteristic, complemented
105#390C2211yescharacteristic
106#390C2211yescharacteristic
107#390C2211yescharacteristic
108#389C2211yescharacteristic, complemented
109#389C2211yescharacteristic, complemented
110#388C2211yescharacteristic
111#388C2211yescharacteristic
112#388C2211yescharacteristic
113#388C2211yescharacteristic
114#388C2211yescharacteristic
115#388C2211yescharacteristic
116#388C2211yescharacteristic, complemented
117#388C2211yescharacteristic, complemented
118#388C2211yescharacteristic, complemented
119#388C2211yescharacteristic, complemented
120#388C2211yescharacteristic, complemented
121#388C2211yescharacteristic, complemented
122#388C2211yescharacteristic, complemented
123#388C2211yescharacteristic, complemented
124#387C2211yescharacteristic, complemented
125#387C2211yescharacteristic, complemented
126#387C2211yescharacteristic, complemented
127#387C2211yescharacteristic, complemented
128#387C2211yescharacteristic, complemented
129#387C2211yescharacteristic, complemented
130#387C2211yescharacteristic, complemented
131#387C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#386C2211yescharacteristic
134#386C2211yescharacteristic
135#386C2211yescharacteristic
136#386C2211yescharacteristic
137#386C2211yescharacteristic
138#386C2211yescharacteristic
139#386C2211yescharacteristic
140#386C2211yescharacteristic
141#386C2211yescharacteristic
142#386C2211yescharacteristic
143#386C2211yescharacteristic
144#386C2211yescharacteristic
145#386C2211yescharacteristic
146#386C2211yescharacteristic
147#386C2211yescharacteristic
148#386C2211yescharacteristic
149#386C2211yescharacteristic
150#386C2211yescharacteristic
151#386C2211yescharacteristic, complemented
152#386C2211yescharacteristic, complemented
153#386C2211yescharacteristic, complemented
154#385C2211yescharacteristic
155#385C2211yescharacteristic
156#385C2211yescharacteristic
157#385C2211yescharacteristic
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic, complemented
162#385C2211yescharacteristic, complemented
163#385C2211yescharacteristic, complemented
164#385C2211yescharacteristic, complemented
165#385C2211yescharacteristic, complemented
166#385C2211yescharacteristic, complemented
167#382C2211yescharacteristic, complemented
168#381C2211yescharacteristic
169#381C2211yescharacteristic
170#381C2211yescharacteristic, complemented
171#380C2211yescharacteristic
172#380C2211yescharacteristic
173#380C2211yescharacteristic
174#380C2211yescharacteristic
175#380C2211yescharacteristic
176#380C2211yescharacteristic
177#380C2211yescharacteristic
178#380C2211yescharacteristic
179#380C2211yescharacteristic
180#380C2211yescharacteristic
181#380C2211yescharacteristic
182#380C2211yescharacteristic
183#379C2211yescharacteristic
184C4×C22⋊C4C2211yescharacteristic
185C2×#95C2211yescharacteristic
186C2×#95C2211yescharacteristic
187C25C2311yescharacteristic
188C22×Q8C2311yescharacteristic
189C22×D4C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C23×C4—24no—
202C23×C4—42no—
203C23×C4—42no—
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216C23×C4C2311yescharacteristic
217#124—42no—
218#123—24no—
219#123—42no—
220#123—42no—
221#123—42no—
222C22⋊Q8—42no—
223C22⋊Q8—42no—
224#121—24no—
225#121—42no—
226#121—42no—
227#121—42no—
228#121—42no—
229#121—42no—
230#121—42no—
231#120—42no—
232#120—42no—
233#120—42no—
234C4×D4—42no—
235C4×D4—42no—
236C4×D4—42no—
237C2×C4⋊C4—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×C4⋊C4C2311yescharacteristic
268C2×C4⋊C4C2311yescharacteristic
269C2×C4⋊C4C2311yescharacteristic
270C2×C22⋊C4—42no—
271C2×C22⋊C4—42no—
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×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
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—22no—
373C24—22no—
374C24—41no—
375C24—41no—
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C24C2411yescharacteristic
380C24C2411yescharacteristic
381C24C2411yescharacteristic
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
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—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—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
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—41no—
436C22×C4—41no—
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—416no—
460C22×C4#4114yes—
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
474C22×C4C2411yescharacteristic
475C22×C4C2411yescharacteristic
476C22×C4C2411yescharacteristic
477C22×C4C2411yescharacteristic
478C22×C4C2411yescharacteristic
479C22×C4C2411yescharacteristic
480C22×C4C2411yescharacteristic
481C22×C4C2411yescharacteristic
482C22×C4C2411yescharacteristic
483C22×C4C2411yescharacteristic
484C22×C4C2411yescharacteristic
485C22×C4C2411yescharacteristic
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
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—
517C22⋊C4—22no—
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—
567C42—41no—
568C42—41no—
569C42—41no—
570C42—41no—
571C42—41no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—28no—
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—44no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23C2×#4112yes—
617C23H(5,𝔽2)12yes—
618C23H(5,𝔽2)12yes—
619C23H(5,𝔽2)12yes—
620C232−1+412yes—
621C23C2511yescharacteristic
622Q8—82no—
623D4—44no—
624D4—44no—
625D4—44no—
626D4—82no—
627D4—82no—
628D4—82no—
629D4—82no—
630D4—82no—
631D4—82no—
632D4—82no—
633D4—82no—
634D4—82no—
635C2×C4—28no—
636C2×C4—21no—
637C2×C4—21no—
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—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—82no—
714C2×C4—82no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—82no—
720C2×C4C2×#4112yes—
721C2×C4C2×#4112yes—
722C2×C4H(5,𝔽2)12yes—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—416no—
736C22—41no—
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#56214yes—
766C22C22×#4111yescharacteristic
767C22C2×H(5,𝔽2)11yescharacteristic
768C22C2×H(5,𝔽2)11yescharacteristic
769C22C2×H(5,𝔽2)11yescharacteristic
770C22C2×H(5,𝔽2)11yescharacteristic
771C22C2×2−1+411yescharacteristic
772C22#58511yescharacteristic
773C4—22no—
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
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—
798C2—24no—
799C2—42no—
800C2—42no—
801C2—81no—
802C2—81no—
803C2—81no—
804C2#349011yescharacteristic
805C2#349211yescharacteristic
806C2#349411yescharacteristic
807C2C2×#56211yescharacteristic
808C2#353411yescharacteristic
809C2#353711yescharacteristic
810C2#354111yescharacteristic
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. #2849C2semidirect
2. #2847C2semidirect
3. #2841C2semidirect
4. #2813C2semidirect
5. #2781C2semidirect
6. #2779C2semidirect
7. #2747C2semidirect
8. #2743C2semidirect
9. #2741C2semidirect
10. #2740C2semidirect
11. #2708C2semidirect
12. #2706C2semidirect
13. #2696C2semidirect
14. #2686C2semidirect
15. #2672C2semidirect
16. #2671C2semidirect
17. #2591C2semidirect
18. #2579C2semidirect
19. #2564C2semidirect
20. #2543C2semidirect
21. #2505C2semidirect
22. #2472C2semidirect
23. #2449C2semidirect
24. #2444C2semidirect
25. #2443C2semidirect
26. #2424C2semidirect
27. #2424C2semidirect
28. #2418C2semidirect
29. #2377C2semidirect
30. #2376C2semidirect
31. C2×#380C2semidirect
37. C2×#123C22semidirect
39. C2×C22⋊Q8C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #400C22semidirect
62. #400C22semidirect
63. #400C22semidirect
65. #399C22semidirect
66. #399C22semidirect
67. #399C22semidirect
68. #398C22semidirect
69. #398C22semidirect
70. #398C22semidirect
71. #398C22semidirect
72. #398C22semidirect
73. #398C22semidirect
76. #397C22semidirect
77. #397C22semidirect
78. #397C22semidirect
79. #397C22semidirect
82. #396C22semidirect
83. #396C22semidirect
84. #396C22semidirect
85. #395C22semidirect
86. #395C22semidirect
95. #394C22semidirect
96. #394C22semidirect
97. #394C22semidirect
98. #394C22semidirect
99. #394C22semidirect
101. #393C22semidirect
104. #392C22semidirect
108. #389C22semidirect
109. #389C22semidirect
116. #388C22semidirect
117. #388C22semidirect
118. #388C22semidirect
119. #388C22semidirect
120. #388C22semidirect
121. #388C22semidirect
122. #388C22semidirect
123. #388C22semidirect
124. #387C22semidirect
125. #387C22semidirect
126. #387C22semidirect
127. #387C22semidirect
128. #387C22semidirect
129. #387C22semidirect
130. #387C22semidirect
131. #387C22semidirect
132. #387C22semidirect
151. #386C22semidirect
152. #386C22semidirect
153. #386C22semidirect
161. #385C22semidirect
162. #385C22semidirect
163. #385C22semidirect
164. #385C22semidirect
165. #385C22semidirect
166. #385C22semidirect
167. #382C22semidirect
170. #381C22semidirect

Maximal subgroups

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

subgroupindex
#28492
#28472
#28412
#28132
#27812
#27792
#27472
#27432
#27412
#27402
#27082
#27062
#26962
#26862
#26722
#26712
#25912
#25792
#25642
#25432
#25052
#24722
#24492
#24442
#24432
#24242
#24182
#23772
#23762
C2×#3802