Finite Group Databasebeta

← #53165

Subgroups — #53165

Order 256.

974 conjugacy classes of subgroups.

The subgroup lattice has 803 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2849C211yesmaximal, characteristic, complemented
2#2848C211yesmaximal, characteristic, complemented
3#2847C211yesmaximal, characteristic, complemented
4#2796C211yesmaximal, characteristic, complemented
5#2788C211yesmaximal, characteristic, complemented
6#2784C211yesmaximal, characteristic, complemented
7#2784C211yesmaximal, characteristic, complemented
8#2778C211yesmaximal, characteristic, complemented
9#2746C211yesmaximal, characteristic, complemented
10#2745C211yesmaximal, characteristic, complemented
11#2743C211yesmaximal, characteristic, complemented
12#2730C211yesmaximal, characteristic, complemented
13#2717C211yesmaximal, characteristic, complemented
14#2712C211yesmaximal, characteristic, complemented
15#2711C211yesmaximal, characteristic, complemented
16#2707C211yesmaximal, characteristic, complemented
17#2700C211yesmaximal, characteristic, complemented
18#2697C211yesmaximal, characteristic, complemented
19#2696C211yesmaximal, characteristic, complemented
20#2693C211yesmaximal, characteristic, complemented
21#2692C211yesmaximal, characteristic, complemented
22#2690C211yesmaximal, characteristic, complemented
23#2688C211yesmaximal, characteristic, complemented
24#2686C211yesmaximal, characteristic, complemented
25#2684C211yesmaximal, characteristic, complemented
26#2678C211yesmaximal, characteristic, complemented
27#2676C211yesmaximal, characteristic, complemented
28#2672C211yesmaximal, characteristic, complemented
29#2672C211yesmaximal, characteristic, complemented
30#2671C211yesmaximal, characteristic, complemented
31#2670C211yesmaximal, characteristic, complemented
32C24×C4C2211yescharacteristic
33C2×#125C2211yescharacteristic, complemented
34C2×#124C2211yescharacteristic
35C2×#124C2211yescharacteristic
36C2×#124C2211yescharacteristic
37C2×#124C2211yescharacteristic, complemented
38C2×#123C2211yescharacteristic
39C2×#123C2211yescharacteristic
40C2×#123C2211yescharacteristic
41C2×#123C2211yescharacteristic
42C2×C22⋊Q8C2211yescharacteristic
43C2×C22⋊Q8C2211yescharacteristic
44C2×C22⋊Q8C2211yescharacteristic
45C2×C22⋊Q8C2211yescharacteristic, complemented
46C2×#121C2211yescharacteristic
47C2×#121C2211yescharacteristic
48C2×#121C2211yescharacteristic
49C2×#121C2211yescharacteristic
50C2×#121C2211yescharacteristic, complemented
51C2×#120C2211yescharacteristic
52C2×#120C2211yescharacteristic
53C2×#120C2211yescharacteristic
54#401C2211yescharacteristic, complemented
55#400C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#399C2211yescharacteristic, complemented
62#399C2211yescharacteristic, complemented
63#399C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#398C2211yescharacteristic, complemented
66#397C2211yescharacteristic
67#397C2211yescharacteristic
68#397C2211yescharacteristic
69#397C2211yescharacteristic
70#397C2211yescharacteristic
71#397C2211yescharacteristic, complemented
72#397C2211yescharacteristic, complemented
73#397C2211yescharacteristic, complemented
74#397C2211yescharacteristic, complemented
75#396C2211yescharacteristic
76#396C2211yescharacteristic
77#396C2211yescharacteristic
78#396C2211yescharacteristic, complemented
79#396C2211yescharacteristic, complemented
80#396C2211yescharacteristic, complemented
81#396C2211yescharacteristic, complemented
82#395C2211yescharacteristic, complemented
83#395C2211yescharacteristic, complemented
84#395C2211yescharacteristic, complemented
85#395C2211yescharacteristic, complemented
86#394C2211yescharacteristic
87#394C2211yescharacteristic
88#394C2211yescharacteristic
89#394C2211yescharacteristic
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic, complemented
95#394C2211yescharacteristic, complemented
96#394C2211yescharacteristic, complemented
97#394C2211yescharacteristic, complemented
98#394C2211yescharacteristic, complemented
99#393C2211yescharacteristic
100#393C2211yescharacteristic
101#393C2211yescharacteristic
102#393C2211yescharacteristic, complemented
103#393C2211yescharacteristic, complemented
104#393C2211yescharacteristic, complemented
105#392C2211yescharacteristic
106#392C2211yescharacteristic
107#392C2211yescharacteristic
108#392C2211yescharacteristic
109#392C2211yescharacteristic
110#391C2211yescharacteristic, complemented
111#391C2211yescharacteristic, complemented
112#391C2211yescharacteristic, complemented
113#390C2211yescharacteristic
114#390C2211yescharacteristic
115#390C2211yescharacteristic
116#390C2211yescharacteristic
117#390C2211yescharacteristic
118#389C2211yescharacteristic, complemented
119#389C2211yescharacteristic, complemented
120#388C2211yescharacteristic
121#388C2211yescharacteristic
122#388C2211yescharacteristic
123#388C2211yescharacteristic
124#388C2211yescharacteristic
125#388C2211yescharacteristic
126#388C2211yescharacteristic
127#388C2211yescharacteristic, complemented
128#388C2211yescharacteristic, complemented
129#388C2211yescharacteristic, complemented
130#388C2211yescharacteristic, complemented
131#388C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#387C2211yescharacteristic, complemented
134#387C2211yescharacteristic, complemented
135#387C2211yescharacteristic, complemented
136#387C2211yescharacteristic, complemented
137#387C2211yescharacteristic, complemented
138#387C2211yescharacteristic, complemented
139#387C2211yescharacteristic, complemented
140#386C2211yescharacteristic
141#386C2211yescharacteristic
142#386C2211yescharacteristic
143#386C2211yescharacteristic
144#386C2211yescharacteristic
145#386C2211yescharacteristic
146#386C2211yescharacteristic
147#386C2211yescharacteristic
148#386C2211yescharacteristic
149#386C2211yescharacteristic
150#386C2211yescharacteristic
151#386C2211yescharacteristic
152#386C2211yescharacteristic
153#386C2211yescharacteristic
154#386C2211yescharacteristic
155#386C2211yescharacteristic
156#386C2211yescharacteristic, complemented
157#386C2211yescharacteristic, complemented
158#386C2211yescharacteristic, complemented
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic
162#385C2211yescharacteristic
163#385C2211yescharacteristic
164#385C2211yescharacteristic
165#385C2211yescharacteristic
166#385C2211yescharacteristic
167#385C2211yescharacteristic
168#385C2211yescharacteristic
169#385C2211yescharacteristic, complemented
170#385C2211yescharacteristic, complemented
171#385C2211yescharacteristic, complemented
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
185#379C2211yescharacteristic
186#379C2211yescharacteristic
187C25C2311yescharacteristic
188C22×Q8C2311yescharacteristic
189C22×Q8C2311yescharacteristic
190C22×Q8C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C22×D4C2311yescharacteristic
202C22×D4C2311yescharacteristic
203C23×C4—42no—
204C23×C4—42no—
205C23×C4—42no—
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215#125—42no—
216#124—42no—
217#124—42no—
218#124—42no—
219#124—42no—
220#123—42no—
221#123—42no—
222#123—42no—
223#123—42no—
224C22⋊Q8—42no—
225C22⋊Q8—42no—
226C22⋊Q8—42no—
227C22⋊Q8—42no—
228#121—42no—
229#121—42no—
230#121—42no—
231#121—42no—
232#121—42no—
233#120—42no—
234#120—42no—
235#120—42no—
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×C4⋊C4C2311yescharacteristic
261C2×C4⋊C4C2311yescharacteristic
262C2×C4⋊C4C2311yescharacteristic
263C2×C4⋊C4C2311yescharacteristic
264C2×C4⋊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×C42C2311yescharacteristic
320C2×C42C2311yescharacteristic
321C2×C42C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324#95C2311yescharacteristic
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
366C24—22no—
367C24—22no—
368C24—22no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C2×Q8—22no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
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—41no—
399C2×D4—41no—
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—
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—41no—
433C22×C4—41no—
434C22×C4—41no—
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—416no—
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
474C22×C4C2411yescharacteristic
475C22×C4C2411yescharacteristic
476C22×C4C2411yescharacteristic
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
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—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
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—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
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—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
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—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23H(5,𝔽2)12yes—
612C23H(5,𝔽2)12yes—
613C232−1+412yes—
614C23C2511yescharacteristic
615Q8—82no—
616Q8—82no—
617Q8—82no—
618D4—82no—
619D4—82no—
620D4—82no—
621D4—82no—
622D4—82no—
623D4—82no—
624D4—82no—
625D4—82no—
626D4—82no—
627D4—82no—
628D4—82no—
629D4—82no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
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—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4H(5,𝔽2)12yes—
713C2×C4H(5,𝔽2)12yes—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—416no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
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—
757C22C2×H(5,𝔽2)11yescharacteristic
758C22C2×H(5,𝔽2)11yescharacteristic
759C22C2×H(5,𝔽2)11yescharacteristic
760C22C2×H(5,𝔽2)11yescharacteristic
761C22C2×2−1+411yescharacteristic
762C22#58511yescharacteristic
763C22#58511yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—41no—
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—
789C2—42no—
790C2—42no—
791C2—42no—
792C2—81no—
793C2—81no—
794C2—81no—
795C2#353211yescharacteristic
796C2#353411yescharacteristic
797C2#353511yescharacteristic
798C2#353611yescharacteristic
799C2#354011yescharacteristic
800C2#354111yescharacteristic
801C2#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. #2849C2semidirect
2. #2848C2semidirect
3. #2847C2semidirect
4. #2796C2semidirect
5. #2788C2semidirect
6. #2784C2semidirect
7. #2784C2semidirect
8. #2778C2semidirect
9. #2746C2semidirect
10. #2745C2semidirect
11. #2743C2semidirect
12. #2730C2semidirect
13. #2717C2semidirect
14. #2712C2semidirect
15. #2711C2semidirect
16. #2707C2semidirect
17. #2700C2semidirect
18. #2697C2semidirect
19. #2696C2semidirect
20. #2693C2semidirect
21. #2692C2semidirect
22. #2690C2semidirect
23. #2688C2semidirect
24. #2686C2semidirect
25. #2684C2semidirect
26. #2678C2semidirect
27. #2676C2semidirect
28. #2672C2semidirect
29. #2672C2semidirect
30. #2671C2semidirect
31. #2670C2semidirect
33. C2×#125C22semidirect
37. C2×#124C22semidirect
45. C2×C22⋊Q8C22semidirect
50. C2×#121C22semidirect
54. #401C22semidirect
55. #400C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #399C22semidirect
62. #399C22semidirect
63. #399C22semidirect
64. #398C22semidirect
65. #398C22semidirect
71. #397C22semidirect
72. #397C22semidirect
73. #397C22semidirect
74. #397C22semidirect
78. #396C22semidirect
79. #396C22semidirect
80. #396C22semidirect
81. #396C22semidirect
82. #395C22semidirect
83. #395C22semidirect
84. #395C22semidirect
85. #395C22semidirect
94. #394C22semidirect
95. #394C22semidirect
96. #394C22semidirect
97. #394C22semidirect
98. #394C22semidirect
102. #393C22semidirect
103. #393C22semidirect
104. #393C22semidirect
110. #391C22semidirect
111. #391C22semidirect
112. #391C22semidirect
118. #389C22semidirect
119. #389C22semidirect
127. #388C22semidirect
128. #388C22semidirect
129. #388C22semidirect
130. #388C22semidirect
131. #388C22semidirect
132. #387C22semidirect
133. #387C22semidirect
134. #387C22semidirect
135. #387C22semidirect
136. #387C22semidirect
137. #387C22semidirect
138. #387C22semidirect
139. #387C22semidirect
156. #386C22semidirect
157. #386C22semidirect
158. #386C22semidirect
169. #385C22semidirect
170. #385C22semidirect
171. #385C22semidirect
174. #381C22semidirect
181. #380C22semidirect
182. #380C22semidirect
183. #380C22semidirect

Maximal subgroups

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

subgroupindex
#28492
#28482
#28472
#27962
#27882
#27842
#27782
#27462
#27452
#27432
#27302
#27172
#27122
#27112
#27072
#27002
#26972
#26962
#26932
#26922
#26902
#26882
#26862
#26842
#26782
#26762
#26722
#26712
#26702