Finite Group Databasebeta

← #45745

Subgroups — #45745

Order 256.

1017 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2848C211yesmaximal, characteristic, complemented
2#2847C211yesmaximal, characteristic
3#2827C211yesmaximal, characteristic, complemented
4#2827C211yesmaximal, characteristic, complemented
5#2788C211yesmaximal, characteristic, complemented
6#2781C211yesmaximal, characteristic, complemented
7#2779C211yesmaximal, characteristic, complemented
8#2768C211yesmaximal, characteristic, complemented
9#2747C211yesmaximal, characteristic, complemented
10#2732C211yesmaximal, characteristic, complemented
11#2711C211yesmaximal, characteristic, complemented
12#2708C211yesmaximal, characteristic, complemented
13#2704C211yesmaximal, characteristic, complemented
14#2692C211yesmaximal, characteristic, complemented
15#2681C211yesmaximal, characteristic, complemented
16#2672C211yesmaximal, characteristic, complemented
17#2534C211yesmaximal, characteristic, complemented
18#2498C211yesmaximal, characteristic, complemented
19#2488C211yesmaximal, characteristic, complemented
20#2472C211yesmaximal, characteristic, complemented
21#2449C211yesmaximal, characteristic, complemented
22#2443C211yesmaximal, characteristic, complemented
23#2442C211yesmaximal, characteristic, complemented
24#2438C211yesmaximal, characteristic, complemented
25#2425C211yesmaximal, characteristic, complemented
26#2418C211yesmaximal, characteristic, complemented
27#2417C211yesmaximal, characteristic, complemented
28#2411C211yesmaximal, characteristic, complemented
29#2379C211yesmaximal, characteristic, complemented
30#2376C211yesmaximal, characteristic, complemented
31C2×#385C211yesmaximal, characteristic, complemented
32C24×C4C2211yescharacteristic
33C2×#125C2211yescharacteristic, complemented
34C2×#124C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic, complemented
39C2×C22⋊Q8C2211yescharacteristic
40C2×C22⋊Q8C2211yescharacteristic
41C2×C22⋊Q8C2211yescharacteristic
42C2×C22⋊Q8C2211yescharacteristic
43C2×C22⋊Q8C2211yescharacteristic, complemented
44C2×C22⋊Q8C2211yescharacteristic, complemented
45C2×#121C2211yescharacteristic
46C2×#121C2211yescharacteristic
47C2×#121C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic
52C2×#117C2211yescharacteristic
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#399C2211yescharacteristic
64#399C2211yescharacteristic, complemented
65#399C2211yescharacteristic, complemented
66#399C2211yescharacteristic, complemented
67#398C2211yescharacteristic, complemented
68#398C2211yescharacteristic, complemented
69#398C2211yescharacteristic, complemented
70#398C2211yescharacteristic, complemented
71#398C2211yescharacteristic, complemented
72#398C2211yescharacteristic, complemented
73#398C2211yescharacteristic, complemented
74#398C2211yescharacteristic, complemented
75#398C2211yescharacteristic, complemented
76#398C2211yescharacteristic, complemented
77#397C2211yescharacteristic
78#397C2211yescharacteristic
79#397C2211yescharacteristic, complemented
80#397C2211yescharacteristic, complemented
81#397C2211yescharacteristic, complemented
82#397C2211yescharacteristic, complemented
83#396C2211yescharacteristic
84#396C2211yescharacteristic
85#396C2211yescharacteristic
86#396C2211yescharacteristic
87#396C2211yescharacteristic, complemented
88#396C2211yescharacteristic, complemented
89#396C2211yescharacteristic, complemented
90#396C2211yescharacteristic, complemented
91#395C2211yescharacteristic, complemented
92#395C2211yescharacteristic, complemented
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic
101#394C2211yescharacteristic, complemented
102#394C2211yescharacteristic, complemented
103#393C2211yescharacteristic
104#393C2211yescharacteristic, complemented
105#391C2211yescharacteristic, complemented
106#391C2211yescharacteristic, complemented
107#391C2211yescharacteristic, complemented
108#390C2211yescharacteristic
109#390C2211yescharacteristic
110#390C2211yescharacteristic
111#389C2211yescharacteristic, complemented
112#389C2211yescharacteristic, complemented
113#389C2211yescharacteristic, complemented
114#389C2211yescharacteristic, complemented
115#389C2211yescharacteristic, complemented
116#389C2211yescharacteristic, complemented
117#388C2211yescharacteristic
118#388C2211yescharacteristic
119#388C2211yescharacteristic
120#388C2211yescharacteristic
121#388C2211yescharacteristic
122#388C2211yescharacteristic
123#388C2211yescharacteristic
124#388C2211yescharacteristic
125#388C2211yescharacteristic, complemented
126#388C2211yescharacteristic, complemented
127#388C2211yescharacteristic, complemented
128#388C2211yescharacteristic, complemented
129#388C2211yescharacteristic, complemented
130#388C2211yescharacteristic, complemented
131#387C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#387C2211yescharacteristic, complemented
134#387C2211yescharacteristic, complemented
135#387C2211yescharacteristic, complemented
136#387C2211yescharacteristic, complemented
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, complemented
151#385C2211yescharacteristic
152#385C2211yescharacteristic
153#385C2211yescharacteristic
154#385C2211yescharacteristic
155#385C2211yescharacteristic
156#385C2211yescharacteristic
157#385C2211yescharacteristic
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic
162#385C2211yescharacteristic
163#385C2211yescharacteristic
164#385C2211yescharacteristic
165#385C2211yescharacteristic
166#385C2211yescharacteristic
167#385C2211yescharacteristic, complemented
168#385C2211yescharacteristic, complemented
169#382C2211yescharacteristic, complemented
170#382C2211yescharacteristic, complemented
171#381C2211yescharacteristic
172#380C2211yescharacteristic
173#380C2211yescharacteristic
174#380C2211yescharacteristic
175#380C2211yescharacteristic
176#380C2211yescharacteristic
177#380C2211yescharacteristic
178#380C2211yescharacteristic
179#380C2211yescharacteristic
180#380C2211yescharacteristic, complemented
181#380C2211yescharacteristic, complemented
182#379C2211yescharacteristic
183#379C2211yescharacteristic
184C4×C22⋊C4C2211yescharacteristic
185C2×#95C2211yescharacteristic
186C2×#95C2211yescharacteristic
187C25C2311yescharacteristic
188C22×Q8C2311yescharacteristic
189C22×Q8C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C23×C4—42no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4C2311yescharacteristic
201C23×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212#125—42no—
213#124—24no—
214#123—24no—
215#123—42no—
216#123—42no—
217#123—42no—
218C22⋊Q8—42no—
219C22⋊Q8—42no—
220C22⋊Q8—42no—
221C22⋊Q8—42no—
222C22⋊Q8—42no—
223C22⋊Q8—42no—
224#121—42no—
225#121—42no—
226#121—42no—
227#120—42no—
228#120—42no—
229C4×D4—42no—
230C4×D4—42no—
231#117—42no—
232C2×C4⋊C4—42no—
233C2×C4⋊C4—42no—
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×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×C4⋊C4C2311yescharacteristic
271C2×C4⋊C4C2311yescharacteristic
272C2×C4⋊C4C2311yescharacteristic
273C2×C22⋊C4—24no—
274C2×C22⋊C4—42no—
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×C42C2311yescharacteristic
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
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
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—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—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
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—416no—
445C22×C4C2411yescharacteristic
446C22×C4C2411yescharacteristic
447C22×C4C2411yescharacteristic
448C22×C4C2411yescharacteristic
449C22×C4C2411yescharacteristic
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
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
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—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
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—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—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#4114yes—
556C42—22no—
557C42—41no—
558C42—41no—
559C42—41no—
560C42—41no—
561C42—41no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—28no—
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—44no—
594C23—44no—
595C23—44no—
596C23—44no—
597C23—44no—
598C23—44no—
599C23C2×#4112yes—
600C23H(5,𝔽2)12yes—
601C23H(5,𝔽2)12yes—
602C232−1+412yes—
603C232−1+412yes—
604C23C2511yescharacteristic
605Q8—82no—
606Q8—82no—
607D4—44no—
608D4—44no—
609D4—82no—
610D4—82no—
611D4—82no—
612D4—82no—
613D4—82no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
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—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—82no—
698C2×C4—82no—
699C2×C4—82no—
700C2×C4C2×#4112yes—
701C2×C4C2×#4112yes—
702C2×C4H(5,𝔽2)12yes—
703C2×C4H(5,𝔽2)12yes—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—416no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
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#56214yes—
740C22C22×#4111yescharacteristic
741C22C2×H(5,𝔽2)11yescharacteristic
742C22C2×H(5,𝔽2)11yescharacteristic
743C22C2×H(5,𝔽2)11yescharacteristic
744C22C2×H(5,𝔽2)11yescharacteristic
745C22C2×2−1+411yescharacteristic
746C22C2×2−1+411yescharacteristic
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C2—24no—
774C2—42no—
775C2—42no—
776C2—81no—
777C2—81no—
778C2#349211yescharacteristic
779C2#351911yescharacteristic
780C2#352011yescharacteristic
781C2C2×#56211yescharacteristic
782C2#353211yescharacteristic
783C2#353611yescharacteristic
784C2#353811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C25
prime radical#2847C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #2848C2semidirect
3. #2827C2semidirect
4. #2827C2semidirect
5. #2788C2semidirect
6. #2781C2semidirect
7. #2779C2semidirect
8. #2768C2semidirect
9. #2747C2semidirect
10. #2732C2semidirect
11. #2711C2semidirect
12. #2708C2semidirect
13. #2704C2semidirect
14. #2692C2semidirect
15. #2681C2semidirect
16. #2672C2semidirect
17. #2534C2semidirect
18. #2498C2semidirect
19. #2488C2semidirect
20. #2472C2semidirect
21. #2449C2semidirect
22. #2443C2semidirect
23. #2442C2semidirect
24. #2438C2semidirect
25. #2425C2semidirect
26. #2418C2semidirect
27. #2417C2semidirect
28. #2411C2semidirect
29. #2379C2semidirect
30. #2376C2semidirect
31. C2×#385C2semidirect
33. C2×#125C22semidirect
38. C2×#123C22semidirect
43. C2×C22⋊Q8C22semidirect
44. C2×C22⋊Q8C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #400C22semidirect
62. #400C22semidirect
64. #399C22semidirect
65. #399C22semidirect
66. #399C22semidirect
67. #398C22semidirect
68. #398C22semidirect
69. #398C22semidirect
70. #398C22semidirect
71. #398C22semidirect
72. #398C22semidirect
73. #398C22semidirect
74. #398C22semidirect
75. #398C22semidirect
76. #398C22semidirect
79. #397C22semidirect
80. #397C22semidirect
81. #397C22semidirect
82. #397C22semidirect
87. #396C22semidirect
88. #396C22semidirect
89. #396C22semidirect
90. #396C22semidirect
91. #395C22semidirect
92. #395C22semidirect
101. #394C22semidirect
102. #394C22semidirect
104. #393C22semidirect
105. #391C22semidirect
106. #391C22semidirect
107. #391C22semidirect
111. #389C22semidirect
112. #389C22semidirect
113. #389C22semidirect
114. #389C22semidirect
115. #389C22semidirect
116. #389C22semidirect
125. #388C22semidirect
126. #388C22semidirect
127. #388C22semidirect
128. #388C22semidirect
129. #388C22semidirect
130. #388C22semidirect
131. #387C22semidirect
132. #387C22semidirect
133. #387C22semidirect
134. #387C22semidirect
135. #387C22semidirect
136. #387C22semidirect
150. #386C22semidirect
167. #385C22semidirect
168. #385C22semidirect
169. #382C22semidirect
170. #382C22semidirect
180. #380C22semidirect
181. #380C22semidirect

Maximal subgroups

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

subgroupindex
#28482
#28472
#28272
#27882
#27812
#27792
#27682
#27472
#27322
#27112
#27082
#27042
#26922
#26812
#26722
#25342
#24982
#24882
#24722
#24492
#24432
#24422
#24382
#24252
#24182
#24172
#24112
#23792
#23762
C2×#3852