Finite Group Databasebeta

← #58172

Subgroups — #58172

Order 256.

925 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2842C211yesmaximal, characteristic, complemented
2#2836C211yesmaximal, characteristic, complemented
3#2829C211yesmaximal, characteristic, complemented
4#2800C211yesmaximal, characteristic, complemented
5#2795C211yesmaximal, characteristic, complemented
6#2775C211yesmaximal, characteristic, complemented
7#2761C211yesmaximal, characteristic, complemented
8#2757C211yesmaximal, characteristic, complemented
9#2748C211yesmaximal, characteristic, complemented
10#2732C211yesmaximal, characteristic, complemented
11#2711C211yesmaximal, characteristic, complemented
12#2707C211yesmaximal, characteristic, complemented
13#2706C211yesmaximal, characteristic, complemented
14#2682C211yesmaximal, characteristic, complemented
15#2681C211yesmaximal, characteristic, complemented
16#2678C211yesmaximal, characteristic, complemented
17#2678C211yesmaximal, characteristic, complemented
18#2672C211yesmaximal, characteristic, complemented
19#2668C211yesmaximal, characteristic, complemented
20#2635C211yesmaximal, characteristic, complemented
21#2630C211yesmaximal, characteristic, complemented
22#2620C211yesmaximal, characteristic, complemented
23#2598C211yesmaximal, characteristic, complemented
24#2472C211yesmaximal, characteristic, complemented
25#2471C211yesmaximal, characteristic, complemented
26#2449C211yesmaximal, characteristic, complemented
27#2441C211yesmaximal, characteristic, complemented
28#2418C211yesmaximal, characteristic, complemented
29#2416C211yesmaximal, characteristic, complemented
30#2413C211yesmaximal, characteristic, complemented
31#2411C211yesmaximal, characteristic, complemented
32C2×#125C2211yescharacteristic, complemented
33C2×#124C2211yescharacteristic
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic, complemented
39C2×C22⋊Q8C2211yescharacteristic
40C2×C22⋊Q8C2211yescharacteristic, complemented
41C2×C22⋊Q8C2211yescharacteristic, complemented
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#121C2211yescharacteristic
46C2×#121C2211yescharacteristic, complemented
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic, complemented
52C2×#117C2211yescharacteristic
53C2×#117C2211yescharacteristic, complemented
54C22×C4⋊C4C2211yescharacteristic, complemented
55C22×C22⋊C4C2211yescharacteristic
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#399C2211yescharacteristic
59#399C2211yescharacteristic
60#399C2211yescharacteristic
61#399C2211yescharacteristic
62#399C2211yescharacteristic
63#399C2211yescharacteristic
64#399C2211yescharacteristic, complemented
65#398C2211yescharacteristic, complemented
66#398C2211yescharacteristic, complemented
67#398C2211yescharacteristic, complemented
68#398C2211yescharacteristic, complemented
69#398C2211yescharacteristic, complemented
70#398C2211yescharacteristic, complemented
71#397C2211yescharacteristic
72#397C2211yescharacteristic
73#397C2211yescharacteristic
74#397C2211yescharacteristic
75#397C2211yescharacteristic
76#397C2211yescharacteristic
77#397C2211yescharacteristic, complemented
78#397C2211yescharacteristic, complemented
79#396C2211yescharacteristic
80#396C2211yescharacteristic
81#396C2211yescharacteristic
82#396C2211yescharacteristic
83#396C2211yescharacteristic
84#396C2211yescharacteristic
85#396C2211yescharacteristic
86#396C2211yescharacteristic
87#396C2211yescharacteristic
88#396C2211yescharacteristic
89#396C2211yescharacteristic
90#396C2211yescharacteristic
91#396C2211yescharacteristic, complemented
92#396C2211yescharacteristic, complemented
93#396C2211yescharacteristic, complemented
94#396C2211yescharacteristic, complemented
95#396C2211yescharacteristic, complemented
96#395C2211yescharacteristic, complemented
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic
101#394C2211yescharacteristic
102#394C2211yescharacteristic
103#394C2211yescharacteristic
104#394C2211yescharacteristic
105#394C2211yescharacteristic
106#394C2211yescharacteristic
107#394C2211yescharacteristic
108#394C2211yescharacteristic
109#394C2211yescharacteristic, complemented
110#394C2211yescharacteristic, complemented
111#394C2211yescharacteristic, complemented
112#394C2211yescharacteristic, complemented
113#394C2211yescharacteristic, complemented
114#393C2211yescharacteristic
115#392C2211yescharacteristic
116#392C2211yescharacteristic
117#392C2211yescharacteristic
118#392C2211yescharacteristic
119#392C2211yescharacteristic
120#391C2211yescharacteristic, complemented
121#390C2211yescharacteristic
122#390C2211yescharacteristic
123#390C2211yescharacteristic
124#390C2211yescharacteristic
125#390C2211yescharacteristic
126#390C2211yescharacteristic
127#390C2211yescharacteristic
128#390C2211yescharacteristic, complemented
129#389C2211yescharacteristic, complemented
130#389C2211yescharacteristic, complemented
131#389C2211yescharacteristic, complemented
132#389C2211yescharacteristic, complemented
133#389C2211yescharacteristic, complemented
134#389C2211yescharacteristic, complemented
135#388C2211yescharacteristic
136#388C2211yescharacteristic
137#388C2211yescharacteristic
138#388C2211yescharacteristic
139#388C2211yescharacteristic
140#388C2211yescharacteristic
141#388C2211yescharacteristic
142#388C2211yescharacteristic
143#388C2211yescharacteristic, complemented
144#388C2211yescharacteristic, complemented
145#388C2211yescharacteristic, complemented
146#388C2211yescharacteristic, complemented
147#388C2211yescharacteristic, complemented
148#388C2211yescharacteristic, complemented
149#387C2211yescharacteristic, complemented
150#387C2211yescharacteristic, complemented
151#387C2211yescharacteristic, complemented
152#387C2211yescharacteristic, complemented
153#387C2211yescharacteristic, complemented
154#387C2211yescharacteristic, complemented
155#387C2211yescharacteristic, complemented
156#386C2211yescharacteristic
157#386C2211yescharacteristic
158#386C2211yescharacteristic
159#386C2211yescharacteristic
160#386C2211yescharacteristic
161#386C2211yescharacteristic
162#386C2211yescharacteristic
163#386C2211yescharacteristic
164#386C2211yescharacteristic
165#386C2211yescharacteristic
166#386C2211yescharacteristic
167#386C2211yescharacteristic, complemented
168#385C2211yescharacteristic
169#385C2211yescharacteristic
170#385C2211yescharacteristic, complemented
171#385C2211yescharacteristic, complemented
172#385C2211yescharacteristic, complemented
173#385C2211yescharacteristic, complemented
174#385C2211yescharacteristic, complemented
175#385C2211yescharacteristic, complemented
176#384C2211yescharacteristic, complemented
177#383C2211yescharacteristic, complemented
178#382C2211yescharacteristic, complemented
179#381C2211yescharacteristic, complemented
180#380C2211yescharacteristic
181#380C2211yescharacteristic, complemented
182#380C2211yescharacteristic, complemented
183#379C2211yescharacteristic
184#379C2211yescharacteristic
185#379C2211yescharacteristic
186C4×C22⋊C4C2211yescharacteristic
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×C4C2311yescharacteristic
202C23×C4C2311yescharacteristic
203C23×C4C2311yescharacteristic
204C23×C4C2311yescharacteristic
205C23×C4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208#125—42no—
209#124—42no—
210#123—42no—
211#123—42no—
212#123—42no—
213#123—42no—
214#123—42no—
215C22⋊Q8—42no—
216C22⋊Q8—42no—
217C22⋊Q8—42no—
218#121—42no—
219#121—42no—
220#121—42no—
221#121—42no—
222#121—42no—
223#120—42no—
224#120—42no—
225#120—42no—
226C4×D4—42no—
227C4×D4—42no—
228#117—42no—
229#117—42no—
230C2×C4⋊C4—42no—
231C2×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
261C2×C4⋊C4C2311yescharacteristic
262C2×C4⋊C4C2311yescharacteristic
263C2×C4⋊C4C2311yescharacteristic
264C2×C4⋊C4C2311yescharacteristic
265C2×C4⋊C4C2311yescharacteristic
266C2×C4⋊C4C2311yescharacteristic
267C2×C4⋊C4C2311yescharacteristic
268C2×C22⋊C4—42no—
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×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328C2×C42C2311yescharacteristic
329C2×C42C2311yescharacteristic
330C2×C42C2311yescharacteristic
331C2×C42C2311yescharacteristic
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—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C2×Q8—22no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
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—
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×C4C2411yescharacteristic
440C22×C4C2411yescharacteristic
441C22×C4C2411yescharacteristic
442C22×C4C2411yescharacteristic
443C22×C4C2411yescharacteristic
444C22×C4C2411yescharacteristic
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
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
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—
501C22⋊C4—22no—
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—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
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—
557C42—22no—
558C42—22no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C23—21no—
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—82no—
606C23—82no—
607C23—82no—
608C23—82no—
609C23—82no—
610C23—82no—
611C23H(5,𝔽2)12yes—
612C232−1+412yes—
613C23C2511yescharacteristic
614Q8—82no—
615D4—44no—
616D4—44no—
617D4—82no—
618D4—82no—
619D4—82no—
620D4—82no—
621D4—82no—
622D4—82no—
623D4—82no—
624D4—82no—
625D4—82no—
626D4—82no—
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—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—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4H(5,𝔽2)12yes—
707C2×C4H(5,𝔽2)12yes—
708C2×C4H(5,𝔽2)12yes—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
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—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—88no—
752C22C2×H(5,𝔽2)11yescharacteristic
753C22C2×H(5,𝔽2)11yescharacteristic
754C22C2×H(5,𝔽2)11yescharacteristic
755C22C2×H(5,𝔽2)11yescharacteristic
756C22C2×2−1+411yescharacteristic
757C22#58511yescharacteristic
758C22#58511yescharacteristic
759C4—22no—
760C4—22no—
761C4—22no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
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—
784C2—42no—
785C2—42no—
786C2—81no—
787C2—81no—
788C2—81no—
789C2—81no—
790C2#353511yescharacteristic
791C2#353611yescharacteristic
792C2#353711yescharacteristic
793C2#353911yescharacteristic
794C2#354211yescharacteristic
795C2#354211yescharacteristic
796C2#356111yescharacteristic
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. #2842C2semidirect
2. #2836C2semidirect
3. #2829C2semidirect
4. #2800C2semidirect
5. #2795C2semidirect
6. #2775C2semidirect
7. #2761C2semidirect
8. #2757C2semidirect
9. #2748C2semidirect
10. #2732C2semidirect
11. #2711C2semidirect
12. #2707C2semidirect
13. #2706C2semidirect
14. #2682C2semidirect
15. #2681C2semidirect
16. #2678C2semidirect
17. #2678C2semidirect
18. #2672C2semidirect
19. #2668C2semidirect
20. #2635C2semidirect
21. #2630C2semidirect
22. #2620C2semidirect
23. #2598C2semidirect
24. #2472C2semidirect
25. #2471C2semidirect
26. #2449C2semidirect
27. #2441C2semidirect
28. #2418C2semidirect
29. #2416C2semidirect
30. #2413C2semidirect
31. #2411C2semidirect
32. C2×#125C22semidirect
38. C2×#123C22semidirect
40. C2×C22⋊Q8C22semidirect
41. C2×C22⋊Q8C22semidirect
46. C2×#121C22semidirect
51. C2×C4×D4C22semidirect
53. C2×#117C22semidirect
54. C22×C4⋊C4C22semidirect
56. #400C22semidirect
57. #400C22semidirect
64. #399C22semidirect
65. #398C22semidirect
66. #398C22semidirect
67. #398C22semidirect
68. #398C22semidirect
69. #398C22semidirect
70. #398C22semidirect
77. #397C22semidirect
78. #397C22semidirect
91. #396C22semidirect
92. #396C22semidirect
93. #396C22semidirect
94. #396C22semidirect
95. #396C22semidirect
96. #395C22semidirect
109. #394C22semidirect
110. #394C22semidirect
111. #394C22semidirect
112. #394C22semidirect
113. #394C22semidirect
120. #391C22semidirect
128. #390C22semidirect
129. #389C22semidirect
130. #389C22semidirect
131. #389C22semidirect
132. #389C22semidirect
133. #389C22semidirect
134. #389C22semidirect
143. #388C22semidirect
144. #388C22semidirect
145. #388C22semidirect
146. #388C22semidirect
147. #388C22semidirect
148. #388C22semidirect
149. #387C22semidirect
150. #387C22semidirect
151. #387C22semidirect
152. #387C22semidirect
153. #387C22semidirect
154. #387C22semidirect
155. #387C22semidirect
167. #386C22semidirect
170. #385C22semidirect
171. #385C22semidirect
172. #385C22semidirect
173. #385C22semidirect
174. #385C22semidirect
175. #385C22semidirect
176. #384C22semidirect
177. #383C22semidirect
178. #382C22semidirect
179. #381C22semidirect
181. #380C22semidirect
182. #380C22semidirect

Maximal subgroups

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

subgroupindex
#28422
#28362
#28292
#28002
#27952
#27752
#27612
#27572
#27482
#27322
#27112
#27072
#27062
#26822
#26812
#26782
#26722
#26682
#26352
#26302
#26202
#25982
#24722
#24712
#24492
#24412
#24182
#24162
#24132
#24112