Finite Group Databasebeta

← #53607

Subgroups — #53607

Order 256.

956 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2836C211yesmaximal, characteristic, complemented
2#2829C211yesmaximal, characteristic, complemented
3#2825C211yesmaximal, characteristic, complemented
4#2797C211yesmaximal, characteristic, complemented
5#2787C211yesmaximal, characteristic, complemented
6#2778C211yesmaximal, characteristic, complemented
7#2749C211yesmaximal, characteristic, complemented
8#2746C211yesmaximal, characteristic, complemented
9#2746C211yesmaximal, characteristic, complemented
10#2711C211yesmaximal, characteristic, complemented
11#2709C211yesmaximal, characteristic, complemented
12#2708C211yesmaximal, characteristic, complemented
13#2708C211yesmaximal, characteristic, complemented
14#2688C211yesmaximal, characteristic, complemented
15#2671C211yesmaximal, characteristic, complemented
16#2671C211yesmaximal, characteristic, complemented
17#2671C211yesmaximal, characteristic, complemented
18#2669C211yesmaximal, characteristic, complemented
19#2668C211yesmaximal, characteristic, complemented
20#2633C211yesmaximal, characteristic, complemented
21#2630C211yesmaximal, characteristic, complemented
22#2622C211yesmaximal, characteristic, complemented
23#2543C211yesmaximal, characteristic, complemented
24#2510C211yesmaximal, characteristic, complemented
25#2460C211yesmaximal, characteristic, complemented
26#2444C211yesmaximal, characteristic, complemented
27#2428C211yesmaximal, characteristic, complemented
28#2424C211yesmaximal, characteristic, complemented
29#2424C211yesmaximal, characteristic, complemented
30#2418C211yesmaximal, characteristic, complemented
31#2412C211yesmaximal, characteristic, complemented
32C2×#127C2211yescharacteristic
33C2×#125C2211yescharacteristic, complemented
34C2×#123C2211yescharacteristic
35C2×#123C2211yescharacteristic
36C2×#123C2211yescharacteristic, complemented
37C2×#121C2211yescharacteristic
38C2×#121C2211yescharacteristic
39C2×#121C2211yescharacteristic
40C2×#121C2211yescharacteristic
41C2×#121C2211yescharacteristic
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic
44C2×#121C2211yescharacteristic
45C2×#121C2211yescharacteristic, complemented
46C2×#121C2211yescharacteristic, complemented
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×#120C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic
52C2×C4×D4C2211yescharacteristic
53C2×C4×D4C2211yescharacteristic
54C22×C22⋊C4C2211yescharacteristic
55C22×C22⋊C4C2211yescharacteristic
56#401C2211yescharacteristic, complemented
57#401C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#400C2211yescharacteristic, complemented
62#399C2211yescharacteristic
63#399C2211yescharacteristic
64#399C2211yescharacteristic, complemented
65#399C2211yescharacteristic, complemented
66#398C2211yescharacteristic, complemented
67#398C2211yescharacteristic, complemented
68#398C2211yescharacteristic, complemented
69#398C2211yescharacteristic, complemented
70#398C2211yescharacteristic, complemented
71#398C2211yescharacteristic, complemented
72#397C2211yescharacteristic
73#397C2211yescharacteristic
74#397C2211yescharacteristic
75#397C2211yescharacteristic
76#397C2211yescharacteristic
77#397C2211yescharacteristic
78#397C2211yescharacteristic
79#397C2211yescharacteristic
80#397C2211yescharacteristic
81#397C2211yescharacteristic, complemented
82#397C2211yescharacteristic, complemented
83#397C2211yescharacteristic, complemented
84#397C2211yescharacteristic, complemented
85#397C2211yescharacteristic, complemented
86#396C2211yescharacteristic
87#396C2211yescharacteristic
88#396C2211yescharacteristic, complemented
89#396C2211yescharacteristic, complemented
90#394C2211yescharacteristic
91#394C2211yescharacteristic
92#394C2211yescharacteristic
93#394C2211yescharacteristic
94#394C2211yescharacteristic
95#394C2211yescharacteristic
96#394C2211yescharacteristic
97#394C2211yescharacteristic
98#394C2211yescharacteristic
99#394C2211yescharacteristic
100#394C2211yescharacteristic
101#394C2211yescharacteristic
102#394C2211yescharacteristic
103#394C2211yescharacteristic
104#394C2211yescharacteristic
105#394C2211yescharacteristic
106#394C2211yescharacteristic, complemented
107#394C2211yescharacteristic, complemented
108#394C2211yescharacteristic, complemented
109#394C2211yescharacteristic, complemented
110#394C2211yescharacteristic, complemented
111#394C2211yescharacteristic, complemented
112#392C2211yescharacteristic
113#392C2211yescharacteristic
114#392C2211yescharacteristic
115#392C2211yescharacteristic
116#392C2211yescharacteristic
117#392C2211yescharacteristic
118#392C2211yescharacteristic
119#392C2211yescharacteristic, complemented
120#390C2211yescharacteristic
121#390C2211yescharacteristic
122#390C2211yescharacteristic, complemented
123#389C2211yescharacteristic, complemented
124#388C2211yescharacteristic
125#388C2211yescharacteristic
126#388C2211yescharacteristic
127#388C2211yescharacteristic
128#388C2211yescharacteristic
129#388C2211yescharacteristic
130#388C2211yescharacteristic, complemented
131#388C2211yescharacteristic, complemented
132#388C2211yescharacteristic, complemented
133#388C2211yescharacteristic, 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#386C2211yescharacteristic, complemented
160#386C2211yescharacteristic, complemented
161#386C2211yescharacteristic, complemented
162#386C2211yescharacteristic, complemented
163#385C2211yescharacteristic
164#385C2211yescharacteristic
165#385C2211yescharacteristic
166#385C2211yescharacteristic
167#385C2211yescharacteristic
168#385C2211yescharacteristic
169#385C2211yescharacteristic, complemented
170#385C2211yescharacteristic, complemented
171#385C2211yescharacteristic, complemented
172#385C2211yescharacteristic, complemented
173#385C2211yescharacteristic, complemented
174#385C2211yescharacteristic, complemented
175#385C2211yescharacteristic, complemented
176#383C2211yescharacteristic, complemented
177#381C2211yescharacteristic
178#381C2211yescharacteristic, complemented
179#380C2211yescharacteristic
180#380C2211yescharacteristic
181#380C2211yescharacteristic
182#380C2211yescharacteristic, complemented
183#380C2211yescharacteristic, complemented
184#379C2211yescharacteristic
185C4×C22⋊C4C2211yescharacteristic, complemented
186C2×#95C2211yescharacteristic, complemented
187C25C2311yescharacteristic
188C22×D4C2311yescharacteristic
189C22×D4C2311yescharacteristic
190C22×D4C2311yescharacteristic
191C22×D4C2311yescharacteristic
192C22×D4C2311yescharacteristic
193C22×D4C2311yescharacteristic
194C22×D4C2311yescharacteristic
195C22×D4C2311yescharacteristic
196C22×D4C2311yescharacteristic
197C22×D4C2311yescharacteristic
198C22×D4C2311yescharacteristic
199C22×D4C2311yescharacteristic
200C22×D4C2311yescharacteristic
201C22×D4C2311yescharacteristic
202C22×D4C2311yescharacteristic
203C22×D4C2311yescharacteristic
204C22×D4C2311yescharacteristic
205C22×D4C2311yescharacteristic
206C23×C4C2311yescharacteristic
207C23×C4C2311yescharacteristic
208C23×C4C2311yescharacteristic
209C23×C4C2311yescharacteristic
210C23×C4C2311yescharacteristic
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216#127—42no—
217#125—42no—
218#123—42no—
219#123—42no—
220#123—42no—
221#121—42no—
222#121—42no—
223#121—42no—
224#121—42no—
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—
234#120—42no—
235C4×D4—42no—
236C4×D4—42no—
237C4×D4—42no—
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×C22⋊C4—42no—
265C2×C22⋊C4—42no—
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×C22⋊C4C2311yescharacteristic
320C2×C22⋊C4C2311yescharacteristic
321C2×C22⋊C4C2311yescharacteristic
322C2×C42C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
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—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24C2411yescharacteristic
374C24C2411yescharacteristic
375C24C2411yescharacteristic
376C24C2411yescharacteristic
377C24C2411yescharacteristic
378C24C2411yescharacteristic
379C24C2411yescharacteristic
380C2×D4—22no—
381C2×D4—22no—
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—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
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—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—41no—
434C22×C4—22no—
435C22×C4—22no—
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—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
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
486C22×C4C2411yescharacteristic
487C22×C4C2411yescharacteristic
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
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—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
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—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—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C42—22no—
571C42—41no—
572C42—41no—
573C42—41no—
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—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—44no—
621C23—44no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23—82no—
626C23—82no—
627C23H(5,𝔽2)12yes—
628C23H(5,𝔽2)12yes—
629C23H(5,𝔽2)12yes—
630C23C2511yescharacteristic
631D4—44no—
632D4—44no—
633D4—44no—
634D4—82no—
635D4—82no—
636D4—82no—
637D4—82no—
638D4—82no—
639D4—82no—
640D4—82no—
641D4—82no—
642D4—82no—
643D4—82no—
644D4—82no—
645D4—82no—
646D4—82no—
647D4—82no—
648D4—82no—
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—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4—82no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4H(5,𝔽2)12yes—
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—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—88no—
781C22C2×H(5,𝔽2)11yescharacteristic
782C22C2×H(5,𝔽2)11yescharacteristic
783C22C2×H(5,𝔽2)11yescharacteristic
784C22C2×H(5,𝔽2)11yescharacteristic
785C22#58511yescharacteristic
786C22#58511yescharacteristic
787C22#58511yescharacteristic
788C4—22no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—41no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C2—42no—
813C2—42no—
814C2—42no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2—81no—
819C2#353311yescharacteristic
820C2#353411yescharacteristic
821C2#353411yescharacteristic
822C2#353411yescharacteristic
823C2#353711yescharacteristic
824C2#356011yescharacteristic
825C2#356211yescharacteristic
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. #2836C2semidirect
2. #2829C2semidirect
3. #2825C2semidirect
4. #2797C2semidirect
5. #2787C2semidirect
6. #2778C2semidirect
7. #2749C2semidirect
8. #2746C2semidirect
9. #2746C2semidirect
10. #2711C2semidirect
11. #2709C2semidirect
12. #2708C2semidirect
13. #2708C2semidirect
14. #2688C2semidirect
15. #2671C2semidirect
16. #2671C2semidirect
17. #2671C2semidirect
18. #2669C2semidirect
19. #2668C2semidirect
20. #2633C2semidirect
21. #2630C2semidirect
22. #2622C2semidirect
23. #2543C2semidirect
24. #2510C2semidirect
25. #2460C2semidirect
26. #2444C2semidirect
27. #2428C2semidirect
28. #2424C2semidirect
29. #2424C2semidirect
30. #2418C2semidirect
31. #2412C2semidirect
33. C2×#125C22semidirect
36. C2×#123C22semidirect
45. C2×#121C22semidirect
46. C2×#121C22semidirect
56. #401C22semidirect
57. #401C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #400C22semidirect
64. #399C22semidirect
65. #399C22semidirect
66. #398C22semidirect
67. #398C22semidirect
68. #398C22semidirect
69. #398C22semidirect
70. #398C22semidirect
71. #398C22semidirect
81. #397C22semidirect
82. #397C22semidirect
83. #397C22semidirect
84. #397C22semidirect
85. #397C22semidirect
88. #396C22semidirect
89. #396C22semidirect
106. #394C22semidirect
107. #394C22semidirect
108. #394C22semidirect
109. #394C22semidirect
110. #394C22semidirect
111. #394C22semidirect
119. #392C22semidirect
122. #390C22semidirect
123. #389C22semidirect
130. #388C22semidirect
131. #388C22semidirect
132. #388C22semidirect
133. #388C22semidirect
134. #387C22semidirect
135. #387C22semidirect
136. #387C22semidirect
137. #387C22semidirect
138. #387C22semidirect
139. #387C22semidirect
156. #386C22semidirect
157. #386C22semidirect
158. #386C22semidirect
159. #386C22semidirect
160. #386C22semidirect
161. #386C22semidirect
162. #386C22semidirect
169. #385C22semidirect
170. #385C22semidirect
171. #385C22semidirect
172. #385C22semidirect
173. #385C22semidirect
174. #385C22semidirect
175. #385C22semidirect
176. #383C22semidirect
178. #381C22semidirect
182. #380C22semidirect
183. #380C22semidirect
185. C4×C22⋊C4C22semidirect
186. C2×#95C22semidirect

Maximal subgroups

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

subgroupindex
#28362
#28292
#28252
#27972
#27872
#27782
#27492
#27462
#27112
#27092
#27082
#26882
#26712
#26692
#26682
#26332
#26302
#26222
#25432
#25102
#24602
#24442
#24282
#24242
#24182
#24122