Finite Group Databasebeta

← #36758

Subgroups — #36758

Order 256.

1105 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2848C211yesmaximal, characteristic, complemented
2#2847C211yesmaximal, characteristic, complemented
3#2797C211yesmaximal, characteristic, complemented
4#2781C211yesmaximal, characteristic, complemented
5#2779C211yesmaximal, characteristic, complemented
6#2778C211yesmaximal, characteristic, complemented
7#2778C211yesmaximal, characteristic, complemented
8#2756C211yesmaximal, characteristic, complemented
9#2753C211yesmaximal, characteristic, complemented
10#2749C211yesmaximal, characteristic, complemented
11#2741C211yesmaximal, characteristic, complemented
12#2730C211yesmaximal, characteristic, complemented
13#2714C211yesmaximal, characteristic, complemented
14#2703C211yesmaximal, characteristic, complemented
15#2702C211yesmaximal, characteristic, complemented
16#2696C211yesmaximal, characteristic, complemented
17#2688C211yesmaximal, characteristic, complemented
18#2676C211yesmaximal, characteristic, complemented
19#2613C211yesmaximal, characteristic, complemented
20#2613C211yesmaximal, characteristic, complemented
21#2493C211yesmaximal, characteristic, complemented
22#2488C211yesmaximal, characteristic, complemented
23#2480C211yesmaximal, characteristic, complemented
24#2472C211yesmaximal, characteristic, complemented
25#2425C211yesmaximal, characteristic, complemented
26#2424C211yesmaximal, characteristic, complemented
27#2419C211yesmaximal, characteristic, complemented
28#2418C211yesmaximal, characteristic, complemented
29#2321C211yesmaximal, characteristic, complemented
30#2321C211yesmaximal, characteristic, complemented
31C2×#386C211yesmaximal, characteristic, complemented
32C23×D4C2211yescharacteristic
33C24×C4C2211yescharacteristic
34C2×#126C2211yescharacteristic, complemented
35C2×#124C2211yescharacteristic, complemented
36C2×#123C2211yescharacteristic
37C2×#123C2211yescharacteristic
38C2×#123C2211yescharacteristic, complemented
39C2×C22⋊Q8C2211yescharacteristic
40C2×C22⋊Q8C2211yescharacteristic, complemented
41C2×C22⋊Q8C2211yescharacteristic, complemented
42C2×#121C2211yescharacteristic
43C2×#121C2211yescharacteristic, complemented
44C2×#121C2211yescharacteristic, complemented
45C2×#121C2211yescharacteristic, complemented
46C2×#120C2211yescharacteristic
47C2×#120C2211yescharacteristic
48C2×#120C2211yescharacteristic
49C2×#120C2211yescharacteristic
50C2×C4×D4C2211yescharacteristic
51C2×C4×D4C2211yescharacteristic
52C22×C22⋊C4C2211yescharacteristic
53C22×C22⋊C4C2211yescharacteristic
54C22×C22⋊C4C2211yescharacteristic
55#401C2211yescharacteristic, complemented
56#400C2211yescharacteristic, complemented
57#400C2211yescharacteristic, complemented
58#400C2211yescharacteristic, complemented
59#400C2211yescharacteristic, complemented
60#400C2211yescharacteristic, complemented
61#400C2211yescharacteristic, complemented
62#399C2211yescharacteristic, complemented
63#398C2211yescharacteristic, complemented
64#398C2211yescharacteristic, complemented
65#397C2211yescharacteristic, complemented
66#397C2211yescharacteristic, complemented
67#397C2211yescharacteristic, complemented
68#397C2211yescharacteristic, complemented
69#397C2211yescharacteristic, complemented
70#397C2211yescharacteristic, complemented
71#397C2211yescharacteristic, complemented
72#397C2211yescharacteristic, complemented
73#397C2211yescharacteristic, complemented
74#396C2211yescharacteristic, complemented
75#396C2211yescharacteristic, complemented
76#396C2211yescharacteristic, complemented
77#394C2211yescharacteristic
78#394C2211yescharacteristic
79#394C2211yescharacteristic
80#394C2211yescharacteristic
81#394C2211yescharacteristic
82#394C2211yescharacteristic
83#394C2211yescharacteristic
84#394C2211yescharacteristic
85#394C2211yescharacteristic, complemented
86#394C2211yescharacteristic, complemented
87#394C2211yescharacteristic, complemented
88#394C2211yescharacteristic, complemented
89#394C2211yescharacteristic, complemented
90#394C2211yescharacteristic, complemented
91#394C2211yescharacteristic, complemented
92#393C2211yescharacteristic, complemented
93#393C2211yescharacteristic, complemented
94#392C2211yescharacteristic
95#392C2211yescharacteristic
96#392C2211yescharacteristic
97#392C2211yescharacteristic
98#392C2211yescharacteristic
99#392C2211yescharacteristic
100#392C2211yescharacteristic
101#392C2211yescharacteristic
102#392C2211yescharacteristic, complemented
103#391C2211yescharacteristic, complemented
104#390C2211yescharacteristic, complemented
105#390C2211yescharacteristic, complemented
106#390C2211yescharacteristic, complemented
107#390C2211yescharacteristic, complemented
108#390C2211yescharacteristic, complemented
109#390C2211yescharacteristic, complemented
110#389C2211yescharacteristic, complemented
111#388C2211yescharacteristic, complemented
112#388C2211yescharacteristic, complemented
113#388C2211yescharacteristic, complemented
114#388C2211yescharacteristic, complemented
115#388C2211yescharacteristic, complemented
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#388C2211yescharacteristic, complemented
125#388C2211yescharacteristic, complemented
126#388C2211yescharacteristic, complemented
127#388C2211yescharacteristic, complemented
128#388C2211yescharacteristic, complemented
129#388C2211yescharacteristic, complemented
130#387C2211yescharacteristic, complemented
131#387C2211yescharacteristic, complemented
132#387C2211yescharacteristic, complemented
133#387C2211yescharacteristic, complemented
134#387C2211yescharacteristic, complemented
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, complemented
148#386C2211yescharacteristic, complemented
149#386C2211yescharacteristic, complemented
150#386C2211yescharacteristic, complemented
151#386C2211yescharacteristic, complemented
152#386C2211yescharacteristic, complemented
153#386C2211yescharacteristic, complemented
154#386C2211yescharacteristic, complemented
155#386C2211yescharacteristic, complemented
156#386C2211yescharacteristic, complemented
157#386C2211yescharacteristic, complemented
158#385C2211yescharacteristic
159#385C2211yescharacteristic
160#385C2211yescharacteristic
161#385C2211yescharacteristic
162#385C2211yescharacteristic, complemented
163#385C2211yescharacteristic, complemented
164#385C2211yescharacteristic, complemented
165#385C2211yescharacteristic, complemented
166#385C2211yescharacteristic, complemented
167#383C2211yescharacteristic, complemented
168#382C2211yescharacteristic, complemented
169#381C2211yescharacteristic
170#381C2211yescharacteristic
171#381C2211yescharacteristic, complemented
172#380C2211yescharacteristic
173#380C2211yescharacteristic
174#380C2211yescharacteristic, complemented
175#380C2211yescharacteristic, complemented
176#380C2211yescharacteristic, complemented
177#380C2211yescharacteristic, complemented
178#380C2211yescharacteristic, complemented
179#379C2211yescharacteristic
180#379C2211yescharacteristic
181#379C2211yescharacteristic
182#379C2211yescharacteristic
183C4×C22⋊C4C2211yescharacteristic
184C4×C22⋊C4C2211yescharacteristic
185C2×#95C2211yescharacteristic
186C2×#95C2211yescharacteristic
187C25C2311yescharacteristic
188C25C2311yescharacteristic
189C22×Q8C2311yescharacteristic
190C22×D4—24no—
191C22×D4—42no—
192C22×D4—42no—
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
206C22×D4C2311yescharacteristic
207C22×D4C2311yescharacteristic
208C23×C4—42no—
209C23×C4—42no—
210C23×C4—42no—
211C23×C4C2311yescharacteristic
212C23×C4C2311yescharacteristic
213C23×C4C2311yescharacteristic
214C23×C4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216C23×C4C2311yescharacteristic
217C23×C4C2311yescharacteristic
218C23×C4C2311yescharacteristic
219C23×C4C2311yescharacteristic
220C23×C4C2311yescharacteristic
221C23×C4C2311yescharacteristic
222#126—42no—
223#124—42no—
224#123—42no—
225#123—42no—
226#123—42no—
227C22⋊Q8—42no—
228C22⋊Q8—42no—
229C22⋊Q8—42no—
230#121—42no—
231#121—42no—
232#121—42no—
233#121—42no—
234#120—24no—
235#120—24no—
236#120—42no—
237#120—42no—
238C4×D4—42no—
239C4×D4—42no—
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×C22⋊C4—42no—
263C2×C22⋊C4—42no—
264C2×C22⋊C4—42no—
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×C22⋊C4C2311yescharacteristic
320C2×C22⋊C4C2311yescharacteristic
321C2×C22⋊C4C2311yescharacteristic
322C2×C22⋊C4C2311yescharacteristic
323C2×C42C2311yescharacteristic
324C2×C42C2311yescharacteristic
325C2×C42C2311yescharacteristic
326C2×C42C2311yescharacteristic
327C2×C42C2311yescharacteristic
328C2×C42C2311yescharacteristic
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—
376C24—41no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24—41no—
382C24#4114yes—
383C24C2411yescharacteristic
384C24C2411yescharacteristic
385C24C2411yescharacteristic
386C24C2411yescharacteristic
387C24C2411yescharacteristic
388C24C2411yescharacteristic
389C24C2411yescharacteristic
390C2×Q8—22no—
391C2×Q8—41no—
392C2×Q8—41no—
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—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
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—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—416no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
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×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—416no—
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
488C22×C4C2411yescharacteristic
489C22×C4C2411yescharacteristic
490C22×C4C2411yescharacteristic
491C22×C4C2411yescharacteristic
492C22×C4C2411yescharacteristic
493C22×C4C2411yescharacteristic
494C22×C4C2411yescharacteristic
495C22×C4C2411yescharacteristic
496C22×C4C2411yescharacteristic
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
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—
517C4⋊C4—41no—
518C4⋊C4—41no—
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—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—41no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C42—41no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—28no—
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—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—82no—
638C23—82no—
639C23—82no—
640C23—82no—
641C23C2×#4112yes—
642C23C2×#4112yes—
643C23C2×#4112yes—
644C23H(5,𝔽2)12yes—
645C23H(5,𝔽2)12yes—
646C23C2511yescharacteristic
647Q8—82no—
648D4—44no—
649D4—44no—
650D4—44no—
651D4—44no—
652D4—44no—
653D4—44no—
654D4—82no—
655D4—82no—
656D4—82no—
657D4—82no—
658D4—82no—
659D4—82no—
660D4—82no—
661D4—82no—
662D4—82no—
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—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4—82no—
744C2×C4H(5,𝔽2)12yes—
745C2×C4H(5,𝔽2)12yes—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—416no—
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—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—88no—
796C22#53814yes—
797C22C22×#4111yescharacteristic
798C22C2×H(5,𝔽2)11yescharacteristic
799C22C2×H(5,𝔽2)11yescharacteristic
800C22C2×H(5,𝔽2)11yescharacteristic
801C22C2×H(5,𝔽2)11yescharacteristic
802C22#58511yescharacteristic
803C22#58511yescharacteristic
804C4—22no—
805C4—22no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C2—24no—
829C2—42no—
830C2—42no—
831C2—81no—
832C2—81no—
833C2—81no—
834C2—81no—
835C2C2×#53811yescharacteristic
836C2#350511yescharacteristic
837C2#350511yescharacteristic
838C2#353211yescharacteristic
839C2#353311yescharacteristic
840C2#354211yescharacteristic
841C2#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. #2848C2semidirect
2. #2847C2semidirect
3. #2797C2semidirect
4. #2781C2semidirect
5. #2779C2semidirect
6. #2778C2semidirect
7. #2778C2semidirect
8. #2756C2semidirect
9. #2753C2semidirect
10. #2749C2semidirect
11. #2741C2semidirect
12. #2730C2semidirect
13. #2714C2semidirect
14. #2703C2semidirect
15. #2702C2semidirect
16. #2696C2semidirect
17. #2688C2semidirect
18. #2676C2semidirect
19. #2613C2semidirect
20. #2613C2semidirect
21. #2493C2semidirect
22. #2488C2semidirect
23. #2480C2semidirect
24. #2472C2semidirect
25. #2425C2semidirect
26. #2424C2semidirect
27. #2419C2semidirect
28. #2418C2semidirect
29. #2321C2semidirect
30. #2321C2semidirect
31. C2×#386C2semidirect
34. C2×#126C22semidirect
35. C2×#124C22semidirect
38. C2×#123C22semidirect
40. C2×C22⋊Q8C22semidirect
41. C2×C22⋊Q8C22semidirect
43. C2×#121C22semidirect
44. C2×#121C22semidirect
45. C2×#121C22semidirect
55. #401C22semidirect
56. #400C22semidirect
57. #400C22semidirect
58. #400C22semidirect
59. #400C22semidirect
60. #400C22semidirect
61. #400C22semidirect
62. #399C22semidirect
63. #398C22semidirect
64. #398C22semidirect
65. #397C22semidirect
66. #397C22semidirect
67. #397C22semidirect
68. #397C22semidirect
69. #397C22semidirect
70. #397C22semidirect
71. #397C22semidirect
72. #397C22semidirect
73. #397C22semidirect
74. #396C22semidirect
75. #396C22semidirect
76. #396C22semidirect
85. #394C22semidirect
86. #394C22semidirect
87. #394C22semidirect
88. #394C22semidirect
89. #394C22semidirect
90. #394C22semidirect
91. #394C22semidirect
92. #393C22semidirect
93. #393C22semidirect
102. #392C22semidirect
103. #391C22semidirect
104. #390C22semidirect
105. #390C22semidirect
106. #390C22semidirect
107. #390C22semidirect
108. #390C22semidirect
109. #390C22semidirect
110. #389C22semidirect
111. #388C22semidirect
112. #388C22semidirect
113. #388C22semidirect
114. #388C22semidirect
115. #388C22semidirect
116. #388C22semidirect
117. #388C22semidirect
118. #388C22semidirect
119. #388C22semidirect
120. #388C22semidirect
121. #388C22semidirect
122. #388C22semidirect
123. #388C22semidirect
124. #388C22semidirect
125. #388C22semidirect
126. #388C22semidirect
127. #388C22semidirect
128. #388C22semidirect
129. #388C22semidirect
130. #387C22semidirect
131. #387C22semidirect
132. #387C22semidirect
133. #387C22semidirect
134. #387C22semidirect
147. #386C22semidirect
148. #386C22semidirect
149. #386C22semidirect
150. #386C22semidirect
151. #386C22semidirect
152. #386C22semidirect
153. #386C22semidirect
154. #386C22semidirect
155. #386C22semidirect
156. #386C22semidirect
157. #386C22semidirect
162. #385C22semidirect
163. #385C22semidirect
164. #385C22semidirect
165. #385C22semidirect
166. #385C22semidirect
167. #383C22semidirect
168. #382C22semidirect
171. #381C22semidirect
174. #380C22semidirect
175. #380C22semidirect
176. #380C22semidirect
177. #380C22semidirect
178. #380C22semidirect

Maximal subgroups

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

subgroupindex
#28482
#28472
#27972
#27812
#27792
#27782
#27562
#27532
#27492
#27412
#27302
#27142
#27032
#27022
#26962
#26882
#26762
#26132
#24932
#24882
#24802
#24722
#24252
#24242
#24192
#24182
#23212
C2×#3862