Finite Group Databasebeta

← C2×#55400 #8102384

Subgroups — C2×#55400 #8102384

Order 512.

4750 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#55400C2132yesmaximal, direct product factor
2C2×#2789C211yesmaximal, characteristic, complemented
3C2×#2784C211yesmaximal, characteristic, complemented
4C2×#2765C211yesmaximal, characteristic, complemented
5C2×#2762C211yesmaximal, characteristic, complemented
6C2×#2762C211yesmaximal, characteristic, complemented
7C2×#2761C211yesmaximal, characteristic, complemented
8C2×#2760C211yesmaximal, characteristic
9C2×#2754C211yesmaximal, characteristic, complemented
10C2×#2753C211yesmaximal, characteristic
11C2×#2751C211yesmaximal, characteristic, complemented
12C2×#2748C211yesmaximal, characteristic, complemented
13C2×#2744C211yesmaximal, characteristic, complemented
14C2×#2744C211yesmaximal, characteristic, complemented
15C2×#2730C211yesmaximal, characteristic
16C2×#2716C211yesmaximal, characteristic, complemented
17C2×#2715C211yesmaximal, characteristic, complemented
18C2×#2821C211yesmaximal, characteristic, complemented
19C2×#2831C211yesmaximal, characteristic, complemented
20C2×#2827C211yesmaximal, characteristic, complemented
21C2×#2578C211yesmaximal, characteristic, complemented
22C2×#2578C211yesmaximal, characteristic, complemented
23C2×#2575C211yesmaximal, characteristic, complemented
24C2×#2574C211yesmaximal, characteristic, complemented
25C2×#2515C211yesmaximal, characteristic, complemented
26C2×#2492C211yesmaximal, characteristic, complemented
27C2×#2521C211yesmaximal, characteristic, complemented
28C2×#2481C211yesmaximal, characteristic, complemented
29C2×#2481C211yesmaximal, characteristic, complemented
30C2×#2655C211yesmaximal, characteristic, complemented
31C2×#2653C211yesmaximal, characteristic, complemented
32C2×#2627C211yesmaximal, characteristic, complemented
33C22×C4⋊Q8C2211yescharacteristic
34C22×#126C2211yescharacteristic
35C22×#126C2211yescharacteristic
36C22×#124C2211yescharacteristic
37C22×C22⋊Q8C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39#2831C22116yescomplemented
40#2827C22116yescomplemented
41#2821C22116yescomplemented
42#2789C22116yescomplemented
43#2784C22116yescomplemented
44#2765C22116yescomplemented
45#2762C22116yescomplemented
46#2762C22116yescomplemented
47#2761C22116yescomplemented
48#2760C22116yes—
49#2754C22116yescomplemented
50#2753C22116yes—
51#2751C22116yescomplemented
52#2748C22116yescomplemented
53#2744C22116yescomplemented
54#2744C22116yescomplemented
55#2730C22116yes—
56#2716C22116yescomplemented
57#2715C22116yescomplemented
58#2655C22116yescomplemented
59#2653C22116yescomplemented
60#2627C22116yescomplemented
61#2578C22116yescomplemented
62#2578C22116yescomplemented
63#2575C22116yescomplemented
64#2574C22116yescomplemented
65#2521C22116yescomplemented
66#2515C22116yescomplemented
67#2492C22116yescomplemented
68#2481C22116yescomplemented
69#2481C22116yescomplemented
70C2×#401C2211yescharacteristic
71C2×#401C2211yescharacteristic
72C2×#401C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#400C2211yescharacteristic
80C2×#400C2211yescharacteristic
81C2×#400C2211yescharacteristic
82C2×#400C2211yescharacteristic
83C2×#400C2211yescharacteristic
84C2×#400C2211yescharacteristic
85C2×#400C2211yescharacteristic
86C2×#400C2211yescharacteristic
87C2×#399C2211yescharacteristic
88C2×#399C2211yescharacteristic
89C2×#399C2211yescharacteristic
90C2×#398C2211yescharacteristic
91C2×#398C2211yescharacteristic
92C2×#398C2211yescharacteristic
93C2×#398C2211yescharacteristic
94C2×#398C2211yescharacteristic
95C2×#398C2211yescharacteristic
96C2×#398C2211yescharacteristic
97C2×#398C2211yescharacteristic
98C2×#398C2211yescharacteristic
99C2×#398C2211yescharacteristic
100C2×#397C2211yescharacteristic
101C2×#397C2211yescharacteristic
102C2×#397C2211yescharacteristic
103C2×#397C2211yescharacteristic
104C2×#397C2211yescharacteristic
105C2×#397C2211yescharacteristic
106C2×#397C2211yescharacteristic
107C2×#397C2211yescharacteristic
108C2×#397C2211yescharacteristic
109C2×#397C2211yescharacteristic
110C2×#397C2211yescharacteristic
111C2×#396C2211yescharacteristic
112C2×#396C2211yescharacteristic
113C2×#396C2211yescharacteristic
114C2×#396C2211yescharacteristic
115C2×#396C2211yescharacteristic
116C2×#396C2211yescharacteristic
117C2×#396C2211yescharacteristic
118C2×#395C2211yescharacteristic
119C2×#395C2211yescharacteristic
120C2×#395C2211yescharacteristic
121C2×#395C2211yescharacteristic
122C2×#394C2211yescharacteristic
123C2×#394C2211yescharacteristic
124C2×#394C2211yescharacteristic
125C2×#394C2211yescharacteristic
126C2×#394C2211yescharacteristic
127C2×#393C2211yescharacteristic
128C2×#393C2211yescharacteristic
129C2×#393C2211yescharacteristic
130C2×#393C2211yescharacteristic
131C2×#393C2211yescharacteristic
132C2×#393C2211yescharacteristic
133C2×#392C2211yescharacteristic
134C2×#391C2211yescharacteristic
135C2×#391C2211yescharacteristic
136C2×#391C2211yescharacteristic
137C2×#391C2211yescharacteristic
138C2×#391C2211yescharacteristic
139C2×#391C2211yescharacteristic
140C2×#391C2211yescharacteristic
141C2×#390C2211yescharacteristic
142C2×#390C2211yescharacteristic
143C2×#389C2211yescharacteristic
144C2×#388C2211yescharacteristic
145C2×#388C2211yescharacteristic
146C2×#388C2211yescharacteristic
147C2×#388C2211yescharacteristic
148C2×#388C2211yescharacteristic
149C2×#388C2211yescharacteristic
150C2×#388C2211yescharacteristic
151C2×#388C2211yescharacteristic
152C2×#388C2211yescharacteristic
153C2×#388C2211yescharacteristic
154C2×#388C2211yescharacteristic
155C2×#388C2211yescharacteristic
156C2×#388C2211yescharacteristic
157C2×#388C2211yescharacteristic
158C2×#387C2211yescharacteristic
159C2×#387C2211yescharacteristic
160C2×#387C2211yescharacteristic
161C2×#387C2211yescharacteristic
162C2×#387C2211yescharacteristic
163C2×#387C2211yescharacteristic
164C2×#387C2211yescharacteristic
165C2×#387C2211yescharacteristic
166C2×#387C2211yescharacteristic
167C2×#387C2211yescharacteristic
168C2×#387C2211yescharacteristic
169C2×#387C2211yescharacteristic
170C2×#387C2211yescharacteristic
171C2×#387C2211yescharacteristic
172C2×#387C2211yescharacteristic
173C2×#387C2211yescharacteristic
174C2×#387C2211yescharacteristic
175C2×#387C2211yescharacteristic
176C2×#387C2211yescharacteristic
177C2×#387C2211yescharacteristic
178C2×#387C2211yescharacteristic
179C2×#387C2211yescharacteristic
180C2×#386C2211yescharacteristic
181C2×#386C2211yescharacteristic
182C2×#386C2211yescharacteristic
183C2×#386C2211yescharacteristic
184C2×#386C2211yescharacteristic
185C2×#386C2211yescharacteristic
186C2×#386C2211yescharacteristic
187C2×#386C2211yescharacteristic
188C2×#386C2211yescharacteristic
189C2×#386C2211yescharacteristic
190C2×#385C2211yescharacteristic
191C2×#385C2211yescharacteristic
192C2×#385C2211yescharacteristic
193C2×#385C2211yescharacteristic
194C2×#385C2211yescharacteristic
195C2×#385C2211yescharacteristic
196C2×#385C2211yescharacteristic
197C2×#385C2211yescharacteristic
198C2×#383C2211yescharacteristic
199C2×#383C2211yescharacteristic
200C2×#382C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C2×#382C2211yescharacteristic
203C2×#382C2211yescharacteristic
204C2×#381C2211yescharacteristic
205C2×#381C2211yescharacteristic
206C2×#381C2211yescharacteristic
207C2×#381C2211yescharacteristic
208C2×#380C2211yescharacteristic
209C2×#380C2211yescharacteristic
210C2×#380C2211yescharacteristic
211C2×#380C2211yescharacteristic
212C2×#380C2211yescharacteristic
213C2×C4×C4⋊C4C2211yescharacteristic
214C2×C4×C4⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×C4×C22⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C23×D4C2311yescharacteristic
224C23×D4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C24×C4C2311yescharacteristic
227C24×C4C2311yescharacteristic
228C24×C4C2311yescharacteristic
229C24×C4C2311yescharacteristic
230C2×C4⋊Q8—44no—
231C2×C4⋊Q8C2318yes—
232C2×#126—44no—
233C2×#126—44no—
234C2×#126C2318yes—
235C2×#126C2318yes—
236C2×#124—44no—
237C2×#124C2318yes—
238C2×C22⋊Q8—44no—
239C2×C22⋊Q8C2318yes—
240C22×C4⋊C4—44no—
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2318yes—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2311yescharacteristic
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2311yescharacteristic
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322#401C2318yes—
323#401C2318yes—
324#401C2318yes—
325#400C2318yes—
326#400C2318yes—
327#400C2318yes—
328#400C2318yes—
329#400C2318yes—
330#400C2318yes—
331#400C2318yes—
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#400C2318yes—
336#400C2318yes—
337#400C2318yes—
338#400C2318yes—
339#399C2318yes—
340#399C2318yes—
341#399C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#397C2318yes—
353#397C2318yes—
354#397C2318yes—
355#397C2318yes—
356#397C2318yes—
357#397C2318yes—
358#397C2318yes—
359#397C2318yes—
360#397C2318yes—
361#397C2318yes—
362#397C2318yes—
363#396C2318yes—
364#396C2318yes—
365#396C2318yes—
366#396C2318yes—
367#396C2318yes—
368#396C2318yes—
369#396C2318yes—
370#395C2318yes—
371#395C2318yes—
372#395C2318yes—
373#395C2318yes—
374#394C2318yes—
375#394C2318yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#393C2318yes—
380#393C2318yes—
381#393C2318yes—
382#393C2318yes—
383#393C2318yes—
384#393C2318yes—
385#392C2318yes—
386#391C2318yes—
387#391C2318yes—
388#391C2318yes—
389#391C2318yes—
390#391C2318yes—
391#391C2318yes—
392#391C2318yes—
393#390C2318yes—
394#390C2318yes—
395#389C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2318yes—
438#386C2318yes—
439#386C2318yes—
440#386C2318yes—
441#386C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#383C2318yes—
451#383C2318yes—
452#382C2318yes—
453#382C2318yes—
454#382C2318yes—
455#382C2318yes—
456#381C2318yes—
457#381C2318yes—
458#381C2318yes—
459#381C2318yes—
460#380C2318yes—
461#380C2318yes—
462#380C2318yes—
463#380C2318yes—
464#380C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2318yes—
470C4×C22⋊C4C2318yes—
471C2×#95C2311yescharacteristic
472C2×#95C2311yescharacteristic
473C2×#95C2311yescharacteristic
474C2×#95C2311yescharacteristic
475C2×#95C2311yescharacteristic
476C2×#95C2311yescharacteristic
477C2×#95C2311yescharacteristic
478C2×#95C2311yescharacteristic
479C2×#95C2311yescharacteristic
480C2×#95C2311yescharacteristic
481C2×#95C2311yescharacteristic
482C2×#95C2311yescharacteristic
483C2×#95C2311yescharacteristic
484C2×#95C2311yescharacteristic
485C2×#95C2311yescharacteristic
486C2×#95C2311yescharacteristic
487C2×#95C2311yescharacteristic
488C2×#95C2311yescharacteristic
489C2×#95C2311yescharacteristic
490C2×#95C2311yescharacteristic
491C2×#95C2311yescharacteristic
492C2×#95C2311yescharacteristic
493C2×#95C2311yescharacteristic
494C2×#95C2311yescharacteristic
495C2×#95C2311yescharacteristic
496C2×#95C2311yescharacteristic
497C2×#95C2311yescharacteristic
498C2×#95C2311yescharacteristic
499C2×#95C2311yescharacteristic
500C2×#95C2311yescharacteristic
501C2×#95C2311yescharacteristic
502C2×#95C2311yescharacteristic
503C2×#95C2311yescharacteristic
504C2×#95C2311yescharacteristic
505C2×#95C2311yescharacteristic
506C2×#95C2311yescharacteristic
507C2×#95C2311yescharacteristic
508C2×#95C2311yescharacteristic
509C2×#95C2311yescharacteristic
510C2×#95C2311yescharacteristic
511C2×#95C2311yescharacteristic
512C2×#95C2311yescharacteristic
513C2×#95C2311yescharacteristic
514C2×#95C2311yescharacteristic
515C2×#95C2311yescharacteristic
516C2×#95C2311yescharacteristic
517C2×#95C2311yescharacteristic
518C2×#95C2311yescharacteristic
519C2×#95C2311yescharacteristic
520C2×#95C2311yescharacteristic
521C2×#95C2311yescharacteristic
522C2×#95C2311yescharacteristic
523C2×#95C2311yescharacteristic
524C2×#95C2311yescharacteristic
525C2×#95C2311yescharacteristic
526C2×#95C2311yescharacteristic
527C2×#95C2311yescharacteristic
528C2×#95C2311yescharacteristic
529C2×#95C2311yescharacteristic
530C2×#95C2311yescharacteristic
531C2×#95C2311yescharacteristic
532C2×#95C2311yescharacteristic
533C2×#95C2311yescharacteristic
534C2×#95C2311yescharacteristic
535C25C2411yescharacteristic
536C25C2411yescharacteristic
537C25C2411yescharacteristic
538C22×Q8—24no—
539C22×Q8—42no—
540C22×Q8—42no—
541C22×Q8—42no—
542C22×Q8—42no—
543C22×Q8—42no—
544C22×Q8—42no—
545C22×Q8—42no—
546C22×Q8—42no—
547C22×Q8C2414yes—
548C22×Q8C2414yes—
549C22×Q8C2414yes—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—42no—
553C22×D4—42no—
554C22×D4—42no—
555C22×D4—42no—
556C22×D4—42no—
557C22×D4—42no—
558C22×D4—42no—
559C22×D4C2414yes—
560C22×D4C2414yes—
561C22×D4C2414yes—
562C23×C4—24no—
563C23×C4—24no—
564C23×C4—42no—
565C23×C4—42no—
566C23×C4—42no—
567C23×C4—42no—
568C23×C4—42no—
569C23×C4—42no—
570C23×C4—42no—
571C23×C4—42no—
572C23×C4—42no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4—42no—
576C23×C4—42no—
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C23×C4C2411yescharacteristic
580C23×C4C2411yescharacteristic
581C23×C4C2411yescharacteristic
582C23×C4C2411yescharacteristic
583C23×C4C2411yescharacteristic
584C23×C4C2411yescharacteristic
585C23×C4C2411yescharacteristic
586C23×C4C2411yescharacteristic
587C23×C4C2411yescharacteristic
588C23×C4C2411yescharacteristic
589C23×C4C2411yescharacteristic
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2411yescharacteristic
601C23×C4C2411yescharacteristic
602C23×C4C2411yescharacteristic
603C23×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2414yes—
606C23×C4C2414yes—
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2414yes—
610C4⋊Q8—416no—
611#126—416no—
612#126—416no—
613#124—416no—
614C22⋊Q8—416no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—416no—
620C2×C4⋊C4—42no—
621C2×C4⋊C4—42no—
622C2×C4⋊C4—42no—
623C2×C4⋊C4—42no—
624C2×C4⋊C4—42no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4—42no—
629C2×C4⋊C4—42no—
630C2×C4⋊C4—42no—
631C2×C4⋊C4—42no—
632C2×C4⋊C4—42no—
633C2×C4⋊C4—42no—
634C2×C4⋊C4—42no—
635C2×C4⋊C4—42no—
636C2×C4⋊C4—42no—
637C2×C4⋊C4—42no—
638C2×C4⋊C4—42no—
639C2×C4⋊C4—42no—
640C2×C4⋊C4—42no—
641C2×C4⋊C4—42no—
642C2×C4⋊C4—42no—
643C2×C4⋊C4—42no—
644C2×C4⋊C4—42no—
645C2×C4⋊C4—42no—
646C2×C4⋊C4—42no—
647C2×C4⋊C4—42no—
648C2×C4⋊C4—42no—
649C2×C4⋊C4—42no—
650C2×C4⋊C4—42no—
651C2×C4⋊C4—42no—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C22⋊C4—24no—
689C2×C22⋊C4—24no—
690C2×C22⋊C4—24no—
691C2×C22⋊C4—24no—
692C2×C22⋊C4—42no—
693C2×C22⋊C4—42no—
694C2×C22⋊C4—42no—
695C2×C22⋊C4—42no—
696C2×C22⋊C4—42no—
697C2×C22⋊C4—42no—
698C2×C22⋊C4—42no—
699C2×C22⋊C4—42no—
700C2×C22⋊C4—42no—
701C2×C22⋊C4—42no—
702C2×C22⋊C4—42no—
703C2×C22⋊C4—42no—
704C2×C22⋊C4—42no—
705C2×C22⋊C4—42no—
706C2×C22⋊C4—42no—
707C2×C22⋊C4—42no—
708C2×C22⋊C4—42no—
709C2×C22⋊C4—42no—
710C2×C22⋊C4—42no—
711C2×C22⋊C4—42no—
712C2×C22⋊C4—42no—
713C2×C22⋊C4—42no—
714C2×C22⋊C4—42no—
715C2×C22⋊C4—42no—
716C2×C22⋊C4—42no—
717C2×C22⋊C4—42no—
718C2×C22⋊C4—42no—
719C2×C22⋊C4—42no—
720C2×C22⋊C4—42no—
721C2×C22⋊C4—42no—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C22⋊C4C2414yes—
741C2×C22⋊C4C2414yes—
742C2×C22⋊C4C2414yes—
743C2×C22⋊C4C2414yes—
744C2×C22⋊C4C2414yes—
745C2×C22⋊C4C2414yes—
746C2×C22⋊C4C2414yes—
747C2×C22⋊C4C2414yes—
748C2×C22⋊C4C2414yes—
749C2×C22⋊C4C2414yes—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C42—24no—
757C2×C42—42no—
758C2×C42—42no—
759C2×C42—42no—
760C2×C42—42no—
761C2×C42—42no—
762C2×C42—42no—
763C2×C42—42no—
764C2×C42—42no—
765C2×C42—42no—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840C24—22no—
841C24—22no—
842C24—22no—
843C24—22no—
844C24—22no—
845C24—22no—
846C24—22no—
847C24—22no—
848C24—22no—
849C24—22no—
850C24—22no—
851C24—22no—
852C24—22no—
853C24—22no—
854C24—22no—
855C24—22no—
856C24—22no—
857C24—22no—
858C24—22no—
859C24—22no—
860C242−1+414yes—
861C24C2512yes—
862C24C2512yes—
863C24C2512yes—
864C24C2511yescharacteristic
865C2×Q8—28no—
866C2×Q8—44no—
867C2×Q8—44no—
868C2×Q8—44no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—88no—
875C2×Q8—88no—
876C2×Q8—88no—
877C2×D4—28no—
878C2×D4—28no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—88no—
887C2×D4—88no—
888C2×D4—88no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—28no—
911C22×C4—22no—
912C22×C4—22no—
913C22×C4—22no—
914C22×C4—22no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—22no—
919C22×C4—22no—
920C22×C4—22no—
921C22×C4—22no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—22no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—22no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—22no—
966C22×C4—22no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—22no—
973C22×C4—28no—
974C22×C4—44no—
975C22×C4—44no—
976C22×C4—44no—
977C22×C4—44no—
978C22×C4—44no—
979C22×C4—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—416no—
988C22×C4—88no—
989C22×C4—88no—
990C22×C4—88no—
991C22×C4—88no—
992C22×C4H(5,𝔽2)14yes—
993C22×C4C2512yes—
994C22×C4C2512yes—
995C22×C4C2512yes—
996C22×C4C2512yes—
997C22×C4C2512yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C22⋊C4—44no—
1073C22⋊C4—44no—
1074C22⋊C4—44no—
1075C22⋊C4—44no—
1076C22⋊C4—44no—
1077C22⋊C4—44no—
1078C22⋊C4—44no—
1079C22⋊C4—44no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—44no—
1084C22⋊C4—44no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C42—28no—
1092C42—44no—
1093C42—44no—
1094C42—44no—
1095C42—44no—
1096C42—44no—
1097C42—44no—
1098C42—44no—
1099C42—44no—
1100C42—44no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—22no—
1106C23—22no—
1107C23—28no—
1108C23—28no—
1109C23—28no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—44no—
1125C23—44no—
1126C23—44no—
1127C23—44no—
1128C23—44no—
1129C23—44no—
1130C23—44no—
1131C23—44no—
1132C23—44no—
1133C23—44no—
1134C23—44no—
1135C23—44no—
1136C23—44no—
1137C23—44no—
1138C23—44no—
1139C23—44no—
1140C23—44no—
1141C23—44no—
1142C23C2×H(5,𝔽2)12yes—
1143C23C2×2−1+414yes—
1144C23C2×2−1+412yes—
1145C23#58512yes—
1146C23#58512yes—
1147C23#58512yes—
1148C23#58512yes—
1149C23#58512yes—
1150C23C2611yescharacteristic
1151Q8—88no—
1152Q8—88no—
1153Q8—88no—
1154D4—88no—
1155D4—88no—
1156D4—88no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—28no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—416no—
1242C2×C4—44no—
1243C2×C4—44no—
1244C2×C4—44no—
1245C2×C4—44no—
1246C2×C4—44no—
1247C2×C4—44no—
1248C2×C4—44no—
1249C2×C4—44no—
1250C2×C4—44no—
1251C2×C4—44no—
1252C2×C4—44no—
1253C2×C4—44no—
1254C2×C4—44no—
1255C2×C4—44no—
1256C2×C4—44no—
1257C2×C4—44no—
1258C2×C4—44no—
1259C2×C4—44no—
1260C2×C4—44no—
1261C2×C4—44no—
1262C2×C4—44no—
1263C2×C4—44no—
1264C2×C4—44no—
1265C2×C4—44no—
1266C2×C4—44no—
1267C2×C4—44no—
1268C2×C4—44no—
1269C2×C4—88no—
1270C2×C4—88no—
1271C2×C4—88no—
1272C2×C4—88no—
1273C2×C4C2×H(5,𝔽2)14yes—
1274C22—24no—
1275C22—24no—
1276C22—24no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—416no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—88no—
1297C22—88no—
1298C22#354114yes—
1299C22#354514yes—
1300C22#356214yes—
1301C22#356414yes—
1302C22#356414yes—
1303C22#356614yes—
1304C22#356614yes—
1305C22C22×H(5,𝔽2)11yescharacteristic
1306C22C22×2−1+411yescharacteristic
1307C22C2×#58511yescharacteristic
1308C22C2×#58511yescharacteristic
1309C22C2×#58511yescharacteristic
1310C22C2×#58511yescharacteristic
1311C22C2×#58511yescharacteristic
1312C4—24no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C2—44no—
1341C2—82no—
1342C2—82no—
1343C2#5540018yesdirect product factor
1344C2C2×#354111yescharacteristic
1345C2C2×#356411yescharacteristic
1346C2C2×#356411yescharacteristic
1347C2C2×#356211yescharacteristic
1348C2C2×#356611yescharacteristic
1349C2C2×#356611yescharacteristic
1350C2C2×#354511yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC2×#392C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #55400C2direct (N × H)
2. C2×#2789C2semidirect
3. C2×#2784C2semidirect
4. C2×#2765C2semidirect
5. C2×#2762C2semidirect
6. C2×#2762C2semidirect
7. C2×#2761C2semidirect
9. C2×#2754C2semidirect
11. C2×#2751C2semidirect
12. C2×#2748C2semidirect
13. C2×#2744C2semidirect
14. C2×#2744C2semidirect
16. C2×#2716C2semidirect
17. C2×#2715C2semidirect
18. C2×#2821C2semidirect
19. C2×#2831C2semidirect
20. C2×#2827C2semidirect
21. C2×#2578C2semidirect
22. C2×#2578C2semidirect
23. C2×#2575C2semidirect
24. C2×#2574C2semidirect
25. C2×#2515C2semidirect
26. C2×#2492C2semidirect
27. C2×#2521C2semidirect
28. C2×#2481C2semidirect
29. C2×#2481C2semidirect
30. C2×#2655C2semidirect
31. C2×#2653C2semidirect
32. C2×#2627C2semidirect
39. #2831C22semidirect
40. #2827C22semidirect
41. #2821C22semidirect
42. #2789C22semidirect
43. #2784C22semidirect
44. #2765C22semidirect
45. #2762C22semidirect
46. #2762C22semidirect
47. #2761C22semidirect
49. #2754C22semidirect
51. #2751C22semidirect
52. #2748C22semidirect
53. #2744C22semidirect
54. #2744C22semidirect
56. #2716C22semidirect
57. #2715C22semidirect
58. #2655C22semidirect
59. #2653C22semidirect
60. #2627C22semidirect
61. #2578C22semidirect
62. #2578C22semidirect
63. #2575C22semidirect
64. #2574C22semidirect
65. #2521C22semidirect
66. #2515C22semidirect
67. #2492C22semidirect
68. #2481C22semidirect
69. #2481C22semidirect
1343. C2#55400direct (N × H)

Maximal subgroups

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

subgroupindex
#554002
C2×#27892
C2×#27842
C2×#27652
C2×#27622
C2×#27612
C2×#27602
C2×#27542
C2×#27532
C2×#27512
C2×#27482
C2×#27442
C2×#27302
C2×#27162
C2×#27152
C2×#28212
C2×#28312
C2×#28272
C2×#25782
C2×#25752
C2×#25742
C2×#25152
C2×#24922
C2×#25212
C2×#24812
C2×#26552
C2×#26532
C2×#26272