Finite Group Databasebeta

← C2×#38103 #7635658

Subgroups — C2×#38103 #7635658

Order 512.

5310 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2806C211yesmaximal, characteristic, complemented
2C2×#2805C211yesmaximal, characteristic, complemented
3C2×#2802C211yesmaximal, characteristic, complemented
4C2×#2802C211yesmaximal, characteristic, complemented
5C2×#2792C211yesmaximal, characteristic, complemented
6C2×#2791C211yesmaximal, characteristic, complemented
7C2×#2774C211yesmaximal, characteristic, complemented
8C2×#2755C211yesmaximal, characteristic, complemented
9#38103C2132yesmaximal, direct product factor
10C2×#2855C211yesmaximal, characteristic
11C2×#2569C211yesmaximal, characteristic
12C2×#2590C211yesmaximal, characteristic, complemented
13C2×#2588C211yesmaximal, characteristic, complemented
14C2×#2586C211yesmaximal, characteristic, complemented
15C2×#2585C211yesmaximal, characteristic, complemented
16C2×#2549C211yesmaximal, characteristic
17C2×#2511C211yesmaximal, characteristic, complemented
18C2×#2507C211yesmaximal, characteristic, complemented
19C2×#2520C211yesmaximal, characteristic, complemented
20C2×#2520C211yesmaximal, characteristic, complemented
21C2×#2438C211yesmaximal, characteristic
22C2×#2438C211yesmaximal, characteristic
23C2×#2438C211yesmaximal, characteristic
24C2×#2438C211yesmaximal, characteristic
25C2×#2646C211yesmaximal, characteristic
26C2×#2627C211yesmaximal, characteristic
27C2×#2344C211yesmaximal, characteristic
28C2×#2344C211yesmaximal, characteristic
29C2×#2329C211yesmaximal, characteristic
30C2×#2317C211yesmaximal, characteristic
31C2×#2296C211yesmaximal, characteristic
32C22×#387C211yesmaximal, characteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×#117C2211yescharacteristic
37C22×#117C2211yescharacteristic
38C22×#117C2211yescharacteristic
39C22×#117C2211yescharacteristic
40C23×C4⋊C4C2211yescharacteristic
41C23×C4⋊C4C2211yescharacteristic
42C23×C42C2211yescharacteristic
43#2855C22116yes—
44#2806C22116yescomplemented
45#2805C22116yescomplemented
46#2802C22116yescomplemented
47#2802C22116yescomplemented
48#2792C22116yescomplemented
49#2791C22116yescomplemented
50#2774C22116yescomplemented
51#2755C22116yescomplemented
52#2646C22116yes—
53#2627C22116yes—
54#2590C22116yescomplemented
55#2588C22116yescomplemented
56#2586C22116yescomplemented
57#2585C22116yescomplemented
58#2569C22116yes—
59#2549C22116yes—
60#2520C22116yescomplemented
61#2520C22116yescomplemented
62#2511C22116yescomplemented
63#2507C22116yescomplemented
64#2438C22116yes—
65#2438C22116yes—
66#2438C22116yes—
67#2438C22116yes—
68C2×#400C2211yescharacteristic
69C2×#400C2211yescharacteristic
70C2×#400C2211yescharacteristic
71C2×#400C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#400C2211yescharacteristic
80C2×#398C2211yescharacteristic
81C2×#398C2211yescharacteristic
82C2×#398C2211yescharacteristic
83C2×#398C2211yescharacteristic
84C2×#398C2211yescharacteristic
85C2×#398C2211yescharacteristic
86C2×#398C2211yescharacteristic
87C2×#398C2211yescharacteristic
88C2×#398C2211yescharacteristic
89C2×#398C2211yescharacteristic
90C2×#398C2211yescharacteristic
91C2×#398C2211yescharacteristic
92C2×#398C2211yescharacteristic
93C2×#398C2211yescharacteristic
94C2×#398C2211yescharacteristic
95C2×#398C2211yescharacteristic
96C2×#398C2211yescharacteristic
97C2×#398C2211yescharacteristic
98C2×#398C2211yescharacteristic
99C2×#398C2211yescharacteristic
100C2×#395C2211yescharacteristic
101C2×#395C2211yescharacteristic
102C2×#395C2211yescharacteristic
103C2×#395C2211yescharacteristic
104C2×#395C2211yescharacteristic
105C2×#395C2211yescharacteristic
106C2×#395C2211yescharacteristic
107C2×#395C2211yescharacteristic
108#2344C22116yes—
109#2344C22116yes—
110#2329C22116yes—
111#2317C22116yes—
112#2296C22116yes—
113C2×#391C2211yescharacteristic
114C2×#391C2211yescharacteristic
115C2×#391C2211yescharacteristic
116C2×#391C2211yescharacteristic
117C2×#391C2211yescharacteristic
118C2×#391C2211yescharacteristic
119C2×#391C2211yescharacteristic
120C2×#391C2211yescharacteristic
121C2×#391C2211yescharacteristic
122C2×#391C2211yescharacteristic
123C2×#389C2211yescharacteristic
124C2×#389C2211yescharacteristic
125C2×#389C2211yescharacteristic
126C2×#389C2211yescharacteristic
127C2×#389C2211yescharacteristic
128C2×#389C2211yescharacteristic
129C2×#389C2211yescharacteristic
130C2×#389C2211yescharacteristic
131C2×#389C2211yescharacteristic
132C2×#389C2211yescharacteristic
133C2×#389C2211yescharacteristic
134C2×#389C2211yescharacteristic
135C2×#389C2211yescharacteristic
136C2×#389C2211yescharacteristic
137C2×#389C2211yescharacteristic
138C2×#389C2211yescharacteristic
139C2×#389C2211yescharacteristic
140C2×#389C2211yescharacteristic
141C2×#389C2211yescharacteristic
142C2×#389C2211yescharacteristic
143C2×#389C2211yescharacteristic
144C2×#389C2211yescharacteristic
145C2×#387C2211yescharacteristic
146C2×#387C2211yescharacteristic
147C2×#387C2211yescharacteristic
148C2×#387C2211yescharacteristic
149C2×#387C2211yescharacteristic
150C2×#387C2211yescharacteristic
151C2×#387C2211yescharacteristic
152C2×#387C2211yescharacteristic
153C2×#387C2211yescharacteristic
154C2×#387C2211yescharacteristic
155C2×#387C2211yescharacteristic
156C2×#387C2211yescharacteristic
157C2×#387C2211yescharacteristic
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×#387C2211yescharacteristic
181C2×#387C22116yes—
182C2×#385C2211yescharacteristic
183C2×#385C2211yescharacteristic
184C2×#385C2211yescharacteristic
185C2×#385C2211yescharacteristic
186C2×#385C2211yescharacteristic
187C2×#385C2211yescharacteristic
188C2×#385C2211yescharacteristic
189C2×#385C2211yescharacteristic
190C2×#385C2211yescharacteristic
191C2×#385C2211yescharacteristic
192C2×#384C2211yescharacteristic
193C2×#384C2211yescharacteristic
194C2×#382C2211yescharacteristic
195C2×#382C2211yescharacteristic
196C2×#381C2211yescharacteristic
197C2×#381C2211yescharacteristic
198C2×#381C2211yescharacteristic
199C2×#381C2211yescharacteristic
200C2×#380C2211yescharacteristic
201C2×#380C2211yescharacteristic
202C2×#380C2211yescharacteristic
203C2×#380C2211yescharacteristic
204C2×#380C2211yescharacteristic
205C2×C4×C4⋊C4C2211yescharacteristic
206C2×C4×C4⋊C4C2211yescharacteristic
207C2×C4×C4⋊C4C2211yescharacteristic
208C2×C4×C4⋊C4C2211yescharacteristic
209C2×C4×C4⋊C4C2211yescharacteristic
210C2×C4×C4⋊C4C2211yescharacteristic
211C2×C4×C4⋊C4C2211yescharacteristic
212C2×C4×C4⋊C4C2211yescharacteristic
213C2×C4×C22⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C22×#95C2211yescharacteristic
216C22×#95C2211yescharacteristic
217C22×#95C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C24×C4C2311yescharacteristic
227C24×C4C2311yescharacteristic
228C24×C4C2311yescharacteristic
229C2×C22⋊Q8—28no—
230C2×C22⋊Q8—44no—
231C2×C22⋊Q8—44no—
232C2×C22⋊Q8C2318yes—
233C2×C22⋊Q8C2318yes—
234C2×C22⋊Q8C2318yes—
235C2×#117—28no—
236C2×#117—28no—
237C2×#117—44no—
238C2×#117—44no—
239C2×#117C2318yes—
240C2×#117C2318yes—
241C2×#117C2318yes—
242C2×#117C2318yes—
243C22×C4⋊C4—44no—
244C22×C4⋊C4Q8116yescomplemented
245C22×C4⋊C4C2311yescharacteristic
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⋊C4C2318yes—
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×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2318yes—
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×C42—44no—
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2318yes—
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328#400C2318yes—
329#400C2318yes—
330#400C2318yes—
331#400C2318yes—
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#400C2318yes—
336#400C2318yes—
337#400C2318yes—
338#400C2318yes—
339#400C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#398C2318yes—
353#398C2318yes—
354#398C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#398C2318yes—
360#395C2318yes—
361#395C2318yes—
362#395C2318yes—
363#395C2318yes—
364#395C2318yes—
365#395C2318yes—
366#395C2318yes—
367#395C2318yes—
368#391C2318yes—
369#391C2318yes—
370#391C2318yes—
371#391C2318yes—
372#391C2318yes—
373#391C2318yes—
374#391C2318yes—
375#391C2318yes—
376#391C2318yes—
377#391C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2318yes—
393#389C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
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#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#384C2318yes—
447#384C2318yes—
448#382C2318yes—
449#382C2318yes—
450#381C2318yes—
451#381C2318yes—
452#381C2318yes—
453#381C2318yes—
454#380C2318yes—
455#380C2318yes—
456#380C2318yes—
457#380C2318yes—
458#380C2318yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2318yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C2×#95C2318yes—
470C2×#95C2318yes—
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×#95C2318yes—
530C2×#95C2318yes—
531C2×#95C2311yescharacteristic
532C2×#95C2311yescharacteristic
533C2×#95C2311yescharacteristic
534C2×#95C2311yescharacteristic
535C2×#95C2311yescharacteristic
536C2×#95C2311yescharacteristic
537C2×#95C2311yescharacteristic
538C2×#95C2311yescharacteristic
539C25C2411yescharacteristic
540C22×Q8—24no—
541C22×Q8—24no—
542C22×Q8—42no—
543C22×Q8—42no—
544C22×Q8—42no—
545C22×Q8—42no—
546C22×Q8—42no—
547C22×Q8—42no—
548C22×Q8—42no—
549C22×Q8C2414yes—
550C22×Q8C2414yes—
551C22×Q8C2414yes—
552C23×C4—24no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—24no—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—24no—
559C23×C4—24no—
560C23×C4—24no—
561C23×C4—42no—
562C23×C4—42no—
563C23×C4—42no—
564C23×C4—42no—
565C23×C4—42no—
566C23×C4—42no—
567C23×C4—42no—
568C23×C4—42no—
569C23×C4—42no—
570C23×C4C2×Q818yes—
571C23×C4C2×Q818yes—
572C23×C4C2×Q818yes—
573C23×C4C2411yescharacteristic
574C23×C4C2411yescharacteristic
575C23×C4C2411yescharacteristic
576C23×C4C2411yescharacteristic
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×C4C2414yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2411yescharacteristic
601C23×C4C2411yescharacteristic
602C23×C4C2411yescharacteristic
603C23×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2411yescharacteristic
606C23×C4C2414yes—
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2414yes—
610C22⋊Q8—232no—
611C22⋊Q8—416no—
612C22⋊Q8—416no—
613#117—232no—
614#117—232no—
615#117—416no—
616#117—416no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4—42no—
629C2×C4⋊C4—42no—
630C2×C4⋊C4—42no—
631C2×C4⋊C4—416no—
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⋊C4—42no—
653C2×C4⋊C4—42no—
654C2×C4⋊C4—42no—
655C2×C4⋊C4—42no—
656C2×C4⋊C4—42no—
657C2×C4⋊C4—42no—
658C2×C4⋊C4—42no—
659C2×C4⋊C4—42no—
660C2×C4⋊C4—42no—
661C2×C4⋊C4—42no—
662C2×C4⋊C4—42no—
663C2×C4⋊C4—42no—
664C2×C4⋊C4—42no—
665C2×C4⋊C4—42no—
666C2×C4⋊C4—42no—
667C2×C4⋊C4—42no—
668C2×C4⋊C4—42no—
669C2×C4⋊C4C2×Q818yes—
670C2×C4⋊C4C2×Q818yes—
671C2×C4⋊C4C2×Q818yes—
672C2×C4⋊C4C2×Q818yes—
673C2×C4⋊C4C2×Q8164yescomplemented
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×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2414yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2414yes—
695C2×C4⋊C4C2414yes—
696C2×C4⋊C4C2414yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2414yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2414yes—
702C2×C4⋊C4C2414yes—
703C2×C4⋊C4C2414yes—
704C2×C4⋊C4C2414yes—
705C2×C4⋊C4C2414yes—
706C2×C4⋊C4C2414yes—
707C2×C4⋊C4C2414yes—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2414yes—
710C2×C4⋊C4C2414yes—
711C2×C4⋊C4C2414yes—
712C2×C4⋊C4C2414yes—
713C2×C4⋊C4C2414yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C22⋊C4—24no—
730C2×C22⋊C4—24no—
731C2×C22⋊C4—24no—
732C2×C22⋊C4—24no—
733C2×C22⋊C4—24no—
734C2×C22⋊C4—24no—
735C2×C22⋊C4—24no—
736C2×C22⋊C4#4118yes—
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×C42—24no—
746C2×C42—24no—
747C2×C42—24no—
748C2×C42—24no—
749C2×C42—42no—
750C2×C42—42no—
751C2×C42—42no—
752C2×C42—42no—
753C2×C42—42no—
754C2×C42—42no—
755C2×C42—42no—
756C2×C42—42no—
757C2×C42—416no—
758C2×C42—42no—
759C2×C42—42no—
760C2×C42—42no—
761C2×C42—42no—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
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—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844C24—22no—
845C24—22no—
846C24—22no—
847C24—22no—
848C24C22×Q814yes—
849C24C2×#4114yes—
850C24H(5,𝔽2)14yes—
851C24C2512yes—
852C24C2511yescharacteristic
853C2×Q8—28no—
854C2×Q8—28no—
855C2×Q8—44no—
856C2×Q8—44no—
857C2×Q8—44no—
858C2×Q8—44no—
859C2×Q8—44no—
860C2×Q8—44no—
861C2×Q8—44no—
862C2×Q8—88no—
863C2×Q8—88no—
864C2×Q8—88no—
865C22×C4—232no—
866C22×C4—232no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—28no—
872C22×C4—28no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—28no—
878C22×C4—22no—
879C22×C4—28no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
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—28no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—28no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
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—28no—
955C22×C4—28no—
956C22×C4—28no—
957C22×C4—416no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—416no—
968C22×C4—416no—
969C22×C4—88no—
970C22×C4—88no—
971C22×C4C22×Q814yes—
972C22×C4C22×Q814yes—
973C22×C4C22×Q814yes—
974C22×C4C22×Q814yes—
975C22×C4C22×Q814yes—
976C22×C4C22×Q814yes—
977C22×C4C22×Q8116yes—
978C22×C4C22×Q8116yes—
979C22×C4C22×Q8116yes—
980C22×C4C2×#4114yes—
981C22×C4C2×#4114yes—
982C22×C42−1+414yes—
983C22×C4C2512yes—
984C22×C4C2512yes—
985C22×C4C2512yes—
986C22×C4C2512yes—
987C22×C4C2512yes—
988C22×C4C2512yes—
989C22×C4C2512yes—
990C22×C4C2512yes—
991C22×C4C2512yes—
992C22×C4C2512yes—
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—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
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—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4C22×Q8116yes—
1065C4⋊C4C22×Q8116yes—
1066C4⋊C4C22×Q8116yes—
1067C4⋊C4C22×Q8116yes—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4C2×#41116yes—
1076C42—28no—
1077C42—28no—
1078C42—28no—
1079C42—28no—
1080C42—44no—
1081C42—44no—
1082C42—44no—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C42—44no—
1090C42—44no—
1091C42—44no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—28no—
1097C23—28no—
1098C23—28no—
1099C23—28no—
1100C23—28no—
1101C23—28no—
1102C23#554116yes—
1103C23C23×Q814yes—
1104C23C23×Q812yes—
1105C23C22×#4114yes—
1106C23C22×#4112yes—
1107C23C2×H(5,𝔽2)14yes—
1108C23C2×H(5,𝔽2)12yes—
1109C23C2×2−1+412yes—
1110C23#58512yes—
1111C23#58512yes—
1112C23#58512yes—
1113C23C2611yescharacteristic
1114Q8—88no—
1115Q8—88no—
1116Q8—88no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—28no—
1136C2×C4—28no—
1137C2×C4—232no—
1138C2×C4—232no—
1139C2×C4—28no—
1140C2×C4—28no—
1141C2×C4—28no—
1142C2×C4—28no—
1143C2×C4—28no—
1144C2×C4—28no—
1145C2×C4—28no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
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—416no—
1210C2×C4—416no—
1211C2×C4—416no—
1212C2×C4—44no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—44no—
1216C2×C4—44no—
1217C2×C4—44no—
1218C2×C4—44no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—44no—
1227C2×C4—44no—
1228C2×C4—44no—
1229C2×C4—44no—
1230C2×C4—44no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—88no—
1234C2×C4—88no—
1235C2×C4C23×Q814yes—
1236C2×C4C23×Q814yes—
1237C2×C4C23×Q814yes—
1238C2×C4C23×Q814yes—
1239C2×C4C23×Q814yes—
1240C2×C4C23×Q814yes—
1241C2×C4C22×#4114yes—
1242C2×C4C22×#4114yes—
1243C2×C4C2×2−1+414yes—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—232no—
1250C22—24no—
1251C22#345814yes—
1252C22C2×#55418yes—
1253C22C2×#55414yes—
1254C22#350214yes—
1255C22#351514yes—
1256C22#352114yes—
1257C22#353314yes—
1258C22#353514yes—
1259C22C24×Q811yescharacteristic
1260C22C23×#4111yescharacteristic
1261C22C22×H(5,𝔽2)11yescharacteristic
1262C22C22×2−1+411yescharacteristic
1263C22C2×#58511yescharacteristic
1264C22C2×#58511yescharacteristic
1265C22C2×#58511yescharacteristic
1266C4—24no—
1267C4—24no—
1268C4—24no—
1269C4—24no—
1270C4—24no—
1271C4—24no—
1272C4—24no—
1273C4—24no—
1274C4—24no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—42no—
1283C4—42no—
1284C4—42no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C2—28no—
1297C2#3810318yesdirect product factor
1298C2C2×#345811yescharacteristic
1299C2C22×#55411yescharacteristic
1300C2C2×#353511yescharacteristic
1301C2C2×#353311yescharacteristic
1302C2C2×#351511yescharacteristic
1303C2C2×#352111yescharacteristic
1304C2C2×#350211yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2806C2semidirect
2. C2×#2805C2semidirect
3. C2×#2802C2semidirect
4. C2×#2802C2semidirect
5. C2×#2792C2semidirect
6. C2×#2791C2semidirect
7. C2×#2774C2semidirect
8. C2×#2755C2semidirect
9. #38103C2direct (N × H)
12. C2×#2590C2semidirect
13. C2×#2588C2semidirect
14. C2×#2586C2semidirect
15. C2×#2585C2semidirect
17. C2×#2511C2semidirect
18. C2×#2507C2semidirect
19. C2×#2520C2semidirect
20. C2×#2520C2semidirect
44. #2806C22semidirect
45. #2805C22semidirect
46. #2802C22semidirect
47. #2802C22semidirect
48. #2792C22semidirect
49. #2791C22semidirect
50. #2774C22semidirect
51. #2755C22semidirect
54. #2590C22semidirect
55. #2588C22semidirect
56. #2586C22semidirect
57. #2585C22semidirect
60. #2520C22semidirect
61. #2520C22semidirect
62. #2511C22semidirect
63. #2507C22semidirect
244. C22×C4⋊C4Q8semidirect
673. C2×C4⋊C4C2×Q8semidirect
1297. C2#38103direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28062
C2×#28052
C2×#28022
C2×#27922
C2×#27912
C2×#27742
C2×#27552
#381032
C2×#28552
C2×#25692
C2×#25902
C2×#25882
C2×#25862
C2×#25852
C2×#25492
C2×#25112
C2×#25072
C2×#25202
C2×#24382
C2×#26462
C2×#26272
C2×#23442
C2×#23292
C2×#23172
C2×#22962
C22×#3872