Finite Group Databasebeta

← C2×#38881 #7635948

Subgroups — C2×#38881 #7635948

Order 512.

5246 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2799C211yesmaximal, characteristic, complemented
2C2×#2793C211yesmaximal, characteristic, complemented
3C2×#2775C211yesmaximal, characteristic, complemented
4C2×#2745C211yesmaximal, characteristic, complemented
5C2×#2734C211yesmaximal, characteristic, complemented
6C2×#2731C211yesmaximal, characteristic
7C2×#2731C211yesmaximal, characteristic
8C2×#2720C211yesmaximal, characteristic, complemented
9#38881C2132yesmaximal, direct product factor
10C2×#2865C211yesmaximal, characteristic, complemented
11C2×#2604C211yesmaximal, characteristic, complemented
12C2×#2594C211yesmaximal, characteristic, complemented
13C2×#2593C211yesmaximal, characteristic
14C2×#2588C211yesmaximal, characteristic, complemented
15C2×#2585C211yesmaximal, characteristic, complemented
16C2×#2574C211yesmaximal, characteristic, complemented
17C2×#2528C211yesmaximal, characteristic, complemented
18C2×#2525C211yesmaximal, characteristic, complemented
19C2×#2475C211yesmaximal, characteristic, complemented
20C2×#2415C211yesmaximal, characteristic
21C2×#2469C211yesmaximal, characteristic, complemented
22C2×#2465C211yesmaximal, characteristic, complemented
23C2×#2465C211yesmaximal, characteristic, complemented
24C2×#2466C211yesmaximal, characteristic
25C2×#2650C211yesmaximal, characteristic, complemented
26C2×#2651C211yesmaximal, characteristic
27C2×#2367C211yesmaximal, characteristic
28C2×#2365C211yesmaximal, characteristic, complemented
29C2×#2336C211yesmaximal, characteristic, complemented
30C2×#2332C211yesmaximal, characteristic, complemented
31C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
32C2×#2298C211yesmaximal, characteristic, complemented
33C22×C4⋊Q8C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C22×#126C2211yescharacteristic
36C22×#125C2211yescharacteristic
37C22×#124C2211yescharacteristic
38C22×C22⋊Q8C2211yescharacteristic
39C22×C22⋊Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×D4C2211yescharacteristic
44C22×#117C2211yescharacteristic
45#2865C22116yescomplemented
46#2799C22116yescomplemented
47#2793C22116yescomplemented
48#2775C22116yescomplemented
49#2745C22116yescomplemented
50#2734C22116yescomplemented
51#2731C22116yes—
52#2731C22116yes—
53#2720C22116yescomplemented
54#2651C22116yes—
55#2650C22116yescomplemented
56#2604C22116yescomplemented
57#2594C22116yescomplemented
58#2593C22116yes—
59#2588C22116yescomplemented
60#2585C22116yescomplemented
61#2574C22116yescomplemented
62#2528C22116yescomplemented
63#2525C22116yescomplemented
64#2475C22116yescomplemented
65#2469C22116yescomplemented
66#2466C22116yes—
67#2465C22116yescomplemented
68#2465C22116yescomplemented
69#2415C22116yes—
70C2×#401C2211yescharacteristic
71C2×#400C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#399C2211yescharacteristic
79C2×#398C2211yescharacteristic
80C2×#398C2211yescharacteristic
81C2×#398C2211yescharacteristic
82C2×#398C2211yescharacteristic
83C2×#398C2211yescharacteristic
84C2×#398C2211yescharacteristic
85C2×#397C2211yescharacteristic
86C2×#397C2211yescharacteristic
87C2×#397C2211yescharacteristic
88C2×#397C2211yescharacteristic
89C2×#397C2211yescharacteristic
90C2×#396C2211yescharacteristic
91C2×#396C2211yescharacteristic
92C2×#396C2211yescharacteristic
93C2×#396C2211yescharacteristic
94C2×#396C2211yescharacteristic
95C2×#396C2211yescharacteristic
96C2×#395C2211yescharacteristic
97C2×#395C2211yescharacteristic
98C2×#395C2211yescharacteristic
99C2×#395C2211yescharacteristic
100C2×#395C2211yescharacteristic
101C2×#395C2211yescharacteristic
102C2×#394C2211yescharacteristic
103C2×#394C2211yescharacteristic
104C2×#394C2211yescharacteristic
105C2×#394C2211yescharacteristic
106C2×#393C2211yescharacteristic
107C2×#393C2211yescharacteristic
108C2×#393C2211yescharacteristic
109C2×#393C2211yescharacteristic
110#2367C22116yes—
111#2365C22116yescomplemented
112#2336C22116yescomplemented
113#2332C22116yescomplemented
114C4×C4⋊Q8C22116yescomplemented
115#2298C22116yescomplemented
116C2×#391C2211yescharacteristic
117C2×#391C2211yescharacteristic
118C2×#391C2211yescharacteristic
119C2×#391C2211yescharacteristic
120C2×#391C2211yescharacteristic
121C2×#391C2211yescharacteristic
122C2×#391C2211yescharacteristic
123C2×#391C2211yescharacteristic
124C2×#390C2211yescharacteristic
125C2×#389C2211yescharacteristic
126C2×#389C2211yescharacteristic
127C2×#389C2211yescharacteristic
128C2×#389C2211yescharacteristic
129C2×#389C2211yescharacteristic
130C2×#389C2211yescharacteristic
131C2×#389C2211yescharacteristic
132C2×#389C2211yescharacteristic
133C2×#389C2211yescharacteristic
134C2×#389C2211yescharacteristic
135C2×#388C2211yescharacteristic
136C2×#388C2211yescharacteristic
137C2×#388C2211yescharacteristic
138C2×#388C2211yescharacteristic
139C2×#388C2211yescharacteristic
140C2×#388C2211yescharacteristic
141C2×#388C2211yescharacteristic
142C2×#388C2211yescharacteristic
143C2×#388C2211yescharacteristic
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×#388C2211yescharacteristic
159C2×#388C2211yescharacteristic
160C2×#388C2211yescharacteristic
161C2×#388C2211yescharacteristic
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×#387C2211yescharacteristic
182C2×#387C2211yescharacteristic
183C2×#387C2211yescharacteristic
184C2×#387C2211yescharacteristic
185C2×#387C2211yescharacteristic
186C2×#387C2211yescharacteristic
187C2×#387C2211yescharacteristic
188C2×#387C2211yescharacteristic
189C2×#387C2211yescharacteristic
190C2×#387C2211yescharacteristic
191C2×#387C2211yescharacteristic
192C2×#387C2211yescharacteristic
193C2×#387C2211yescharacteristic
194C2×#385C2211yescharacteristic
195C2×#385C2211yescharacteristic
196C2×#385C2211yescharacteristic
197C2×#385C2211yescharacteristic
198C2×#384C2211yescharacteristic
199C2×#383C2211yescharacteristic
200C2×#382C2211yescharacteristic
201C2×#381C2211yescharacteristic
202C2×#380C2211yescharacteristic
203C2×C4×C4⋊C4C2211yescharacteristic
204C2×C4×C4⋊C4C2211yescharacteristic
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×C4⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×#376C2211yescharacteristic
218C2×C43C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×Q8C2311yescharacteristic
223C23×D4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C2×C4⋊Q8—28no—
227C2×C4⋊Q8—28no—
228C2×C4⋊Q8C2318yes—
229C2×C4⋊Q8C2318yes—
230C2×#126—44no—
231C2×#126C2318yes—
232C2×#125—28no—
233C2×#125C2318yes—
234C2×#124—28no—
235C2×#124C2318yes—
236C2×C22⋊Q8—28no—
237C2×C22⋊Q8—44no—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2318yes—
240C2×C4×Q8—44no—
241C2×C4×Q8—44no—
242C2×C4×Q8—44no—
243C2×C4×Q8C2318yes—
244C2×C4×Q8C2318yes—
245C2×C4×Q8C2318yes—
246C2×C4×D4—44no—
247C2×C4×D4C2318yes—
248C2×#117—28no—
249C2×#117C2318yes—
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×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×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×C22⋊C4C2311yescharacteristic
313C22×C22⋊C4C2311yescharacteristic
314C22×C22⋊C4C2311yescharacteristic
315C22×C22⋊C4C2311yescharacteristic
316C22×C22⋊C4C2311yescharacteristic
317C22×C22⋊C4C2311yescharacteristic
318C22×C22⋊C4C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340#401C2318yes—
341#400C2318yes—
342#400C2318yes—
343#400C2318yes—
344#400C2318yes—
345#400C2318yes—
346#400C2318yes—
347#400C2318yes—
348#399C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#398C2318yes—
353#398C2318yes—
354#398C2318yes—
355#397C2318yes—
356#397C2318yes—
357#397C2318yes—
358#397C2318yes—
359#397C2318yes—
360#396C2318yes—
361#396C2318yes—
362#396C2318yes—
363#396C2318yes—
364#396C2318yes—
365#396C2318yes—
366#395C2318yes—
367#395C2318yes—
368#395C2318yes—
369#395C2318yes—
370#395C2318yes—
371#395C2318yes—
372#394C2318yes—
373#394C2318yes—
374#394C2318yes—
375#394C2318yes—
376#393C2318yes—
377#393C2318yes—
378#393C2318yes—
379#393C2318yes—
380#391C2318yes—
381#391C2318yes—
382#391C2318yes—
383#391C2318yes—
384#391C2318yes—
385#391C2318yes—
386#391C2318yes—
387#391C2318yes—
388#390C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2318yes—
393#389C2318yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2318yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#387C2318yes—
449#387C2318yes—
450#387C2318yes—
451#387C2318yes—
452#387C2318yes—
453#387C2318yes—
454#387C2318yes—
455#387C2318yes—
456#387C2318yes—
457#387C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#384C2318yes—
463#383C2318yes—
464#382C2318yes—
465#381C2318yes—
466#380C2318yes—
467C4×C4⋊C4C2318yes—
468C4×C4⋊C4C2318yes—
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2318yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2318yes—
477C4×C4⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2318yes—
481#376C2318yes—
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
535C2×#95C2311yescharacteristic
536C2×#95C2311yescharacteristic
537C2×#95C2311yescharacteristic
538C2×#95C2311yescharacteristic
539C2×#95C2311yescharacteristic
540C43C2318yes—
541C25C2411yescharacteristic
542C25C2411yescharacteristic
543C22×Q8—24no—
544C22×Q8—24no—
545C22×Q8—24no—
546C22×Q8—42no—
547C22×Q8—42no—
548C22×Q8—42no—
549C22×Q8—42no—
550C22×Q8—42no—
551C22×Q8—42no—
552C22×Q8—42no—
553C22×Q8—42no—
554C22×Q8#4118yes—
555C22×Q8C2414yes—
556C22×Q8C2414yes—
557C22×Q8C2414yes—
558C22×Q8C2414yes—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4C2414yes—
563C23×C4—24no—
564C23×C4—24no—
565C23×C4—24no—
566C23×C4—42no—
567C23×C4—42no—
568C23×C4—42no—
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2411yescharacteristic
572C23×C4C2411yescharacteristic
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×C4C2414yes—
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2414yes—
600C4⋊Q8—232no—
601C4⋊Q8—232no—
602#126—416no—
603#125—232no—
604#124—232no—
605C22⋊Q8—232no—
606C22⋊Q8—416no—
607C4×Q8—416no—
608C4×Q8—416no—
609C4×Q8—416no—
610C4×D4—416no—
611#117—232no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
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—24no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—24no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—24no—
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#4118yes—
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×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×C22⋊C4—24no—
699C2×C22⋊C4—24no—
700C2×C22⋊C4—24no—
701C2×C22⋊C4—24no—
702C2×C22⋊C4—24no—
703C2×C22⋊C4—24no—
704C2×C22⋊C4—24no—
705C2×C22⋊C4—24no—
706C2×C22⋊C4—24no—
707C2×C22⋊C4—24no—
708C2×C22⋊C4—24no—
709C2×C22⋊C4—24no—
710C2×C22⋊C4—24no—
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⋊C4—42no—
723C2×C22⋊C4—42no—
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×C42—24no—
751C2×C42—24no—
752C2×C42—24no—
753C2×C42—24no—
754C2×C42—24no—
755C2×C42—24no—
756C2×C42—24no—
757C2×C42—24no—
758C2×C42—24no—
759C2×C42—24no—
760C2×C42—42no—
761C2×C42—42no—
762C2×C42—42no—
763C2×C42—42no—
764C2×C42—42no—
765C2×C42—42no—
766C2×C42—42no—
767C2×C42—42no—
768C2×C42—42no—
769C2×C42—42no—
770C2×C42—42no—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
774C2×C42C2414yes—
775C2×C42C2414yes—
776C2×C42C2414yes—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
784C2×C42C2414yes—
785C2×C42C2414yes—
786C2×C42C2414yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
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—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850C24—22no—
851C24—22no—
852C24—22no—
853C24—22no—
854C24—22no—
855C24—22no—
856C24—22no—
857C24—22no—
858C24—22no—
859C24—22no—
860C24—22no—
861C24—22no—
862C24—22no—
863C24—22no—
864C24C2512yes—
865C24C2512yes—
866C24C2511yescharacteristic
867C2×Q8—28no—
868C2×Q8—28no—
869C2×Q8—28no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—44no—
873C2×Q8—416no—
874C2×Q8—44no—
875C2×Q8—44no—
876C2×Q8—44no—
877C2×Q8—44no—
878C2×Q8—44no—
879C2×Q8—416no—
880C2×Q8—416no—
881C2×Q8—88no—
882C2×Q8C2×#41116yes—
883C2×D4—28no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—416no—
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—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—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—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—28no—
966C22×C4—28no—
967C22×C4—28no—
968C22×C4—44no—
969C22×C4—416no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—88no—
973C22×C4C2×#4114yes—
974C22×C4C2×#4114yes—
975C22×C4C2×#4114yes—
976C22×C4C2×#4114yes—
977C22×C4C2×#4114yes—
978C22×C4C2×#4114yes—
979C22×C4H(5,𝔽2)14yes—
980C22×C42−1+414yes—
981C22×C42−1+414yes—
982C22×C4C2512yes—
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—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
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—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—28no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—28no—
1033C4⋊C4—28no—
1034C4⋊C4—28no—
1035C4⋊C4—28no—
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⋊C4C2×#41116yes—
1054C22⋊C4—28no—
1055C22⋊C4—28no—
1056C22⋊C4—28no—
1057C22⋊C4—28no—
1058C22⋊C4—28no—
1059C22⋊C4—28no—
1060C22⋊C4—28no—
1061C22⋊C4—28no—
1062C22⋊C4—28no—
1063C22⋊C4—28no—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
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—
1080C42—28no—
1081C42—28no—
1082C42—28no—
1083C42—28no—
1084C42—28no—
1085C42—28no—
1086C42—28no—
1087C42—28no—
1088C42—28no—
1089C42—28no—
1090C42—44no—
1091C42—44no—
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—22no—
1108C23—22no—
1109C23—22no—
1110C23—22no—
1111C23—22no—
1112C23—22no—
1113C23—22no—
1114C23—22no—
1115C23—44no—
1116C23—44no—
1117C23—44no—
1118C23—44no—
1119C23—44no—
1120C23—44no—
1121C23—44no—
1122C23—44no—
1123C23—44no—
1124C23—44no—
1125C23—44no—
1126C23—44no—
1127C23—44no—
1128C23—44no—
1129C23C22×#4112yes—
1130C23C22×#4112yes—
1131C23C2×H(5,𝔽2)12yes—
1132C23C2×2−1+412yes—
1133C23C2×2−1+412yes—
1134C23#58512yes—
1135C23#58512yes—
1136C23C2611yescharacteristic
1137Q8—416no—
1138Q8—416no—
1139Q8—416no—
1140Q8—88no—
1141D4—416no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
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—28no—
1161C2×C4—28no—
1162C2×C4—28no—
1163C2×C4—28no—
1164C2×C4—28no—
1165C2×C4—28no—
1166C2×C4—28no—
1167C2×C4—28no—
1168C2×C4—28no—
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—416no—
1230C2×C4—44no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—44no—
1234C2×C4—44no—
1235C2×C4—44no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—44no—
1239C2×C4—44no—
1240C2×C4—44no—
1241C2×C4—44no—
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—88no—
1251C2×C4C22×#4114yes—
1252C2×C4C22×#4114yes—
1253C2×C4C22×#4114yes—
1254C2×C4C22×#4114yes—
1255C2×C4C22×#4114yes—
1256C2×C4C22×#4114yes—
1257C2×C4C2×H(5,𝔽2)14yes—
1258C2×C4C2×2−1+414yes—
1259C2×C4C2×2−1+414yes—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—88no—
1275C22—88no—
1276C22#345914yes—
1277C22#348214yes—
1278C22#349414yes—
1279C22#351614yes—
1280C22#351814yes—
1281C22#355214yes—
1282C22#355714yes—
1283C22C23×#4111yescharacteristic
1284C22C23×#4111yescharacteristic
1285C22C22×H(5,𝔽2)11yescharacteristic
1286C22C22×2−1+411yescharacteristic
1287C22C22×2−1+411yescharacteristic
1288C22C2×#58511yescharacteristic
1289C22C2×#58511yescharacteristic
1290C4—24no—
1291C4—24no—
1292C4—24no—
1293C4—24no—
1294C4—24no—
1295C4—24no—
1296C4—24no—
1297C4—24no—
1298C4—24no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C2—82no—
1320C2—82no—
1321C2#3888118yesdirect product factor
1322C2C2×#345911yescharacteristic
1323C2C2×#348211yescharacteristic
1324C2C2×#355711yescharacteristic
1325C2C2×#355211yescharacteristic
1326C2C2×#351611yescharacteristic
1327C2C2×#351811yescharacteristic
1328C2C2×#349411yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC23×D4C23
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×#2799C2semidirect
2. C2×#2793C2semidirect
3. C2×#2775C2semidirect
4. C2×#2745C2semidirect
5. C2×#2734C2semidirect
8. C2×#2720C2semidirect
9. #38881C2direct (N × H)
10. C2×#2865C2semidirect
11. C2×#2604C2semidirect
12. C2×#2594C2semidirect
14. C2×#2588C2semidirect
15. C2×#2585C2semidirect
16. C2×#2574C2semidirect
17. C2×#2528C2semidirect
18. C2×#2525C2semidirect
19. C2×#2475C2semidirect
21. C2×#2469C2semidirect
22. C2×#2465C2semidirect
23. C2×#2465C2semidirect
25. C2×#2650C2semidirect
28. C2×#2365C2semidirect
29. C2×#2336C2semidirect
30. C2×#2332C2semidirect
31. C2×C4×C4⋊Q8C2semidirect
32. C2×#2298C2semidirect
45. #2865C22semidirect
46. #2799C22semidirect
47. #2793C22semidirect
48. #2775C22semidirect
49. #2745C22semidirect
50. #2734C22semidirect
53. #2720C22semidirect
55. #2650C22semidirect
56. #2604C22semidirect
57. #2594C22semidirect
59. #2588C22semidirect
60. #2585C22semidirect
61. #2574C22semidirect
62. #2528C22semidirect
63. #2525C22semidirect
64. #2475C22semidirect
65. #2469C22semidirect
67. #2465C22semidirect
68. #2465C22semidirect
111. #2365C22semidirect
112. #2336C22semidirect
113. #2332C22semidirect
114. C4×C4⋊Q8C22semidirect
115. #2298C22semidirect
1321. C2#38881direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27992
C2×#27932
C2×#27752
C2×#27452
C2×#27342
C2×#27312
C2×#27202
#388812
C2×#28652
C2×#26042
C2×#25942
C2×#25932
C2×#25882
C2×#25852
C2×#25742
C2×#25282
C2×#25252
C2×#24752
C2×#24152
C2×#24692
C2×#24652
C2×#24662
C2×#26502
C2×#26512
C2×#23672
C2×#23652
C2×#23362
C2×#23322
C2×C4×C4⋊Q82
C2×#22982