Finite Group Databasebeta

← C2×#48110 #7704039

Subgroups — C2×#48110 #7704039

Order 512.

5342 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
1C2×#2805C211yesmaximal, characteristic, complemented
2C2×#2788C211yesmaximal, characteristic, complemented
3C2×#2776C211yesmaximal, characteristic, complemented
4C2×#2776C211yesmaximal, characteristic, complemented
5C2×#2774C211yesmaximal, characteristic, complemented
6C2×#2743C211yesmaximal, characteristic
7C2×#2739C211yesmaximal, characteristic, complemented
8C2×#2739C211yesmaximal, characteristic, complemented
9C2×#2738C211yesmaximal, characteristic, complemented
10C2×#2713C211yesmaximal, characteristic, complemented
11C2×#2690C211yesmaximal, characteristic, complemented
12C2×#2677C211yesmaximal, characteristic, complemented
13#48110C2132yesmaximal, direct product factor
14C2×#2565C211yesmaximal, characteristic, complemented
15C2×#2576C211yesmaximal, characteristic
16C2×#2573C211yesmaximal, characteristic, complemented
17C2×#2572C211yesmaximal, characteristic
18C2×#2484C211yesmaximal, characteristic, complemented
19C2×#2441C211yesmaximal, characteristic, complemented
20C2×#2477C211yesmaximal, characteristic
21C2×#2429C211yesmaximal, characteristic, complemented
22C2×#2465C211yesmaximal, characteristic, complemented
23C2×#2465C211yesmaximal, characteristic, complemented
24C2×#2417C211yesmaximal, characteristic
25C2×#2440C211yesmaximal, characteristic, complemented
26C2×#2460C211yesmaximal, characteristic
27C2×#2449C211yesmaximal, characteristic
28C2×#2634C211yesmaximal, characteristic, complemented
29C2×#2665C211yesmaximal, characteristic, complemented
30C2×#2381C211yesmaximal, characteristic, complemented
31C2×#2360C211yesmaximal, characteristic, complemented
32C2×#2313C211yesmaximal, characteristic, complemented
33C22×C4⋊Q8C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C22×#125C2211yescharacteristic
36C22×#125C2211yescharacteristic
37C22×C22⋊Q8C2211yescharacteristic
38C22×C22⋊Q8C2211yescharacteristic
39C22×C22⋊Q8C2211yescharacteristic
40C22×C22⋊Q8C2211yescharacteristic
41C22×C22⋊Q8C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44C22×C4×D4C2211yescharacteristic
45C22×#117C2211yescharacteristic
46C23×C4⋊C4C2211yescharacteristic
47C23×C4⋊C4C2211yescharacteristic
48#2805C22116yescomplemented
49#2788C22116yescomplemented
50#2776C22116yescomplemented
51#2776C22116yescomplemented
52#2774C22116yescomplemented
53#2743C22116yes—
54#2739C22116yescomplemented
55#2739C22116yescomplemented
56#2738C22116yescomplemented
57#2713C22116yescomplemented
58#2690C22116yescomplemented
59#2677C22116yescomplemented
60#2665C22116yescomplemented
61#2634C22116yescomplemented
62#2576C22116yes—
63#2573C22116yescomplemented
64#2572C22116yes—
65#2565C22116yescomplemented
66#2484C22116yescomplemented
67#2477C22116yes—
68#2465C22116yescomplemented
69#2465C22116yescomplemented
70#2460C22116yes—
71#2449C22116yes—
72#2441C22116yescomplemented
73#2440C22116yescomplemented
74#2429C22116yescomplemented
75#2417C22116yes—
76C2×#401C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#400C2211yescharacteristic
80C2×#400C2211yescharacteristic
81C2×#400C2211yescharacteristic
82C2×#400C2211yescharacteristic
83C2×#400C2211yescharacteristic
84C2×#400C2211yescharacteristic
85C2×#400C2211yescharacteristic
86C2×#400C2211yescharacteristic
87C2×#400C2211yescharacteristic
88C2×#400C2211yescharacteristic
89C2×#400C2211yescharacteristic
90C2×#400C2211yescharacteristic
91C2×#399C2211yescharacteristic
92C2×#399C2211yescharacteristic
93C2×#398C2211yescharacteristic
94C2×#398C2211yescharacteristic
95C2×#398C2211yescharacteristic
96C2×#398C2211yescharacteristic
97C2×#398C2211yescharacteristic
98C2×#398C2211yescharacteristic
99C2×#398C2211yescharacteristic
100C2×#398C2211yescharacteristic
101C2×#398C2211yescharacteristic
102C2×#398C2211yescharacteristic
103C2×#397C2211yescharacteristic
104C2×#397C2211yescharacteristic
105C2×#397C2211yescharacteristic
106C2×#396C2211yescharacteristic
107C2×#396C2211yescharacteristic
108C2×#396C2211yescharacteristic
109C2×#396C2211yescharacteristic
110C2×#396C2211yescharacteristic
111C2×#396C2211yescharacteristic
112C2×#395C2211yescharacteristic
113C2×#395C2211yescharacteristic
114C2×#395C2211yescharacteristic
115C2×#395C2211yescharacteristic
116C2×#395C2211yescharacteristic
117C2×#395C2211yescharacteristic
118C2×#395C2211yescharacteristic
119C2×#394C2211yescharacteristic
120C2×#394C2211yescharacteristic
121C2×#393C2211yescharacteristic
122C2×#393C2211yescharacteristic
123C2×#393C2211yescharacteristic
124#2381C22116yescomplemented
125#2360C22116yescomplemented
126#2313C22116yescomplemented
127C2×#391C2211yescharacteristic
128C2×#391C2211yescharacteristic
129C2×#391C2211yescharacteristic
130C2×#391C2211yescharacteristic
131C2×#391C2211yescharacteristic
132C2×#391C2211yescharacteristic
133C2×#391C2211yescharacteristic
134C2×#389C2211yescharacteristic
135C2×#389C2211yescharacteristic
136C2×#389C2211yescharacteristic
137C2×#389C2211yescharacteristic
138C2×#389C2211yescharacteristic
139C2×#389C2211yescharacteristic
140C2×#389C2211yescharacteristic
141C2×#389C2211yescharacteristic
142C2×#389C2211yescharacteristic
143C2×#389C2211yescharacteristic
144C2×#389C2211yescharacteristic
145C2×#389C2211yescharacteristic
146C2×#388C2211yescharacteristic
147C2×#388C2211yescharacteristic
148C2×#388C2211yescharacteristic
149C2×#388C2211yescharacteristic
150C2×#388C2211yescharacteristic
151C2×#388C2211yescharacteristic
152C2×#388C2211yescharacteristic
153C2×#388C2211yescharacteristic
154C2×#388C2211yescharacteristic
155C2×#388C2211yescharacteristic
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×#387C2211yescharacteristic
182C2×#387C2211yescharacteristic
183C2×#387C2211yescharacteristic
184C2×#387C2211yescharacteristic
185C2×#386C2211yescharacteristic
186C2×#386C2211yescharacteristic
187C2×#386C2211yescharacteristic
188C2×#386C2211yescharacteristic
189C2×#385C2211yescharacteristic
190C2×#385C2211yescharacteristic
191C2×#385C2211yescharacteristic
192C2×#385C2211yescharacteristic
193C2×#385C2211yescharacteristic
194C2×#385C2211yescharacteristic
195C2×#385C2211yescharacteristic
196C2×#385C2211yescharacteristic
197C2×#384C2211yescharacteristic
198C2×#383C2211yescharacteristic
199C2×#383C2211yescharacteristic
200C2×#383C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C2×#381C2211yescharacteristic
203C2×#381C2211yescharacteristic
204C2×#381C2211yescharacteristic
205C2×#381C2211yescharacteristic
206C2×#381C2211yescharacteristic
207C2×#380C2211yescharacteristic
208C2×#380C2211yescharacteristic
209C2×#380C2211yescharacteristic
210C2×#380C2211yescharacteristic
211C2×#380C2211yescharacteristic
212C2×C4×C4⋊C4C2211yescharacteristic
213C2×C4×C22⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×C4×C22⋊C4C2211yescharacteristic
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×Q8C2311yescharacteristic
223C23×D4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C24×C4C2311yescharacteristic
227C24×C4C2311yescharacteristic
228C24×C4C2311yescharacteristic
229C24×C4C2311yescharacteristic
230C2×C4⋊Q8—28no—
231C2×C4⋊Q8—44no—
232C2×C4⋊Q8C2318yes—
233C2×C4⋊Q8C2318yes—
234C2×#125—44no—
235C2×#125—44no—
236C2×#125C2318yes—
237C2×#125C2318yes—
238C2×C22⋊Q8—28no—
239C2×C22⋊Q8—44no—
240C2×C22⋊Q8—44no—
241C2×C22⋊Q8—44no—
242C2×C22⋊Q8—44no—
243C2×C22⋊Q8C2318yes—
244C2×C22⋊Q8C2318yes—
245C2×C22⋊Q8C2318yes—
246C2×C22⋊Q8C2318yes—
247C2×C22⋊Q8C2318yes—
248C2×C4×Q8—44no—
249C2×C4×Q8—44no—
250C2×C4×Q8C2318yes—
251C2×C4×Q8C2318yes—
252C2×C4×D4—44no—
253C2×C4×D4C2318yes—
254C2×#117—44no—
255C2×#117C2318yes—
256C22×C4⋊C4—28no—
257C22×C4⋊C4—44no—
258C22×C4⋊C4C2318yes—
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⋊C4C2318yes—
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⋊C4C2311yescharacteristic
302C22×C4⋊C4C2311yescharacteristic
303C22×C4⋊C4C2311yescharacteristic
304C22×C4⋊C4C2311yescharacteristic
305C22×C4⋊C4C2311yescharacteristic
306C22×C4⋊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×C22⋊C4C2311yescharacteristic
320C22×C22⋊C4C2311yescharacteristic
321C22×C22⋊C4C2311yescharacteristic
322C22×C22⋊C4C2311yescharacteristic
323C22×C22⋊C4C2311yescharacteristic
324C22×C22⋊C4C2311yescharacteristic
325C22×C22⋊C4C2311yescharacteristic
326C22×C22⋊C4C2311yescharacteristic
327C22×C22⋊C4C2311yescharacteristic
328C22×C22⋊C4C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2311yescharacteristic
333C22×C42C2311yescharacteristic
334C22×C42C2311yescharacteristic
335C22×C42C2311yescharacteristic
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2311yescharacteristic
339C22×C42C2311yescharacteristic
340C22×C42C2311yescharacteristic
341C22×C42C2311yescharacteristic
342#401C2318yes—
343#400C2318yes—
344#400C2318yes—
345#400C2318yes—
346#400C2318yes—
347#400C2318yes—
348#400C2318yes—
349#400C2318yes—
350#400C2318yes—
351#400C2318yes—
352#400C2318yes—
353#400C2318yes—
354#400C2318yes—
355#400C2318yes—
356#400C2318yes—
357#399C2318yes—
358#399C2318yes—
359#398C2318yes—
360#398C2318yes—
361#398C2318yes—
362#398C2318yes—
363#398C2318yes—
364#398C2318yes—
365#398C2318yes—
366#398C2318yes—
367#398C2318yes—
368#398C2318yes—
369#397C2318yes—
370#397C2318yes—
371#397C2318yes—
372#396C2318yes—
373#396C2318yes—
374#396C2318yes—
375#396C2318yes—
376#396C2318yes—
377#396C2318yes—
378#395C2318yes—
379#395C2318yes—
380#395C2318yes—
381#395C2318yes—
382#395C2318yes—
383#395C2318yes—
384#395C2318yes—
385#394C2318yes—
386#394C2318yes—
387#393C2318yes—
388#393C2318yes—
389#393C2318yes—
390#391C2318yes—
391#391C2318yes—
392#391C2318yes—
393#391C2318yes—
394#391C2318yes—
395#391C2318yes—
396#391C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2318yes—
400#389C2318yes—
401#389C2318yes—
402#389C2318yes—
403#389C2318yes—
404#389C2318yes—
405#389C2318yes—
406#389C2318yes—
407#389C2318yes—
408#389C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
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#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#387C2318yes—
444#387C2318yes—
445#387C2318yes—
446#387C2318yes—
447#387C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#386C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2318yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#384C2318yes—
461#383C2318yes—
462#383C2318yes—
463#383C2318yes—
464#382C2318yes—
465#381C2318yes—
466#381C2318yes—
467#381C2318yes—
468#381C2318yes—
469#381C2318yes—
470#380C2318yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2318yes—
475C4×C4⋊C4C2318yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2318yes—
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
540C2×#95C2311yescharacteristic
541C2×#95C2311yescharacteristic
542C2×#95C2311yescharacteristic
543C2×#95C2311yescharacteristic
544C25C2411yescharacteristic
545C25C2411yescharacteristic
546C22×Q8—24no—
547C22×Q8—24no—
548C22×Q8—24no—
549C22×Q8—24no—
550C22×Q8—24no—
551C22×Q8—42no—
552C22×Q8—42no—
553C22×Q8—42no—
554C22×Q8—42no—
555C22×Q8—42no—
556C22×Q8—42no—
557C22×Q8—42no—
558C22×Q8C2414yes—
559C22×Q8C2414yes—
560C22×Q8C2414yes—
561C22×Q8C2414yes—
562C22×D4—24no—
563C22×D4—24no—
564C22×D4—42no—
565C22×D4C2414yes—
566C23×C4—24no—
567C23×C4—24no—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4—24no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—24no—
574C23×C4—24no—
575C23×C4—42no—
576C23×C4—42no—
577C23×C4—42no—
578C23×C4—42no—
579C23×C4—42no—
580C23×C4—42no—
581C23×C4—42no—
582C23×C4—42no—
583C23×C4—42no—
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×C4C2411yescharacteristic
606C23×C4C2411yescharacteristic
607C23×C4C2414yes—
608C23×C4C2414yes—
609C23×C4C2414yes—
610C23×C4C2411yescharacteristic
611C23×C4C2411yescharacteristic
612C23×C4C2411yescharacteristic
613C23×C4C2411yescharacteristic
614C23×C4C2411yescharacteristic
615C23×C4C2411yescharacteristic
616C23×C4C2414yes—
617C23×C4C2414yes—
618C23×C4C2414yes—
619C4⋊Q8—232no—
620C4⋊Q8—416no—
621#125—416no—
622#125—416no—
623C22⋊Q8—232no—
624C22⋊Q8—416no—
625C22⋊Q8—416no—
626C22⋊Q8—416no—
627C22⋊Q8—416no—
628C4×Q8—416no—
629C4×Q8—416no—
630C4×D4—416no—
631#117—416no—
632C2×C4⋊C4—24no—
633C2×C4⋊C4—24no—
634C2×C4⋊C4—24no—
635C2×C4⋊C4—24no—
636C2×C4⋊C4—24no—
637C2×C4⋊C4—24no—
638C2×C4⋊C4—24no—
639C2×C4⋊C4—24no—
640C2×C4⋊C4—24no—
641C2×C4⋊C4—24no—
642C2×C4⋊C4—24no—
643C2×C4⋊C4—24no—
644C2×C4⋊C4—24no—
645C2×C4⋊C4—24no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—24no—
649C2×C4⋊C4—24no—
650C2×C4⋊C4—24no—
651C2×C4⋊C4—24no—
652C2×C4⋊C4—24no—
653C2×C4⋊C4—232no—
654C2×C4⋊C4—416no—
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⋊C4—42no—
670C2×C4⋊C4—42no—
671C2×C4⋊C4—42no—
672C2×C4⋊C4—42no—
673C2×C4⋊C4—42no—
674C2×C4⋊C4—42no—
675C2×C4⋊C4—42no—
676C2×C4⋊C4—42no—
677C2×C4⋊C4—42no—
678C2×C4⋊C4—42no—
679C2×C4⋊C4—42no—
680C2×C4⋊C4#4118yes—
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×C22⋊C4—24no—
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—24no—
737C2×C22⋊C4—24no—
738C2×C22⋊C4—24no—
739C2×C22⋊C4—42no—
740C2×C22⋊C4—42no—
741C2×C22⋊C4—42no—
742C2×C22⋊C4—42no—
743C2×C22⋊C4—42no—
744C2×C22⋊C4—42no—
745C2×C22⋊C4—42no—
746C2×C22⋊C4—42no—
747C2×C22⋊C4—42no—
748C2×C22⋊C4—42no—
749C2×C22⋊C4—42no—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C22⋊C4C2414yes—
771C2×C22⋊C4C2414yes—
772C2×C42—24no—
773C2×C42—24no—
774C2×C42—24no—
775C2×C42—42no—
776C2×C42—42no—
777C2×C42—42no—
778C2×C42—42no—
779C2×C42—42no—
780C2×C42—42no—
781C2×C42—42no—
782C2×C42—42no—
783C2×C42—42no—
784C2×C42—42no—
785C2×C42C2414yes—
786C2×C42C2414yes—
787C2×C42C2414yes—
788C2×C42C2414yes—
789C2×C42C2414yes—
790C2×C42C2414yes—
791C2×C42C2414yes—
792C2×C42C2414yes—
793C2×C42C2414yes—
794C2×C42C2414yes—
795C2×C42C2414yes—
796C2×C42C2414yes—
797C2×C42C2414yes—
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—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2414yes—
855#95C2414yes—
856#95C2414yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860C24—22no—
861C24—22no—
862C24—22no—
863C24—22no—
864C24—22no—
865C24—22no—
866C24—22no—
867C24—22no—
868C24—22no—
869C24—22no—
870C24—22no—
871C24—22no—
872C242−1+414yes—
873C242−1+414yes—
874C24C2512yes—
875C24C2512yes—
876C24C2511yescharacteristic
877C2×Q8—28no—
878C2×Q8—28no—
879C2×Q8—28no—
880C2×Q8—28no—
881C2×Q8—28no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—44no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—416no—
890C2×Q8—416no—
891C2×Q8—88no—
892C2×Q8—88no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—44no—
896C2×D4—416no—
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—28no—
961C22×C4—28no—
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—22no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—22no—
980C22×C4—28no—
981C22×C4—28no—
982C22×C4—28no—
983C22×C4—28no—
984C22×C4—28no—
985C22×C4—28no—
986C22×C4—28no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—416no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—416no—
998C22×C4—416no—
999C22×C4—88no—
1000C22×C4—88no—
1001C22×C4—88no—
1002C22×C4C2×#4114yes—
1003C22×C4C2×#4114yes—
1004C22×C4C2×#4114yes—
1005C22×C4H(5,𝔽2)14yes—
1006C22×C4H(5,𝔽2)14yes—
1007C22×C42−1+414yes—
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—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C4⋊C4—28no—
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—28no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—28no—
1054C4⋊C4—28no—
1055C4⋊C4—28no—
1056C4⋊C4—28no—
1057C4⋊C4—28no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4C2×#41116yes—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—28no—
1092C22⋊C4—28no—
1093C22⋊C4—28no—
1094C22⋊C4—28no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C42—28no—
1107C42—28no—
1108C42—28no—
1109C42—44no—
1110C42—44no—
1111C42—44no—
1112C42—44no—
1113C42—44no—
1114C42—44no—
1115C42—44no—
1116C42—44no—
1117C42—44no—
1118C42—44no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—22no—
1123C23—22no—
1124C23—22no—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—22no—
1130C23—22no—
1131C23—28no—
1132C23—28no—
1133C23—28no—
1134C23—28no—
1135C23—28no—
1136C23—28no—
1137C23—44no—
1138C23—44no—
1139C23—44no—
1140C23—44no—
1141C23—44no—
1142C23—44no—
1143C23—44no—
1144C23—44no—
1145C23C22×#4112yes—
1146C23C2×H(5,𝔽2)12yes—
1147C23C2×H(5,𝔽2)12yes—
1148C23C2×2−1+414yes—
1149C23C2×2−1+414yes—
1150C23C2×2−1+412yes—
1151C23C2×2−1+412yes—
1152C23C2×2−1+412yes—
1153C23#58512yes—
1154C23C2611yescharacteristic
1155Q8—416no—
1156Q8—416no—
1157Q8—88no—
1158Q8—88no—
1159D4—416no—
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—28no—
1173C2×C4—28no—
1174C2×C4—28no—
1175C2×C4—28no—
1176C2×C4—28no—
1177C2×C4—28no—
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—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—416no—
1248C2×C4—416no—
1249C2×C4—416no—
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—44no—
1270C2×C4—44no—
1271C2×C4—44no—
1272C2×C4—44no—
1273C2×C4—88no—
1274C2×C4—88no—
1275C2×C4—88no—
1276C2×C4C22×#4114yes—
1277C2×C4C22×#4114yes—
1278C2×C4C22×#4114yes—
1279C2×C4C2×H(5,𝔽2)14yes—
1280C2×C4C2×H(5,𝔽2)14yes—
1281C2×C4C2×2−1+414yes—
1282C22—24no—
1283C22—24no—
1284C22—24no—
1285C22—24no—
1286C22—24no—
1287C22—24no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—416no—
1297C22—416no—
1298C22#349514yes—
1299C22#351914yes—
1300C22#352314yes—
1301C22#353514yes—
1302C22#353814yes—
1303C22#354114yes—
1304C22#355214yes—
1305C22C23×#4111yescharacteristic
1306C22C22×H(5,𝔽2)11yescharacteristic
1307C22C22×H(5,𝔽2)11yescharacteristic
1308C22C22×2−1+411yescharacteristic
1309C22C22×2−1+411yescharacteristic
1310C22C22×2−1+411yescharacteristic
1311C22C2×#58511yescharacteristic
1312C4—24no—
1313C4—24no—
1314C4—24no—
1315C4—24no—
1316C4—24no—
1317C4—24no—
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—
1340C4—42no—
1341C2—44no—
1342C2—44no—
1343C2#4811018yesdirect product factor
1344C2C2×#354111yescharacteristic
1345C2C2×#353511yescharacteristic
1346C2C2×#353811yescharacteristic
1347C2C2×#355211yescharacteristic
1348C2C2×#351911yescharacteristic
1349C2C2×#352311yescharacteristic
1350C2C2×#349511yescharacteristic
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×#2805C2semidirect
2. C2×#2788C2semidirect
3. C2×#2776C2semidirect
4. C2×#2776C2semidirect
5. C2×#2774C2semidirect
7. C2×#2739C2semidirect
8. C2×#2739C2semidirect
9. C2×#2738C2semidirect
10. C2×#2713C2semidirect
11. C2×#2690C2semidirect
12. C2×#2677C2semidirect
13. #48110C2direct (N × H)
14. C2×#2565C2semidirect
16. C2×#2573C2semidirect
18. C2×#2484C2semidirect
19. C2×#2441C2semidirect
21. C2×#2429C2semidirect
22. C2×#2465C2semidirect
23. C2×#2465C2semidirect
25. C2×#2440C2semidirect
28. C2×#2634C2semidirect
29. C2×#2665C2semidirect
30. C2×#2381C2semidirect
31. C2×#2360C2semidirect
32. C2×#2313C2semidirect
48. #2805C22semidirect
49. #2788C22semidirect
50. #2776C22semidirect
51. #2776C22semidirect
52. #2774C22semidirect
54. #2739C22semidirect
55. #2739C22semidirect
56. #2738C22semidirect
57. #2713C22semidirect
58. #2690C22semidirect
59. #2677C22semidirect
60. #2665C22semidirect
61. #2634C22semidirect
63. #2573C22semidirect
65. #2565C22semidirect
66. #2484C22semidirect
68. #2465C22semidirect
69. #2465C22semidirect
72. #2441C22semidirect
73. #2440C22semidirect
74. #2429C22semidirect
124. #2381C22semidirect
125. #2360C22semidirect
126. #2313C22semidirect
1343. C2#48110direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28052
C2×#27882
C2×#27762
C2×#27742
C2×#27432
C2×#27392
C2×#27382
C2×#27132
C2×#26902
C2×#26772
#481102
C2×#25652
C2×#25762
C2×#25732
C2×#25722
C2×#24842
C2×#24412
C2×#24772
C2×#24292
C2×#24652
C2×#24172
C2×#24402
C2×#24602
C2×#24492
C2×#26342
C2×#26652
C2×#23812
C2×#23602
C2×#23132