Finite Group Databasebeta

← C2×#38001 #7635286

Subgroups — C2×#38001 #7635286

Order 512.

5050 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2766C211yesmaximal, characteristic, complemented
2C2×#2763C211yesmaximal, characteristic, complemented
3C2×#2762C211yesmaximal, characteristic, complemented
4C2×#2745C211yesmaximal, characteristic, complemented
5C2×#2739C211yesmaximal, characteristic, complemented
6C2×#2698C211yesmaximal, characteristic, complemented
7C2×#2695C211yesmaximal, characteristic
8C2×#2687C211yesmaximal, characteristic
9#38001C2132yesmaximal, direct product factor
10C2×#2855C211yesmaximal, characteristic, complemented
11C2×#2612C211yesmaximal, characteristic, complemented
12C2×#2605C211yesmaximal, characteristic, complemented
13C2×#2576C211yesmaximal, characteristic
14C2×#2572C211yesmaximal, characteristic
15C2×#2527C211yesmaximal, characteristic, complemented
16C2×#2527C211yesmaximal, characteristic, complemented
17C2×#2530C211yesmaximal, characteristic, complemented
18C2×#2514C211yesmaximal, characteristic, complemented
19C2×#2515C211yesmaximal, characteristic, complemented
20C2×#2524C211yesmaximal, characteristic, complemented
21C2×#2524C211yesmaximal, characteristic, complemented
22C2×#2520C211yesmaximal, characteristic, complemented
23C2×#2523C211yesmaximal, characteristic, complemented
24C2×#2493C211yesmaximal, characteristic, complemented
25C2×#2665C211yesmaximal, characteristic, complemented
26C2×#2638C211yesmaximal, characteristic
27C2×#2373C211yesmaximal, characteristic, complemented
28C2×#2368C211yesmaximal, characteristic, complemented
29C2×#2332C211yesmaximal, characteristic, complemented
30C2×#2318C211yesmaximal, characteristic
31C2×C4×#123C211yesmaximal, characteristic
32C2×#2283C211yesmaximal, characteristic, complemented
33C22×#126C2211yescharacteristic
34C22×#123C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×C22⋊Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38C23×C42C2211yescharacteristic
39#2855C22116yescomplemented
40#2766C22116yescomplemented
41#2763C22116yescomplemented
42#2762C22116yescomplemented
43#2745C22116yescomplemented
44#2739C22116yescomplemented
45#2698C22116yescomplemented
46#2695C22116yes—
47#2687C22116yes—
48#2665C22116yescomplemented
49#2638C22116yes—
50#2612C22116yescomplemented
51#2605C22116yescomplemented
52#2576C22116yes—
53#2572C22116yes—
54#2530C22116yescomplemented
55#2527C22116yescomplemented
56#2527C22116yescomplemented
57#2524C22116yescomplemented
58#2524C22116yescomplemented
59#2523C22116yescomplemented
60#2520C22116yescomplemented
61#2515C22116yescomplemented
62#2514C22116yescomplemented
63#2493C22116yescomplemented
64C2×#401C2211yescharacteristic
65C2×#401C2211yescharacteristic
66C2×#401C2211yescharacteristic
67C2×#400C2211yescharacteristic
68C2×#400C2211yescharacteristic
69C2×#400C2211yescharacteristic
70C2×#400C2211yescharacteristic
71C2×#400C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#398C2211yescharacteristic
80C2×#398C2211yescharacteristic
81C2×#398C2211yescharacteristic
82C2×#398C2211yescharacteristic
83C2×#398C2211yescharacteristic
84C2×#398C2211yescharacteristic
85C2×#398C2211yescharacteristic
86C2×#397C2211yescharacteristic
87C2×#397C2211yescharacteristic
88C2×#397C2211yescharacteristic
89C2×#397C2211yescharacteristic
90C2×#397C2211yescharacteristic
91C2×#397C2211yescharacteristic
92C2×#396C2211yescharacteristic
93C2×#396C2211yescharacteristic
94C2×#395C2211yescharacteristic
95C2×#395C2211yescharacteristic
96C2×#395C2211yescharacteristic
97C2×#395C2211yescharacteristic
98C2×#394C2211yescharacteristic
99C2×#394C2211yescharacteristic
100C2×#393C2211yescharacteristic
101C2×#393C2211yescharacteristic
102C2×#393C2211yescharacteristic
103C2×#393C2211yescharacteristic
104#2373C22116yescomplemented
105#2368C22116yescomplemented
106#2332C22116yescomplemented
107#2318C22116yes—
108C4×#123C22116yes—
109C2×#391C2211yescharacteristic
110C2×#391C2211yescharacteristic
111C2×#391C2211yescharacteristic
112C2×#391C2211yescharacteristic
113C2×#391C2211yescharacteristic
114C2×#391C2211yescharacteristic
115C2×#391C2211yescharacteristic
116C2×#391C2211yescharacteristic
117C2×#391C2211yescharacteristic
118C2×#391C2211yescharacteristic
119C2×#391C2211yescharacteristic
120C2×#389C2211yescharacteristic
121C2×#389C2211yescharacteristic
122C2×#389C2211yescharacteristic
123C2×#389C2211yescharacteristic
124C2×#388C2211yescharacteristic
125C2×#388C2211yescharacteristic
126C2×#388C2211yescharacteristic
127C2×#388C2211yescharacteristic
128C2×#388C2211yescharacteristic
129C2×#388C2211yescharacteristic
130C2×#388C2211yescharacteristic
131C2×#388C2211yescharacteristic
132C2×#388C2211yescharacteristic
133C2×#388C2211yescharacteristic
134C2×#388C2211yescharacteristic
135C2×#387C2211yescharacteristic
136C2×#387C2211yescharacteristic
137C2×#387C2211yescharacteristic
138C2×#387C2211yescharacteristic
139C2×#387C2211yescharacteristic
140C2×#387C2211yescharacteristic
141C2×#387C2211yescharacteristic
142C2×#387C2211yescharacteristic
143C2×#387C2211yescharacteristic
144C2×#387C2211yescharacteristic
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×#386C2211yescharacteristic
166C2×#386C2211yescharacteristic
167C2×#386C2211yescharacteristic
168C2×#385C2211yescharacteristic
169C2×#385C2211yescharacteristic
170C2×#385C2211yescharacteristic
171C2×#385C2211yescharacteristic
172C2×#385C2211yescharacteristic
173C2×#385C2211yescharacteristic
174C2×#385C2211yescharacteristic
175C2×#385C2211yescharacteristic
176C2×#385C2211yescharacteristic
177#2283C22116yescomplemented
178C2×#383C2211yescharacteristic
179C2×#383C2211yescharacteristic
180C2×#383C2211yescharacteristic
181C2×#383C2211yescharacteristic
182C2×#383C2211yescharacteristic
183C2×#383C2211yescharacteristic
184C2×#382C2211yescharacteristic
185C2×#382C2211yescharacteristic
186C2×#382C2211yescharacteristic
187C2×#382C2211yescharacteristic
188C2×#382C2211yescharacteristic
189C2×#381C2211yescharacteristic
190C2×#381C2211yescharacteristic
191C2×#381C2211yescharacteristic
192C2×#381C2211yescharacteristic
193C2×#381C2211yescharacteristic
194C2×#381C2211yescharacteristic
195C2×#381C2211yescharacteristic
196C2×#380C2211yescharacteristic
197C2×#380C2211yescharacteristic
198C2×#380C2211yescharacteristic
199C2×#380C2211yescharacteristic
200C2×C4×C4⋊C4C2211yescharacteristic
201C2×C4×C4⋊C4C2211yescharacteristic
202C2×C4×C4⋊C4C2211yescharacteristic
203C2×C4×C4⋊C4C2211yescharacteristic
204C2×C4×C4⋊C4C2211yescharacteristic
205C2×C4×C4⋊C4C2211yescharacteristic
206C2×C4×C4⋊C4C2211yescharacteristic
207C2×C4×C22⋊C4C2211yescharacteristic
208C2×C4×C22⋊C4C2211yescharacteristic
209C2×C4×C22⋊C4C2211yescharacteristic
210C2×C4×C22⋊C4C2211yescharacteristic
211C2×C4×C22⋊C4C2211yescharacteristic
212C2×C4×C22⋊C4C2211yescharacteristic
213C2×C4×C22⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×#376C2211yescharacteristic
216C2×#376C2211yescharacteristic
217C2×#376C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×D4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C24×C4C2311yescharacteristic
227C24×C4C2311yescharacteristic
228C24×C4C2311yescharacteristic
229C2×#126—28no—
230C2×#126C2318yes—
231C2×#123—28no—
232C2×#123C2318yes—
233C2×C22⋊Q8—28no—
234C2×C22⋊Q8—28no—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×C4×D4—28no—
238C2×C4×D4C2318yes—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2311yescharacteristic
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⋊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×C22⋊C4C2311yescharacteristic
274C22×C22⋊C4C2311yescharacteristic
275C22×C22⋊C4C2311yescharacteristic
276C22×C22⋊C4C2311yescharacteristic
277C22×C22⋊C4C2311yescharacteristic
278C22×C22⋊C4C2311yescharacteristic
279C22×C22⋊C4C2311yescharacteristic
280C22×C22⋊C4C2311yescharacteristic
281C22×C22⋊C4C2311yescharacteristic
282C22×C22⋊C4C2311yescharacteristic
283C22×C22⋊C4C2311yescharacteristic
284C22×C22⋊C4C2311yescharacteristic
285C22×C22⋊C4C2311yescharacteristic
286C22×C22⋊C4C2311yescharacteristic
287C22×C22⋊C4C2311yescharacteristic
288C22×C22⋊C4C2311yescharacteristic
289C22×C22⋊C4C2311yescharacteristic
290C22×C22⋊C4C2311yescharacteristic
291C22×C22⋊C4C2311yescharacteristic
292C22×C22⋊C4C2311yescharacteristic
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2311yescharacteristic
295C22×C42—28no—
296C22×C42C2318yes—
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299C22×C42C2311yescharacteristic
300C22×C42C2311yescharacteristic
301C22×C42C2311yescharacteristic
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314#401C2318yes—
315#401C2318yes—
316#401C2318yes—
317#400C2318yes—
318#400C2318yes—
319#400C2318yes—
320#400C2318yes—
321#400C2318yes—
322#400C2318yes—
323#400C2318yes—
324#400C2318yes—
325#400C2318yes—
326#400C2318yes—
327#400C2318yes—
328#400C2318yes—
329#398C2318yes—
330#398C2318yes—
331#398C2318yes—
332#398C2318yes—
333#398C2318yes—
334#398C2318yes—
335#398C2318yes—
336#397C2318yes—
337#397C2318yes—
338#397C2318yes—
339#397C2318yes—
340#397C2318yes—
341#397C2318yes—
342#396C2318yes—
343#396C2318yes—
344#395C2318yes—
345#395C2318yes—
346#395C2318yes—
347#395C2318yes—
348#394C2318yes—
349#394C2318yes—
350#393C2318yes—
351#393C2318yes—
352#393C2318yes—
353#393C2318yes—
354#391C2318yes—
355#391C2318yes—
356#391C2318yes—
357#391C2318yes—
358#391C2318yes—
359#391C2318yes—
360#391C2318yes—
361#391C2318yes—
362#391C2318yes—
363#391C2318yes—
364#391C2318yes—
365#389C2318yes—
366#389C2318yes—
367#389C2318yes—
368#389C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#385C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#383C2318yes—
423#383C2318yes—
424#383C2318yes—
425#383C2318yes—
426#383C2318yes—
427#383C2318yes—
428#382C2318yes—
429#382C2318yes—
430#382C2318yes—
431#382C2318yes—
432#382C2318yes—
433#381C2318yes—
434#381C2318yes—
435#381C2318yes—
436#381C2318yes—
437#381C2318yes—
438#381C2318yes—
439#381C2318yes—
440#380C2318yes—
441#380C2318yes—
442#380C2318yes—
443#380C2318yes—
444C4×C4⋊C4C2318yes—
445C4×C4⋊C4C2318yes—
446C4×C4⋊C4C2318yes—
447C4×C4⋊C4C2318yes—
448C4×C4⋊C4C2318yes—
449C4×C4⋊C4C2318yes—
450C4×C4⋊C4C2318yes—
451C4×C22⋊C4C2318yes—
452C4×C22⋊C4C2318yes—
453C4×C22⋊C4C2318yes—
454C4×C22⋊C4C2318yes—
455C4×C22⋊C4C2318yes—
456C4×C22⋊C4C2318yes—
457C4×C22⋊C4C2318yes—
458C4×C22⋊C4C2318yes—
459#376C2318yes—
460#376C2318yes—
461#376C2318yes—
462C2×#95C2318yes—
463C2×#95C2311yescharacteristic
464C2×#95C2311yescharacteristic
465C2×#95C2311yescharacteristic
466C2×#95C2311yescharacteristic
467C2×#95C2311yescharacteristic
468C2×#95C2311yescharacteristic
469C2×#95C2311yescharacteristic
470C2×#95C2311yescharacteristic
471C2×#95C2311yescharacteristic
472C2×#95C2311yescharacteristic
473C2×#95C2311yescharacteristic
474C2×#95C2311yescharacteristic
475C2×#95C2311yescharacteristic
476C2×#95C2311yescharacteristic
477C2×#95C2311yescharacteristic
478C2×#95C2311yescharacteristic
479C2×#95C2311yescharacteristic
480C2×#95C2311yescharacteristic
481C2×#95C2311yescharacteristic
482C2×#95C2311yescharacteristic
483C2×#95C2311yescharacteristic
484C2×#95C2311yescharacteristic
485C2×#95C2311yescharacteristic
486C2×#95C2311yescharacteristic
487C2×#95C2311yescharacteristic
488C2×#95C2311yescharacteristic
489C2×#95C2311yescharacteristic
490C2×#95C2311yescharacteristic
491C2×#95C2311yescharacteristic
492C2×#95C2311yescharacteristic
493C2×#95C2311yescharacteristic
494C2×#95C2311yescharacteristic
495C2×#95C2311yescharacteristic
496C2×#95C2311yescharacteristic
497C2×#95C2311yescharacteristic
498C2×#95C2311yescharacteristic
499C2×#95C2311yescharacteristic
500C2×#95C2311yescharacteristic
501C2×#95C2311yescharacteristic
502C2×#95C2311yescharacteristic
503C2×#95C2311yescharacteristic
504C2×#95C2311yescharacteristic
505C2×#95C2311yescharacteristic
506C2×#95C2311yescharacteristic
507C2×#95C2311yescharacteristic
508C2×#95C2311yescharacteristic
509C2×#95C2311yescharacteristic
510C2×#95C2311yescharacteristic
511C2×#95C2311yescharacteristic
512C2×#95C2311yescharacteristic
513C2×#95C2311yescharacteristic
514C2×#95C2311yescharacteristic
515C2×#95C2311yescharacteristic
516C2×#95C2311yescharacteristic
517C2×#95C2311yescharacteristic
518C2×#95C2311yescharacteristic
519C2×#95C2311yescharacteristic
520C2×#95C2311yescharacteristic
521C2×#95C2311yescharacteristic
522C2×#95C2311yescharacteristic
523C2×#95C2311yescharacteristic
524C2×#95C2311yescharacteristic
525C2×#95C2311yescharacteristic
526C2×#95C2311yescharacteristic
527C2×#95C2311yescharacteristic
528C2×#95C2311yescharacteristic
529C2×#95C2311yescharacteristic
530C2×#95C2311yescharacteristic
531C2×#95C2311yescharacteristic
532C2×#95C2311yescharacteristic
533C2×#95C2311yescharacteristic
534C2×#95C2311yescharacteristic
535C25C2411yescharacteristic
536C25C2411yescharacteristic
537C22×Q8—24no—
538C22×Q8—24no—
539C22×Q8—42no—
540C22×Q8—42no—
541C22×Q8—42no—
542C22×Q8—42no—
543C22×Q8—42no—
544C22×Q8—42no—
545C22×Q8—42no—
546C22×Q8C2414yes—
547C22×Q8C2414yes—
548C22×Q8C2414yes—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—42no—
552C22×D4C2414yes—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—24no—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—24no—
559C23×C4—42no—
560C23×C4—42no—
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×C4#4118yes—
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×C4C2411yescharacteristic
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2411yescharacteristic
595C23×C4C2414yes—
596C23×C4C2414yes—
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2411yescharacteristic
601C23×C4C2411yescharacteristic
602C23×C4C2414yes—
603C23×C4C2414yes—
604C23×C4C2414yes—
605C23×C4C2414yes—
606#126—232no—
607#123—232no—
608C22⋊Q8—232no—
609C22⋊Q8—232no—
610C4×D4—232no—
611C2×C4⋊C4—24no—
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—42no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4—42no—
629C2×C4⋊C4—42no—
630C2×C4⋊C4—42no—
631C2×C4⋊C4—42no—
632C2×C4⋊C4—42no—
633C2×C4⋊C4—42no—
634C2×C4⋊C4—42no—
635C2×C4⋊C4—42no—
636C2×C4⋊C4—42no—
637C2×C4⋊C4—42no—
638C2×C4⋊C4—42no—
639C2×C4⋊C4—42no—
640C2×C4⋊C4—42no—
641C2×C4⋊C4—42no—
642C2×C4⋊C4—42no—
643C2×C4⋊C4—42no—
644C2×C4⋊C4—42no—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C22⋊C4—24no—
680C2×C22⋊C4—24no—
681C2×C22⋊C4—24no—
682C2×C22⋊C4—24no—
683C2×C22⋊C4—24no—
684C2×C22⋊C4—24no—
685C2×C22⋊C4—24no—
686C2×C22⋊C4—24no—
687C2×C22⋊C4—24no—
688C2×C22⋊C4—24no—
689C2×C22⋊C4—42no—
690C2×C22⋊C4—42no—
691C2×C22⋊C4—42no—
692C2×C22⋊C4—42no—
693C2×C22⋊C4—42no—
694C2×C22⋊C4—42no—
695C2×C22⋊C4—42no—
696C2×C22⋊C4—42no—
697C2×C22⋊C4—42no—
698C2×C22⋊C4—42no—
699C2×C22⋊C4—42no—
700C2×C22⋊C4#4118yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C42—24no—
724C2×C42—24no—
725C2×C42—24no—
726C2×C42—24no—
727C2×C42—24no—
728C2×C42—24no—
729C2×C42—232no—
730C2×C42—24no—
731C2×C42—24no—
732C2×C42—42no—
733C2×C42—42no—
734C2×C42—42no—
735C2×C42—42no—
736C2×C42—42no—
737C2×C42—42no—
738C2×C42—42no—
739C2×C42—42no—
740C2×C42—42no—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2414yes—
745C2×C42C2414yes—
746C2×C42C2414yes—
747C2×C42C2414yes—
748C2×C42C2414yes—
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2414yes—
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2414yes—
775#95C2414yes—
776#95C2414yes—
777#95C2414yes—
778#95C2414yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2414yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2414yes—
800#95C2414yes—
801#95C2414yes—
802#95C2414yes—
803#95C2414yes—
804#95C2414yes—
805#95C2414yes—
806#95C2414yes—
807#95C2414yes—
808#95C2414yes—
809#95C2414yes—
810#95C2414yes—
811#95C2414yes—
812#95C2414yes—
813#95C2414yes—
814#95C2414yes—
815#95C2414yes—
816#95C2414yes—
817#95C2414yes—
818#95C2414yes—
819#95C2414yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2414yes—
826#95C2414yes—
827#95C2414yes—
828#95C2414yes—
829#95C2414yes—
830C24—22no—
831C24—22no—
832C24—22no—
833C24—22no—
834C24—22no—
835C24—22no—
836C24—22no—
837C24—22no—
838C24—22no—
839C24—22no—
840C24—22no—
841C24—22no—
842C24C2×#4114yes—
843C24C2×#4114yes—
844C24C2512yes—
845C24C2512yes—
846C24C2511yescharacteristic
847C2×Q8—28no—
848C2×Q8—28no—
849C2×Q8—44no—
850C2×Q8—44no—
851C2×Q8—44no—
852C2×Q8—44no—
853C2×Q8—44no—
854C2×Q8—44no—
855C2×Q8—44no—
856C2×Q8—88no—
857C2×Q8—88no—
858C2×Q8—88no—
859C2×D4—28no—
860C2×D4—28no—
861C2×D4—44no—
862C2×D4—416no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—28no—
874C22×C4—28no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
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—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—28no—
948C22×C4—28no—
949C22×C4—28no—
950C22×C4—28no—
951C22×C4—416no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—44no—
955C22×C4—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—416no—
964C22×C4—416no—
965C22×C4—88no—
966C22×C4—88no—
967C22×C4—88no—
968C22×C4C2×#4114yes—
969C22×C4C2×#4114yes—
970C22×C4C2×#4114yes—
971C22×C4C2×#4114yes—
972C22×C4C2×#41116yes—
973C22×C42−1+414yes—
974C22×C4C2512yes—
975C22×C4C2512yes—
976C22×C4C2512yes—
977C22×C4C2512yes—
978C22×C4C2512yes—
979C22×C4C2512yes—
980C22×C4C2512yes—
981C22×C4C2512yes—
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—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—44no—
1019C4⋊C4—44no—
1020C4⋊C4—44no—
1021C4⋊C4—44no—
1022C4⋊C4—44no—
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—
1037C22⋊C4—28no—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—28no—
1042C22⋊C4—28no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—44no—
1048C22⋊C4—44no—
1049C22⋊C4—44no—
1050C22⋊C4—44no—
1051C22⋊C4—44no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4C2×#41116yes—
1059C42—28no—
1060C42—28no—
1061C42—28no—
1062C42—28no—
1063C42—28no—
1064C42—28no—
1065C42—28no—
1066C42—28no—
1067C42—44no—
1068C42—44no—
1069C42—44no—
1070C42—44no—
1071C42—44no—
1072C42—44no—
1073C42—44no—
1074C42—44no—
1075C42—44no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—28no—
1089C23—28no—
1090C23—28no—
1091C23—28no—
1092C23—28no—
1093C23—28no—
1094C23—44no—
1095C23—44no—
1096C23—44no—
1097C23—44no—
1098C23—44no—
1099C23—44no—
1100C23—44no—
1101C23—44no—
1102C23C22×#4114yes—
1103C23C22×#4114yes—
1104C23C22×#4112yes—
1105C23C22×#4112yes—
1106C23C2×2−1+412yes—
1107C23#58512yes—
1108C23#58512yes—
1109C23#58512yes—
1110C23#58512yes—
1111C23C2611yescharacteristic
1112Q8—88no—
1113Q8—88no—
1114Q8—88no—
1115D4—416no—
1116C2×C4—22no—
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—28no—
1127C2×C4—28no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—28no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
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—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—416no—
1204C2×C4—416no—
1205C2×C4—416no—
1206C2×C4—44no—
1207C2×C4—44no—
1208C2×C4—44no—
1209C2×C4—44no—
1210C2×C4—44no—
1211C2×C4—44no—
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—88no—
1231C2×C4—88no—
1232C2×C4—88no—
1233C2×C4C22×#4114yes—
1234C2×C4C22×#4114yes—
1235C2×C4C22×#4114yes—
1236C2×C4C22×#4114yes—
1237C2×C4C2×2−1+414yes—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—416no—
1252C22—416no—
1253C22—42no—
1254C22#346114yes—
1255C22#347514yes—
1256C22#349114yes—
1257C22#349514yes—
1258C22#352114yes—
1259C22#356514yes—
1260C22#356814yes—
1261C22C23×#4111yescharacteristic
1262C22C23×#4111yescharacteristic
1263C22C22×2−1+411yescharacteristic
1264C22C2×#58511yescharacteristic
1265C22C2×#58511yescharacteristic
1266C22C2×#58511yescharacteristic
1267C22C2×#58511yescharacteristic
1268C4—24no—
1269C4—24no—
1270C4—24no—
1271C4—24no—
1272C4—24no—
1273C4—42no—
1274C4—42no—
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—
1296C4—42no—
1297C2—44no—
1298C2—44no—
1299C2#3800118yesdirect product factor
1300C2C2×#346111yescharacteristic
1301C2C2×#347511yescharacteristic
1302C2C2×#356811yescharacteristic
1303C2C2×#356511yescharacteristic
1304C2C2×#349111yescharacteristic
1305C2C2×#352111yescharacteristic
1306C2C2×#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×#2766C2semidirect
2. C2×#2763C2semidirect
3. C2×#2762C2semidirect
4. C2×#2745C2semidirect
5. C2×#2739C2semidirect
6. C2×#2698C2semidirect
9. #38001C2direct (N × H)
10. C2×#2855C2semidirect
11. C2×#2612C2semidirect
12. C2×#2605C2semidirect
15. C2×#2527C2semidirect
16. C2×#2527C2semidirect
17. C2×#2530C2semidirect
18. C2×#2514C2semidirect
19. C2×#2515C2semidirect
20. C2×#2524C2semidirect
21. C2×#2524C2semidirect
22. C2×#2520C2semidirect
23. C2×#2523C2semidirect
24. C2×#2493C2semidirect
25. C2×#2665C2semidirect
27. C2×#2373C2semidirect
28. C2×#2368C2semidirect
29. C2×#2332C2semidirect
32. C2×#2283C2semidirect
39. #2855C22semidirect
40. #2766C22semidirect
41. #2763C22semidirect
42. #2762C22semidirect
43. #2745C22semidirect
44. #2739C22semidirect
45. #2698C22semidirect
48. #2665C22semidirect
50. #2612C22semidirect
51. #2605C22semidirect
54. #2530C22semidirect
55. #2527C22semidirect
56. #2527C22semidirect
57. #2524C22semidirect
58. #2524C22semidirect
59. #2523C22semidirect
60. #2520C22semidirect
61. #2515C22semidirect
62. #2514C22semidirect
63. #2493C22semidirect
104. #2373C22semidirect
105. #2368C22semidirect
106. #2332C22semidirect
177. #2283C22semidirect
1299. C2#38001direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#27662
C2×#27632
C2×#27622
C2×#27452
C2×#27392
C2×#26982
C2×#26952
C2×#26872
#380012
C2×#28552
C2×#26122
C2×#26052
C2×#25762
C2×#25722
C2×#25272
C2×#25302
C2×#25142
C2×#25152
C2×#25242
C2×#25202
C2×#25232
C2×#24932
C2×#26652
C2×#26382
C2×#23732
C2×#23682
C2×#23322
C2×#23182
C2×C4×#1232
C2×#22832