Finite Group Databasebeta

← C2×#46169 #7702736

Subgroups — C2×#46169 #7702736

Order 512.

4930 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2810C211yesmaximal, characteristic, complemented
2C2×#2767C211yesmaximal, characteristic, complemented
3C2×#2767C211yesmaximal, characteristic, complemented
4C2×#2767C211yesmaximal, characteristic, complemented
5C2×#2767C211yesmaximal, characteristic, complemented
6C2×#2767C211yesmaximal, characteristic, complemented
7C2×#2767C211yesmaximal, characteristic, complemented
8C2×#2726C211yesmaximal, characteristic, complemented
9C2×#2719C211yesmaximal, characteristic, complemented
10C2×#2719C211yesmaximal, characteristic, complemented
11C2×#2719C211yesmaximal, characteristic, complemented
12C2×#2719C211yesmaximal, characteristic, complemented
13#46169C2132yesmaximal, direct product factor
14C2×#2839C211yesmaximal, characteristic, complemented
15C2×#2839C211yesmaximal, characteristic, complemented
16C2×#2851C211yesmaximal, characteristic
17C2×#2851C211yesmaximal, characteristic
18C2×#2569C211yesmaximal, characteristic
19C2×#2569C211yesmaximal, characteristic
20C2×#2505C211yesmaximal, characteristic
21C2×#2505C211yesmaximal, characteristic
22C2×#2505C211yesmaximal, characteristic
23C2×#2505C211yesmaximal, characteristic
24C2×#2505C211yesmaximal, characteristic
25C2×#2505C211yesmaximal, characteristic
26C2×#2442C211yesmaximal, characteristic
27C2×#2442C211yesmaximal, characteristic
28C2×#2473C211yesmaximal, characteristic
29C2×#2473C211yesmaximal, characteristic
30C2×#2382C211yesmaximal, characteristic, complemented
31C2×#2382C211yesmaximal, characteristic, complemented
32C22×#387C211yesmaximal, characteristic
33C22×#125C2211yescharacteristic
34C22×#125C2211yescharacteristic
35C22×#125C2211yescharacteristic
36C22×#125C2211yescharacteristic
37C22×#125C2211yescharacteristic
38C22×#125C2211yescharacteristic
39C23×C4⋊C4C2211yescharacteristic
40C23×C4⋊C4C2211yescharacteristic
41C23×C42C2211yescharacteristic
42#2851C22116yes—
43#2851C22116yes—
44#2839C22116yescomplemented
45#2839C22116yescomplemented
46#2810C22116yescomplemented
47#2767C22116yescomplemented
48#2767C22116yescomplemented
49#2767C22116yescomplemented
50#2767C22116yescomplemented
51#2767C22116yescomplemented
52#2767C22116yescomplemented
53#2726C22116yescomplemented
54#2719C22116yescomplemented
55#2719C22116yescomplemented
56#2719C22116yescomplemented
57#2719C22116yescomplemented
58#2569C22116yes—
59#2569C22116yes—
60#2505C22116yes—
61#2505C22116yes—
62#2505C22116yes—
63#2505C22116yes—
64#2505C22116yes—
65#2505C22116yes—
66#2473C22116yes—
67#2473C22116yes—
68#2442C22116yes—
69#2442C22116yes—
70C2×#400C2211yescharacteristic
71C2×#400C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#400C2211yescharacteristic
80C2×#400C2211yescharacteristic
81C2×#400C2211yescharacteristic
82C2×#400C2211yescharacteristic
83C2×#400C2211yescharacteristic
84C2×#400C2211yescharacteristic
85C2×#400C2211yescharacteristic
86C2×#400C2211yescharacteristic
87C2×#400C2211yescharacteristic
88C2×#400C2211yescharacteristic
89C2×#400C2211yescharacteristic
90C2×#400C2211yescharacteristic
91C2×#400C2211yescharacteristic
92C2×#400C2211yescharacteristic
93C2×#400C2211yescharacteristic
94C2×#400C2211yescharacteristic
95C2×#400C2211yescharacteristic
96C2×#400C2211yescharacteristic
97C2×#400C2211yescharacteristic
98C2×#398C2211yescharacteristic
99C2×#398C2211yescharacteristic
100C2×#398C2211yescharacteristic
101C2×#398C2211yescharacteristic
102C2×#398C2211yescharacteristic
103C2×#398C2211yescharacteristic
104C2×#398C2211yescharacteristic
105C2×#398C2211yescharacteristic
106C2×#398C2211yescharacteristic
107C2×#398C2211yescharacteristic
108C2×#398C2211yescharacteristic
109C2×#398C2211yescharacteristic
110C2×#398C2211yescharacteristic
111C2×#398C2211yescharacteristic
112C2×#398C2211yescharacteristic
113C2×#398C2211yescharacteristic
114C2×#398C2211yescharacteristic
115C2×#398C2211yescharacteristic
116C2×#398C2211yescharacteristic
117C2×#398C2211yescharacteristic
118#2382C22116yescomplemented
119#2382C22116yescomplemented
120C2×#389C2211yescharacteristic
121C2×#389C2211yescharacteristic
122C2×#389C2211yescharacteristic
123C2×#389C2211yescharacteristic
124C2×#389C2211yescharacteristic
125C2×#389C2211yescharacteristic
126C2×#389C2211yescharacteristic
127C2×#389C2211yescharacteristic
128C2×#389C2211yescharacteristic
129C2×#389C2211yescharacteristic
130C2×#389C2211yescharacteristic
131C2×#389C2211yescharacteristic
132C2×#389C2211yescharacteristic
133C2×#389C2211yescharacteristic
134C2×#389C2211yescharacteristic
135C2×#389C2211yescharacteristic
136C2×#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×#387C22116yes—
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×#385C2211yescharacteristic
178C2×#385C2211yescharacteristic
179C2×#385C2211yescharacteristic
180C2×#385C2211yescharacteristic
181C2×#385C2211yescharacteristic
182C2×#385C2211yescharacteristic
183C2×#385C2211yescharacteristic
184C2×#385C2211yescharacteristic
185C2×#385C2211yescharacteristic
186C2×#385C2211yescharacteristic
187C2×#385C2211yescharacteristic
188C2×#385C2211yescharacteristic
189C2×#385C2211yescharacteristic
190C2×#385C2211yescharacteristic
191C2×#385C2211yescharacteristic
192C2×#385C2211yescharacteristic
193C2×#382C2211yescharacteristic
194C2×#382C2211yescharacteristic
195C2×#382C2211yescharacteristic
196C2×#382C2211yescharacteristic
197C2×#382C2211yescharacteristic
198C2×#382C2211yescharacteristic
199C2×#382C2211yescharacteristic
200C2×#382C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C2×#382C2211yescharacteristic
203C2×#380C2211yescharacteristic
204C2×#380C2211yescharacteristic
205C2×#380C2211yescharacteristic
206C2×#380C2211yescharacteristic
207C2×#380C2211yescharacteristic
208C2×#380C2211yescharacteristic
209C2×#380C2211yescharacteristic
210C2×#380C2211yescharacteristic
211C2×C4×C22⋊C4C2211yescharacteristic
212C2×C4×C22⋊C4C2211yescharacteristic
213C2×C4×C22⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C22×#95C2211yescharacteristic
216C22×#95C2211yescharacteristic
217C22×#95C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C24×C4C2311yescharacteristic
220C24×C4C2311yescharacteristic
221C24×C4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C2×#125—28no—
227C2×#125—28no—
228C2×#125—44no—
229C2×#125—44no—
230C2×#125—44no—
231C2×#125—44no—
232C2×#125C2318yes—
233C2×#125C2318yes—
234C2×#125C2318yes—
235C2×#125C2318yes—
236C2×#125C2318yes—
237C2×#125C2318yes—
238C22×C4⋊C4—28no—
239C22×C4⋊C4—44no—
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⋊C4C2318yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2318yes—
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊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×C42—44no—
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2318yes—
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320#400C2318yes—
321#400C2318yes—
322#400C2318yes—
323#400C2318yes—
324#400C2318yes—
325#400C2318yes—
326#400C2318yes—
327#400C2318yes—
328#400C2318yes—
329#400C2318yes—
330#400C2318yes—
331#400C2318yes—
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#400C2318yes—
336#400C2318yes—
337#400C2318yes—
338#400C2318yes—
339#400C2318yes—
340#400C2318yes—
341#400C2318yes—
342#400C2318yes—
343#400C2318yes—
344#400C2318yes—
345#400C2318yes—
346#400C2318yes—
347#400C2318yes—
348#398C2318yes—
349#398C2318yes—
350#398C2318yes—
351#398C2318yes—
352#398C2318yes—
353#398C2318yes—
354#398C2318yes—
355#398C2318yes—
356#398C2318yes—
357#398C2318yes—
358#398C2318yes—
359#398C2318yes—
360#398C2318yes—
361#398C2318yes—
362#398C2318yes—
363#398C2318yes—
364#398C2318yes—
365#398C2318yes—
366#398C2318yes—
367#398C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2318yes—
374#389C2318yes—
375#389C2318yes—
376#389C2318yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2318yes—
383#389C2318yes—
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#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2318yes—
429#385C2318yes—
430#385C2318yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2318yes—
436#385C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#382C2318yes—
441#382C2318yes—
442#382C2318yes—
443#382C2318yes—
444#382C2318yes—
445#382C2318yes—
446#382C2318yes—
447#382C2318yes—
448#382C2318yes—
449#382C2318yes—
450#380C2318yes—
451#380C2318yes—
452#380C2318yes—
453#380C2318yes—
454#380C2318yes—
455#380C2318yes—
456#380C2318yes—
457#380C2318yes—
458C4×C22⋊C4C2318yes—
459C4×C22⋊C4C2318yes—
460C4×C22⋊C4C2318yes—
461C4×C22⋊C4C2318yes—
462C2×#95C2318yes—
463C2×#95C2318yes—
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×#95C2318yes—
533C2×#95C2318yes—
534C2×#95C2311yescharacteristic
535C2×#95C2311yescharacteristic
536C2×#95C2311yescharacteristic
537C2×#95C2311yescharacteristic
538C25C2411yescharacteristic
539C23×C4—24no—
540C23×C4—24no—
541C23×C4—24no—
542C23×C4—24no—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—24no—
546C23×C4—24no—
547C23×C4—24no—
548C23×C4—24no—
549C23×C4—24no—
550C23×C4—42no—
551C23×C4—42no—
552C23×C4—42no—
553C23×C4—42no—
554C23×C4—42no—
555C23×C4—42no—
556C23×C4—42no—
557C23×C4—42no—
558C23×C4—42no—
559C23×C4—42no—
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2411yescharacteristic
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
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×C4C2414yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2414yes—
590C23×C4C2411yescharacteristic
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2411yescharacteristic
594C23×C4C2414yes—
595C23×C4C2414yes—
596C23×C4C2414yes—
597#125—232no—
598#125—232no—
599#125—416no—
600#125—416no—
601#125—416no—
602#125—416no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
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—232no—
623C2×C4⋊C4—416no—
624C2×C4⋊C4—42no—
625C2×C4⋊C4—42no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4—42no—
629C2×C4⋊C4—42no—
630C2×C4⋊C4—42no—
631C2×C4⋊C4—42no—
632C2×C4⋊C4—42no—
633C2×C4⋊C4—42no—
634C2×C4⋊C4—42no—
635C2×C4⋊C4—42no—
636C2×C4⋊C4—42no—
637C2×C4⋊C4—42no—
638C2×C4⋊C4—42no—
639C2×C4⋊C4—42no—
640C2×C4⋊C4—42no—
641C2×C4⋊C4—42no—
642C2×C4⋊C4—42no—
643C2×C4⋊C4—42no—
644C2×C4⋊C4—42no—
645C2×C4⋊C4—42no—
646C2×C4⋊C4—42no—
647C2×C4⋊C4—42no—
648C2×C4⋊C4—42no—
649C2×C4⋊C4—42no—
650C2×C4⋊C4—42no—
651C2×C4⋊C4—42no—
652C2×C4⋊C4—42no—
653C2×C4⋊C4—42no—
654C2×C4⋊C4—42no—
655C2×C4⋊C4—42no—
656C2×C4⋊C4—42no—
657C2×C4⋊C4—42no—
658C2×C4⋊C4—42no—
659C2×C4⋊C4—42no—
660C2×C4⋊C4#4118yes—
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×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×C22⋊C4—24no—
718C2×C22⋊C4—24no—
719C2×C22⋊C4—24no—
720C2×C22⋊C4—24no—
721C2×C22⋊C4—24no—
722C2×C22⋊C4—24no—
723C2×C22⋊C4—24no—
724C2×C22⋊C4—24no—
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×C42—24no—
734C2×C42—24no—
735C2×C42—24no—
736C2×C42—24no—
737C2×C42—416no—
738C2×C42—42no—
739C2×C42—42no—
740C2×C42—42no—
741C2×C42—42no—
742C2×C42—42no—
743C2×C42—42no—
744C2×C42—42no—
745C2×C42—42no—
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—
834C242−1+414yes—
835C242−1+414yes—
836C242−1+414yes—
837C24C2512yes—
838C24C2511yescharacteristic
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
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—22no—
874C22×C4—22no—
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—28no—
890C22×C4—28no—
891C22×C4—28no—
892C22×C4—28no—
893C22×C4—28no—
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—28no—
931C22×C4—28no—
932C22×C4—28no—
933C22×C4—28no—
934C22×C4—28no—
935C22×C4—28no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—44no—
945C22×C4—44no—
946C22×C4—416no—
947C22×C4—416no—
948C22×C4—416no—
949C22×C4—416no—
950C22×C4—416no—
951C22×C4—88no—
952C22×C4—88no—
953C22×C4C2×#4114yes—
954C22×C4C2×#4114yes—
955C22×C4C2×#4114yes—
956C22×C4H(5,𝔽2)14yes—
957C22×C4C2512yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2512yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2512yes—
967C22×C4C2512yes—
968C22×C4C2512yes—
969C22×C4C2512yes—
970C22×C4C2512yes—
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2512yes—
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—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—28no—
992C4⋊C4—28no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—44no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—44no—
1010C4⋊C4—44no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
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—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4C2×#41116yes—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C42—28no—
1052C42—28no—
1053C42—28no—
1054C42—28no—
1055C42—44no—
1056C42—44no—
1057C42—44no—
1058C42—44no—
1059C42—44no—
1060C42—44no—
1061C42—44no—
1062C42—44no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—28no—
1068C23—28no—
1069C23—28no—
1070C23—28no—
1071C23—28no—
1072C23—28no—
1073C23#564116yes—
1074C23C22×#4112yes—
1075C23C2×H(5,𝔽2)12yes—
1076C23C2×2−1+414yes—
1077C23C2×2−1+414yes—
1078C23C2×2−1+414yes—
1079C23C2×2−1+412yes—
1080C23C2×2−1+412yes—
1081C23C2×2−1+412yes—
1082C23#58512yes—
1083C23#58512yes—
1084C23C2611yescharacteristic
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—28no—
1094C2×C4—28no—
1095C2×C4—28no—
1096C2×C4—28no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
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—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—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—416no—
1176C2×C4—416no—
1177C2×C4—416no—
1178C2×C4—416no—
1179C2×C4—416no—
1180C2×C4—44no—
1181C2×C4—44no—
1182C2×C4—44no—
1183C2×C4—44no—
1184C2×C4—44no—
1185C2×C4—44no—
1186C2×C4—44no—
1187C2×C4—44no—
1188C2×C4—44no—
1189C2×C4—44no—
1190C2×C4—44no—
1191C2×C4—44no—
1192C2×C4—44no—
1193C2×C4—44no—
1194C2×C4—44no—
1195C2×C4—44no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—44no—
1199C2×C4—44no—
1200C2×C4—44no—
1201C2×C4—44no—
1202C2×C4—44no—
1203C2×C4—44no—
1204C2×C4—44no—
1205C2×C4—44no—
1206C2×C4—88no—
1207C2×C4—88no—
1208C2×C4C22×#4114yes—
1209C2×C4C22×#4114yes—
1210C2×C4C22×#4114yes—
1211C2×C4C2×H(5,𝔽2)14yes—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—232no—
1219C22#349514yes—
1220C22#351614yes—
1221C22#352014yes—
1222C22C2×#56418yes—
1223C22C2×#56414yes—
1224C22#353514yes—
1225C22#354114yes—
1226C22#356414yes—
1227C22C23×#4111yescharacteristic
1228C22C22×H(5,𝔽2)11yescharacteristic
1229C22C22×2−1+411yescharacteristic
1230C22C22×2−1+411yescharacteristic
1231C22C22×2−1+411yescharacteristic
1232C22C2×#58511yescharacteristic
1233C22C2×#58511yescharacteristic
1234C4—24no—
1235C4—24no—
1236C4—24no—
1237C4—24no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—42no—
1242C4—42no—
1243C4—42no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—42no—
1248C4—42no—
1249C4—42no—
1250C4—42no—
1251C4—42no—
1252C4—42no—
1253C4—42no—
1254C4—42no—
1255C4—42no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—42no—
1263C4—42no—
1264C2—28no—
1265C2#4616918yesdirect product factor
1266C2C22×#56411yescharacteristic
1267C2C2×#354111yescharacteristic
1268C2C2×#353511yescharacteristic
1269C2C2×#356411yescharacteristic
1270C2C2×#352011yescharacteristic
1271C2C2×#351611yescharacteristic
1272C2C2×#349511yescharacteristic
subgroupG/H
center, socleC24C25
commutator, Frattini, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2810C2semidirect
2. C2×#2767C2semidirect
3. C2×#2767C2semidirect
4. C2×#2767C2semidirect
5. C2×#2767C2semidirect
6. C2×#2767C2semidirect
7. C2×#2767C2semidirect
8. C2×#2726C2semidirect
9. C2×#2719C2semidirect
10. C2×#2719C2semidirect
11. C2×#2719C2semidirect
12. C2×#2719C2semidirect
13. #46169C2direct (N × H)
14. C2×#2839C2semidirect
15. C2×#2839C2semidirect
30. C2×#2382C2semidirect
31. C2×#2382C2semidirect
44. #2839C22semidirect
45. #2839C22semidirect
46. #2810C22semidirect
47. #2767C22semidirect
48. #2767C22semidirect
49. #2767C22semidirect
50. #2767C22semidirect
51. #2767C22semidirect
52. #2767C22semidirect
53. #2726C22semidirect
54. #2719C22semidirect
55. #2719C22semidirect
56. #2719C22semidirect
57. #2719C22semidirect
118. #2382C22semidirect
119. #2382C22semidirect
1265. C2#46169direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28102
C2×#27672
C2×#27262
C2×#27192
#461692
C2×#28392
C2×#28512
C2×#25692
C2×#25052
C2×#24422
C2×#24732
C2×#23822
C22×#3872