Finite Group Databasebeta

← C2×#47534 #7700906

Subgroups — C2×#47534 #7700906

Order 512.

4930 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2811C211yesmaximal, characteristic, complemented
2C2×#2798C211yesmaximal, characteristic, complemented
3C2×#2763C211yesmaximal, characteristic, complemented
4C2×#2759C211yesmaximal, characteristic, complemented
5C2×#2759C211yesmaximal, characteristic, complemented
6C2×#2758C211yesmaximal, characteristic, complemented
7C2×#2751C211yesmaximal, characteristic
8C2×#2737C211yesmaximal, characteristic
9C2×#2731C211yesmaximal, characteristic
10C2×#2723C211yesmaximal, characteristic
11C2×#2698C211yesmaximal, characteristic, complemented
12C2×#2689C211yesmaximal, characteristic, complemented
13#47534C2132yesmaximal, direct product factor
14C2×#2838C211yesmaximal, characteristic, complemented
15C2×#2607C211yesmaximal, characteristic, complemented
16C2×#2604C211yesmaximal, characteristic, complemented
17C2×#2574C211yesmaximal, characteristic, complemented
18C2×#2560C211yesmaximal, characteristic
19C2×#2556C211yesmaximal, characteristic, complemented
20C2×#2527C211yesmaximal, characteristic, complemented
21C2×#2532C211yesmaximal, characteristic, complemented
22C2×#2532C211yesmaximal, characteristic, complemented
23C2×#2514C211yesmaximal, characteristic, complemented
24C2×#2489C211yesmaximal, characteristic, complemented
25C2×#2520C211yesmaximal, characteristic, complemented
26C2×#2448C211yesmaximal, characteristic
27C2×#2469C211yesmaximal, characteristic, complemented
28C2×#2446C211yesmaximal, characteristic, complemented
29C2×#2462C211yesmaximal, characteristic, complemented
30C2×#2337C211yesmaximal, characteristic
31C2×#2331C211yesmaximal, characteristic, complemented
32C2×#2320C211yesmaximal, characteristic, complemented
33C22×C4⋊Q8C2211yescharacteristic
34C22×#126C2211yescharacteristic
35C22×#126C2211yescharacteristic
36C22×#125C2211yescharacteristic
37C22×#124C2211yescharacteristic
38C22×C22⋊Q8C2211yescharacteristic
39C22×C22⋊Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2838C22116yescomplemented
43#2811C22116yescomplemented
44#2798C22116yescomplemented
45#2763C22116yescomplemented
46#2759C22116yescomplemented
47#2759C22116yescomplemented
48#2758C22116yescomplemented
49#2751C22116yes—
50#2737C22116yes—
51#2731C22116yes—
52#2723C22116yes—
53#2698C22116yescomplemented
54#2689C22116yescomplemented
55#2607C22116yescomplemented
56#2604C22116yescomplemented
57#2574C22116yescomplemented
58#2560C22116yes—
59#2556C22116yescomplemented
60#2532C22116yescomplemented
61#2532C22116yescomplemented
62#2527C22116yescomplemented
63#2520C22116yescomplemented
64#2514C22116yescomplemented
65#2489C22116yescomplemented
66#2469C22116yescomplemented
67#2462C22116yescomplemented
68#2448C22116yes—
69#2446C22116yescomplemented
70C2×#401C2211yescharacteristic
71C2×#401C2211yescharacteristic
72C2×#400C2211yescharacteristic
73C2×#400C2211yescharacteristic
74C2×#400C2211yescharacteristic
75C2×#400C2211yescharacteristic
76C2×#400C2211yescharacteristic
77C2×#400C2211yescharacteristic
78C2×#400C2211yescharacteristic
79C2×#400C2211yescharacteristic
80C2×#400C2211yescharacteristic
81C2×#399C2211yescharacteristic
82C2×#399C2211yescharacteristic
83C2×#399C2211yescharacteristic
84C2×#398C2211yescharacteristic
85C2×#398C2211yescharacteristic
86C2×#398C2211yescharacteristic
87C2×#398C2211yescharacteristic
88C2×#398C2211yescharacteristic
89C2×#397C2211yescharacteristic
90C2×#397C2211yescharacteristic
91C2×#397C2211yescharacteristic
92C2×#397C2211yescharacteristic
93C2×#397C2211yescharacteristic
94C2×#397C2211yescharacteristic
95C2×#397C2211yescharacteristic
96C2×#397C2211yescharacteristic
97C2×#397C2211yescharacteristic
98C2×#396C2211yescharacteristic
99C2×#396C2211yescharacteristic
100C2×#395C2211yescharacteristic
101C2×#395C2211yescharacteristic
102C2×#395C2211yescharacteristic
103C2×#395C2211yescharacteristic
104C2×#395C2211yescharacteristic
105C2×#395C2211yescharacteristic
106C2×#395C2211yescharacteristic
107C2×#395C2211yescharacteristic
108C2×#394C2211yescharacteristic
109C2×#394C2211yescharacteristic
110C2×#393C2211yescharacteristic
111C2×#393C2211yescharacteristic
112C2×#393C2211yescharacteristic
113C2×#393C2211yescharacteristic
114C2×#393C2211yescharacteristic
115C2×#393C2211yescharacteristic
116C2×#393C2211yescharacteristic
117C2×#393C2211yescharacteristic
118#2337C22116yes—
119#2331C22116yescomplemented
120#2320C22116yescomplemented
121C2×#391C2211yescharacteristic
122C2×#391C2211yescharacteristic
123C2×#391C2211yescharacteristic
124C2×#391C2211yescharacteristic
125C2×#391C2211yescharacteristic
126C2×#391C2211yescharacteristic
127C2×#391C2211yescharacteristic
128C2×#391C2211yescharacteristic
129C2×#391C2211yescharacteristic
130C2×#391C2211yescharacteristic
131C2×#391C2211yescharacteristic
132C2×#391C2211yescharacteristic
133C2×#391C2211yescharacteristic
134C2×#391C2211yescharacteristic
135C2×#391C2211yescharacteristic
136C2×#391C2211yescharacteristic
137C2×#391C2211yescharacteristic
138C2×#391C2211yescharacteristic
139C2×#391C2211yescharacteristic
140C2×#390C2211yescharacteristic
141C2×#390C2211yescharacteristic
142C2×#389C2211yescharacteristic
143C2×#389C2211yescharacteristic
144C2×#389C2211yescharacteristic
145C2×#389C2211yescharacteristic
146C2×#389C2211yescharacteristic
147C2×#389C2211yescharacteristic
148C2×#389C2211yescharacteristic
149C2×#388C2211yescharacteristic
150C2×#388C2211yescharacteristic
151C2×#388C2211yescharacteristic
152C2×#388C2211yescharacteristic
153C2×#388C2211yescharacteristic
154C2×#388C2211yescharacteristic
155C2×#388C2211yescharacteristic
156C2×#388C2211yescharacteristic
157C2×#388C2211yescharacteristic
158C2×#388C2211yescharacteristic
159C2×#388C2211yescharacteristic
160C2×#388C2211yescharacteristic
161C2×#388C2211yescharacteristic
162C2×#388C2211yescharacteristic
163C2×#388C2211yescharacteristic
164C2×#388C2211yescharacteristic
165C2×#388C2211yescharacteristic
166C2×#388C2211yescharacteristic
167C2×#388C2211yescharacteristic
168C2×#388C2211yescharacteristic
169C2×#387C2211yescharacteristic
170C2×#387C2211yescharacteristic
171C2×#387C2211yescharacteristic
172C2×#387C2211yescharacteristic
173C2×#387C2211yescharacteristic
174C2×#387C2211yescharacteristic
175C2×#387C2211yescharacteristic
176C2×#387C2211yescharacteristic
177C2×#387C2211yescharacteristic
178C2×#387C2211yescharacteristic
179C2×#387C2211yescharacteristic
180C2×#387C2211yescharacteristic
181C2×#387C2211yescharacteristic
182C2×#387C2211yescharacteristic
183C2×#387C2211yescharacteristic
184C2×#387C2211yescharacteristic
185C2×#387C2211yescharacteristic
186C2×#387C2211yescharacteristic
187C2×#387C2211yescharacteristic
188C2×#387C2211yescharacteristic
189C2×#387C2211yescharacteristic
190C2×#387C2211yescharacteristic
191C2×#386C2211yescharacteristic
192C2×#386C2211yescharacteristic
193C2×#385C2211yescharacteristic
194C2×#385C2211yescharacteristic
195C2×#385C2211yescharacteristic
196C2×#385C2211yescharacteristic
197C2×#383C2211yescharacteristic
198C2×#383C2211yescharacteristic
199C2×#383C2211yescharacteristic
200C2×#383C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C2×#382C2211yescharacteristic
203C2×#382C2211yescharacteristic
204C2×#382C2211yescharacteristic
205C2×#381C2211yescharacteristic
206C2×#381C2211yescharacteristic
207C2×#380C2211yescharacteristic
208C2×C4×C4⋊C4C2211yescharacteristic
209C2×C4×C4⋊C4C2211yescharacteristic
210C2×C4×C4⋊C4C2211yescharacteristic
211C2×C4×C4⋊C4C2211yescharacteristic
212C2×C4×C4⋊C4C2211yescharacteristic
213C2×C4×C4⋊C4C2211yescharacteristic
214C2×C4×C22⋊C4C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C2×C4×C22⋊C4C2211yescharacteristic
217C2×#376C2211yescharacteristic
218C2×#376C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×Q8C2311yescharacteristic
223C23×Q8C2311yescharacteristic
224C23×Q8C2311yescharacteristic
225C23×D4C2311yescharacteristic
226C24×C4C2311yescharacteristic
227C24×C4C2311yescharacteristic
228C2×C4⋊Q8—28no—
229C2×C4⋊Q8C2318yes—
230C2×#126—44no—
231C2×#126—44no—
232C2×#126C2318yes—
233C2×#126C2318yes—
234C2×#125—44no—
235C2×#125C2318yes—
236C2×#124—28no—
237C2×#124C2318yes—
238C2×C22⋊Q8—44no—
239C2×C22⋊Q8—44no—
240C2×C22⋊Q8C2318yes—
241C2×C22⋊Q8C2318yes—
242C2×C4×Q8—28no—
243C2×C4×Q8—44no—
244C2×C4×Q8C2318yes—
245C2×C4×Q8C2318yes—
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×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×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×C22⋊C4C2311yescharacteristic
296C22×C22⋊C4C2311yescharacteristic
297C22×C22⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321C22×C42C2311yescharacteristic
322C22×C42C2311yescharacteristic
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2311yescharacteristic
326#401C2318yes—
327#401C2318yes—
328#400C2318yes—
329#400C2318yes—
330#400C2318yes—
331#400C2318yes—
332#400C2318yes—
333#400C2318yes—
334#400C2318yes—
335#400C2318yes—
336#400C2318yes—
337#399C2318yes—
338#399C2318yes—
339#399C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#397C2318yes—
346#397C2318yes—
347#397C2318yes—
348#397C2318yes—
349#397C2318yes—
350#397C2318yes—
351#397C2318yes—
352#397C2318yes—
353#397C2318yes—
354#396C2318yes—
355#396C2318yes—
356#395C2318yes—
357#395C2318yes—
358#395C2318yes—
359#395C2318yes—
360#395C2318yes—
361#395C2318yes—
362#395C2318yes—
363#395C2318yes—
364#394C2318yes—
365#394C2318yes—
366#393C2318yes—
367#393C2318yes—
368#393C2318yes—
369#393C2318yes—
370#393C2318yes—
371#393C2318yes—
372#393C2318yes—
373#393C2318yes—
374#391C2318yes—
375#391C2318yes—
376#391C2318yes—
377#391C2318yes—
378#391C2318yes—
379#391C2318yes—
380#391C2318yes—
381#391C2318yes—
382#391C2318yes—
383#391C2318yes—
384#391C2318yes—
385#391C2318yes—
386#391C2318yes—
387#391C2318yes—
388#391C2318yes—
389#391C2318yes—
390#391C2318yes—
391#391C2318yes—
392#391C2318yes—
393#390C2318yes—
394#390C2318yes—
395#389C2318yes—
396#389C2318yes—
397#389C2318yes—
398#389C2318yes—
399#389C2318yes—
400#389C2318yes—
401#389C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#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#386C2318yes—
445#386C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#383C2318yes—
451#383C2318yes—
452#383C2318yes—
453#383C2318yes—
454#382C2318yes—
455#382C2318yes—
456#382C2318yes—
457#382C2318yes—
458#381C2318yes—
459#381C2318yes—
460#380C2318yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2318yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C22⋊C4C2318yes—
468C4×C22⋊C4C2318yes—
469C4×C22⋊C4C2318yes—
470#376C2318yes—
471#376C2318yes—
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
535C2×#95C2311yescharacteristic
536C2×#95C2311yescharacteristic
537C2×#95C2311yescharacteristic
538C25C2411yescharacteristic
539C25C2411yescharacteristic
540C22×Q8—24no—
541C22×Q8—24no—
542C22×Q8—24no—
543C22×Q8—42no—
544C22×Q8—42no—
545C22×Q8—42no—
546C22×Q8—42no—
547C22×Q8—42no—
548C22×Q8—42no—
549C22×Q8—42no—
550C22×Q8—42no—
551C22×Q8—42no—
552C22×Q8—42no—
553C22×Q8—42no—
554C22×Q8—42no—
555C22×Q8—42no—
556C22×Q8—42no—
557C22×Q8#4118yes—
558C22×Q8C2414yes—
559C22×Q8C2414yes—
560C22×Q8C2414yes—
561C22×Q8C2414yes—
562C22×Q8C2414yes—
563C22×Q8C2414yes—
564C22×D4—24no—
565C22×D4—42no—
566C22×D4—42no—
567C22×D4C2414yes—
568C23×C4—24no—
569C23×C4—42no—
570C23×C4—42no—
571C23×C4—42no—
572C23×C4—42no—
573C23×C4—42no—
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×C4C2411yescharacteristic
596C23×C4C2411yescharacteristic
597C23×C4C2411yescharacteristic
598C23×C4C2411yescharacteristic
599C23×C4C2411yescharacteristic
600C23×C4C2411yescharacteristic
601C23×C4C2411yescharacteristic
602C23×C4C2411yescharacteristic
603C23×C4C2414yes—
604C23×C4C2414yes—
605C4⋊Q8—232no—
606#126—416no—
607#126—416no—
608#125—416no—
609#124—232no—
610C22⋊Q8—416no—
611C22⋊Q8—416no—
612C4×Q8—232no—
613C4×Q8—416no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—24no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—24no—
628C2×C4⋊C4—24no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—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⋊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×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×C22⋊C4—24no—
689C2×C22⋊C4—24no—
690C2×C22⋊C4—24no—
691C2×C22⋊C4—24no—
692C2×C22⋊C4—24no—
693C2×C22⋊C4—24no—
694C2×C22⋊C4—24no—
695C2×C22⋊C4—24no—
696C2×C22⋊C4—24no—
697C2×C22⋊C4—42no—
698C2×C22⋊C4—42no—
699C2×C22⋊C4—42no—
700C2×C22⋊C4—42no—
701C2×C22⋊C4—42no—
702C2×C22⋊C4—42no—
703C2×C22⋊C4—42no—
704C2×C22⋊C4—42no—
705C2×C22⋊C4—42no—
706C2×C22⋊C4—42no—
707C2×C22⋊C4—42no—
708C2×C22⋊C4—42no—
709C2×C22⋊C4—42no—
710C2×C22⋊C4—42no—
711C2×C22⋊C4—42no—
712C2×C22⋊C4—42no—
713C2×C22⋊C4—42no—
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×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2414yes—
730C2×C22⋊C4C2414yes—
731C2×C22⋊C4C2414yes—
732C2×C22⋊C4C2414yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2414yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2414yes—
739C2×C22⋊C4C2414yes—
740C2×C42—24no—
741C2×C42—24no—
742C2×C42—24no—
743C2×C42—24no—
744C2×C42—24no—
745C2×C42—24no—
746C2×C42—24no—
747C2×C42—42no—
748C2×C42—42no—
749C2×C42—42no—
750C2×C42—42no—
751C2×C42—42no—
752C2×C42—42no—
753C2×C42—42no—
754C2×C42—42no—
755C2×C42—42no—
756C2×C42—42no—
757C2×C42C2414yes—
758C2×C42C2414yes—
759C2×C42C2414yes—
760C2×C42C2414yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2414yes—
767C2×C42C2414yes—
768C2×C42C2414yes—
769C2×C42C2414yes—
770C2×C42C2414yes—
771C2×C42C2414yes—
772C2×C42C2414yes—
773C2×C42C2414yes—
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—
830#95C2414yes—
831#95C2414yes—
832#95C2414yes—
833#95C2414yes—
834#95C2414yes—
835#95C2414yes—
836#95C2414yes—
837#95C2414yes—
838#95C2414yes—
839#95C2414yes—
840C24—22no—
841C24—22no—
842C24—22no—
843C24—22no—
844C24—22no—
845C24—22no—
846C24—22no—
847C24—22no—
848C24—22no—
849C24—22no—
850C24—22no—
851C24—22no—
852C24—22no—
853C24—22no—
854C24C2512yes—
855C24C2512yes—
856C24C2511yescharacteristic
857C2×Q8—28no—
858C2×Q8—28no—
859C2×Q8—28no—
860C2×Q8—44no—
861C2×Q8—416no—
862C2×Q8—44no—
863C2×Q8—44no—
864C2×Q8—44no—
865C2×Q8—44no—
866C2×Q8—44no—
867C2×Q8—44no—
868C2×Q8—44no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—44no—
873C2×Q8—44no—
874C2×Q8—44no—
875C2×Q8—416no—
876C2×Q8—88no—
877C2×Q8—88no—
878C2×Q8—88no—
879C2×Q8—88no—
880C2×Q8C2×#41116yes—
881C2×D4—28no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—88no—
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—22no—
948C22×C4—22no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—22no—
952C22×C4—22no—
953C22×C4—22no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—22no—
966C22×C4—28no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4—88no—
973C22×C4—88no—
974C22×C4C2×#4114yes—
975C22×C4C2×#4114yes—
976C22×C4C2×#4114yes—
977C22×C4H(5,𝔽2)14yes—
978C22×C42−1+414yes—
979C22×C42−1+414yes—
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—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—28no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—28no—
1015C4⋊C4—28no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—28no—
1019C4⋊C4—28no—
1020C4⋊C4—28no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—44no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—44no—
1029C4⋊C4—44no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4—44no—
1035C4⋊C4—44no—
1036C4⋊C4—44no—
1037C4⋊C4—44no—
1038C4⋊C4—44no—
1039C4⋊C4—44no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—28no—
1052C22⋊C4—28no—
1053C22⋊C4—28no—
1054C22⋊C4—28no—
1055C22⋊C4—44no—
1056C22⋊C4—44no—
1057C22⋊C4—44no—
1058C22⋊C4—44no—
1059C22⋊C4—44no—
1060C22⋊C4—44no—
1061C22⋊C4—44no—
1062C22⋊C4—44no—
1063C22⋊C4—44no—
1064C22⋊C4—44no—
1065C22⋊C4—44no—
1066C22⋊C4—44no—
1067C22⋊C4—44no—
1068C22⋊C4—44no—
1069C22⋊C4—44no—
1070C22⋊C4—44no—
1071C22⋊C4—44no—
1072C42—28no—
1073C42—28no—
1074C42—28no—
1075C42—28no—
1076C42—28no—
1077C42—28no—
1078C42—28no—
1079C42—44no—
1080C42—44no—
1081C42—44no—
1082C42—44no—
1083C42—44no—
1084C42—44no—
1085C42—44no—
1086C42—44no—
1087C42—44no—
1088C42—44no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—44no—
1104C23—44no—
1105C23—44no—
1106C23—44no—
1107C23—44no—
1108C23—44no—
1109C23—44no—
1110C23—44no—
1111C23—44no—
1112C23—44no—
1113C23—44no—
1114C23—44no—
1115C23—44no—
1116C23—44no—
1117C23C22×#4112yes—
1118C23C2×H(5,𝔽2)12yes—
1119C23C2×2−1+412yes—
1120C23C2×2−1+412yes—
1121C23#58512yes—
1122C23#58512yes—
1123C23#58512yes—
1124C23C2611yescharacteristic
1125Q8—416no—
1126Q8—416no—
1127Q8—88no—
1128Q8—88no—
1129Q8—88no—
1130Q8—88no—
1131D4—88no—
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—28no—
1145C2×C4—28no—
1146C2×C4—28no—
1147C2×C4—28no—
1148C2×C4—28no—
1149C2×C4—28no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—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—44no—
1220C2×C4—44no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—44no—
1224C2×C4—44no—
1225C2×C4—44no—
1226C2×C4—44no—
1227C2×C4—44no—
1228C2×C4—44no—
1229C2×C4—44no—
1230C2×C4—44no—
1231C2×C4—44no—
1232C2×C4—44no—
1233C2×C4—44no—
1234C2×C4—44no—
1235C2×C4—44no—
1236C2×C4—44no—
1237C2×C4—44no—
1238C2×C4—44no—
1239C2×C4—44no—
1240C2×C4—44no—
1241C2×C4—44no—
1242C2×C4—88no—
1243C2×C4—88no—
1244C2×C4C22×#4114yes—
1245C2×C4C22×#4114yes—
1246C2×C4C22×#4114yes—
1247C2×C4C2×H(5,𝔽2)14yes—
1248C2×C4C2×2−1+414yes—
1249C2×C4C2×2−1+414yes—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—88no—
1265C22—88no—
1266C22#349114yes—
1267C22#351814yes—
1268C22#352214yes—
1269C22#354014yes—
1270C22#355514yes—
1271C22#356114yes—
1272C22#356414yes—
1273C22C23×#4111yescharacteristic
1274C22C22×H(5,𝔽2)11yescharacteristic
1275C22C22×2−1+411yescharacteristic
1276C22C22×2−1+411yescharacteristic
1277C22C2×#58511yescharacteristic
1278C22C2×#58511yescharacteristic
1279C22C2×#58511yescharacteristic
1280C4—24no—
1281C4—24no—
1282C4—24no—
1283C4—24no—
1284C4—24no—
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C2—82no—
1310C2—82no—
1311C2#4753418yesdirect product factor
1312C2C2×#354011yescharacteristic
1313C2C2×#356111yescharacteristic
1314C2C2×#356411yescharacteristic
1315C2C2×#355511yescharacteristic
1316C2C2×#349111yescharacteristic
1317C2C2×#352211yescharacteristic
1318C2C2×#351811yescharacteristic
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×#2811C2semidirect
2. C2×#2798C2semidirect
3. C2×#2763C2semidirect
4. C2×#2759C2semidirect
5. C2×#2759C2semidirect
6. C2×#2758C2semidirect
11. C2×#2698C2semidirect
12. C2×#2689C2semidirect
13. #47534C2direct (N × H)
14. C2×#2838C2semidirect
15. C2×#2607C2semidirect
16. C2×#2604C2semidirect
17. C2×#2574C2semidirect
19. C2×#2556C2semidirect
20. C2×#2527C2semidirect
21. C2×#2532C2semidirect
22. C2×#2532C2semidirect
23. C2×#2514C2semidirect
24. C2×#2489C2semidirect
25. C2×#2520C2semidirect
27. C2×#2469C2semidirect
28. C2×#2446C2semidirect
29. C2×#2462C2semidirect
31. C2×#2331C2semidirect
32. C2×#2320C2semidirect
42. #2838C22semidirect
43. #2811C22semidirect
44. #2798C22semidirect
45. #2763C22semidirect
46. #2759C22semidirect
47. #2759C22semidirect
48. #2758C22semidirect
53. #2698C22semidirect
54. #2689C22semidirect
55. #2607C22semidirect
56. #2604C22semidirect
57. #2574C22semidirect
59. #2556C22semidirect
60. #2532C22semidirect
61. #2532C22semidirect
62. #2527C22semidirect
63. #2520C22semidirect
64. #2514C22semidirect
65. #2489C22semidirect
66. #2469C22semidirect
67. #2462C22semidirect
69. #2446C22semidirect
119. #2331C22semidirect
120. #2320C22semidirect
1311. C2#47534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#28112
C2×#27982
C2×#27632
C2×#27592
C2×#27582
C2×#27512
C2×#27372
C2×#27312
C2×#27232
C2×#26982
C2×#26892
#475342
C2×#28382
C2×#26072
C2×#26042
C2×#25742
C2×#25602
C2×#25562
C2×#25272
C2×#25322
C2×#25142
C2×#24892
C2×#25202
C2×#24482
C2×#24692
C2×#24462
C2×#24622
C2×#23372
C2×#23312
C2×#23202