Finite Group Databasebeta

← C2×#52722 #8092564

Subgroups — C2×#52722 #8092564

Order 512.

5080 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52722C2132yesmaximal, direct product factor
2C2×#2806C211yesmaximal, characteristic, complemented
3C2×#2802C211yesmaximal, characteristic, complemented
4C2×#2768C211yesmaximal, characteristic, complemented
5C2×#2755C211yesmaximal, characteristic, complemented
6C2×#2755C211yesmaximal, characteristic, complemented
7C2×#2754C211yesmaximal, characteristic, complemented
8C2×#2747C211yesmaximal, characteristic, complemented
9C2×#2744C211yesmaximal, characteristic, complemented
10C2×#2845C211yesmaximal, characteristic, complemented
11C2×#2841C211yesmaximal, characteristic, complemented
12C2×#2831C211yesmaximal, characteristic, complemented
13C2×#2831C211yesmaximal, characteristic, complemented
14C2×#2839C211yesmaximal, characteristic, complemented
15C2×#2839C211yesmaximal, characteristic, complemented
16C2×#2839C211yesmaximal, characteristic, complemented
17C2×#2836C211yesmaximal, characteristic, complemented
18C2×#2484C211yesmaximal, characteristic, complemented
19C2×#2484C211yesmaximal, characteristic, complemented
20C2×#2503C211yesmaximal, characteristic, complemented
21C2×#2486C211yesmaximal, characteristic
22C2×#2505C211yesmaximal, characteristic, complemented
23C2×#2488C211yesmaximal, characteristic
24C2×#2413C211yesmaximal, characteristic
25C2×#2413C211yesmaximal, characteristic
26C2×#2438C211yesmaximal, characteristic, complemented
27C2×#2438C211yesmaximal, characteristic, complemented
28C2×#2450C211yesmaximal, characteristic
29C2×#2419C211yesmaximal, characteristic
30C2×#2623C211yesmaximal, characteristic
31C2×#2627C211yesmaximal, characteristic, complemented
32C22×#398C211yesmaximal, characteristic, complemented
33C22×#123C2211yescharacteristic
34C22×#123C2211yescharacteristic
35C22×#123C2211yescharacteristic
36C22×C22⋊Q8C2211yescharacteristic
37C22×C22⋊Q8C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39C22×#117C2211yescharacteristic
40C22×#117C2211yescharacteristic
41C23×C4⋊C4C2211yescharacteristic
42C23×C4⋊C4C2211yescharacteristic
43C23×C4⋊C4C2211yescharacteristic
44C23×C4⋊C4C2211yescharacteristic
45#2845C22116yescomplemented
46#2841C22116yescomplemented
47#2839C22116yescomplemented
48#2839C22116yescomplemented
49#2839C22116yescomplemented
50#2836C22116yescomplemented
51#2831C22116yescomplemented
52#2831C22116yescomplemented
53#2806C22116yescomplemented
54#2802C22116yescomplemented
55#2768C22116yescomplemented
56#2755C22116yescomplemented
57#2755C22116yescomplemented
58#2754C22116yescomplemented
59#2747C22116yescomplemented
60#2744C22116yescomplemented
61#2627C22116yescomplemented
62#2623C22116yes—
63#2505C22116yescomplemented
64#2503C22116yescomplemented
65#2488C22116yes—
66#2486C22116yes—
67#2484C22116yescomplemented
68#2484C22116yescomplemented
69#2450C22116yes—
70#2438C22116yescomplemented
71#2438C22116yescomplemented
72#2419C22116yes—
73#2413C22116yes—
74#2413C22116yes—
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×#399C2211yescharacteristic
97C2×#399C2211yescharacteristic
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
118C2×#398C2211yescharacteristic
119C2×#398C2211yescharacteristic
120C2×#398C2211yescharacteristic
121C2×#398C2211yescharacteristic
122C2×#398C2211yescharacteristic
123C2×#398C2211yescharacteristic
124C2×#398C2211yescharacteristic
125C2×#398C2211yescharacteristic
126C2×#398C2211yescharacteristic
127C2×#398C2211yescharacteristic
128C2×#398C2211yescharacteristic
129C2×#398C22116yescomplemented
130C2×#397C2211yescharacteristic
131C2×#397C2211yescharacteristic
132C2×#397C2211yescharacteristic
133C2×#397C2211yescharacteristic
134C2×#397C2211yescharacteristic
135C2×#397C2211yescharacteristic
136C2×#397C2211yescharacteristic
137C2×#396C2211yescharacteristic
138C2×#396C2211yescharacteristic
139C2×#396C2211yescharacteristic
140C2×#396C2211yescharacteristic
141C2×#396C2211yescharacteristic
142C2×#395C2211yescharacteristic
143C2×#395C2211yescharacteristic
144C2×#395C2211yescharacteristic
145C2×#395C2211yescharacteristic
146C2×#393C2211yescharacteristic
147C2×#393C2211yescharacteristic
148C2×#391C2211yescharacteristic
149C2×#391C2211yescharacteristic
150C2×#391C2211yescharacteristic
151C2×#391C2211yescharacteristic
152C2×#391C2211yescharacteristic
153C2×#391C2211yescharacteristic
154C2×#389C2211yescharacteristic
155C2×#389C2211yescharacteristic
156C2×#389C2211yescharacteristic
157C2×#389C2211yescharacteristic
158C2×#389C2211yescharacteristic
159C2×#389C2211yescharacteristic
160C2×#389C2211yescharacteristic
161C2×#389C2211yescharacteristic
162C2×#389C2211yescharacteristic
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×#386C2211yescharacteristic
187C2×#386C2211yescharacteristic
188C2×#386C2211yescharacteristic
189C2×#385C2211yescharacteristic
190C2×#385C2211yescharacteristic
191C2×#385C2211yescharacteristic
192C2×#385C2211yescharacteristic
193C2×#385C2211yescharacteristic
194C2×#385C2211yescharacteristic
195C2×#385C2211yescharacteristic
196C2×#385C2211yescharacteristic
197C2×#385C2211yescharacteristic
198C2×#382C2211yescharacteristic
199C2×#382C2211yescharacteristic
200C2×#382C2211yescharacteristic
201C2×#382C2211yescharacteristic
202C2×#381C2211yescharacteristic
203C2×#381C2211yescharacteristic
204C2×#381C2211yescharacteristic
205C2×#381C2211yescharacteristic
206C2×#381C2211yescharacteristic
207C2×#381C2211yescharacteristic
208C2×#381C2211yescharacteristic
209C2×#381C2211yescharacteristic
210C2×#380C2211yescharacteristic
211C2×#380C2211yescharacteristic
212C2×#380C2211yescharacteristic
213C2×#380C2211yescharacteristic
214C2×#380C2211yescharacteristic
215C2×C4×C22⋊C4C2211yescharacteristic
216C22×#95C2211yescharacteristic
217C22×#95C2211yescharacteristic
218C22×#95C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×Q8C2311yescharacteristic
221C23×D4C2311yescharacteristic
222C24×C4C2311yescharacteristic
223C24×C4C2311yescharacteristic
224C24×C4C2311yescharacteristic
225C24×C4C2311yescharacteristic
226C24×C4C2311yescharacteristic
227C24×C4C2311yescharacteristic
228C24×C4C2311yescharacteristic
229C24×C4C2311yescharacteristic
230C2×#123—44no—
231C2×#123—44no—
232C2×#123—44no—
233C2×#123C2318yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×C22⋊Q8—44no—
237C2×C22⋊Q8—44no—
238C2×C22⋊Q8C2318yes—
239C2×C22⋊Q8C2318yes—
240C2×C4×D4—44no—
241C2×C4×D4C2318yes—
242C2×#117—44no—
243C2×#117—44no—
244C2×#117C2318yes—
245C2×#117C2318yes—
246C22×C4⋊C4—44no—
247C22×C4⋊C4—44no—
248C22×C4⋊C4—44no—
249C22×C4⋊C4—44no—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2318yes—
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2311yescharacteristic
272C22×C4⋊C4C2311yescharacteristic
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2311yescharacteristic
302C22×C4⋊C4C2318yes—
303C22×C4⋊C4C2318yes—
304C22×C4⋊C4C2318yes—
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2311yescharacteristic
310C22×C22⋊C4C2311yescharacteristic
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2311yescharacteristic
313C22×C22⋊C4C2311yescharacteristic
314C22×C22⋊C4C2311yescharacteristic
315C22×C22⋊C4C2311yescharacteristic
316C22×C22⋊C4C2311yescharacteristic
317C22×C22⋊C4C2311yescharacteristic
318C22×C22⋊C4C2311yescharacteristic
319C22×C22⋊C4C2311yescharacteristic
320C22×C22⋊C4C2311yescharacteristic
321C22×C22⋊C4C2311yescharacteristic
322C22×C22⋊C4C2311yescharacteristic
323C22×C22⋊C4C2311yescharacteristic
324C22×C22⋊C4C2311yescharacteristic
325C22×C42C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2311yescharacteristic
329C22×C42C2311yescharacteristic
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
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#400C2318yes—
349#400C2318yes—
350#400C2318yes—
351#400C2318yes—
352#400C2318yes—
353#399C2318yes—
354#399C2318yes—
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#398C2318yes—
369#398C2318yes—
370#398C2318yes—
371#398C2318yes—
372#398C2318yes—
373#398C2318yes—
374#398C2318yes—
375#398C2318yes—
376#398C2318yes—
377#398C2318yes—
378#398C2318yes—
379#398C2318yes—
380#398C2318yes—
381#398C2318yes—
382#398C2318yes—
383#398C2318yes—
384#398C2318yes—
385#398C2318yes—
386#397C2318yes—
387#397C2318yes—
388#397C2318yes—
389#397C2318yes—
390#397C2318yes—
391#397C2318yes—
392#397C2318yes—
393#396C2318yes—
394#396C2318yes—
395#396C2318yes—
396#396C2318yes—
397#396C2318yes—
398#395C2318yes—
399#395C2318yes—
400#395C2318yes—
401#395C2318yes—
402#393C2318yes—
403#393C2318yes—
404#391C2318yes—
405#391C2318yes—
406#391C2318yes—
407#391C2318yes—
408#391C2318yes—
409#391C2318yes—
410#389C2318yes—
411#389C2318yes—
412#389C2318yes—
413#389C2318yes—
414#389C2318yes—
415#389C2318yes—
416#389C2318yes—
417#389C2318yes—
418#389C2318yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
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#386C2318yes—
443#386C2318yes—
444#386C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#382C2318yes—
455#382C2318yes—
456#382C2318yes—
457#382C2318yes—
458#381C2318yes—
459#381C2318yes—
460#381C2318yes—
461#381C2318yes—
462#381C2318yes—
463#381C2318yes—
464#381C2318yes—
465#381C2318yes—
466#380C2318yes—
467#380C2318yes—
468#380C2318yes—
469#380C2318yes—
470#380C2318yes—
471C4×C22⋊C4C2318yes—
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×#95C2318yes—
536C2×#95C2318yes—
537C2×#95C2318yes—
538C2×#95C2311yescharacteristic
539C2×#95C2311yescharacteristic
540C2×#95C2311yescharacteristic
541C25C2411yescharacteristic
542C25C2411yescharacteristic
543C22×Q8—24no—
544C22×Q8—42no—
545C22×Q8—42no—
546C22×Q8—42no—
547C22×Q8—42no—
548C22×Q8—42no—
549C22×Q8C2414yes—
550C22×Q8C2414yes—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—24no—
554C22×D4C2414yes—
555C23×C4—24no—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—24no—
559C23×C4—24no—
560C23×C4—24no—
561C23×C4—24no—
562C23×C4—24no—
563C23×C4—24no—
564C23×C4—24no—
565C23×C4—24no—
566C23×C4—24no—
567C23×C4—24no—
568C23×C4—24no—
569C23×C4—24no—
570C23×C4—24no—
571C23×C4—42no—
572C23×C4—42no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4—42no—
576C23×C4—42no—
577C23×C4—42no—
578C23×C4—42no—
579C23×C4C2414yes—
580C23×C4C2414yes—
581C23×C4C2414yes—
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×C4C2411yescharacteristic
604C23×C4C2411yescharacteristic
605C23×C4C2411yescharacteristic
606C23×C4C2411yescharacteristic
607C23×C4C2411yescharacteristic
608C23×C4C2411yescharacteristic
609C23×C4C2414yes—
610C23×C4C2414yes—
611C23×C4C2411yescharacteristic
612C23×C4C2411yescharacteristic
613C23×C4C2414yes—
614C23×C4C2414yes—
615C23×C4C2414yes—
616#123—416no—
617#123—416no—
618#123—416no—
619C22⋊Q8—416no—
620C22⋊Q8—416no—
621C4×D4—416no—
622#117—416no—
623#117—416no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—24no—
627C2×C4⋊C4—24no—
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—416no—
645C2×C4⋊C4—416no—
646C2×C4⋊C4—416no—
647C2×C4⋊C4—416no—
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—42no—
661C2×C4⋊C4—42no—
662C2×C4⋊C4—42no—
663C2×C4⋊C4—42no—
664C2×C4⋊C4—42no—
665C2×C4⋊C4—42no—
666C2×C4⋊C4—42no—
667C2×C4⋊C4—42no—
668C2×C4⋊C4—42no—
669C2×C4⋊C4—42no—
670C2×C4⋊C4—42no—
671C2×C4⋊C4—42no—
672C2×C4⋊C4—42no—
673C2×C4⋊C4—42no—
674C2×C4⋊C4—42no—
675C2×C4⋊C4—42no—
676C2×C4⋊C4—42no—
677C2×C4⋊C4—42no—
678C2×C4⋊C4—42no—
679C2×C4⋊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×C4⋊C4C2414yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2414yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2414yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C22⋊C4—24no—
731C2×C22⋊C4—24no—
732C2×C22⋊C4—24no—
733C2×C22⋊C4—24no—
734C2×C22⋊C4—24no—
735C2×C22⋊C4—24no—
736C2×C22⋊C4—24no—
737C2×C22⋊C4—24no—
738C2×C22⋊C4—42no—
739C2×C22⋊C4—42no—
740C2×C22⋊C4—42no—
741C2×C22⋊C4—42no—
742C2×C22⋊C4—42no—
743C2×C22⋊C4—42no—
744C2×C22⋊C4—42no—
745C2×C22⋊C4—42no—
746C2×C22⋊C4—42no—
747C2×C22⋊C4—42no—
748C2×C22⋊C4—42no—
749C2×C22⋊C4—42no—
750C2×C22⋊C4C2414yes—
751C2×C22⋊C4C2414yes—
752C2×C22⋊C4C2414yes—
753C2×C22⋊C4C2414yes—
754C2×C22⋊C4C2414yes—
755C2×C22⋊C4C2414yes—
756C2×C22⋊C4C2414yes—
757C2×C22⋊C4C2414yes—
758C2×C22⋊C4C2414yes—
759C2×C22⋊C4C2414yes—
760C2×C22⋊C4C2414yes—
761C2×C22⋊C4C2414yes—
762C2×C22⋊C4C2414yes—
763C2×C22⋊C4C2414yes—
764C2×C22⋊C4C2414yes—
765C2×C22⋊C4C2414yes—
766C2×C22⋊C4C2414yes—
767C2×C22⋊C4C2414yes—
768C2×C22⋊C4C2414yes—
769C2×C22⋊C4C2414yes—
770C2×C42—24no—
771C2×C42—42no—
772C2×C42—42no—
773C2×C42—42no—
774C2×C42—42no—
775C2×C42—42no—
776C2×C42—42no—
777C2×C42C2414yes—
778C2×C42C2414yes—
779C2×C42C2414yes—
780C2×C42C2414yes—
781C2×C42C2414yes—
782C2×C42C2414yes—
783C2×C42C2414yes—
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—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2414yes—
845#95C2414yes—
846#95C2414yes—
847#95C2414yes—
848#95C2414yes—
849#95C2414yes—
850C24—22no—
851C24—22no—
852C24—22no—
853C24—22no—
854C24—22no—
855C24—22no—
856C24—22no—
857C24—22no—
858C24—22no—
859C24—22no—
860C24—22no—
861C24H(5,𝔽2)14yes—
862C24H(5,𝔽2)14yes—
863C242−1+414yes—
864C24C2512yes—
865C24C2512yes—
866C24C2511yescharacteristic
867C2×Q8—28no—
868C2×Q8—44no—
869C2×Q8—44no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—44no—
873C2×Q8—88no—
874C2×Q8—88no—
875C2×D4—28no—
876C2×D4—28no—
877C2×D4—28no—
878C2×D4—416no—
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—28no—
906C22×C4—28no—
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—28no—
918C22×C4—28no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—28no—
923C22×C4—28no—
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—28no—
938C22×C4—28no—
939C22×C4—28no—
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—22no—
967C22×C4—22no—
968C22×C4—22no—
969C22×C4—22no—
970C22×C4—22no—
971C22×C4—22no—
972C22×C4—22no—
973C22×C4—22no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—28no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—28no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4—44no—
985C22×C4—44no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—416no—
989C22×C4—416no—
990C22×C4—416no—
991C22×C4—416no—
992C22×C4—416no—
993C22×C4—416no—
994C22×C4—88no—
995C22×C4—88no—
996C22×C42−1+414yes—
997C22×C42−1+414yes—
998C22×C4C2512yes—
999C22×C4C2512yes—
1000C22×C4C2512yes—
1001C22×C4C2512yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2512yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2512yes—
1010C22×C4C2512yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2512yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
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—
1046C4⋊C4—44no—
1047C4⋊C4—44no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—44no—
1051C4⋊C4—44no—
1052C4⋊C4—44no—
1053C4⋊C4—44no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—44no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
1089C22⋊C4—44no—
1090C22⋊C4—44no—
1091C22⋊C4—44no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C42—28no—
1099C42—44no—
1100C42—44no—
1101C42—44no—
1102C42—44no—
1103C42—44no—
1104C42—44no—
1105C23—22no—
1106C23—22no—
1107C23—22no—
1108C23—22no—
1109C23—28no—
1110C23—28no—
1111C23—28no—
1112C23—28no—
1113C23—28no—
1114C23—28no—
1115C23—22no—
1116C23—22no—
1117C23—22no—
1118C23—22no—
1119C23—22no—
1120C23—22no—
1121C23—22no—
1122C23—44no—
1123C23—44no—
1124C23—44no—
1125C23—44no—
1126C23—44no—
1127C23—44no—
1128C23—44no—
1129C23#562116yes—
1130C23C2×H(5,𝔽2)14yes—
1131C23C2×H(5,𝔽2)14yes—
1132C23C2×H(5,𝔽2)12yes—
1133C23C2×H(5,𝔽2)12yes—
1134C23C2×2−1+414yes—
1135C23C2×2−1+412yes—
1136C23C2×2−1+412yes—
1137C23C2×2−1+412yes—
1138C23#58512yes—
1139C23#58512yes—
1140C23C2611yescharacteristic
1141Q8—88no—
1142Q8—88no—
1143D4—416no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
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—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—416no—
1232C2×C4—416no—
1233C2×C4—416no—
1234C2×C4—416no—
1235C2×C4—416no—
1236C2×C4—416no—
1237C2×C4—44no—
1238C2×C4—44no—
1239C2×C4—44no—
1240C2×C4—44no—
1241C2×C4—44no—
1242C2×C4—44no—
1243C2×C4—44no—
1244C2×C4—44no—
1245C2×C4—44no—
1246C2×C4—44no—
1247C2×C4—44no—
1248C2×C4—44no—
1249C2×C4—44no—
1250C2×C4—44no—
1251C2×C4—44no—
1252C2×C4—44no—
1253C2×C4—44no—
1254C2×C4—44no—
1255C2×C4—44no—
1256C2×C4—44no—
1257C2×C4—44no—
1258C2×C4—44no—
1259C2×C4—44no—
1260C2×C4—44no—
1261C2×C4—44no—
1262C2×C4—44no—
1263C2×C4—44no—
1264C2×C4—88no—
1265C2×C4—88no—
1266C2×C4C2×2−1+414yes—
1267C2×C4C2×2−1+414yes—
1268C22—24no—
1269C22—24no—
1270C22—24no—
1271C22—24no—
1272C22—24no—
1273C22—24no—
1274C22—232no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—88no—
1283C22C2×#56218yes—
1284C22C2×#56214yes—
1285C22#353314yes—
1286C22#353514yes—
1287C22#353514yes—
1288C22#354414yes—
1289C22#356314yes—
1290C22#356314yes—
1291C22C22×H(5,𝔽2)11yescharacteristic
1292C22C22×H(5,𝔽2)11yescharacteristic
1293C22C22×2−1+411yescharacteristic
1294C22C22×2−1+411yescharacteristic
1295C22C22×2−1+411yescharacteristic
1296C22C2×#58511yescharacteristic
1297C22C2×#58511yescharacteristic
1298C4—24no—
1299C4—24no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—42no—
1305C4—42no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C2—28no—
1328C2—82no—
1329C2#5272218yesdirect product factor
1330C2C22×#56211yescharacteristic
1331C2C2×#353511yescharacteristic
1332C2C2×#353511yescharacteristic
1333C2C2×#353311yescharacteristic
1334C2C2×#356311yescharacteristic
1335C2C2×#356311yescharacteristic
1336C2C2×#354411yescharacteristic
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. #52722C2direct (N × H)
2. C2×#2806C2semidirect
3. C2×#2802C2semidirect
4. C2×#2768C2semidirect
5. C2×#2755C2semidirect
6. C2×#2755C2semidirect
7. C2×#2754C2semidirect
8. C2×#2747C2semidirect
9. C2×#2744C2semidirect
10. C2×#2845C2semidirect
11. C2×#2841C2semidirect
12. C2×#2831C2semidirect
13. C2×#2831C2semidirect
14. C2×#2839C2semidirect
15. C2×#2839C2semidirect
16. C2×#2839C2semidirect
17. C2×#2836C2semidirect
18. C2×#2484C2semidirect
19. C2×#2484C2semidirect
20. C2×#2503C2semidirect
22. C2×#2505C2semidirect
26. C2×#2438C2semidirect
27. C2×#2438C2semidirect
31. C2×#2627C2semidirect
32. C22×#398C2semidirect
45. #2845C22semidirect
46. #2841C22semidirect
47. #2839C22semidirect
48. #2839C22semidirect
49. #2839C22semidirect
50. #2836C22semidirect
51. #2831C22semidirect
52. #2831C22semidirect
53. #2806C22semidirect
54. #2802C22semidirect
55. #2768C22semidirect
56. #2755C22semidirect
57. #2755C22semidirect
58. #2754C22semidirect
59. #2747C22semidirect
60. #2744C22semidirect
61. #2627C22semidirect
63. #2505C22semidirect
64. #2503C22semidirect
67. #2484C22semidirect
68. #2484C22semidirect
70. #2438C22semidirect
71. #2438C22semidirect
129. C2×#398C22semidirect
1329. C2#52722direct (N × H)

Maximal subgroups

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

subgroupindex
#527222
C2×#28062
C2×#28022
C2×#27682
C2×#27552
C2×#27542
C2×#27472
C2×#27442
C2×#28452
C2×#28412
C2×#28312
C2×#28392
C2×#28362
C2×#24842
C2×#25032
C2×#24862
C2×#25052
C2×#24882
C2×#24132
C2×#24382
C2×#24502
C2×#24192
C2×#26232
C2×#26272
C22×#3982