Finite Group Databasebeta

← C2×#62889 #10586224

Subgroups — C2×#62889 #10586224

Order 512.

30734 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62889C2164yesmaximal, direct product factor
2C2×#3504C212yesmaximal, complemented
3C2×#3509C212yesmaximal, complemented
4C2×#3495C214yesmaximal, complemented
5C2×#3502C212yesmaximal, complemented
6C2×#3507C212yesmaximal, complemented
7C2×#3556C214yesmaximal, complemented
8C2×#3555C218yesmaximal, complemented
9C2×#3555C218yesmaximal, complemented
10C2×#3557C214yesmaximal, complemented
11C2×#3564C218yesmaximal, complemented
12C2×#3563C218yesmaximal, complemented
13C2×#3563C218yesmaximal, complemented
14C2×#3455C211yesmaximal, characteristic
15C2×#3458C211yesmaximal, characteristic, complemented
16C22×#541C211yesmaximal, characteristic, complemented
17#3564C221256yescomplemented
18#3563C221256yescomplemented
19#3563C221256yescomplemented
20#3557C221128yescomplemented
21#3556C221128yescomplemented
22#3555C221256yescomplemented
23#3555C221256yescomplemented
24C2×#564C22116yescomplemented
25C2×#563C22116yes—
26C2×#563C22116yes—
27C2×#563C22116yescomplemented
28#3509C22164yescomplemented
29#3507C22164yescomplemented
30#3504C22164yescomplemented
31#3502C22164yescomplemented
32#3495C221128yescomplemented
33C2×#559C2214yescomplemented
34C2×Q82C2214yescomplemented
35C2×Q82C2214yescomplemented
36C2×#557C2214yescomplemented
37C2×#557C22116yescomplemented
38C2×#557C2218yescomplemented
39C2×#557C2218yescomplemented
40C2×#557C2214yescomplemented
41C2×#557C2218yescomplemented
42C2×#557C2218yescomplemented
43C2×#557C2214yescomplemented
44C2×#556C22116yes—
45C2×#556C2218yes—
46C2×#556C2218yescomplemented
47C2×#556C2214yescomplemented
48C2×#556C2218yescomplemented
49C2×#554C22116yes—
50C2×#554C2218yes—
51C2×#554C2214yescomplemented
52C2×#554C2218yescomplemented
53C2×#552C2218yes—
54C2×#552C22116yes—
55C2×#552C22116yes—
56C2×#552C22116yes—
57C2×#552C2218yes—
58C2×#552C22116yescomplemented
59C2×#552C2218yescomplemented
60C2×#551C22116yes—
61#3458C22132yescomplemented
62C2×#544C2214yes—
63C2×#544C2214yes—
64C2×#544C2218yes—
65C2×#544C2214yes—
66C2×#544C2214yes—
67C2×#544C22116yescomplemented
68C2×#544C2218yescomplemented
69C2×#543C2214yes—
70#3455C22132yes—
71C2×#542C22116yes—
72C2×#542C2218yes—
73C2×#542C2214yes—
74C2×#541C22116yes—
75C2×#541C2218yes—
76C2×#541C22116yes—
77C2×#541C2214yes—
78C2×#541C2214yes—
79C2×#541C2218yes—
80C2×#541C2212yes—
81C2×#541C22132yescomplemented
82C2×#541C22116yescomplemented
83C2×#541C2214yescomplemented
84C2×#541C22116yescomplemented
85C2×#541C22116yescomplemented
86C2×#541C2214yescomplemented
87C2×#540C2212yes—
88C2×#539C2214yes—
89C2×#539C22116yes—
90C2×#539C2218yes—
91C2×#538C2214yes—
92C2×#536C2214yes—
93C2×#533C2218yes—
94C2×#533C2214yes—
95C2×#533C2214yes—
96C2×#533C2218yes—
97C2×#533C2212yes—
98C2×#533C2211yescharacteristic
99C2×#533C2212yes—
100C2×#533C2218yescomplemented
101C2×#533C2214yescomplemented
102C2×#532C2211yescharacteristic
103C22×C4⋊Q8C2211yescharacteristic
104C2×#529C2218yes—
105C2×#529C2218yes—
106C2×#529C2218yes—
107C22×#126C2214yes—
108C22×#125C2214yes—
109C22×#125C2211yescharacteristic
110C22×#125C2214yescomplemented
111C2×#525C2212yes—
112C22×C22⋊Q8C2212yes—
113C2×#520C2214yes—
114C2×#519C2214yes—
115C2×C4×#41C2212yes—
116C22×C4×Q8C2212yes—
117C22×#117C2212yes—
118C22×#117C2211yescharacteristic
119C22×#41C2312yes—
120C23×Q8C2312yes—
121C24×C4C2311yescharacteristic
122#564C231256yescomplemented
123#563C231256yes—
124#563C231256yes—
125#563C231256yescomplemented
126#559C23164yescomplemented
127Q82C23164yescomplemented
128Q82C23164yescomplemented
129#557C23164yescomplemented
130#557C231128yescomplemented
131#557C231128yescomplemented
132#557C23164yescomplemented
133#557C231128yescomplemented
134#557C23164yescomplemented
135#557C231128yescomplemented
136#557C231256yescomplemented
137#556C231128yes—
138#556C231256yes—
139#556C23164yescomplemented
140#556C231128yescomplemented
141#556C231128yescomplemented
142#554C231128yes—
143#554C231256yes—
144#554C231128yescomplemented
145#554C23164yescomplemented
146#552C231128yes—
147#552C231128yes—
148#552C231256yes—
149#552C231256yes—
150#552C231256yes—
151#552C231128yescomplemented
152#552C231256yescomplemented
153#551C231256yes—
154#544C23164yes—
155#544C23164yes—
156#544C23164yes—
157#544C23164yes—
158#544C231128yes—
159#544C231128yescomplemented
160#544C231256yescomplemented
161#543C23164yes—
162#542C23164yes—
163#542C231128yes—
164#542C231256yes—
165#541C23164yes—
166#541C231128yes—
167#541C23164yes—
168#541C23132yes—
169#541C231128yes—
170#541C231256yes—
171#541C231256yes—
172#541C23164yescomplemented
173#541C23164yescomplemented
174#541C231256yescomplemented
175#541C231256yescomplemented
176#541C231256yescomplemented
177#540C23132yes—
178#539C23164yes—
179#539C231128yes—
180#539C231256yes—
181#538C23164yes—
182#536C23164yes—
183#533C23116yes—
184#533C23132yes—
185#533C23132yes—
186#533C23164yes—
187#533C23164yes—
188#533C231128yes—
189#533C231128yes—
190#533C23164yescomplemented
191#533C231128yescomplemented
192#532C23116yes—
193C2×C4⋊Q8C2314yes—
194C2×C4⋊Q8C2314yes—
195C2×C4⋊Q8C23116yes—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2314yes—
198C2×C4⋊Q8C2318yes—
199C2×C4⋊Q8C2318yes—
200C2×C4⋊Q8C2318yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2318yes—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2318yes—
206C2×C4⋊Q8C2318yes—
207C2×C4⋊Q8C2318yes—
208C2×C4⋊Q8C23116yes—
209C2×C4⋊Q8C23116yes—
210C2×C4⋊Q8C23116yes—
211C2×#127C2311yescharacteristic
212#529C231128yes—
213#529C231128yes—
214#529C231128yes—
215C2×#126C23116yes—
216C2×#126C23116yes—
217C2×#126C23164yes—
218C2×#126C2318yes—
219C2×#126C2318yes—
220C2×#126C23116yes—
221C2×#126C23116yes—
222C2×#126C23116yes—
223C2×#126C23116yes—
224C2×#126C23116yes—
225C2×#126C23116yes—
226C2×#126C23116yes—
227C2×#126C23116yes—
228C2×#125C2314yes—
229C2×#125C23116yes—
230C2×#125C23116yes—
231C2×#125C2314yes—
232C2×#125C23116yes—
233C2×#125C23164yes—
234C2×#125C2312yes—
235C2×#125C23116yes—
236C2×#125C2318yes—
237C2×#125C2318yes—
238C2×#125C2318yes—
239C2×#125C2318yes—
240C2×#125C2312yes—
241C2×#125C23116yes—
242C2×#125C2312yes—
243C2×#125C2318yes—
244C2×#125C23116yes—
245C2×#125C2314yes—
246C2×#125C2318yes—
247C2×#125C23116yes—
248C2×#125C23116yes—
249C2×#125C23116yes—
250C2×#125C23116yes—
251C2×#125C23116yes—
252C2×#125C23116yes—
253C2×#125C23116yes—
254C2×#125C23116yes—
255C2×#125C23116yes—
256C2×#125C23164yescomplemented
257C2×#124C2318yes—
258C2×#124C2318yes—
259C2×#124C2318yes—
260C2×#124C2312yes—
261C2×#124C23116yes—
262#525C23132yes—
263C2×#123C2314yes—
264C2×#123C23116yes—
265C2×#123C2318yes—
266C2×#123C2318yes—
267C2×#123C23116yes—
268C2×#123C23116yes—
269C2×#123C23116yes—
270C2×C22⋊Q8C2318yes—
271C2×C22⋊Q8C2318yes—
272C2×C22⋊Q8C23132yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2318yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2318yes—
279C2×C22⋊Q8C2318yes—
280C2×C22⋊Q8C23116yes—
281C2×C22⋊Q8C2318yes—
282C2×C22⋊Q8C2318yes—
283C2×C22⋊Q8C2318yes—
284C2×C22⋊Q8C23116yes—
285C2×C22⋊Q8C2318yes—
286C2×C22⋊Q8C2318yes—
287C2×C22⋊Q8C23116yes—
288C2×C22⋊Q8C23116yes—
289C2×C22⋊Q8C23116yes—
290C2×C22⋊Q8C23116yes—
291C2×C22⋊Q8C23116yes—
292C2×C22⋊Q8C23116yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2318yes—
296C2×#120C2314yes—
297#520C23164yes—
298#519C23164yes—
299C4×#41C23132yes—
300C2×C4×Q8C2314yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C23132yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2318yes—
307C2×C4×Q8C2318yes—
308C2×C4×Q8C2318yes—
309C2×C4×Q8C2318yes—
310C2×C4×Q8C2318yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2318yes—
313C2×C4×Q8C2318yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2314yes—
316C2×C4×Q8C23116yes—
317C2×C4×Q8C2318yes—
318C2×C4×Q8C23116yes—
319C2×C4×Q8C2318yes—
320C2×C4×Q8C23116yes—
321C2×C4×Q8C23116yes—
322C2×C4×D4C2318yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C23116yes—
325C2×C4×D4C2318yes—
326C2×C4×D4C2318yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2318yes—
329C2×C4×D4C23116yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2314yes—
335C2×#117C23116yes—
336C2×#117C2312yes—
337C2×#117C2314yes—
338C2×#117C2312yes—
339C2×#117C23132yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C2×#117C23116yes—
343C2×#117C2318yes—
344C2×#117C23116yes—
345C2×#117C23116yes—
346C2×#117C23116yes—
347C2×#117C23116yes—
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2314yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2314yes—
352C22×C4⋊C4C2318yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C23116yes—
357C22×C22⋊C4C2312yes—
358C22×C22⋊C4C2314yes—
359C22×C22⋊C4C2314yes—
360C22×C42C2311yescharacteristic
361C22×C42C2311yescharacteristic
362C22×C42C2314yes—
363C22×C42C2314yes—
364C22×C42C2314yes—
365C25C2411yescharacteristic
366C2×#41—216no—
367C2×#41C24116yes—
368C22×Q8—216no—
369C22×Q8C2414yes—
370C22×Q8C2414yes—
371C22×Q8C2412yes—
372C22×Q8C24116yes—
373C22×Q8C2418yes—
374C22×Q8C2414yes—
375C22×Q8C24116yes—
376C22×Q8C2414yes—
377C22×Q8C2414yes—
378C22×D4C2414yes—
379C22×D4C2412yes—
380C22×D4C2418yes—
381C22×D4C2414yes—
382C23×C4—28no—
383C23×C4C2414yes—
384C23×C4C2411yescharacteristic
385C23×C4C2412yes—
386C23×C4C2414yes—
387C23×C4C2418yes—
388C23×C4C2412yes—
389C23×C4C2412yes—
390C23×C4C2414yes—
391C23×C4C2412yes—
392C23×C4C2418yes—
393C23×C4C24116yes—
394C23×C4C2418yes—
395C23×C4C2411yescharacteristic
396C4⋊Q8C24132yes—
397C4⋊Q8C24132yes—
398C4⋊Q8C2418yes—
399C4⋊Q8C24132yes—
400C4⋊Q8C24164yes—
401C4⋊Q8C24164yes—
402C4⋊Q8C24164yes—
403C4⋊Q8C24116yes—
404C4⋊Q8C24164yes—
405C4⋊Q8C24116yes—
406C4⋊Q8C24116yes—
407C4⋊Q8C24164yes—
408C4⋊Q8C24164yes—
409C4⋊Q8C24164yes—
410C4⋊Q8C241128yes—
411C4⋊Q8C241128yes—
412C4⋊Q8C241128yes—
413#127C2418yes—
414#126C241128yes—
415#126C241128yes—
416#126C24164yes—
417#126C24164yes—
418#126C241128yes—
419#126C241128yes—
420#126C241128yes—
421#126C241128yes—
422#126C241128yes—
423#126C241128yes—
424#126C241128yes—
425#126C241128yes—
426#125C24132yes—
427#125C241128yes—
428#125C241128yes—
429#125C24132yes—
430#125C24116yes—
431#125C241128yes—
432#125C24164yes—
433#125C24164yes—
434#125C24164yes—
435#125C24164yes—
436#125C24116yes—
437#125C241128yes—
438#125C24116yes—
439#125C24164yes—
440#125C241128yes—
441#125C24132yes—
442#125C24164yes—
443#125C241128yes—
444#125C241128yes—
445#125C241128yes—
446#125C241128yes—
447#125C241128yes—
448#125C241128yes—
449#125C241128yes—
450#125C241128yes—
451#125C241128yes—
452#124C24164yes—
453#124C24164yes—
454#124C24164yes—
455#124C24116yes—
456#124C241128yes—
457#123C24132yes—
458#123C241128yes—
459#123C24164yes—
460#123C24164yes—
461#123C241128yes—
462#123C241128yes—
463#123C241128yes—
464C22⋊Q8C24164yes—
465C22⋊Q8C24164yes—
466C22⋊Q8C24132yes—
467C22⋊Q8C24132yes—
468C22⋊Q8C24164yes—
469C22⋊Q8C24132yes—
470C22⋊Q8C24132yes—
471C22⋊Q8C24164yes—
472C22⋊Q8C24164yes—
473C22⋊Q8C241128yes—
474C22⋊Q8C24164yes—
475C22⋊Q8C24164yes—
476C22⋊Q8C24164yes—
477C22⋊Q8C241128yes—
478C22⋊Q8C24164yes—
479C22⋊Q8C24164yes—
480C22⋊Q8C241128yes—
481C22⋊Q8C241128yes—
482C22⋊Q8C241128yes—
483C22⋊Q8C241128yes—
484C22⋊Q8C241128yes—
485C22⋊Q8C241128yes—
486#121C24132yes—
487#121C24132yes—
488#121C24164yes—
489#120C24132yes—
490C4×Q8C24132yes—
491C4×Q8C24132yes—
492C4×Q8C24132yes—
493C4×Q8C24132yes—
494C4×Q8C24132yes—
495C4×Q8C24164yes—
496C4×Q8C24164yes—
497C4×Q8C24164yes—
498C4×Q8C24164yes—
499C4×Q8C24164yes—
500C4×Q8C24132yes—
501C4×Q8C24164yes—
502C4×Q8C24164yes—
503C4×Q8C24132yes—
504C4×Q8C24132yes—
505C4×Q8C241128yes—
506C4×Q8C24164yes—
507C4×Q8C241128yes—
508C4×Q8C24164yes—
509C4×Q8C241128yes—
510C4×Q8C241128yes—
511C4×D4C24164yes—
512C4×D4C24132yes—
513C4×D4C241128yes—
514C4×D4C24164yes—
515C4×D4C24164yes—
516C4×D4C24132yes—
517C4×D4C24164yes—
518C4×D4C241128yes—
519#117C24132yes—
520#117C24132yes—
521#117C24116yes—
522#117C24116yes—
523#117C24132yes—
524#117C24116yes—
525#117C24132yes—
526#117C24116yes—
527#117C24116yes—
528#117C24132yes—
529#117C241128yes—
530#117C24164yes—
531#117C241128yes—
532#117C241128yes—
533#117C241128yes—
534#117C241128yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C24116yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C24116yes—
544C2×C4⋊C4C24132yes—
545C2×C4⋊C4C24116yes—
546C2×C4⋊C4C24116yes—
547C2×C4⋊C4C24116yes—
548C2×C4⋊C4C24116yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C24116yes—
551C2×C4⋊C4C24116yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C24132yes—
555C2×C4⋊C4C24164yes—
556C2×C4⋊C4C24132yes—
557C2×C4⋊C4C24132yes—
558C2×C4⋊C4C24132yes—
559C2×C4⋊C4C241128yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C24116yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C24116yes—
566C2×C4⋊C4C24116yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2414yes—
569C2×C4⋊C4C24116yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2418yes—
572C2×C4⋊C4C2418yes—
573C2×C4⋊C4C2418yes—
574C2×C4⋊C4C2414yes—
575C2×C4⋊C4C24116yes—
576C2×C4⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C24116yes—
583C2×C22⋊C4C24132yes—
584C2×C22⋊C4C24116yes—
585C2×C22⋊C4C24132yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C24116yes—
591C2×C22⋊C4C24116yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C24116yes—
594C2×C42C2414yes—
595C2×C42C2412yes—
596C2×C42C24116yes—
597C2×C42C24116yes—
598C2×C42C24116yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2412yes—
602C2×C42C2418yes—
603C2×C42C2411yescharacteristic
604C2×C42C2411yescharacteristic
605C2×C42C2418yes—
606C2×C42C2414yes—
607C2×C42C2418yes—
608C2×C42C2418yes—
609C2×C42C24132yes—
610C2×C42C2418yes—
611C2×C42C2418yes—
612C2×C42C24132yes—
613C2×C42C24132yes—
614C24—24no—
615C24—44no—
616C24C2512yes—
617C24C2514yes—
618C24C2511yescharacteristic
619C24C2514yes—
620#41—264no—
621C2×Q8—216no—
622C2×Q8—216no—
623C2×Q8—264no—
624C2×Q8—28no—
625C2×Q8—416no—
626C2×Q8—48no—
627C2×Q8—432no—
628C2×Q8—48no—
629C2×Q8—48no—
630C2×Q8C25116yes—
631C2×Q8C25116yes—
632C2×Q8C2518yes—
633C2×Q8C25132yes—
634C2×Q8C25116yes—
635C2×Q8C25164yes—
636C2×Q8C25116yes—
637C2×Q8C25116yes—
638C2×D4—216no—
639C2×D4—28no—
640C2×D4—48no—
641C2×D4—416no—
642C2×D4C25116yes—
643C2×D4C2518yes—
644C2×D4C25132yes—
645C2×D4C25116yes—
646C22×C4—24no—
647C22×C4—216no—
648C22×C4—28no—
649C22×C4—28no—
650C22×C4—232no—
651C22×C4—216no—
652C22×C4—44no—
653C22×C4—48no—
654C22×C4—432no—
655C22×C4—416no—
656C22×C4—416no—
657C22×C4—44no—
658C22×C42−1+418yes—
659C22×C4C2518yes—
660C22×C4C25116yes—
661C22×C4C25116yes—
662C22×C4C2514yes—
663C22×C4C2518yes—
664C22×C4C2518yes—
665C22×C4C2518yes—
666C22×C4C2512yes—
667C22×C4C2514yes—
668C22×C4C2518yes—
669C22×C4C2512yes—
670C22×C4C2512yes—
671C22×C4C2518yes—
672C22×C4C2514yes—
673C22×C4C2518yes—
674C22×C4C2518yes—
675C22×C4C2518yes—
676C22×C4C25116yes—
677C22×C4C25132yes—
678C22×C4C25132yes—
679C22×C4C25164yes—
680C22×C4C2514yes—
681C22×C4C2511yescharacteristic
682C22×C4C2511yescharacteristic
683C4⋊C4C25116yes—
684C4⋊C4C25116yes—
685C4⋊C4C25164yes—
686C4⋊C4C25132yes—
687C4⋊C4C25116yes—
688C4⋊C4C25116yes—
689C4⋊C4C25132yes—
690C4⋊C4C25116yes—
691C4⋊C4C25164yes—
692C4⋊C4C25164yes—
693C4⋊C4C25164yes—
694C4⋊C4C25164yes—
695C4⋊C4C25116yes—
696C4⋊C4C25164yes—
697C4⋊C4C25132yes—
698C4⋊C4C25132yes—
699C4⋊C4C25132yes—
700C4⋊C4C25132yes—
701C4⋊C4C25164yes—
702C4⋊C4C25116yes—
703C4⋊C4C25132yes—
704C4⋊C4C25164yes—
705C4⋊C4C25164yes—
706C4⋊C4C25116yes—
707C4⋊C4C25116yes—
708C4⋊C4C25164yes—
709C4⋊C4C25132yes—
710C4⋊C4C25132yes—
711C4⋊C4C25132yes—
712C4⋊C4C25132yes—
713C4⋊C4C25116yes—
714C4⋊C4C25164yes—
715C4⋊C4C25116yes—
716C22⋊C4C25132yes—
717C22⋊C4C25116yes—
718C22⋊C4C25116yes—
719C22⋊C4C25116yes—
720C22⋊C4C25116yes—
721C22⋊C4C25164yes—
722C22⋊C4C25116yes—
723C22⋊C4C25132yes—
724C22⋊C4C25132yes—
725C22⋊C4C25132yes—
726C22⋊C4C25164yes—
727C22⋊C4C25164yes—
728C22⋊C4C25132yes—
729C22⋊C4C25164yes—
730C42C2518yes—
731C42C25116yes—
732C42C2518yes—
733C42C25116yes—
734C42C2518yes—
735C42C25132yes—
736C42C2514yes—
737C42C2514yes—
738C42C25132yes—
739C42C25116yes—
740C42C25132yes—
741C42C25132yes—
742C42C25164yes—
743C42C25164yes—
744C42C25164yes—
745C23—24no—
746C23—24no—
747C23—28no—
748C23—216no—
749C23—28no—
750C23—28no—
751C23—48no—
752C23—88no—
753C23C2×2−1+414yes—
754C23C2614yes—
755C23C2618yes—
756C23C2612yes—
757C23C2611yescharacteristic
758Q8—232no—
759Q8—232no—
760Q8—216no—
761Q8—432no—
762Q8—416no—
763Q8—464no—
764Q8—416no—
765Q8—416no—
766D4—232no—
767D4—216no—
768D4—416no—
769D4—432no—
770C2×C4—28no—
771C2×C4—24no—
772C2×C4—28no—
773C2×C4—232no—
774C2×C4—216no—
775C2×C4—216no—
776C2×C4—28no—
777C2×C4—216no—
778C2×C4—24no—
779C2×C4—216no—
780C2×C4—216no—
781C2×C4—24no—
782C2×C4—216no—
783C2×C4—216no—
784C2×C4—232no—
785C2×C4—48no—
786C2×C4—416no—
787C2×C4—464no—
788C2×C4—432no—
789C2×C4—432no—
790C2×C4—48no—
791C2×C4C2×2−1+414yes—
792C2×C4C2×2−1+414yes—
793C2×C4C2×2−1+4116yes—
794C2×C4C26116yes—
795C2×C4C2614yes—
796C2×C4C26116yes—
797C2×C4C2618yes—
798C2×C4C26116yes—
799C2×C4C2614yes—
800C2×C4C2614yes—
801C2×C4C2618yes—
802C2×C4C26116yes—
803C2×C4C26116yes—
804C2×C4C2612yes—
805C2×C4C2612yes—
806C22—24no—
807C22—28no—
808C22—24no—
809C22—28no—
810C22—216no—
811C22—28no—
812C22—416no—
813C22—48no—
814C22—88no—
815C22C22×2−1+414yes—
816C22C22×2−1+412yes—
817C222−1+614yes—
818C22C2711yescharacteristic
819C4—24no—
820C4—28no—
821C4—216no—
822C4—216no—
823C4—28no—
824C4—216no—
825C4—24no—
826C4—216no—
827C4—216no—
828C4—24no—
829C4C22×2−1+414yes—
830C4C22×2−1+414yes—
831C2—24no—
832C2—48no—
833C2—44no—
834C2#6288914yesdirect product factor
835C2C23×2−1+411yescharacteristic
836C2C2×2−1+612yes—
subgroupG/H
center, socleC23C26
commutator, Frattini, cosocleC22C27
prime radicalC2×#3455C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62889C2direct (N × H)
2. C2×#3504C2semidirect
3. C2×#3509C2semidirect
4. C2×#3495C2semidirect
5. C2×#3502C2semidirect
6. C2×#3507C2semidirect
7. C2×#3556C2semidirect
8. C2×#3555C2semidirect
9. C2×#3555C2semidirect
10. C2×#3557C2semidirect
11. C2×#3564C2semidirect
12. C2×#3563C2semidirect
13. C2×#3563C2semidirect
15. C2×#3458C2semidirect
16. C22×#541C2semidirect
17. #3564C22semidirect
18. #3563C22semidirect
19. #3563C22semidirect
20. #3557C22semidirect
21. #3556C22semidirect
22. #3555C22semidirect
23. #3555C22semidirect
24. C2×#564C22semidirect
27. C2×#563C22semidirect
28. #3509C22semidirect
29. #3507C22semidirect
30. #3504C22semidirect
31. #3502C22semidirect
32. #3495C22semidirect
33. C2×#559C22semidirect
34. C2×Q82C22semidirect
35. C2×Q82C22semidirect
36. C2×#557C22semidirect
37. C2×#557C22semidirect
38. C2×#557C22semidirect
39. C2×#557C22semidirect
40. C2×#557C22semidirect
41. C2×#557C22semidirect
42. C2×#557C22semidirect
43. C2×#557C22semidirect
46. C2×#556C22semidirect
47. C2×#556C22semidirect
48. C2×#556C22semidirect
51. C2×#554C22semidirect
52. C2×#554C22semidirect
58. C2×#552C22semidirect
59. C2×#552C22semidirect
61. #3458C22semidirect
67. C2×#544C22semidirect
68. C2×#544C22semidirect
81. C2×#541C22semidirect
82. C2×#541C22semidirect
83. C2×#541C22semidirect
84. C2×#541C22semidirect
85. C2×#541C22semidirect
86. C2×#541C22semidirect
100. C2×#533C22semidirect
101. C2×#533C22semidirect
110. C22×#125C22semidirect
122. #564C23semidirect
125. #563C23semidirect
126. #559C23semidirect
127. Q82C23semidirect
128. Q82C23semidirect
129. #557C23semidirect
130. #557C23semidirect
131. #557C23semidirect
132. #557C23semidirect
133. #557C23semidirect
134. #557C23semidirect
135. #557C23semidirect
136. #557C23semidirect
139. #556C23semidirect
140. #556C23semidirect
141. #556C23semidirect
144. #554C23semidirect
145. #554C23semidirect
151. #552C23semidirect
152. #552C23semidirect
159. #544C23semidirect
160. #544C23semidirect
172. #541C23semidirect
173. #541C23semidirect
174. #541C23semidirect
175. #541C23semidirect
176. #541C23semidirect
190. #533C23semidirect
191. #533C23semidirect
256. C2×#125C23semidirect
834. C2#62889direct (N × H)

Maximal subgroups

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

subgroupindex
#628892
C2×#35042
C2×#35092
C2×#34952
C2×#35022
C2×#35072
C2×#35562
C2×#35552
C2×#35572
C2×#35642
C2×#35632
C2×#34552
C2×#34582
C22×#5412