Finite Group Databasebeta

← C2×#62886 #10586221

Subgroups — C2×#62886 #10586221

Order 512.

33854 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62886C2164yesmaximal, direct product factor
2C2×#3495C214yesmaximal, complemented
3C2×#3489C214yesmaximal, complemented
4C2×#3486C212yesmaximal, complemented
5C2×#3493C212yesmaximal, complemented
6C2×#3550C214yesmaximal, complemented
7C2×#3545C214yesmaximal, complemented
8C2×#3547C218yesmaximal, complemented
9C2×#3544C214yesmaximal, complemented
10C2×#3551C214yesmaximal, complemented
11C2×#3540C214yesmaximal, complemented
12C2×#3533C218yesmaximal, complemented
13C2×#3538C214yesmaximal, complemented
14C2×#3541C218yesmaximal, complemented
15C2×#3449C212yesmaximal, complemented
16C22×#536C211yesmaximal, characteristic, complemented
17C22×2−1+4C2212yes—
18C23×#41C2211yescharacteristic
19C23×#41C2212yescomplemented
20C24×Q8C2211yescharacteristic, complemented
21#3551C221128yescomplemented
22#3550C221128yescomplemented
23#3547C221256yescomplemented
24#3545C221128yescomplemented
25#3544C221128yescomplemented
26#3541C221256yescomplemented
27#3540C221128yescomplemented
28#3538C221128yescomplemented
29#3533C221256yescomplemented
30C2×#563C2218yescomplemented
31C2×#563C2214yescomplemented
32C2×#563C2218yescomplemented
33C2×#563C2218yescomplemented
34C2×#562C22116yescomplemented
35C2×#562C2218yescomplemented
36C2×H(3,𝔽4)C2214yescomplemented
37C2×#560C2218yescomplemented
38#3495C221128yescomplemented
39#3493C22164yescomplemented
40#3489C221128yescomplemented
41#3486C22164yescomplemented
42C2×#559C2218yescomplemented
43C2×Q82C2214yescomplemented
44C2×#556C2218yescomplemented
45C2×#556C2218yescomplemented
46C2×#555C2218yescomplemented
47C2×#555C2214yescomplemented
48C2×#555C2218yescomplemented
49C2×#554C2218yescomplemented
50C2×#554C2218yescomplemented
51C2×#553C22116yescomplemented
52C2×#553C2218yescomplemented
53C2×#552C2218yescomplemented
54C2×#552C2218yescomplemented
55C2×#552C2218yescomplemented
56C2×#552C22116yescomplemented
57C2×#551C2218yescomplemented
58C2×#551C2218yescomplemented
59C2×#551C22116yescomplemented
60C2×D4×Q8C2218yescomplemented
61C2×D4×Q8C2218yescomplemented
62C2×D4×Q8C2218yescomplemented
63C2×#548C2218yescomplemented
64C2×#548C2218yescomplemented
65C2×#548C2218yescomplemented
66C2×#547C2218yescomplemented
67C2×#547C22116yescomplemented
68C2×#546C22116yescomplemented
69C2×#546C2218yescomplemented
70C2×#544C22116yescomplemented
71C2×#544C2212yescomplemented
72C2×#542C2218yescomplemented
73C2×#542C22116yescomplemented
74C2×#542C22116yescomplemented
75C2×#542C22116yescomplemented
76C2×#541C2218yescomplemented
77C2×#540C22116yescomplemented
78C2×#539C22116yescomplemented
79C2×#538C22116yescomplemented
80C2×#538C22116yescomplemented
81C2×#538C2218yescomplemented
82#3449C22164yescomplemented
83C2×#537C2214yes—
84C2×#537C2212yes—
85C2×#537C2218yescomplemented
86C2×#537C2214yescomplemented
87C2×#536C2212yes—
88C2×#536C2214yes—
89C2×#536C2214yescomplemented
90C2×#536C2214yescomplemented
91C2×#536C2214yescomplemented
92C2×#536C2218yescomplemented
93C2×#536C2214yescomplemented
94C2×#536C2218yescomplemented
95C2×#536C2212yescomplemented
96C2×#536C2214yescomplemented
97C2×#536C22132yescomplemented
98C2×#535C2214yes—
99C2×#535C2212yes—
100C2×#535C2212yescomplemented
101C2×#534C2214yes—
102C2×#534C2214yescomplemented
103C2×#533C2218yescomplemented
104C2×#532C2214yes—
105C2×#532C2214yescomplemented
106C22×C4⋊Q8C2212yescomplemented
107C2×#529C2218yescomplemented
108C2×#529C2218yescomplemented
109C22×#124C2212yes—
110C2×#525C2214yes—
111C2×#525C2214yes—
112C2×#525C2214yescomplemented
113C2×#525C2218yescomplemented
114C2×#525C2218yescomplemented
115C2×#525C2214yescomplemented
116C22×#123C2214yescomplemented
117C22×C22⋊Q8C2218yescomplemented
118C22×C22⋊Q8C2214yescomplemented
119C2×#520C2214yescomplemented
120C2×#519C2212yescomplemented
121C22×#117C2211yescharacteristic, complemented
122C22×#117C2212yescomplemented
123C2×2−1+4—416no—
124C2×2−1+4C23132yes—
125C22×#41—48no—
126C22×#41—416no—
127C22×#41C2314yes—
128C22×#41C2312yes—
129C22×#41C2312yes—
130C22×#41C2312yes—
131C22×#41C2312yes—
132C22×#41C23116yes—
133C22×#41C2314yes—
134C22×#41C2314yes—
135C22×#41C2314yes—
136C22×#41C2318yes—
137C22×#41C2318yes—
138C22×#41C23132yescomplemented
139C23×Q8—48no—
140C23×Q8C2312yes—
141C23×Q8C2312yes—
142C23×Q8C2314yes—
143C23×Q8C2314yes—
144C23×Q8C2311yescharacteristic
145C23×Q8C2312yes—
146C23×Q8C2318yes—
147C23×Q8C23116yescomplemented
148C23×D4C2312yes—
149C23×D4C2311yescharacteristic
150C23×D4C2314yes—
151C23×D4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2312yes—
154C24×C4C2312yes—
155C24×C4C2314yes—
156#563C231128yescomplemented
157#563C23164yescomplemented
158#563C231128yescomplemented
159#563C231128yescomplemented
160#562C231256yescomplemented
161#562C231128yescomplemented
162H(3,𝔽4)C23164yescomplemented
163#560C231128yescomplemented
164#559C231128yescomplemented
165Q82C23164yescomplemented
166#556C231128yescomplemented
167#556C231128yescomplemented
168#555C231128yescomplemented
169#555C23164yescomplemented
170#555C231128yescomplemented
171#554C231128yescomplemented
172#554C231128yescomplemented
173#553C231128yescomplemented
174#553C231256yescomplemented
175#552C231128yescomplemented
176#552C231256yescomplemented
177#552C231128yescomplemented
178#552C231128yescomplemented
179#551C231256yescomplemented
180#551C231128yescomplemented
181#551C231128yescomplemented
182D4×Q8C231128yescomplemented
183D4×Q8C231128yescomplemented
184D4×Q8C231128yescomplemented
185#548C231128yescomplemented
186#548C231128yescomplemented
187#548C231128yescomplemented
188#547C231256yescomplemented
189#547C231128yescomplemented
190#546C231256yescomplemented
191#546C231128yescomplemented
192#544C23132yescomplemented
193#544C231256yescomplemented
194#542C231128yescomplemented
195#542C231256yescomplemented
196#542C231256yescomplemented
197#542C231256yescomplemented
198#541C231128yescomplemented
199#540C231256yescomplemented
200#539C231256yescomplemented
201#538C231128yescomplemented
202#538C231256yescomplemented
203#538C231256yescomplemented
204#537C23164yes—
205#537C23132yes—
206#537C23164yescomplemented
207#537C231128yescomplemented
208#536C23164yes—
209#536C23132yes—
210#536C23164yescomplemented
211#536C23164yescomplemented
212#536C23164yescomplemented
213#536C23164yescomplemented
214#536C23132yescomplemented
215#536C23164yescomplemented
216#536C231128yescomplemented
217#536C231128yescomplemented
218#535C23164yes—
219#535C23132yes—
220#535C23132yescomplemented
221#534C23164yes—
222#534C23164yescomplemented
223#533C231128yescomplemented
224#532C23164yes—
225#532C23164yescomplemented
226C2×C4⋊Q8C2318yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2314yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2318yes—
232C2×C4⋊Q8C2318yes—
233C2×C4⋊Q8C2318yes—
234C2×C4⋊Q8C23116yes—
235C2×C4⋊Q8C2318yes—
236C2×C4⋊Q8C23132yescomplemented
237C2×#127C2314yes—
238C2×#127C2314yes—
239#529C231128yescomplemented
240#529C231128yescomplemented
241C2×#126C23116yes—
242C2×#126C23116yes—
243C2×#126C23116yes—
244C2×#126C23116yes—
245C2×#126C23116yes—
246C2×#126C23116yes—
247C2×#125C2318yes—
248C2×#125C2318yes—
249C2×#125C23116yes—
250C2×#125C23116yes—
251C2×#125C23116yes—
252C2×#124C2314yes—
253C2×#124C2318yes—
254C2×#124C2314yes—
255C2×#124C23132yes—
256C2×#124C2318yes—
257C2×#124C2318yes—
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#124C2314yes—
261C2×#124C2314yes—
262C2×#124C2318yes—
263C2×#124C23116yes—
264C2×#124C2318yes—
265C2×#124C23116yes—
266C2×#124C23116yes—
267#525C23164yes—
268#525C23164yes—
269#525C23164yescomplemented
270#525C23164yescomplemented
271#525C231128yescomplemented
272#525C231128yescomplemented
273C2×#123C2318yes—
274C2×#123C2318yes—
275C2×#123C2318yes—
276C2×#123C2318yes—
277C2×#123C2314yes—
278C2×#123C2318yes—
279C2×#123C2314yes—
280C2×#123C2318yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C23116yes—
284C2×#123C23116yes—
285C2×#123C23116yes—
286C2×#123C23116yes—
287C2×#123C23116yes—
288C2×#123C23116yes—
289C2×#123C23116yes—
290C2×#123C23164yescomplemented
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2318yes—
293C2×C22⋊Q8C2318yes—
294C2×C22⋊Q8C2318yes—
295C2×C22⋊Q8C2318yes—
296C2×C22⋊Q8C2318yes—
297C2×C22⋊Q8C2318yes—
298C2×C22⋊Q8C23116yes—
299C2×C22⋊Q8C23116yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2318yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2318yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2318yes—
306C2×C22⋊Q8C23116yes—
307C2×C22⋊Q8C2318yes—
308C2×C22⋊Q8C23116yes—
309C2×C22⋊Q8C23116yes—
310C2×C22⋊Q8C23116yes—
311C2×C22⋊Q8C23116yes—
312C2×C22⋊Q8C23116yes—
313C2×C22⋊Q8C23164yescomplemented
314C2×C22⋊Q8C231128yescomplemented
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2318yes—
318C2×#121C2314yes—
319C2×#121C2318yes—
320C2×#121C2314yes—
321C2×#121C2318yes—
322C2×#121C23116yes—
323C2×#121C2318yes—
324C2×#121C2318yes—
325C2×#121C2318yes—
326C2×#121C2318yes—
327C2×#121C2318yes—
328C2×#121C23116yes—
329C2×#121C23116yes—
330C2×#121C23116yes—
331C2×#121C23116yes—
332C2×#120C2318yes—
333C2×#120C2314yes—
334C2×#120C2314yes—
335C2×#120C2318yes—
336C2×#120C2314yes—
337C2×#120C2314yes—
338C2×#120C23116yes—
339#520C23164yescomplemented
340#519C23132yescomplemented
341C2×C4×Q8C2318yes—
342C2×C4×Q8C2318yes—
343C2×C4×Q8C2318yes—
344C2×C4×Q8C2318yes—
345C2×C4×Q8C23116yes—
346C2×C4×D4C23116yes—
347C2×C4×D4C2318yes—
348C2×C4×D4C2318yes—
349C2×C4×D4C2318yes—
350C2×C4×D4C2318yes—
351C2×C4×D4C2318yes—
352C2×C4×D4C23116yes—
353C2×C4×D4C23116yes—
354C2×C4×D4C23116yes—
355C2×C4×D4C23116yes—
356C2×C4×D4C2318yes—
357C2×C4×D4C23116yes—
358C2×#117C2314yes—
359C2×#117C2314yes—
360C2×#117C2314yes—
361C2×#117C2312yes—
362C2×#117C2312yes—
363C2×#117C2314yes—
364C2×#117C2314yes—
365C2×#117C2318yes—
366C2×#117C2318yes—
367C2×#117C23116yes—
368C2×#117C23116yes—
369C2×#117C23116yes—
370C2×#117C23116yescomplemented
371C2×#117C23132yescomplemented
372C22×C4⋊C4C2312yes—
373C22×C4⋊C4C2314yes—
374C22×C4⋊C4C2318yes—
375C22×C4⋊C4C2318yes—
376C22×C4⋊C4C23116yes—
377C22×C22⋊C4C2312yes—
378C22×C22⋊C4C2314yes—
379C22×C22⋊C4C2318yes—
380C22×C22⋊C4C23116yes—
381C22×C42C2312yes—
382C22×C42C2314yes—
383C25C2412yes—
384C25C2411yescharacteristic
385C25C2414yes—
3862−1+4—4128no—
387C2×#41—232no—
388C2×#41—48no—
389C2×#41—48no—
390C2×#41—48no—
391C2×#41—48no—
392C2×#41—464no—
393C2×#41—416no—
394C2×#41—416no—
395C2×#41—432no—
396C2×#41—416no—
397C2×#41—432no—
398C2×#41—4128no—
399C2×#41C24132yes—
400C2×#41C24116yes—
401C2×#41C24116yes—
402C2×#41C24164yes—
403C2×#41C24164yes—
404C2×#41C24116yes—
405C2×#41C24132yes—
406C2×#41C24116yes—
407C2×#41C24132yes—
408C2×#41C24132yes—
409C22×Q8—216no—
410C22×Q8—48no—
411C22×Q8—44no—
412C22×Q8—416no—
413C22×Q8—416no—
414C22×Q8—464no—
415C22×Q8—48no—
416C22×Q8—432no—
417C22×Q8C2418yes—
418C22×Q8C2414yes—
419C22×Q8C24116yes—
420C22×Q8C2418yes—
421C22×Q8C2411yescharacteristic
422C22×Q8C2418yes—
423C22×Q8C2414yes—
424C22×Q8C2414yes—
425C22×Q8C2412yes—
426C22×Q8C2414yes—
427C22×Q8C24164yes—
428C22×Q8C2411yescharacteristic
429C22×Q8C24116yes—
430C22×Q8C2418yes—
431C22×Q8C24132yes—
432C22×Q8C24116yes—
433C22×Q8C24132yes—
434C22×D4—48no—
435C22×D4—44no—
436C22×D4—48no—
437C22×D4—416no—
438C22×D4C2418yes—
439C22×D4C2414yes—
440C22×D4C2418yes—
441C22×D4C2418yes—
442C22×D4C2418yes—
443C22×D4C2418yes—
444C22×D4C2418yes—
445C22×D4C2411yescharacteristic
446C22×D4C2418yes—
447C22×D4C2412yes—
448C22×D4C2412yes—
449C22×D4C2412yes—
450C22×D4C2412yes—
451C22×D4C2418yes—
452C22×D4C2411yescharacteristic
453C22×D4C2412yes—
454C22×D4C2414yes—
455C22×D4C24116yes—
456C22×D4C2418yes—
457C22×D4C24132yes—
458C22×D4C24116yes—
459C23×C4—28no—
460C23×C4—216no—
461C23×C4—416no—
462C23×C4—48no—
463C23×C4C2414yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2418yes—
467C23×C4C2412yes—
468C23×C4C2412yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C24116yes—
472C23×C4C2418yes—
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2414yes—
476C23×C4C24116yes—
477C23×C4C2418yes—
478C23×C4C24116yes—
479C23×C4C2418yes—
480C23×C4C2418yes—
481C23×C4C2414yes—
482C23×C4C24132yes—
483C23×C4C24116yes—
484C23×C4C2411yescharacteristic
485C4⋊Q8C24164yes—
486C4⋊Q8C24132yes—
487C4⋊Q8C24132yes—
488C4⋊Q8C24132yes—
489C4⋊Q8C24132yes—
490C4⋊Q8C24164yes—
491C4⋊Q8C24164yes—
492C4⋊Q8C24164yes—
493C4⋊Q8C241128yes—
494C4⋊Q8C24164yes—
495#127C24132yes—
496#127C24132yes—
497#126C241128yes—
498#126C241128yes—
499#126C241128yes—
500#126C241128yes—
501#126C241128yes—
502#126C241128yes—
503#125C24164yes—
504#125C24164yes—
505#125C241128yes—
506#125C241128yes—
507#125C241128yes—
508#124C24132yes—
509#124C24164yes—
510#124C24132yes—
511#124C24164yes—
512#124C24164yes—
513#124C24132yes—
514#124C24132yes—
515#124C24132yes—
516#124C24132yes—
517#124C24164yes—
518#124C241128yes—
519#124C24164yes—
520#124C241128yes—
521#124C241128yes—
522#123C24164yes—
523#123C24164yes—
524#123C24164yes—
525#123C24164yes—
526#123C24132yes—
527#123C24164yes—
528#123C24132yes—
529#123C24164yes—
530#123C24132yes—
531#123C24132yes—
532#123C241128yes—
533#123C241128yes—
534#123C241128yes—
535#123C241128yes—
536#123C241128yes—
537#123C241128yes—
538#123C241128yes—
539C22⋊Q8C24132yes—
540C22⋊Q8C24164yes—
541C22⋊Q8C24164yes—
542C22⋊Q8C24164yes—
543C22⋊Q8C24164yes—
544C22⋊Q8C24164yes—
545C22⋊Q8C24164yes—
546C22⋊Q8C241128yes—
547C22⋊Q8C241128yes—
548C22⋊Q8C24132yes—
549C22⋊Q8C24164yes—
550C22⋊Q8C24132yes—
551C22⋊Q8C24164yes—
552C22⋊Q8C24132yes—
553C22⋊Q8C24164yes—
554C22⋊Q8C241128yes—
555C22⋊Q8C24164yes—
556C22⋊Q8C241128yes—
557C22⋊Q8C241128yes—
558C22⋊Q8C241128yes—
559C22⋊Q8C241128yes—
560C22⋊Q8C241128yes—
561#121C24132yes—
562#121C24132yes—
563#121C24164yes—
564#121C24132yes—
565#121C24164yes—
566#121C24132yes—
567#121C24164yes—
568#121C241128yes—
569#121C24164yes—
570#121C24164yes—
571#121C24164yes—
572#121C24164yes—
573#121C24164yes—
574#121C241128yes—
575#121C241128yes—
576#121C241128yes—
577#121C241128yes—
578#120C24164yes—
579#120C24132yes—
580#120C24132yes—
581#120C24164yes—
582#120C24132yes—
583#120C24132yes—
584#120C241128yes—
585C4×Q8C24164yes—
586C4×Q8C24164yes—
587C4×Q8C24164yes—
588C4×Q8C24164yes—
589C4×Q8C241128yes—
590C4×D4C241128yes—
591C4×D4C24164yes—
592C4×D4C24164yes—
593C4×D4C24164yes—
594C4×D4C24164yes—
595C4×D4C24164yes—
596C4×D4C241128yes—
597C4×D4C241128yes—
598C4×D4C241128yes—
599C4×D4C241128yes—
600C4×D4C24164yes—
601C4×D4C241128yes—
602#117C24132yes—
603#117C24132yes—
604#117C24132yes—
605#117C24116yes—
606#117C24116yes—
607#117C24132yes—
608#117C24132yes—
609#117C24164yes—
610#117C24164yes—
611#117C241128yes—
612#117C241128yes—
613#117C241128yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C24116yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C24116yes—
622C2×C4⋊C4C24116yes—
623C2×C4⋊C4C24116yes—
624C2×C4⋊C4C24132yes—
625C2×C4⋊C4C24116yes—
626C2×C4⋊C4C24164yes—
627C2×C4⋊C4C24164yes—
628C2×C4⋊C4C241128yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C24116yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C24116yes—
633C2×C4⋊C4C24116yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C24116yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2414yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C24116yes—
643C2×C22⋊C4C24116yes—
644C2×C22⋊C4C24116yes—
645C2×C22⋊C4C24116yes—
646C2×C22⋊C4C24132yes—
647C2×C22⋊C4C24164yes—
648C2×C22⋊C4C241128yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C24116yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C22⋊C4C2418yes—
657C2×C22⋊C4C24116yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2418yes—
661C2×C42C24116yes—
662C2×C42C2418yes—
663C2×C42C2418yes—
664C2×C42C2414yes—
665C2×C42C2414yes—
666C2×C42C24116yes—
667C2×C42C24132yes—
668C24—24no—
669C24—28no—
670C24—44no—
671C24—48no—
672C24—48no—
673C24—416no—
674C24C2512yes—
675C24C2512yes—
676C24C2512yes—
677C24C2518yes—
678C24C2511yescharacteristic
679C24C2518yes—
680C24C2514yes—
681C24C25116yes—
682#41—2128no—
683#41—432no—
684#41—432no—
685#41—432no—
686#41—432no—
687#41—464no—
688#41—464no—
689#41—4128no—
690#41—464no—
691#41—4128no—
692C2×Q8—232no—
693C2×Q8—264no—
694C2×Q8—216no—
695C2×Q8—48no—
696C2×Q8—48no—
697C2×Q8—432no—
698C2×Q8—416no—
699C2×Q8—42no—
700C2×Q8—44no—
701C2×Q8—42no—
702C2×Q8—48no—
703C2×Q8—416no—
704C2×Q8—416no—
705C2×Q8—464no—
706C2×Q8—464no—
707C2×Q8—432no—
708C2×Q8—4128no—
709C2×Q8C25132yes—
710C2×Q8C25116yes—
711C2×Q8C25132yes—
712C2×Q8C2514yes—
713C2×Q8C25132yes—
714C2×Q8C25116yes—
715C2×Q8C25116yes—
716C2×Q8C2518yes—
717C2×Q8C25116yes—
718C2×Q8C2514yes—
719C2×D4—232no—
720C2×D4—216no—
721C2×D4—432no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—42no—
728C2×D4—44no—
729C2×D4—42no—
730C2×D4—416no—
731C2×D4—432no—
732C2×D4—416no—
733C2×D4—416no—
734C2×D4—416no—
735C2×D4—416no—
736C2×D4—416no—
737C2×D4—416no—
738C2×D4—416no—
739C2×D4—464no—
740C2×D4C25132yes—
741C2×D4C25116yes—
742C2×D4C25132yes—
743C2×D4C25132yes—
744C2×D4C25132yes—
745C2×D4C25132yes—
746C2×D4C25132yes—
747C2×D4C2514yes—
748C2×D4C25132yes—
749C2×D4C2518yes—
750C2×D4C2518yes—
751C2×D4C2518yes—
752C2×D4C2518yes—
753C2×D4C25132yes—
754C2×D4C2514yes—
755C2×D4C2518yes—
756C2×D4C25116yes—
757C22×C4—24no—
758C22×C4—28no—
759C22×C4—216no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—232no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—264no—
768C22×C4—232no—
769C22×C4—464no—
770C22×C4—48no—
771C22×C4—416no—
772C22×C4—432no—
773C22×C4—416no—
774C22×C4—432no—
775C22×C4—416no—
776C22×C4—48no—
777C22×C4—432no—
778C22×C4H(5,𝔽2)18yes—
779C22×C4C2518yes—
780C22×C4C2514yes—
781C22×C4C25116yes—
782C22×C4C2518yes—
783C22×C4C2518yes—
784C22×C4C25132yes—
785C22×C4C2518yes—
786C22×C4C2518yes—
787C22×C4C2518yes—
788C22×C4C2518yes—
789C22×C4C2518yes—
790C22×C4C2518yes—
791C22×C4C2518yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2512yes—
795C22×C4C2518yes—
796C22×C4C2518yes—
797C22×C4C2512yes—
798C22×C4C25116yes—
799C22×C4C25132yes—
800C22×C4C25164yes—
801C22×C4C25164yes—
802C22×C4C25132yes—
803C22×C4C25132yes—
804C22×C4C25116yes—
805C22×C4C2514yes—
806C22×C4C2512yes—
807C4⋊C4C25116yes—
808C4⋊C4C25132yes—
809C4⋊C4C25132yes—
810C4⋊C4C25164yes—
811C4⋊C4C25132yes—
812C4⋊C4C25116yes—
813C4⋊C4C25132yes—
814C4⋊C4C25164yes—
815C4⋊C4C25164yes—
816C4⋊C4C25164yes—
817C4⋊C4C25132yes—
818C4⋊C4C25164yes—
819C4⋊C4C25132yes—
820C4⋊C4C25164yes—
821C4⋊C4C25164yes—
822C4⋊C4C25132yes—
823C4⋊C4C25132yes—
824C22⋊C4C25132yes—
825C22⋊C4C25164yes—
826C22⋊C4C25132yes—
827C22⋊C4C25116yes—
828C22⋊C4C25116yes—
829C22⋊C4C25132yes—
830C22⋊C4C25164yes—
831C22⋊C4C25164yes—
832C22⋊C4C25164yes—
833C22⋊C4C25132yes—
834C22⋊C4C25132yes—
835C22⋊C4C25132yes—
836C22⋊C4C25164yes—
837C22⋊C4C25132yes—
838C22⋊C4C25132yes—
839C22⋊C4C25132yes—
840C22⋊C4C25132yes—
841C22⋊C4C25164yes—
842C42C25116yes—
843C42C25116yes—
844C42C25132yes—
845C42C25116yes—
846C42C25116yes—
847C42C25132yes—
848C42C25164yes—
849C42C25132yes—
850C23—24no—
851C23—28no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—216no—
856C23—28no—
857C23—216no—
858C23—28no—
859C23—216no—
860C23—28no—
861C23—216no—
862C23—48no—
863C23—416no—
864C23—416no—
865C23—432no—
866C23—416no—
867C23—816no—
868C23—832no—
869C23C2×H(5,𝔽2)14yes—
870C23C2614yes—
871C23C2614yes—
872C23C2614yes—
873C23C26116yes—
874C23C2612yes—
875C23C2611yescharacteristic
876Q8—264no—
877Q8—232no—
878Q8—416no—
879Q8—416no—
880Q8—432no—
881Q8—44no—
882Q8—48no—
883Q8—44no—
884Q8—416no—
885Q8—432no—
886D4—264no—
887D4—232no—
888D4—48no—
889D4—48no—
890D4—48no—
891D4—48no—
892D4—416no—
893D4—44no—
894D4—48no—
895D4—44no—
896D4—432no—
897D4—432no—
898D4—432no—
899D4—432no—
900D4—432no—
901D4—432no—
902D4—432no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—28no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—216no—
909C2×C4—216no—
910C2×C4—216no—
911C2×C4—232no—
912C2×C4—216no—
913C2×C4—216no—
914C2×C4—216no—
915C2×C4—216no—
916C2×C4—216no—
917C2×C4—216no—
918C2×C4—216no—
919C2×C4—216no—
920C2×C4—216no—
921C2×C4—264no—
922C2×C4—416no—
923C2×C4—432no—
924C2×C4—432no—
925C2×C4—464no—
926C2×C4—432no—
927C2×C4—416no—
928C2×C4—464no—
929C2×C4C2×H(5,𝔽2)18yes—
930C2×C4C2×H(5,𝔽2)116yes—
931C2×C4C26116yes—
932C2×C4C26116yes—
933C2×C4C26116yes—
934C2×C4C2612yes—
935C2×C4C2612yes—
936C2×C4C2614yes—
937C2×C4C26116yes—
938C2×C4C26116yes—
939C2×C4C2614yes—
940C2×C4C2614yes—
941C22—24no—
942C22—28no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—216no—
947C22—28no—
948C22—216no—
949C22—28no—
950C22—216no—
951C22—28no—
952C22—416no—
953C22—48no—
954C22—48no—
955C22—432no—
956C22—48no—
957C22—816no—
958C22—832no—
959C22C22×H(5,𝔽2)14yes—
960C22C22×H(5,𝔽2)12yes—
961C222−1+614yes—
962C22C2711yescharacteristic
963C4—24no—
964C4—24no—
965C4—22no—
966C4—22no—
967C4—216no—
968C4—216no—
969C4—216no—
970C4—216no—
971C4—216no—
972C4C22×H(5,𝔽2)18yes—
973C2—24no—
974C2—44no—
975C2—44no—
976C2—416no—
977C2—44no—
978C2#6288614yesdirect product factor
979C2C23×H(5,𝔽2)11yescharacteristic
980C2C2×2−1+612yes—
subgroupG/H
center, socleC23C26
commutator, Frattini, cosocleC22C27
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62886C2direct (N × H)
2. C2×#3495C2semidirect
3. C2×#3489C2semidirect
4. C2×#3486C2semidirect
5. C2×#3493C2semidirect
6. C2×#3550C2semidirect
7. C2×#3545C2semidirect
8. C2×#3547C2semidirect
9. C2×#3544C2semidirect
10. C2×#3551C2semidirect
11. C2×#3540C2semidirect
12. C2×#3533C2semidirect
13. C2×#3538C2semidirect
14. C2×#3541C2semidirect
15. C2×#3449C2semidirect
16. C22×#536C2semidirect
19. C23×#41C22semidirect
20. C24×Q8C22semidirect
21. #3551C22semidirect
22. #3550C22semidirect
23. #3547C22semidirect
24. #3545C22semidirect
25. #3544C22semidirect
26. #3541C22semidirect
27. #3540C22semidirect
28. #3538C22semidirect
29. #3533C22semidirect
30. C2×#563C22semidirect
31. C2×#563C22semidirect
32. C2×#563C22semidirect
33. C2×#563C22semidirect
34. C2×#562C22semidirect
35. C2×#562C22semidirect
36. C2×H(3,𝔽4)C22semidirect
37. C2×#560C22semidirect
38. #3495C22semidirect
39. #3493C22semidirect
40. #3489C22semidirect
41. #3486C22semidirect
42. C2×#559C22semidirect
43. C2×Q82C22semidirect
44. C2×#556C22semidirect
45. C2×#556C22semidirect
46. C2×#555C22semidirect
47. C2×#555C22semidirect
48. C2×#555C22semidirect
49. C2×#554C22semidirect
50. C2×#554C22semidirect
51. C2×#553C22semidirect
52. C2×#553C22semidirect
53. C2×#552C22semidirect
54. C2×#552C22semidirect
55. C2×#552C22semidirect
56. C2×#552C22semidirect
57. C2×#551C22semidirect
58. C2×#551C22semidirect
59. C2×#551C22semidirect
60. C2×D4×Q8C22semidirect
61. C2×D4×Q8C22semidirect
62. C2×D4×Q8C22semidirect
63. C2×#548C22semidirect
64. C2×#548C22semidirect
65. C2×#548C22semidirect
66. C2×#547C22semidirect
67. C2×#547C22semidirect
68. C2×#546C22semidirect
69. C2×#546C22semidirect
70. C2×#544C22semidirect
71. C2×#544C22semidirect
72. C2×#542C22semidirect
73. C2×#542C22semidirect
74. C2×#542C22semidirect
75. C2×#542C22semidirect
76. C2×#541C22semidirect
77. C2×#540C22semidirect
78. C2×#539C22semidirect
79. C2×#538C22semidirect
80. C2×#538C22semidirect
81. C2×#538C22semidirect
82. #3449C22semidirect
85. C2×#537C22semidirect
86. C2×#537C22semidirect
89. C2×#536C22semidirect
90. C2×#536C22semidirect
91. C2×#536C22semidirect
92. C2×#536C22semidirect
93. C2×#536C22semidirect
94. C2×#536C22semidirect
95. C2×#536C22semidirect
96. C2×#536C22semidirect
97. C2×#536C22semidirect
100. C2×#535C22semidirect
102. C2×#534C22semidirect
103. C2×#533C22semidirect
105. C2×#532C22semidirect
106. C22×C4⋊Q8C22semidirect
107. C2×#529C22semidirect
108. C2×#529C22semidirect
112. C2×#525C22semidirect
113. C2×#525C22semidirect
114. C2×#525C22semidirect
115. C2×#525C22semidirect
116. C22×#123C22semidirect
117. C22×C22⋊Q8C22semidirect
118. C22×C22⋊Q8C22semidirect
119. C2×#520C22semidirect
120. C2×#519C22semidirect
121. C22×#117C22semidirect
122. C22×#117C22semidirect
138. C22×#41C23semidirect
147. C23×Q8C23semidirect
156. #563C23semidirect
157. #563C23semidirect
158. #563C23semidirect
159. #563C23semidirect
160. #562C23semidirect
161. #562C23semidirect
162. H(3,𝔽4)C23semidirect
163. #560C23semidirect
164. #559C23semidirect
165. Q82C23semidirect
166. #556C23semidirect
167. #556C23semidirect
168. #555C23semidirect
169. #555C23semidirect
170. #555C23semidirect
171. #554C23semidirect
172. #554C23semidirect
173. #553C23semidirect
174. #553C23semidirect
175. #552C23semidirect
176. #552C23semidirect
177. #552C23semidirect
178. #552C23semidirect
179. #551C23semidirect
180. #551C23semidirect
181. #551C23semidirect
182. D4×Q8C23semidirect
183. D4×Q8C23semidirect
184. D4×Q8C23semidirect
185. #548C23semidirect
186. #548C23semidirect
187. #548C23semidirect
188. #547C23semidirect
189. #547C23semidirect
190. #546C23semidirect
191. #546C23semidirect
192. #544C23semidirect
193. #544C23semidirect
194. #542C23semidirect
195. #542C23semidirect
196. #542C23semidirect
197. #542C23semidirect
198. #541C23semidirect
199. #540C23semidirect
200. #539C23semidirect
201. #538C23semidirect
202. #538C23semidirect
203. #538C23semidirect
206. #537C23semidirect
207. #537C23semidirect
210. #536C23semidirect
211. #536C23semidirect
212. #536C23semidirect
213. #536C23semidirect
214. #536C23semidirect
215. #536C23semidirect
216. #536C23semidirect
217. #536C23semidirect
220. #535C23semidirect
222. #534C23semidirect
223. #533C23semidirect
225. #532C23semidirect
236. C2×C4⋊Q8C23semidirect
239. #529C23semidirect
240. #529C23semidirect
269. #525C23semidirect
270. #525C23semidirect
271. #525C23semidirect
272. #525C23semidirect
290. C2×#123C23semidirect
313. C2×C22⋊Q8C23semidirect
314. C2×C22⋊Q8C23semidirect
339. #520C23semidirect
340. #519C23semidirect
370. C2×#117C23semidirect
371. C2×#117C23semidirect
978. C2#62886direct (N × H)

Maximal subgroups

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

subgroupindex
#628862
C2×#34952
C2×#34892
C2×#34862
C2×#34932
C2×#35502
C2×#35452
C2×#35472
C2×#35442
C2×#35512
C2×#35402
C2×#35332
C2×#35382
C2×#35412
C2×#34492
C22×#5362