Finite Group Databasebeta

← C2×#62932 #10586275

Subgroups — C2×#62932 #10586275

Order 512.

31352 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62932C2164yesmaximal, direct product factor
2C2×#3510C214yesmaximal, complemented
3C2×#3509C212yesmaximal, complemented
4C2×#3495C214yesmaximal, complemented
5C2×#3523C214yesmaximal, complemented
6C2×#3502C212yesmaximal, complemented
7C2×#3507C214yesmaximal, complemented
8C2×#3501C211yesmaximal, characteristic, complemented
9C2×#3550C214yesmaximal, complemented
10C2×#3555C218yesmaximal, complemented
11C2×#3555C214yesmaximal, complemented
12C2×#3557C218yesmaximal, complemented
13C2×#3564C218yesmaximal, complemented
14C2×#3538C214yesmaximal, complemented
15C2×Q8×#41C212yesmaximal, complemented
16C22×#556C211yesmaximal, characteristic, complemented
17C2×#3461C212yesmaximal, complemented
18C2×#3460C211yesmaximal, characteristic
19#3564C221256yescomplemented
20#3557C221256yescomplemented
21#3555C221128yescomplemented
22#3555C221256yescomplemented
23#3550C221128yescomplemented
24#3538C221128yescomplemented
25C2×#563C22116yescomplemented
26C2×#563C22116yescomplemented
27C2×#563C22116yescomplemented
28#3523C221128yescomplemented
29#3510C221128yescomplemented
30#3509C22164yescomplemented
31#3507C221128yescomplemented
32#3502C22164yescomplemented
33#3501C22132yescomplemented
34#3495C221128yescomplemented
35C2×#559C2218yes—
36C2×#559C2218yes—
37Q8×#41C22164yescomplemented
38C2×Q82C2212yescomplemented
39C2×Q82C2218yescomplemented
40C2×#557C2218yescomplemented
41C2×#557C2218yescomplemented
42C2×#557C2214yescomplemented
43C2×#557C2214yescomplemented
44C2×#557C2218yescomplemented
45C2×#557C2214yescomplemented
46C2×#557C2212yescomplemented
47C2×#556C2218yes—
48C2×#556C2218yes—
49C2×#556C2214yes—
50C2×#556C2218yes—
51C2×#556C2214yes—
52C2×#556C22132yescomplemented
53C2×#556C22116yescomplemented
54C2×#556C2214yescomplemented
55C2×#556C2218yescomplemented
56C2×#556C2214yescomplemented
57C2×#554C2218yes—
58C2×#554C2218yes—
59C2×#554C2214yes—
60C2×#554C2214yes—
61C2×#554C2214yescomplemented
62C2×#554C2212yescomplemented
63C2×#552C2218yes—
64C2×#552C2218yes—
65C2×#552C2218yescomplemented
66C2×#552C22116yescomplemented
67C2×#552C22116yescomplemented
68C2×#552C2218yescomplemented
69C2×#551C22116yes—
70C2×#551C22116yes—
71C2×D4×Q8C2214yes—
72C2×D4×Q8C2214yes—
73C2×D4×Q8C2218yescomplemented
74C2×D4×Q8C2212yescomplemented
75#3461C22164yescomplemented
76#3460C22132yes—
77C2×#544C2218yes—
78C2×#544C2212yes—
79C2×#544C2211yescharacteristic
80C2×#544C2218yescomplemented
81C2×#544C2214yescomplemented
82C2×#543C2214yes—
83C2×#542C2218yes—
84C2×#542C2214yes—
85C2×#542C2218yes—
86C2×#542C22116yescomplemented
87C2×#542C2218yescomplemented
88C2×#542C2218yescomplemented
89C2×#541C2218yescomplemented
90C2×#541C22116yescomplemented
91C2×#541C22116yescomplemented
92C2×#541C2218yescomplemented
93C2×#541C2218yescomplemented
94C2×#541C2218yescomplemented
95C2×#540C2214yes—
96C2×#539C2218yes—
97C2×#539C2218yescomplemented
98C2×#539C22116yescomplemented
99C2×#538C2214yes—
100C2×#537C2211yescharacteristic
101C2×#536C2214yes—
102C2×#536C2218yescomplemented
103C2×#536C2214yescomplemented
104C2×#535C2212yes—
105C2×#533C2218yes—
106C2×#533C2212yes—
107C2×#533C2214yes—
108C2×#533C2218yescomplemented
109C2×#533C2214yescomplemented
110C2×#533C2214yescomplemented
111C2×#533C2218yescomplemented
112C2×#533C2214yescomplemented
113C2×#532C2214yes—
114C22×C4⋊Q8C2211yescharacteristic
115C2×#529C2218yes—
116C2×#529C2218yes—
117C2×#529C2218yes—
118C2×#529C2214yes—
119C2×#529C2218yescomplemented
120C22×#126C2214yes—
121C22×#124C2212yes—
122C2×#525C2214yes—
123C22×C22⋊Q8C2212yes—
124C22×C22⋊Q8C2214yes—
125C2×#520C2214yescomplemented
126C2×#519C2214yes—
127C2×#519C2214yescomplemented
128C2×#518C2212yes—
129C2×C4×#41C2212yes—
130C2×C4×#41C2214yes—
131C22×C4×Q8C2212yes—
132C22×C4×Q8C2211yescharacteristic
133C22×C4×Q8C2214yescomplemented
134C22×C4×D4C2211yescharacteristic
135C22×#117C2212yes—
136C22×#41C2312yes—
137C22×#41C2314yes—
138C23×Q8C2312yes—
139C23×Q8C2311yescharacteristic
140C23×Q8C2314yes—
141C23×Q8C2314yes—
142C23×D4C2311yescharacteristic
143C24×C4C2312yes—
144#563C231256yescomplemented
145#563C231256yescomplemented
146#563C231256yescomplemented
147#559C231128yes—
148#559C231128yes—
149Q82C23132yescomplemented
150Q82C231128yescomplemented
151#557C23132yescomplemented
152#557C23164yescomplemented
153#557C231128yescomplemented
154#557C231128yescomplemented
155#557C231128yescomplemented
156#557C23164yescomplemented
157#557C23164yescomplemented
158#556C23164yes—
159#556C23164yes—
160#556C231128yes—
161#556C231128yes—
162#556C231128yes—
163#556C231128yescomplemented
164#556C23164yescomplemented
165#556C231256yescomplemented
166#556C23164yescomplemented
167#554C23164yes—
168#554C231128yes—
169#554C23164yes—
170#554C231128yes—
171#554C23132yescomplemented
172#554C23164yescomplemented
173#552C231128yes—
174#552C231128yes—
175#552C231128yescomplemented
176#552C231256yescomplemented
177#552C231128yescomplemented
178#552C231256yescomplemented
179#551C231256yes—
180#551C231256yes—
181D4×Q8C23164yes—
182D4×Q8C23164yes—
183D4×Q8C23132yescomplemented
184D4×Q8C231128yescomplemented
185#544C23116yes—
186#544C23132yes—
187#544C231128yes—
188#544C23164yescomplemented
189#544C231128yescomplemented
190#543C23164yes—
191#542C23164yes—
192#542C231128yes—
193#542C231128yes—
194#542C231128yescomplemented
195#542C231128yescomplemented
196#542C231256yescomplemented
197#541C231128yescomplemented
198#541C231128yescomplemented
199#541C231128yescomplemented
200#541C231128yescomplemented
201#541C231256yescomplemented
202#541C231256yescomplemented
203#540C23164yes—
204#539C231128yes—
205#539C231256yescomplemented
206#539C231128yescomplemented
207#538C23164yes—
208#537C23116yes—
209#536C23164yes—
210#536C23164yescomplemented
211#536C231128yescomplemented
212#535C23132yes—
213#533C23132yes—
214#533C23164yes—
215#533C231128yes—
216#533C231128yescomplemented
217#533C23164yescomplemented
218#533C231128yescomplemented
219#533C23164yescomplemented
220#533C23164yescomplemented
221#532C23164yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C2314yes—
224C2×C4⋊Q8C23116yes—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2312yes—
228C2×C4⋊Q8C2318yes—
229C2×C4⋊Q8C2314yes—
230C2×C4⋊Q8C2314yes—
231C2×C4⋊Q8C2318yes—
232C2×C4⋊Q8C2318yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2318yes—
235C2×C4⋊Q8C2318yes—
236C2×C4⋊Q8C2318yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C23116yes—
239C2×C4⋊Q8C23116yes—
240C2×#127C2314yes—
241#529C23164yes—
242#529C231128yes—
243#529C231128yes—
244#529C231128yes—
245#529C231128yescomplemented
246C2×#126C23116yes—
247C2×#126C23116yes—
248C2×#126C23164yes—
249C2×#126C2318yes—
250C2×#126C23116yes—
251C2×#126C23116yes—
252C2×#126C23116yes—
253C2×#126C23116yes—
254C2×#126C23116yes—
255C2×#126C23116yes—
256C2×#126C23116yes—
257C2×#126C23116yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2318yes—
262C2×#125C2318yes—
263C2×#125C23116yes—
264C2×#125C2314yes—
265C2×#125C23116yes—
266C2×#125C2318yes—
267C2×#125C2318yes—
268C2×#125C2318yes—
269C2×#125C2318yes—
270C2×#125C2318yes—
271C2×#125C23116yes—
272C2×#125C23116yes—
273C2×#125C23116yes—
274C2×#125C23116yes—
275C2×#124C2318yes—
276C2×#124C2318yes—
277C2×#124C23132yes—
278C2×#124C2314yes—
279C2×#124C2318yes—
280C2×#124C2318yes—
281C2×#124C2318yes—
282C2×#124C23116yes—
283C2×#124C23116yes—
284#525C23164yes—
285C2×#123C2318yes—
286C2×#123C23116yes—
287C2×#123C23116yes—
288C2×#123C2318yes—
289C2×#123C23116yes—
290C2×#123C23116yes—
291C2×#123C23116yes—
292C2×#123C23116yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2318yes—
295C2×C22⋊Q8C2318yes—
296C2×C22⋊Q8C2318yes—
297C2×C22⋊Q8C2318yes—
298C2×C22⋊Q8C2318yes—
299C2×C22⋊Q8C23132yes—
300C2×C22⋊Q8C23164yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2318yes—
304C2×C22⋊Q8C2318yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2318yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2318yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2318yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C23116yes—
313C2×C22⋊Q8C2318yes—
314C2×C22⋊Q8C2318yes—
315C2×C22⋊Q8C2318yes—
316C2×C22⋊Q8C2318yes—
317C2×C22⋊Q8C2318yes—
318C2×C22⋊Q8C2318yes—
319C2×C22⋊Q8C23116yes—
320C2×C22⋊Q8C23116yes—
321C2×C22⋊Q8C23116yes—
322C2×C22⋊Q8C23116yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2318yes—
329C2×#120C2318yes—
330#520C23164yescomplemented
331#519C23164yes—
332#519C23164yescomplemented
333#518C23132yes—
334C4×#41C23132yes—
335C4×#41C23164yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2318yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2314yes—
340C2×C4×Q8C2318yes—
341C2×C4×Q8C23132yes—
342C2×C4×Q8C23116yes—
343C2×C4×Q8C2314yes—
344C2×C4×Q8C2314yes—
345C2×C4×Q8C2318yes—
346C2×C4×Q8C2314yes—
347C2×C4×Q8C2318yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2314yes—
350C2×C4×Q8C2314yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2318yes—
353C2×C4×Q8C2318yes—
354C2×C4×Q8C2318yes—
355C2×C4×Q8C2318yes—
356C2×C4×Q8C2318yes—
357C2×C4×Q8C2318yes—
358C2×C4×Q8C2318yes—
359C2×C4×Q8C2318yes—
360C2×C4×Q8C2314yes—
361C2×C4×Q8C2318yes—
362C2×C4×Q8C23116yes—
363C2×C4×Q8C2318yes—
364C2×C4×Q8C23164yescomplemented
365C2×C4×D4C2314yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C23116yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2318yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2318yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2318yes—
377C2×C4×D4C2318yes—
378C2×C4×D4C2318yes—
379C2×C4×D4C23116yes—
380C2×C4×D4C2318yes—
381C2×C4×D4C23116yes—
382C2×#117C2314yes—
383C2×#117C2314yes—
384C2×#117C2318yes—
385C2×#117C23132yes—
386C2×#117C2314yes—
387C2×#117C2312yes—
388C2×#117C2314yes—
389C2×#117C2318yes—
390C2×#117C23116yes—
391C2×#117C2314yes—
392C2×#117C23116yes—
393C2×#117C2318yes—
394C2×#117C23116yes—
395C2×#117C23116yes—
396C2×#117C2318yes—
397C22×C4⋊C4C2311yescharacteristic
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2311yescharacteristic
400C22×C4⋊C4C2314yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2314yes—
403C22×C4⋊C4C2318yes—
404C22×C4⋊C4C2314yes—
405C22×C4⋊C4C2318yes—
406C22×C4⋊C4C2312yes—
407C22×C22⋊C4C2314yes—
408C22×C22⋊C4C2312yes—
409C22×C22⋊C4C2318yes—
410C22×C22⋊C4C2314yes—
411C22×C42C2314yes—
412C22×C42C2311yescharacteristic
413C22×C42C2312yes—
414C22×C42C2318yes—
415C22×C42C2314yes—
416C25C2412yes—
417C2×#41—216no—
418C2×#41—416no—
419C2×#41C24116yes—
420C2×#41C24132yes—
421C22×Q8—216no—
422C22×Q8—44no—
423C22×Q8—416no—
424C22×Q8—416no—
425C22×Q8C2418yes—
426C22×Q8C2412yes—
427C22×Q8C2412yes—
428C22×Q8C2414yes—
429C22×Q8C24116yes—
430C22×Q8C2414yes—
431C22×Q8C2418yes—
432C22×Q8C2412yes—
433C22×Q8C2418yes—
434C22×Q8C2418yes—
435C22×Q8C2418yes—
436C22×Q8C2414yes—
437C22×Q8C24132yes—
438C22×Q8C24132yes—
439C22×D4—28no—
440C22×D4C2414yes—
441C22×D4C2414yes—
442C22×D4C2412yes—
443C22×D4C2418yes—
444C22×D4C2418yes—
445C22×D4C2418yes—
446C22×D4C2414yes—
447C23×C4—48no—
448C23×C4C2414yes—
449C23×C4C2411yescharacteristic
450C23×C4C2414yes—
451C23×C4C2414yes—
452C23×C4C2414yes—
453C23×C4C2411yescharacteristic
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2418yes—
458C23×C4C2418yes—
459C23×C4C2418yes—
460C23×C4C2414yes—
461C23×C4C2414yes—
462C23×C4C2418yes—
463C23×C4C24116yes—
464C23×C4C2411yescharacteristic
465C4⋊Q8C24132yes—
466C4⋊Q8C24132yes—
467C4⋊Q8C24132yes—
468C4⋊Q8C24116yes—
469C4⋊Q8C24116yes—
470C4⋊Q8C24164yes—
471C4⋊Q8C24132yes—
472C4⋊Q8C24132yes—
473C4⋊Q8C24164yes—
474C4⋊Q8C24164yes—
475C4⋊Q8C24132yes—
476C4⋊Q8C24164yes—
477C4⋊Q8C24164yes—
478C4⋊Q8C24164yes—
479C4⋊Q8C24132yes—
480C4⋊Q8C241128yes—
481C4⋊Q8C241128yes—
482#127C24132yes—
483#126C241128yes—
484#126C241128yes—
485#126C24164yes—
486#126C241128yes—
487#126C241128yes—
488#126C241128yes—
489#126C241128yes—
490#126C241128yes—
491#126C241128yes—
492#126C241128yes—
493#126C241128yes—
494#125C24132yes—
495#125C24132yes—
496#125C24132yes—
497#125C24164yes—
498#125C24164yes—
499#125C241128yes—
500#125C24132yes—
501#125C241128yes—
502#125C24164yes—
503#125C24164yes—
504#125C24164yes—
505#125C24164yes—
506#125C24164yes—
507#125C241128yes—
508#125C241128yes—
509#125C241128yes—
510#125C241128yes—
511#124C24164yes—
512#124C24164yes—
513#124C24132yes—
514#124C24164yes—
515#124C24164yes—
516#124C24164yes—
517#124C241128yes—
518#124C241128yes—
519#123C24164yes—
520#123C241128yes—
521#123C241128yes—
522#123C24164yes—
523#123C241128yes—
524#123C241128yes—
525#123C241128yes—
526#123C241128yes—
527C22⋊Q8C24132yes—
528C22⋊Q8C24164yes—
529C22⋊Q8C24164yes—
530C22⋊Q8C24164yes—
531C22⋊Q8C24164yes—
532C22⋊Q8C24164yes—
533C22⋊Q8C24132yes—
534C22⋊Q8C24132yes—
535C22⋊Q8C24164yes—
536C22⋊Q8C24164yes—
537C22⋊Q8C24132yes—
538C22⋊Q8C24164yes—
539C22⋊Q8C24132yes—
540C22⋊Q8C24164yes—
541C22⋊Q8C24132yes—
542C22⋊Q8C24164yes—
543C22⋊Q8C24132yes—
544C22⋊Q8C241128yes—
545C22⋊Q8C24164yes—
546C22⋊Q8C24164yes—
547C22⋊Q8C24164yes—
548C22⋊Q8C24164yes—
549C22⋊Q8C24164yes—
550C22⋊Q8C24164yes—
551C22⋊Q8C241128yes—
552C22⋊Q8C241128yes—
553C22⋊Q8C241128yes—
554C22⋊Q8C241128yes—
555#121C24132yes—
556#121C24132yes—
557#121C24132yes—
558#121C24132yes—
559#121C24132yes—
560#121C24164yes—
561#120C24164yes—
562C4×Q8C24116yes—
563C4×Q8C24164yes—
564C4×Q8C24116yes—
565C4×Q8C24132yes—
566C4×Q8C24164yes—
567C4×Q8C24132yes—
568C4×Q8C24132yes—
569C4×Q8C24164yes—
570C4×Q8C24132yes—
571C4×Q8C24164yes—
572C4×Q8C24116yes—
573C4×Q8C24132yes—
574C4×Q8C24132yes—
575C4×Q8C24116yes—
576C4×Q8C24164yes—
577C4×Q8C24164yes—
578C4×Q8C24164yes—
579C4×Q8C24164yes—
580C4×Q8C24164yes—
581C4×Q8C24164yes—
582C4×Q8C24164yes—
583C4×Q8C24164yes—
584C4×Q8C24132yes—
585C4×Q8C24164yes—
586C4×Q8C241128yes—
587C4×Q8C24164yes—
588C4×D4C24132yes—
589C4×D4C24132yes—
590C4×D4C24132yes—
591C4×D4C24164yes—
592C4×D4C24132yes—
593C4×D4C24116yes—
594C4×D4C24132yes—
595C4×D4C24164yes—
596C4×D4C24116yes—
597C4×D4C24132yes—
598C4×D4C24164yes—
599C4×D4C24164yes—
600C4×D4C24164yes—
601C4×D4C241128yes—
602C4×D4C24164yes—
603C4×D4C241128yes—
604#117C24132yes—
605#117C24132yes—
606#117C24164yes—
607#117C24132yes—
608#117C24116yes—
609#117C24132yes—
610#117C24164yes—
611#117C241128yes—
612#117C24132yes—
613#117C241128yes—
614#117C24164yes—
615#117C241128yes—
616#117C241128yes—
617#117C24164yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2418yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C24116yes—
629C2×C4⋊C4C24116yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C24116yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C24132yes—
640C2×C4⋊C4C24116yes—
641C2×C4⋊C4C24132yes—
642C2×C4⋊C4C24164yes—
643C2×C4⋊C4C24132yes—
644C2×C4⋊C4C24164yes—
645C2×C4⋊C4C24116yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C24116yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C24116yes—
660C2×C4⋊C4C24116yes—
661C2×C4⋊C4C24116yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C24132yes—
669C2×C22⋊C4C24116yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C24116yes—
672C2×C22⋊C4C24116yes—
673C2×C22⋊C4C24164yes—
674C2×C22⋊C4C24132yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C24116yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C24116yes—
685C2×C42C2418yes—
686C2×C42C2418yes—
687C2×C42C24116yes—
688C2×C42C24116yes—
689C2×C42C2414yes—
690C2×C42C2412yes—
691C2×C42C2418yes—
692C2×C42C2414yes—
693C2×C42C2418yes—
694C2×C42C2414yes—
695C2×C42C2418yes—
696C2×C42C24132yes—
697C2×C42C2412yes—
698C2×C42C2418yes—
699C2×C42C2414yes—
700C2×C42C2414yes—
701C2×C42C24116yes—
702C2×C42C24164yes—
703C2×C42C24132yes—
704C24—28no—
705C24—44no—
706C24—44no—
707C24C2514yes—
708C24C2514yes—
709C24C2511yescharacteristic
710C24C2518yes—
711#41—264no—
712#41—464no—
713C2×Q8—232no—
714C2×Q8—264no—
715C2×Q8—28no—
716C2×Q8—28no—
717C2×Q8—216no—
718C2×Q8—44no—
719C2×Q8—416no—
720C2×Q8—416no—
721C2×Q8—48no—
722C2×Q8—416no—
723C2×Q8—48no—
724C2×Q8—416no—
725C2×Q8—464no—
726C2×Q8—464no—
727C2×Q8C25132yes—
728C2×Q8C2518yes—
729C2×Q8C2518yes—
730C2×Q8C25116yes—
731C2×Q8C25116yes—
732C2×Q8C25132yes—
733C2×Q8C2518yes—
734C2×Q8C25132yes—
735C2×Q8C25132yes—
736C2×Q8C25116yes—
737C2×D4—216no—
738C2×D4—216no—
739C2×D4—232no—
740C2×D4—28no—
741C2×D4—416no—
742C2×D4—48no—
743C2×D4—416no—
744C2×D4C25116yes—
745C2×D4C25116yes—
746C2×D4C2518yes—
747C2×D4C25132yes—
748C2×D4C25132yes—
749C2×D4C25116yes—
750C22×C4—216no—
751C22×C4—216no—
752C22×C4—24no—
753C22×C4—216no—
754C22×C4—216no—
755C22×C4—432no—
756C22×C4—48no—
757C22×C4—44no—
758C22×C4—416no—
759C22×C4—44no—
760C22×C4—42no—
761C22×C4—416no—
762C22×C4—48no—
763C22×C4—44no—
764C22×C4—416no—
765C22×C4—416no—
766C22×C42−1+418yes—
767C22×C4C25116yes—
768C22×C4C25116yes—
769C22×C4C2514yes—
770C22×C4C25116yes—
771C22×C4C25116yes—
772C22×C4C2512yes—
773C22×C4C2518yes—
774C22×C4C2512yes—
775C22×C4C2514yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2518yes—
779C22×C4C2512yes—
780C22×C4C2518yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2511yescharacteristic
784C22×C4C2518yes—
785C22×C4C2518yes—
786C22×C4C2514yes—
787C22×C4C2518yes—
788C22×C4C25132yes—
789C22×C4C25116yes—
790C22×C4C25132yes—
791C22×C4C25132yes—
792C22×C4C25132yes—
793C22×C4C25116yes—
794C22×C4C2514yes—
795C22×C4C2512yes—
796C22×C4C2511yescharacteristic
797C4⋊C4C2514yes—
798C4⋊C4C25116yes—
799C4⋊C4C25116yes—
800C4⋊C4C25132yes—
801C4⋊C4C2518yes—
802C4⋊C4C25116yes—
803C4⋊C4C2514yes—
804C4⋊C4C25132yes—
805C4⋊C4C25116yes—
806C4⋊C4C25164yes—
807C4⋊C4C25132yes—
808C4⋊C4C25116yes—
809C4⋊C4C25132yes—
810C4⋊C4C25132yes—
811C4⋊C4C25132yes—
812C4⋊C4C25116yes—
813C4⋊C4C25164yes—
814C4⋊C4C25132yes—
815C4⋊C4C25116yes—
816C4⋊C4C25132yes—
817C4⋊C4C25164yes—
818C4⋊C4C25116yes—
819C4⋊C4C25116yes—
820C4⋊C4C2518yes—
821C4⋊C4C2518yes—
822C4⋊C4C25132yes—
823C4⋊C4C25116yes—
824C4⋊C4C25132yes—
825C4⋊C4C25116yes—
826C4⋊C4C25116yes—
827C4⋊C4C25116yes—
828C4⋊C4C25164yes—
829C4⋊C4C25164yes—
830C4⋊C4C25164yes—
831C4⋊C4C25132yes—
832C4⋊C4C25132yes—
833C4⋊C4C25132yes—
834C22⋊C4C25132yes—
835C22⋊C4C25132yes—
836C22⋊C4C25132yes—
837C22⋊C4C25164yes—
838C22⋊C4C25132yes—
839C22⋊C4C25164yes—
840C22⋊C4C25116yes—
841C22⋊C4C25132yes—
842C22⋊C4C25132yes—
843C22⋊C4C25132yes—
844C22⋊C4C25164yes—
845C22⋊C4C25116yes—
846C22⋊C4C25116yes—
847C22⋊C4C25132yes—
848C22⋊C4C25132yes—
849C22⋊C4C25164yes—
850C42C2518yes—
851C42C25116yes—
852C42C25132yes—
853C42C25132yes—
854C42C25116yes—
855C42C2518yes—
856C42C25132yes—
857C42C25116yes—
858C42C25132yes—
859C42C25116yes—
860C42C25132yes—
861C42C25116yes—
862C42C25164yes—
863C42C25164yes—
864C23—22no—
865C23—22no—
866C23—28no—
867C23—28no—
868C23—28no—
869C23—28no—
870C23—28no—
871C23—28no—
872C23—216no—
873C23—48no—
874C23—48no—
875C23—816no—
876C23C2×2−1+414yes—
877C23C2618yes—
878C23C2618yes—
879C23C2612yes—
880C23C2611yescharacteristic
881Q8—264no—
882Q8—216no—
883Q8—216no—
884Q8—232no—
885Q8—48no—
886Q8—432no—
887Q8—432no—
888Q8—416no—
889Q8—432no—
890Q8—416no—
891D4—232no—
892D4—232no—
893D4—216no—
894D4—432no—
895D4—416no—
896D4—432no—
897C2×C4—28no—
898C2×C4—232no—
899C2×C4—216no—
900C2×C4—22no—
901C2×C4—28no—
902C2×C4—28no—
903C2×C4—28no—
904C2×C4—216no—
905C2×C4—24no—
906C2×C4—216no—
907C2×C4—24no—
908C2×C4—28no—
909C2×C4—24no—
910C2×C4—232no—
911C2×C4—28no—
912C2×C4—232no—
913C2×C4—232no—
914C2×C4—416no—
915C2×C4—48no—
916C2×C4—432no—
917C2×C4—48no—
918C2×C4—44no—
919C2×C4—432no—
920C2×C4—416no—
921C2×C4—48no—
922C2×C4—432no—
923C2×C4—432no—
924C2×C4C2×2−1+418yes—
925C2×C4C2×2−1+4116yes—
926C2×C4#58514yes—
927C2×C4C2614yes—
928C2×C4C26116yes—
929C2×C4C2614yes—
930C2×C4C2618yes—
931C2×C4C2618yes—
932C2×C4C2618yes—
933C2×C4C2614yes—
934C2×C4C26116yes—
935C2×C4C2618yes—
936C2×C4C26116yes—
937C2×C4C2618yes—
938C2×C4C2612yes—
939C2×C4C2614yes—
940C2×C4C2612yes—
941C22—22no—
942C22—22no—
943C22—28no—
944C22—28no—
945C22—28no—
946C22—28no—
947C22—28no—
948C22—28no—
949C22—28no—
950C22—416no—
951C22—416no—
952C22—816no—
953C22C22×2−1+414yes—
954C22C22×2−1+412yes—
955C22C2×#58512yes—
956C222−1+612yes—
957C22C2711yescharacteristic
958C4—28no—
959C4—216no—
960C4—22no—
961C4—28no—
962C4—28no—
963C4—28no—
964C4—216no—
965C4—24no—
966C4—216no—
967C4—24no—
968C4—28no—
969C4—24no—
970C4C22×2−1+418yes—
971C4C2×#58514yes—
972C2—24no—
973C2—48no—
974C2—48no—
975C2#6293214yesdirect product factor
976C2C23×2−1+411yescharacteristic
977C2C22×#58511yescharacteristic
978C2C2×2−1+611yescharacteristic
subgroupG/H
center, socleC23C26
commutator, Frattini, cosocleC22C27
prime radicalC2×#3460C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62932C2direct (N × H)
2. C2×#3510C2semidirect
3. C2×#3509C2semidirect
4. C2×#3495C2semidirect
5. C2×#3523C2semidirect
6. C2×#3502C2semidirect
7. C2×#3507C2semidirect
8. C2×#3501C2semidirect
9. C2×#3550C2semidirect
10. C2×#3555C2semidirect
11. C2×#3555C2semidirect
12. C2×#3557C2semidirect
13. C2×#3564C2semidirect
14. C2×#3538C2semidirect
15. C2×Q8×#41C2semidirect
16. C22×#556C2semidirect
17. C2×#3461C2semidirect
19. #3564C22semidirect
20. #3557C22semidirect
21. #3555C22semidirect
22. #3555C22semidirect
23. #3550C22semidirect
24. #3538C22semidirect
25. C2×#563C22semidirect
26. C2×#563C22semidirect
27. C2×#563C22semidirect
28. #3523C22semidirect
29. #3510C22semidirect
30. #3509C22semidirect
31. #3507C22semidirect
32. #3502C22semidirect
33. #3501C22semidirect
34. #3495C22semidirect
37. Q8×#41C22semidirect
38. C2×Q82C22semidirect
39. C2×Q82C22semidirect
40. C2×#557C22semidirect
41. C2×#557C22semidirect
42. C2×#557C22semidirect
43. C2×#557C22semidirect
44. C2×#557C22semidirect
45. C2×#557C22semidirect
46. C2×#557C22semidirect
52. C2×#556C22semidirect
53. C2×#556C22semidirect
54. C2×#556C22semidirect
55. C2×#556C22semidirect
56. C2×#556C22semidirect
61. C2×#554C22semidirect
62. C2×#554C22semidirect
65. C2×#552C22semidirect
66. C2×#552C22semidirect
67. C2×#552C22semidirect
68. C2×#552C22semidirect
73. C2×D4×Q8C22semidirect
74. C2×D4×Q8C22semidirect
75. #3461C22semidirect
80. C2×#544C22semidirect
81. C2×#544C22semidirect
86. C2×#542C22semidirect
87. C2×#542C22semidirect
88. C2×#542C22semidirect
89. C2×#541C22semidirect
90. C2×#541C22semidirect
91. C2×#541C22semidirect
92. C2×#541C22semidirect
93. C2×#541C22semidirect
94. C2×#541C22semidirect
97. C2×#539C22semidirect
98. C2×#539C22semidirect
102. C2×#536C22semidirect
103. C2×#536C22semidirect
108. C2×#533C22semidirect
109. C2×#533C22semidirect
110. C2×#533C22semidirect
111. C2×#533C22semidirect
112. C2×#533C22semidirect
119. C2×#529C22semidirect
125. C2×#520C22semidirect
127. C2×#519C22semidirect
133. C22×C4×Q8C22semidirect
144. #563C23semidirect
145. #563C23semidirect
146. #563C23semidirect
149. Q82C23semidirect
150. Q82C23semidirect
151. #557C23semidirect
152. #557C23semidirect
153. #557C23semidirect
154. #557C23semidirect
155. #557C23semidirect
156. #557C23semidirect
157. #557C23semidirect
163. #556C23semidirect
164. #556C23semidirect
165. #556C23semidirect
166. #556C23semidirect
171. #554C23semidirect
172. #554C23semidirect
175. #552C23semidirect
176. #552C23semidirect
177. #552C23semidirect
178. #552C23semidirect
183. D4×Q8C23semidirect
184. D4×Q8C23semidirect
188. #544C23semidirect
189. #544C23semidirect
194. #542C23semidirect
195. #542C23semidirect
196. #542C23semidirect
197. #541C23semidirect
198. #541C23semidirect
199. #541C23semidirect
200. #541C23semidirect
201. #541C23semidirect
202. #541C23semidirect
205. #539C23semidirect
206. #539C23semidirect
210. #536C23semidirect
211. #536C23semidirect
216. #533C23semidirect
217. #533C23semidirect
218. #533C23semidirect
219. #533C23semidirect
220. #533C23semidirect
245. #529C23semidirect
330. #520C23semidirect
332. #519C23semidirect
364. C2×C4×Q8C23semidirect
975. C2#62932direct (N × H)

Maximal subgroups

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

subgroupindex
#629322
C2×#35102
C2×#35092
C2×#34952
C2×#35232
C2×#35022
C2×#35072
C2×#35012
C2×#35502
C2×#35552
C2×#35572
C2×#35642
C2×#35382
C2×Q8×#412
C22×#5562
C2×#34612
C2×#34602