Finite Group Databasebeta

← C2×#62945 #10586289

Subgroups — C2×#62945 #10586289

Order 512.

31808 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62945C2164yesmaximal, direct product factor
2C2×#3495C214yesmaximal, complemented
3C2×#3503C212yesmaximal, complemented
4C2×#3503C214yesmaximal, complemented
5C2×#3502C211yesmaximal, characteristic, complemented
6C2×#3515C214yesmaximal, complemented
7C2×#3520C214yesmaximal, complemented
8C2×#3492C212yesmaximal, complemented
9C2×#3555C214yesmaximal, complemented
10C2×#3544C214yesmaximal, complemented
11C2×#3552C218yesmaximal, complemented
12C2×#3563C214yesmaximal, complemented
13C2×#3563C218yesmaximal, complemented
14C2×#3538C218yesmaximal, complemented
15C2×#3475C212yesmaximal, complemented
16C22×#554C211yesmaximal, characteristic, complemented
17C2×#3461C211yesmaximal, characteristic, complemented
18C22×#544C212yesmaximal, complemented
19#3563C221128yescomplemented
20#3563C221256yescomplemented
21#3555C221128yescomplemented
22#3552C221256yescomplemented
23#3544C221128yescomplemented
24#3538C221256yescomplemented
25C2×#564C2218yescomplemented
26C2×#563C22116yescomplemented
27C2×#563C22116yescomplemented
28C2×#563C2218yescomplemented
29#3520C221128yescomplemented
30#3515C221128yescomplemented
31#3503C22164yescomplemented
32#3503C221128yescomplemented
33#3502C22132yescomplemented
34#3495C221128yescomplemented
35#3492C22164yescomplemented
36C2×Q82C2214yescomplemented
37C2×Q82C2214yescomplemented
38C2×#557C2214yescomplemented
39C2×#557C2218yescomplemented
40C2×#557C2218yescomplemented
41C2×#557C2214yescomplemented
42#3475C22164yescomplemented
43C2×#556C2214yes—
44C2×#556C2212yes—
45C2×#556C2218yescomplemented
46C2×#555C2212yes—
47C2×#554C2218yes—
48C2×#554C2218yes—
49C2×#554C2214yes—
50C2×#554C2214yes—
51C2×#554C2212yes—
52C2×#554C22132yescomplemented
53C2×#554C2218yescomplemented
54C2×#554C2218yescomplemented
55C2×#554C2214yescomplemented
56C2×#553C2214yes—
57C2×#553C2218yescomplemented
58C2×#552C22116yes—
59C2×#552C2218yes—
60C2×#552C2214yes—
61C2×#552C2214yes—
62C2×#552C22116yescomplemented
63C2×#552C2218yescomplemented
64C2×#552C2218yescomplemented
65C2×#552C2218yescomplemented
66C2×#552C2218yescomplemented
67C2×#551C2218yes—
68C2×#551C22116yes—
69C2×D4×Q8C2218yes—
70C2×D4×Q8C2214yes—
71C2×D4×Q8C22116yescomplemented
72C2×D4×Q8C2214yescomplemented
73C2×#548C2218yes—
74C2×#547C2214yes—
75C2×#547C2214yes—
76C2×#547C2212yes—
77C2×#547C2218yescomplemented
78C2×#546C2214yes—
79#3461C22132yescomplemented
80C2×#544C2214yes—
81C2×#544C2218yes—
82C2×#544C2212yes—
83C2×#544C2214yes—
84C2×#544C2211yescharacteristic
85C2×#544C22116yescomplemented
86C2×#544C2218yescomplemented
87C2×#544C2218yescomplemented
88C2×#544C2218yescomplemented
89C2×#544C2218yescomplemented
90C2×#544C22164yescomplemented
91C2×#542C2218yes—
92C2×#542C2214yescomplemented
93C2×#542C2218yescomplemented
94C2×#541C22116yescomplemented
95C2×#541C22116yescomplemented
96C2×#541C2214yescomplemented
97C2×#541C2218yescomplemented
98C2×#541C2218yescomplemented
99C2×#539C2214yes—
100C2×#539C2218yes—
101C2×#539C22116yes—
102C2×#539C22116yescomplemented
103C2×#537C2211yescharacteristic
104C2×#536C2212yes—
105C2×#536C22116yescomplemented
106C2×#533C2214yes—
107C2×#533C2212yes—
108C2×#533C2218yescomplemented
109C2×#533C2214yescomplemented
110C2×#533C2214yescomplemented
111C22×C4⋊Q8C2211yescharacteristic
112C22×C4⋊Q8C2218yescomplemented
113C22×C4⋊Q8C2214yescomplemented
114C2×#529C2218yes—
115C2×#529C2214yes—
116C2×#529C2214yes—
117C2×#529C2218yescomplemented
118C2×#529C2214yescomplemented
119C22×#125C2212yes—
120C22×#125C2218yescomplemented
121C2×#525C2218yes—
122C2×#525C2214yes—
123C22×C22⋊Q8C2214yes—
124C22×C22⋊Q8C2218yes—
125C22×C22⋊Q8C2212yes—
126C2×#520C2214yes—
127C2×#520C2218yes—
128C2×#519C2212yes—
129C2×C4×#41C2214yes—
130C2×C4×#41C2212yes—
131C22×C4×Q8C2211yescharacteristic
132C22×C4×D4C2212yes—
133C22×C4×D4C2211yescharacteristic
134C22×#117C2214yes—
135C23×C4⋊C4C2212yes—
136C22×#41C2312yes—
137C22×#41C2314yes—
138C22×#41C2318yes—
139C23×Q8C2311yescharacteristic
140C23×Q8C2312yes—
141C23×Q8C2318yes—
142C23×Q8C2318yes—
143C23×D4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2314yes—
146#564C231128yescomplemented
147#563C231256yescomplemented
148#563C231256yescomplemented
149#563C231128yescomplemented
150Q82C23164yescomplemented
151Q82C23164yescomplemented
152#557C23164yescomplemented
153#557C231128yescomplemented
154#557C231128yescomplemented
155#557C23164yescomplemented
156#556C23132yes—
157#556C23164yes—
158#556C231128yescomplemented
159#555C23132yes—
160#554C23164yes—
161#554C23164yes—
162#554C231128yes—
163#554C23132yes—
164#554C231128yes—
165#554C231128yescomplemented
166#554C231128yescomplemented
167#554C23164yescomplemented
168#553C23164yes—
169#553C231128yescomplemented
170#552C23164yes—
171#552C23164yes—
172#552C231256yes—
173#552C231128yes—
174#552C231128yescomplemented
175#552C231128yescomplemented
176#552C231128yescomplemented
177#552C231256yescomplemented
178#552C231128yescomplemented
179#551C231128yes—
180#551C231256yes—
181D4×Q8C23164yes—
182D4×Q8C231128yes—
183D4×Q8C231256yescomplemented
184D4×Q8C23164yescomplemented
185#548C231128yes—
186#547C23132yes—
187#547C23164yes—
188#547C23164yes—
189#547C231128yescomplemented
190#546C23164yes—
191#544C23116yes—
192#544C23132yes—
193#544C23164yes—
194#544C231128yes—
195#544C23164yes—
196#544C231128yescomplemented
197#544C231128yescomplemented
198#544C231256yescomplemented
199#544C231128yescomplemented
200#544C231128yescomplemented
201#542C231128yes—
202#542C23164yescomplemented
203#542C231128yescomplemented
204#541C23164yescomplemented
205#541C231128yescomplemented
206#541C231128yescomplemented
207#541C231256yescomplemented
208#541C231256yescomplemented
209#539C23164yes—
210#539C231128yes—
211#539C231256yes—
212#539C231256yescomplemented
213#537C23116yes—
214#536C23132yes—
215#536C231256yescomplemented
216#533C23132yes—
217#533C23164yes—
218#533C23164yescomplemented
219#533C231128yescomplemented
220#533C23164yescomplemented
221C2×C4⋊Q8C2314yes—
222C2×C4⋊Q8C2314yes—
223C2×C4⋊Q8C23116yes—
224C2×C4⋊Q8C2312yes—
225C2×C4⋊Q8C2314yes—
226C2×C4⋊Q8C2318yes—
227C2×C4⋊Q8C23116yes—
228C2×C4⋊Q8C2318yes—
229C2×C4⋊Q8C2318yes—
230C2×C4⋊Q8C2318yes—
231C2×C4⋊Q8C23116yes—
232C2×C4⋊Q8C2318yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2314yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C23116yes—
238C2×C4⋊Q8C23116yes—
239C2×C4⋊Q8C231128yescomplemented
240C2×C4⋊Q8C23164yescomplemented
241#529C23164yes—
242#529C23164yes—
243#529C231128yes—
244#529C23164yescomplemented
245#529C231128yescomplemented
246C2×#126C2318yes—
247C2×#126C2318yes—
248C2×#126C2318yes—
249C2×#126C2318yes—
250C2×#126C2318yes—
251C2×#126C23116yes—
252C2×#126C23116yes—
253C2×#126C23116yes—
254C2×#126C23116yes—
255C2×#126C23116yes—
256C2×#125C2318yes—
257C2×#125C2318yes—
258C2×#125C23132yes—
259C2×#125C2314yes—
260C2×#125C2318yes—
261C2×#125C23116yes—
262C2×#125C2318yes—
263C2×#125C23116yes—
264C2×#125C2318yes—
265C2×#125C2318yes—
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×#125C2318yes—
269C2×#125C2314yes—
270C2×#125C2318yes—
271C2×#125C23116yes—
272C2×#125C23116yes—
273C2×#125C23116yes—
274C2×#125C23116yes—
275C2×#125C23116yes—
276C2×#125C23116yes—
277C2×#125C231128yescomplemented
278C2×#124C2318yes—
279C2×#124C2314yes—
280C2×#124C2314yes—
281C2×#124C2314yes—
282C2×#124C23116yes—
283#525C23164yes—
284#525C231128yes—
285C2×#123C2318yes—
286C2×#123C23116yes—
287C2×#123C2318yes—
288C2×#123C2318yes—
289C2×#123C2318yes—
290C2×#123C2318yes—
291C2×#123C2318yes—
292C2×#123C23116yes—
293C2×#123C23116yes—
294C2×#123C23116yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2318yes—
297C2×C22⋊Q8C2318yes—
298C2×C22⋊Q8C23116yes—
299C2×C22⋊Q8C23116yes—
300C2×C22⋊Q8C23116yes—
301C2×C22⋊Q8C2318yes—
302C2×C22⋊Q8C23116yes—
303C2×C22⋊Q8C2318yes—
304C2×C22⋊Q8C2318yes—
305C2×C22⋊Q8C231128yes—
306C2×C22⋊Q8C23132yes—
307C2×C22⋊Q8C23164yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2318yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2318yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2318yes—
319C2×C22⋊Q8C23116yes—
320C2×C22⋊Q8C2318yes—
321C2×C22⋊Q8C2318yes—
322C2×C22⋊Q8C23116yes—
323C2×C22⋊Q8C23116yes—
324C2×C22⋊Q8C23116yes—
325C2×C22⋊Q8C23116yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2318yes—
329C2×#121C2314yes—
330C2×#121C2318yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#120C2318yes—
334#520C23164yes—
335#520C231128yes—
336#519C23132yes—
337C4×#41C23132yes—
338C4×#41C23164yes—
339C2×C4×Q8C2314yes—
340C2×C4×Q8C2314yes—
341C2×C4×Q8C23116yes—
342C2×C4×Q8C2314yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2314yes—
346C2×C4×Q8C2318yes—
347C2×C4×Q8C2318yes—
348C2×C4×Q8C2318yes—
349C2×C4×Q8C2318yes—
350C2×C4×Q8C2318yes—
351C2×C4×Q8C2314yes—
352C2×C4×Q8C2314yes—
353C2×C4×Q8C2318yes—
354C2×C4×Q8C2318yes—
355C2×C4×Q8C23116yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2318yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C23116yes—
363C2×C4×D4C23132yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2318yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2318yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C23116yes—
372C2×C4×D4C23116yes—
373C2×C4×D4C23116yes—
374C2×C4×D4C2318yes—
375C2×C4×D4C2318yes—
376C2×C4×D4C2314yes—
377C2×#117C2312yes—
378C2×#117C2314yes—
379C2×#117C2318yes—
380C2×#117C2318yes—
381C2×#117C2314yes—
382C2×#117C2314yes—
383C2×#117C23164yes—
384C2×#117C2314yes—
385C2×#117C2318yes—
386C2×#117C2314yes—
387C2×#117C2318yes—
388C2×#117C2318yes—
389C2×#117C23116yes—
390C2×#117C2318yes—
391C2×#117C2318yes—
392C2×#117C23116yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2314yes—
396C22×C4⋊C4C2318yes—
397C22×C4⋊C4C2318yes—
398C22×C4⋊C4C23132yes—
399C22×C4⋊C4C2314yes—
400C22×C4⋊C4C2314yes—
401C22×C4⋊C4C2311yescharacteristic
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2312yes—
404C22×C4⋊C4C23116yes—
405C22×C4⋊C4C2318yes—
406C22×C4⋊C4C2318yes—
407C22×C4⋊C4C2314yes—
408C22×C4⋊C4C2318yes—
409C22×C22⋊C4C2318yes—
410C22×C22⋊C4C2314yes—
411C22×C22⋊C4C2312yes—
412C22×C42C2318yes—
413C22×C42C2311yescharacteristic
414C22×C42C2312yes—
415C22×C42C2314yes—
416C25C2412yes—
417C2×#41—232no—
418C2×#41—216no—
419C2×#41—816no—
420C2×#41C24116yes—
421C2×#41C24132yes—
422C2×#41C24164yes—
423C22×Q8—28no—
424C22×Q8—84no—
425C22×Q8—816no—
426C22×Q8—816no—
427C22×Q8C2414yes—
428C22×Q8C2412yes—
429C22×Q8C2414yes—
430C22×Q8C2418yes—
431C22×Q8C2418yes—
432C22×Q8C2414yes—
433C22×Q8C24116yes—
434C22×Q8C2418yes—
435C22×Q8C2414yes—
436C22×Q8C24116yes—
437C22×Q8C24164yes—
438C22×Q8C24164yes—
439C22×D4—28no—
440C22×D4C2414yes—
441C22×D4C2418yes—
442C22×D4C2412yes—
443C22×D4C2412yes—
444C22×D4C2411yescharacteristic
445C22×D4C2418yes—
446C22×D4C2418yes—
447C22×D4C2414yes—
448C22×D4C2411yescharacteristic
449C23×C4—216no—
450C23×C4—88no—
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2418yes—
454C23×C4C2414yes—
455C23×C4C2411yescharacteristic
456C23×C4C2414yes—
457C23×C4C24116yes—
458C23×C4C2414yes—
459C23×C4C2414yes—
460C23×C4C2411yescharacteristic
461C23×C4C2414yes—
462C23×C4C2418yes—
463C23×C4C2418yes—
464C23×C4C2412yes—
465C23×C4C24116yes—
466C23×C4C2418yes—
467C23×C4C2414yes—
468C23×C4C24132yes—
469C23×C4C2411yescharacteristic
470C4⋊Q8C24132yes—
471C4⋊Q8C24132yes—
472C4⋊Q8C24116yes—
473C4⋊Q8C24132yes—
474C4⋊Q8C24164yes—
475C4⋊Q8C241128yes—
476C4⋊Q8C24164yes—
477C4⋊Q8C24164yes—
478C4⋊Q8C24164yes—
479C4⋊Q8C241128yes—
480C4⋊Q8C24164yes—
481C4⋊Q8C24116yes—
482C4⋊Q8C24132yes—
483C4⋊Q8C24132yes—
484C4⋊Q8C24132yes—
485C4⋊Q8C241128yes—
486C4⋊Q8C241128yes—
487#126C24164yes—
488#126C24164yes—
489#126C24164yes—
490#126C24164yes—
491#126C24164yes—
492#126C241128yes—
493#126C241128yes—
494#126C241128yes—
495#126C241128yes—
496#126C241128yes—
497#125C24164yes—
498#125C24164yes—
499#125C24132yes—
500#125C24164yes—
501#125C241128yes—
502#125C24164yes—
503#125C241128yes—
504#125C24164yes—
505#125C24164yes—
506#125C24132yes—
507#125C24132yes—
508#125C24164yes—
509#125C24132yes—
510#125C24164yes—
511#125C241128yes—
512#125C241128yes—
513#125C241128yes—
514#125C241128yes—
515#125C241128yes—
516#125C241128yes—
517#124C24164yes—
518#124C24132yes—
519#124C24132yes—
520#124C24132yes—
521#124C241128yes—
522#123C24164yes—
523#123C241128yes—
524#123C24164yes—
525#123C24164yes—
526#123C24164yes—
527#123C24164yes—
528#123C24164yes—
529#123C241128yes—
530#123C241128yes—
531#123C241128yes—
532C22⋊Q8C24132yes—
533C22⋊Q8C24164yes—
534C22⋊Q8C24164yes—
535C22⋊Q8C241128yes—
536C22⋊Q8C241128yes—
537C22⋊Q8C241128yes—
538C22⋊Q8C24164yes—
539C22⋊Q8C241128yes—
540C22⋊Q8C24164yes—
541C22⋊Q8C24164yes—
542C22⋊Q8C24132yes—
543C22⋊Q8C24132yes—
544C22⋊Q8C24164yes—
545C22⋊Q8C24132yes—
546C22⋊Q8C24164yes—
547C22⋊Q8C24132yes—
548C22⋊Q8C24132yes—
549C22⋊Q8C24132yes—
550C22⋊Q8C24132yes—
551C22⋊Q8C24132yes—
552C22⋊Q8C24164yes—
553C22⋊Q8C241128yes—
554C22⋊Q8C24164yes—
555C22⋊Q8C24164yes—
556C22⋊Q8C241128yes—
557C22⋊Q8C241128yes—
558C22⋊Q8C241128yes—
559C22⋊Q8C241128yes—
560#121C24132yes—
561#121C24132yes—
562#121C24164yes—
563#121C24132yes—
564#121C24164yes—
565#121C24132yes—
566#121C24132yes—
567#120C24164yes—
568C4×Q8C24132yes—
569C4×Q8C24132yes—
570C4×Q8C24132yes—
571C4×Q8C24116yes—
572C4×Q8C24116yes—
573C4×Q8C24132yes—
574C4×Q8C24164yes—
575C4×Q8C24164yes—
576C4×Q8C24164yes—
577C4×Q8C24164yes—
578C4×Q8C24164yes—
579C4×Q8C24132yes—
580C4×Q8C24132yes—
581C4×Q8C24164yes—
582C4×Q8C24164yes—
583C4×Q8C241128yes—
584C4×D4C24116yes—
585C4×D4C24132yes—
586C4×D4C24132yes—
587C4×D4C24116yes—
588C4×D4C24164yes—
589C4×D4C24132yes—
590C4×D4C24132yes—
591C4×D4C24164yes—
592C4×D4C24132yes—
593C4×D4C24116yes—
594C4×D4C24132yes—
595C4×D4C24164yes—
596C4×D4C24116yes—
597C4×D4C241128yes—
598C4×D4C241128yes—
599C4×D4C241128yes—
600C4×D4C24164yes—
601C4×D4C24164yes—
602C4×D4C24132yes—
603#117C24116yes—
604#117C24132yes—
605#117C24164yes—
606#117C24164yes—
607#117C24132yes—
608#117C24132yes—
609#117C24132yes—
610#117C24164yes—
611#117C24132yes—
612#117C24164yes—
613#117C24164yes—
614#117C241128yes—
615#117C24164yes—
616#117C24164yes—
617#117C241128yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C24116yes—
624C2×C4⋊C4C24116yes—
625C2×C4⋊C4C24132yes—
626C2×C4⋊C4C24164yes—
627C2×C4⋊C4C24164yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C24116yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C24132yes—
639C2×C4⋊C4C24132yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C24116yes—
642C2×C4⋊C4C24116yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C24116yes—
647C2×C4⋊C4C24116yes—
648C2×C4⋊C4C24116yes—
649C2×C4⋊C4C24116yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C24116yes—
652C2×C4⋊C4C241128yes—
653C2×C4⋊C4C24164yes—
654C2×C4⋊C4C24164yes—
655C2×C4⋊C4C24132yes—
656C2×C4⋊C4C24164yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2418yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C24164yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C24132yes—
679C2×C22⋊C4C24116yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C24116yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C42C2418yes—
691C2×C42C2414yes—
692C2×C42C24116yes—
693C2×C42C24116yes—
694C2×C42C2414yes—
695C2×C42C2418yes—
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2414yes—
700C2×C42C24164yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2418yes—
704C2×C42C24116yes—
705C2×C42C24132yes—
706C24—28no—
707C24—28no—
708C24—44no—
709C24C2512yes—
710C24C2514yes—
711C24C2518yes—
712C24C2511yescharacteristic
713C24C2512yes—
714#41—2128no—
715#41—264no—
716#41—864no—
717C2×Q8—216no—
718C2×Q8—232no—
719C2×Q8—28no—
720C2×Q8—216no—
721C2×Q8—48no—
722C2×Q8—416no—
723C2×Q8—432no—
724C2×Q8—48no—
725C2×Q8—416no—
726C2×Q8—816no—
727C2×Q8—864no—
728C2×Q8—864no—
729C2×Q8C25116yes—
730C2×Q8C2518yes—
731C2×Q8C25116yes—
732C2×Q8C25132yes—
733C2×Q8C25116yes—
734C2×Q8C25164yes—
735C2×Q8C25132yes—
736C2×Q8C25116yes—
737C2×D4—28no—
738C2×D4—216no—
739C2×D4—232no—
740C2×D4—232no—
741C2×D4—24no—
742C2×D4—28no—
743C2×D4—48no—
744C2×D4—416no—
745C2×D42−1+418yes—
746C2×D4C25116yes—
747C2×D4C25132yes—
748C2×D4C2518yes—
749C2×D4C2518yes—
750C2×D4C2514yes—
751C2×D4C25132yes—
752C2×D4C25116yes—
753C2×D4C2514yes—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—232no—
757C22×C4—216no—
758C22×C4—216no—
759C22×C4—264no—
760C22×C4—24no—
761C22×C4—216no—
762C22×C4—216no—
763C22×C4—44no—
764C22×C4—416no—
765C22×C4—48no—
766C22×C4—416no—
767C22×C4—416no—
768C22×C4—42no—
769C22×C4—48no—
770C22×C4—432no—
771C22×C4—832no—
772C22×C42−1+418yes—
773C22×C4C2514yes—
774C22×C4C25116yes—
775C22×C4C2518yes—
776C22×C4C25132yes—
777C22×C4C25116yes—
778C22×C4C25116yes—
779C22×C4C2518yes—
780C22×C4C25116yes—
781C22×C4C2514yes—
782C22×C4C2514yes—
783C22×C4C2518yes—
784C22×C4C2511yescharacteristic
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2512yes—
789C22×C4C2518yes—
790C22×C4C2518yes—
791C22×C4C2514yes—
792C22×C4C2514yes—
793C22×C4C25132yes—
794C22×C4C2518yes—
795C22×C4C25116yes—
796C22×C4C25116yes—
797C22×C4C25132yes—
798C22×C4C25164yes—
799C22×C4C25132yes—
800C22×C4C2514yes—
801C22×C4C2511yescharacteristic
802C22×C4C2512yes—
803C4⋊C4C25116yes—
804C4⋊C4C25132yes—
805C4⋊C4C25116yes—
806C4⋊C4C25116yes—
807C4⋊C4C25164yes—
808C4⋊C4C2518yes—
809C4⋊C4C2518yes—
810C4⋊C4C25116yes—
811C4⋊C4C25132yes—
812C4⋊C4C25164yes—
813C4⋊C4C25116yes—
814C4⋊C4C25116yes—
815C4⋊C4C2518yes—
816C4⋊C4C25132yes—
817C4⋊C4C25132yes—
818C4⋊C4C25132yes—
819C4⋊C4C25164yes—
820C4⋊C4C25164yes—
821C4⋊C4C25116yes—
822C4⋊C4C2518yes—
823C4⋊C4C25164yes—
824C4⋊C4C25164yes—
825C4⋊C4C25164yes—
826C4⋊C4C25132yes—
827C4⋊C4C25132yes—
828C4⋊C4C25116yes—
829C4⋊C4C25116yes—
830C4⋊C4C25132yes—
831C4⋊C4C25132yes—
832C4⋊C4C25116yes—
833C4⋊C4C25132yes—
834C4⋊C4C25132yes—
835C4⋊C4C25132yes—
836C4⋊C4C25132yes—
837C4⋊C4C25132yes—
838C4⋊C4C25116yes—
839C22⋊C4C25116yes—
840C22⋊C4C25132yes—
841C22⋊C4C25132yes—
842C22⋊C4C25116yes—
843C22⋊C4C25132yes—
844C22⋊C4C25132yes—
845C22⋊C4C25132yes—
846C22⋊C4C25116yes—
847C22⋊C4C25132yes—
848C22⋊C4C25132yes—
849C22⋊C4C25132yes—
850C22⋊C4C25132yes—
851C22⋊C4C25132yes—
852C22⋊C4C25116yes—
853C22⋊C4C25164yes—
854C22⋊C4C25132yes—
855C22⋊C4C25116yes—
856C22⋊C4C25132yes—
857C42C25116yes—
858C42C2518yes—
859C42C25132yes—
860C42C25116yes—
861C42C25132yes—
862C42C2518yes—
863C42C25116yes—
864C42C25132yes—
865C42C25116yes—
866C42C25116yes—
867C42C25164yes—
868C42C25164yes—
869C23—24no—
870C23—22no—
871C23—24no—
872C23—22no—
873C23—216no—
874C23—24no—
875C23—28no—
876C23—28no—
877C23—216no—
878C23—24no—
879C23—28no—
880C23—24no—
881C23—48no—
882C23—432no—
883C23C2×2−1+414yes—
884C23C2×2−1+418yes—
885C23C2614yes—
886C23C2618yes—
887C23C2612yes—
888C23C2614yes—
889C23C2611yescharacteristic
890Q8—232no—
891Q8—216no—
892Q8—232no—
893Q8—416no—
894Q8—432no—
895Q8—464no—
896Q8—416no—
897Q8—432no—
898D4—216no—
899D4—232no—
900D4—264no—
901D4—28no—
902D4—216no—
903D4—416no—
904D4—432no—
905D4C2×2−1+4116yes—
906C2×C4—216no—
907C2×C4—28no—
908C2×C4—28no—
909C2×C4—22no—
910C2×C4—216no—
911C2×C4—28no—
912C2×C4—216no—
913C2×C4—28no—
914C2×C4—264no—
915C2×C4—28no—
916C2×C4—216no—
917C2×C4—216no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—232no—
921C2×C4—232no—
922C2×C4—28no—
923C2×C4—232no—
924C2×C4—232no—
925C2×C4—48no—
926C2×C4—432no—
927C2×C4—416no—
928C2×C4—432no—
929C2×C4—432no—
930C2×C4—44no—
931C2×C4—416no—
932C2×C4—464no—
933C2×C4C2×2−1+418yes—
934C2×C4C2×2−1+414yes—
935C2×C4C2×2−1+4116yes—
936C2×C4C2618yes—
937C2×C4C26116yes—
938C2×C4C2618yes—
939C2×C4C2612yes—
940C2×C4C2618yes—
941C2×C4C2618yes—
942C2×C4C2618yes—
943C2×C4C2614yes—
944C2×C4C26116yes—
945C2×C4C26116yes—
946C2×C4C2618yes—
947C2×C4C2612yes—
948C2×C4C2614yes—
949C22—24no—
950C22—22no—
951C22—24no—
952C22—22no—
953C22—28no—
954C22—216no—
955C22—24no—
956C22—28no—
957C22—28no—
958C22—24no—
959C22—28no—
960C22—24no—
961C22—432no—
962C22—416no—
963C22—48no—
964C22C22×2−1+414yes—
965C22C22×2−1+418yes—
966C22C22×2−1+412yes—
967C22C22×2−1+412yes—
968C22H(7,𝔽2)12yes—
969C22C2711yescharacteristic
970C4—28no—
971C4—28no—
972C4—22no—
973C4—216no—
974C4—28no—
975C4—28no—
976C4—28no—
977C4—216no—
978C4—216no—
979C4—28no—
980C4—24no—
981C4C22×2−1+418yes—
982C4C22×2−1+414yes—
983C2—24no—
984C2—28no—
985C2—48no—
986C2—44no—
987C2#6294514yesdirect product factor
988C2C23×2−1+411yescharacteristic
989C2C23×2−1+411yescharacteristic
990C2C2×H(7,𝔽2)11yescharacteristic
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. #62945C2direct (N × H)
2. C2×#3495C2semidirect
3. C2×#3503C2semidirect
4. C2×#3503C2semidirect
5. C2×#3502C2semidirect
6. C2×#3515C2semidirect
7. C2×#3520C2semidirect
8. C2×#3492C2semidirect
9. C2×#3555C2semidirect
10. C2×#3544C2semidirect
11. C2×#3552C2semidirect
12. C2×#3563C2semidirect
13. C2×#3563C2semidirect
14. C2×#3538C2semidirect
15. C2×#3475C2semidirect
16. C22×#554C2semidirect
17. C2×#3461C2semidirect
18. C22×#544C2semidirect
19. #3563C22semidirect
20. #3563C22semidirect
21. #3555C22semidirect
22. #3552C22semidirect
23. #3544C22semidirect
24. #3538C22semidirect
25. C2×#564C22semidirect
26. C2×#563C22semidirect
27. C2×#563C22semidirect
28. C2×#563C22semidirect
29. #3520C22semidirect
30. #3515C22semidirect
31. #3503C22semidirect
32. #3503C22semidirect
33. #3502C22semidirect
34. #3495C22semidirect
35. #3492C22semidirect
36. C2×Q82C22semidirect
37. C2×Q82C22semidirect
38. C2×#557C22semidirect
39. C2×#557C22semidirect
40. C2×#557C22semidirect
41. C2×#557C22semidirect
42. #3475C22semidirect
45. C2×#556C22semidirect
52. C2×#554C22semidirect
53. C2×#554C22semidirect
54. C2×#554C22semidirect
55. C2×#554C22semidirect
57. C2×#553C22semidirect
62. C2×#552C22semidirect
63. C2×#552C22semidirect
64. C2×#552C22semidirect
65. C2×#552C22semidirect
66. C2×#552C22semidirect
71. C2×D4×Q8C22semidirect
72. C2×D4×Q8C22semidirect
77. C2×#547C22semidirect
79. #3461C22semidirect
85. C2×#544C22semidirect
86. C2×#544C22semidirect
87. C2×#544C22semidirect
88. C2×#544C22semidirect
89. C2×#544C22semidirect
90. C2×#544C22semidirect
92. C2×#542C22semidirect
93. C2×#542C22semidirect
94. C2×#541C22semidirect
95. C2×#541C22semidirect
96. C2×#541C22semidirect
97. C2×#541C22semidirect
98. C2×#541C22semidirect
102. C2×#539C22semidirect
105. C2×#536C22semidirect
108. C2×#533C22semidirect
109. C2×#533C22semidirect
110. C2×#533C22semidirect
112. C22×C4⋊Q8C22semidirect
113. C22×C4⋊Q8C22semidirect
117. C2×#529C22semidirect
118. C2×#529C22semidirect
120. C22×#125C22semidirect
146. #564C23semidirect
147. #563C23semidirect
148. #563C23semidirect
149. #563C23semidirect
150. Q82C23semidirect
151. Q82C23semidirect
152. #557C23semidirect
153. #557C23semidirect
154. #557C23semidirect
155. #557C23semidirect
158. #556C23semidirect
165. #554C23semidirect
166. #554C23semidirect
167. #554C23semidirect
169. #553C23semidirect
174. #552C23semidirect
175. #552C23semidirect
176. #552C23semidirect
177. #552C23semidirect
178. #552C23semidirect
183. D4×Q8C23semidirect
184. D4×Q8C23semidirect
189. #547C23semidirect
196. #544C23semidirect
197. #544C23semidirect
198. #544C23semidirect
199. #544C23semidirect
200. #544C23semidirect
202. #542C23semidirect
203. #542C23semidirect
204. #541C23semidirect
205. #541C23semidirect
206. #541C23semidirect
207. #541C23semidirect
208. #541C23semidirect
212. #539C23semidirect
215. #536C23semidirect
218. #533C23semidirect
219. #533C23semidirect
220. #533C23semidirect
239. C2×C4⋊Q8C23semidirect
240. C2×C4⋊Q8C23semidirect
244. #529C23semidirect
245. #529C23semidirect
277. C2×#125C23semidirect
987. C2#62945direct (N × H)

Maximal subgroups

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

subgroupindex
#629452
C2×#34952
C2×#35032
C2×#35022
C2×#35152
C2×#35202
C2×#34922
C2×#35552
C2×#35442
C2×#35522
C2×#35632
C2×#35382
C2×#34752
C22×#5542
C2×#34612
C22×#5442