Finite Group Databasebeta

← C2×#62944 #10586288

Subgroups — C2×#62944 #10586288

Order 512.

34944 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62944C2164yesmaximal, direct product factor
2C2×#3489C214yesmaximal, complemented
3C2×#3511C212yesmaximal, complemented
4C2×#3497C211yesmaximal, characteristic, complemented
5C2×#3519C214yesmaximal, complemented
6C2×#3519C214yesmaximal, complemented
7C2×#3492C212yesmaximal, complemented
8C2×#3501C214yesmaximal, complemented
9C2×#3548C214yesmaximal, complemented
10C2×#3547C214yesmaximal, complemented
11C2×#3559C214yesmaximal, complemented
12C2×#3536C218yesmaximal, complemented
13C2×#3536C218yesmaximal, complemented
14C2×#3541C218yesmaximal, complemented
15C22×#554C211yesmaximal, characteristic, complemented
16C2×D4×#41C212yesmaximal, complemented
17C2×#3461C211yesmaximal, characteristic, complemented
18C22×#537C212yesmaximal, complemented
19C22×2−1+4C2212yescomplemented
20C23×#41C2214yescomplemented
21#3559C221128yescomplemented
22#3548C221128yescomplemented
23#3547C221128yescomplemented
24#3541C221256yescomplemented
25#3536C221256yescomplemented
26#3536C221256yescomplemented
27C2×#563C2218yescomplemented
28C2×#562C22116yescomplemented
29C2×#562C2218yescomplemented
30C2×#562C22116yescomplemented
31#3519C221128yescomplemented
32#3519C221128yescomplemented
33#3511C22164yescomplemented
34#3501C221128yescomplemented
35#3497C22132yescomplemented
36#3492C22164yescomplemented
37#3489C221128yescomplemented
38C2×#556C2214yescomplemented
39C2×#555C2214yescomplemented
40C2×#555C2214yescomplemented
41C2×#554C2214yes—
42C2×#554C2214yes—
43C2×#554C22116yescomplemented
44C2×#554C2218yescomplemented
45C2×#554C2218yescomplemented
46C2×#554C2218yescomplemented
47C2×#554C2214yescomplemented
48C2×#554C2214yescomplemented
49C2×#554C22132yescomplemented
50C2×#553C2218yescomplemented
51C2×#553C2218yescomplemented
52C2×#553C2218yescomplemented
53C2×#553C2218yescomplemented
54C2×#552C2218yescomplemented
55D4×#41C22164yescomplemented
56C2×#550C2214yescomplemented
57C2×#550C2212yescomplemented
58C2×#550C2214yescomplemented
59C2×D4×Q8C2212yes—
60C2×D4×Q8C2218yescomplemented
61C2×D4×Q8C2214yescomplemented
62C2×#548C2214yescomplemented
63C2×#548C2218yescomplemented
64C2×#548C2218yescomplemented
65C2×#548C2218yescomplemented
66C2×#547C2218yescomplemented
67C2×#547C2214yescomplemented
68C2×#547C22116yescomplemented
69C2×#547C2218yescomplemented
70C2×#547C2214yescomplemented
71C2×#547C2212yescomplemented
72C2×#546C22116yescomplemented
73C2×#546C2218yescomplemented
74C2×#546C2218yescomplemented
75C2×#546C2214yescomplemented
76C2×#546C22116yescomplemented
77C2×#546C2218yescomplemented
78C2×D42C2214yes—
79C2×D42C2212yes—
80C2×D42C2214yes—
81#3461C22132yescomplemented
82C2×#544C2218yescomplemented
83C2×#544C2211yescharacteristic, complemented
84C2×#543C22116yescomplemented
85C2×#542C22116yescomplemented
86C2×#542C2218yescomplemented
87C2×#542C2214yescomplemented
88C2×#541C2214yescomplemented
89C2×#540C2218yescomplemented
90C2×#540C2218yescomplemented
91C2×#539C22116yescomplemented
92C2×#539C2214yescomplemented
93C2×#539C2218yescomplemented
94C2×#538C22116yescomplemented
95C2×#538C22116yescomplemented
96C2×#537C2211yescharacteristic
97C2×#537C2218yescomplemented
98C2×#537C22116yescomplemented
99C2×#537C2214yescomplemented
100C2×#537C2218yescomplemented
101C2×#537C2218yescomplemented
102C2×#537C2218yescomplemented
103C2×#537C2212yescomplemented
104C2×#537C2214yescomplemented
105C2×#537C22164yescomplemented
106C2×#536C2218yescomplemented
107C2×#536C2212yescomplemented
108C2×#533C2214yescomplemented
109C2×#533C2214yescomplemented
110C2×#532C2214yescomplemented
111C2×#532C2214yescomplemented
112C2×#532C2214yescomplemented
113C2×#532C2212yescomplemented
114C22×C4⋊Q8C2211yescharacteristic, complemented
115C2×#529C2214yescomplemented
116C2×#529C2214yescomplemented
117C22×#125C2212yescomplemented
118C2×#525C2218yescomplemented
119C2×#525C2218yescomplemented
120C2×#525C2218yescomplemented
121C2×#525C2214yescomplemented
122C22×C22⋊Q8C2218yescomplemented
123C22×C22⋊Q8C2214yescomplemented
124C22×C22⋊Q8C2218yescomplemented
125C22×C22⋊Q8C2212yescomplemented
126C22×#121C2218yescomplemented
127C22×#121C2218yescomplemented
128C2×#520C2214yescomplemented
129C2×#518C2218yes—
130C2×C4×#41C2212yescomplemented
131C22×C4×Q8C2211yescharacteristic, complemented
132C22×C4×D4C2214yes—
133C22×C4×D4C2212yes—
134C22×C4×D4C2211yescharacteristic
135C23×C4⋊C4C2212yescomplemented
136C2×2−1+4—416no—
137C2×2−1+4C23132yescomplemented
138C22×#41—432no—
139C22×#41C2312yes—
140C22×#41C2314yes—
141C22×#41C2318yes—
142C22×#41C2318yes—
143C22×#41C2314yes—
144C22×#41C2314yes—
145C22×#41C2318yes—
146C22×#41C2318yes—
147C22×#41C2318yes—
148C22×#41C2318yes—
149C22×#41C23164yescomplemented
150C23×Q8C2311yescharacteristic
151C23×Q8C2314yes—
152C23×Q8C2318yes—
153C23×Q8C2312yes—
154C23×D4C2311yescharacteristic
155C23×D4C2314yes—
156C23×D4C2314yes—
157C23×D4C2318yes—
158C23×D4C2318yes—
159C24×C4C2312yes—
160C24×C4C2318yes—
161C24×C4C2314yes—
162#563C231128yescomplemented
163#562C231256yescomplemented
164#562C231128yescomplemented
165#562C231256yescomplemented
166#556C23164yescomplemented
167#555C23164yescomplemented
168#555C23164yescomplemented
169#554C23164yes—
170#554C23164yes—
171#554C231128yescomplemented
172#554C23164yescomplemented
173#554C231128yescomplemented
174#554C23164yescomplemented
175#554C231256yescomplemented
176#554C231128yescomplemented
177#553C231128yescomplemented
178#553C231128yescomplemented
179#553C231128yescomplemented
180#553C231128yescomplemented
181#552C231128yescomplemented
182#550C23132yescomplemented
183#550C23164yescomplemented
184#550C23164yescomplemented
185D4×Q8C23132yes—
186D4×Q8C231128yescomplemented
187D4×Q8C23164yescomplemented
188#548C23164yescomplemented
189#548C231128yescomplemented
190#548C231128yescomplemented
191#548C231128yescomplemented
192#547C23132yescomplemented
193#547C23164yescomplemented
194#547C231256yescomplemented
195#547C231128yescomplemented
196#547C231128yescomplemented
197#547C23164yescomplemented
198#546C231128yescomplemented
199#546C23164yescomplemented
200#546C231256yescomplemented
201#546C231128yescomplemented
202#546C231256yescomplemented
203#546C231128yescomplemented
204D42C23132yes—
205D42C23164yes—
206D42C23164yes—
207#544C23116yescomplemented
208#544C231128yescomplemented
209#543C231256yescomplemented
210#542C23164yescomplemented
211#542C231128yescomplemented
212#542C231256yescomplemented
213#541C23164yescomplemented
214#540C231128yescomplemented
215#540C231128yescomplemented
216#539C23164yescomplemented
217#539C231128yescomplemented
218#539C231256yescomplemented
219#538C231256yescomplemented
220#538C231256yescomplemented
221#537C23116yes—
222#537C23164yescomplemented
223#537C23132yescomplemented
224#537C231128yescomplemented
225#537C231128yescomplemented
226#537C231128yescomplemented
227#537C231128yescomplemented
228#537C23164yescomplemented
229#537C231256yescomplemented
230#536C23132yescomplemented
231#536C231128yescomplemented
232#533C23164yescomplemented
233#533C23164yescomplemented
234#532C23132yescomplemented
235#532C23164yescomplemented
236#532C23164yescomplemented
237#532C23164yescomplemented
238C2×C4⋊Q8C2314yes—
239C2×C4⋊Q8C2314yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2314yes—
243C2×C4⋊Q8C2314yes—
244C2×C4⋊Q8C2314yes—
245C2×C4⋊Q8C23116yes—
246C2×C4⋊Q8C23116yescomplemented
247C2×#127C2312yes—
248C2×#127C2314yes—
249C2×#127C2314yes—
250#529C23164yescomplemented
251#529C23164yescomplemented
252C2×#126C2318yes—
253C2×#126C2318yes—
254C2×#126C23116yes—
255C2×#126C23116yes—
256C2×#125C2318yes—
257C2×#125C2318yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2318yes—
261C2×#125C2318yes—
262C2×#125C23116yes—
263C2×#125C23132yescomplemented
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#124C2318yes—
267C2×#124C2318yes—
268C2×#124C2314yes—
269C2×#124C2318yes—
270C2×#124C23116yes—
271C2×#124C23116yes—
272#525C23164yescomplemented
273#525C231128yescomplemented
274#525C231128yescomplemented
275#525C231128yescomplemented
276C2×#123C23116yes—
277C2×#123C23116yes—
278C2×#123C2318yes—
279C2×#123C2318yes—
280C2×#123C2318yes—
281C2×#123C2318yes—
282C2×#123C2318yes—
283C2×#123C23116yes—
284C2×#123C23116yes—
285C2×#123C23116yes—
286C2×#123C23116yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2318yes—
289C2×C22⋊Q8C2318yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2318yes—
293C2×C22⋊Q8C23116yes—
294C2×C22⋊Q8C2318yes—
295C2×C22⋊Q8C2318yes—
296C2×C22⋊Q8C23116yes—
297C2×C22⋊Q8C23116yes—
298C2×C22⋊Q8C23116yes—
299C2×C22⋊Q8C23116yes—
300C2×C22⋊Q8C23116yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2318yes—
305C2×C22⋊Q8C2318yes—
306C2×C22⋊Q8C2318yes—
307C2×C22⋊Q8C2318yes—
308C2×C22⋊Q8C2318yes—
309C2×C22⋊Q8C23116yes—
310C2×C22⋊Q8C23116yes—
311C2×C22⋊Q8C23116yes—
312C2×C22⋊Q8C23116yes—
313C2×C22⋊Q8C231128yescomplemented
314C2×C22⋊Q8C23132yescomplemented
315C2×C22⋊Q8C23164yescomplemented
316C2×C22⋊Q8C231128yescomplemented
317C2×#121C2314yes—
318C2×#121C2314yes—
319C2×#121C2318yes—
320C2×#121C2318yes—
321C2×#121C23116yes—
322C2×#121C23116yes—
323C2×#121C23116yes—
324C2×#121C2318yes—
325C2×#121C23116yes—
326C2×#121C2318yes—
327C2×#121C2318yes—
328C2×#121C2318yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2318yes—
332C2×#121C2318yes—
333C2×#121C2318yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2318yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2318yes—
340C2×#121C23116yes—
341C2×#121C23116yes—
342C2×#121C23116yes—
343C2×#121C23116yes—
344C2×#121C231128yescomplemented
345C2×#121C231128yescomplemented
346C2×#120C2318yes—
347C2×#120C2318yes—
348C2×#120C2318yes—
349C2×#120C23116yes—
350#520C23164yescomplemented
351#518C231128yes—
352C4×#41C23132yescomplemented
353C2×C4×Q8C2314yes—
354C2×C4×Q8C2314yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2318yes—
358C2×C4×Q8C2314yes—
359C2×C4×Q8C2318yes—
360C2×C4×Q8C23116yescomplemented
361C2×C4×D4C2312yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2318yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2318yes—
369C2×C4×D4C2318yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C23116yes—
373C2×C4×D4C23164yes—
374C2×C4×D4C23132yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C23116yes—
380C2×C4×D4C23116yes—
381C2×C4×D4C2318yes—
382C2×C4×D4C2318yes—
383C2×C4×D4C23116yes—
384C2×C4×D4C2318yes—
385C2×C4×D4C2318yes—
386C2×C4×D4C2314yes—
387C2×C4×D4C23116yes—
388C2×C4×D4C2314yes—
389C2×C4×D4C2318yes—
390C2×#117C2312yes—
391C2×#117C2314yes—
392C2×#117C2318yes—
393C2×#117C2318yes—
394C2×#117C2318yes—
395C2×#117C2318yes—
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2318yes—
399C22×C4⋊C4C2314yes—
400C22×C4⋊C4C2318yes—
401C22×C4⋊C4C2311yescharacteristic
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2314yes—
404C22×C4⋊C4C2312yes—
405C22×C4⋊C4C2318yes—
406C22×C4⋊C4C2318yes—
407C22×C4⋊C4C2314yes—
408C22×C4⋊C4C23116yes—
409C22×C4⋊C4C23132yescomplemented
410C22×C22⋊C4C2314yes—
411C22×C22⋊C4C2312yes—
412C22×C22⋊C4C2318yes—
413C22×C22⋊C4C23116yes—
414C22×C22⋊C4C23116yes—
415C22×C42C2311yescharacteristic
416C22×C42C2312yes—
417C22×C42C2314yes—
418C25C2412yes—
419C25C2418yes—
4202−1+4—4128no—
421C2×#41—216no—
422C2×#41—232no—
423C2×#41—432no—
424C2×#41—432no—
425C2×#41—432no—
426C2×#41—416no—
427C2×#41—416no—
428C2×#41—432no—
429C2×#41—4256no—
430C2×#41—816no—
431C2×#41—816no—
432C2×#41C24116yes—
433C2×#41C24132yes—
434C2×#41C24164yes—
435C2×#41C24164yes—
436C2×#41C24164yes—
437C2×#41C24164yes—
438C2×#41C24132yes—
439C2×#41C24132yes—
440C2×#41C24164yes—
441C2×#41C24164yes—
442C22×Q8—28no—
443C22×Q8—416no—
444C22×Q8—432no—
445C22×Q8—84no—
446C22×Q8C2414yes—
447C22×Q8C2414yes—
448C22×Q8C2412yes—
449C22×Q8C2418yes—
450C22×Q8C2414yes—
451C22×Q8C2418yes—
452C22×Q8C2418yes—
453C22×Q8C2418yes—
454C22×Q8C24132yes—
455C22×Q8C24164yes—
456C22×Q8C24116yes—
457C22×D4—28no—
458C22×D4—232no—
459C22×D4—416no—
460C22×D4—432no—
461C22×D4—816no—
462C22×D4C2412yes—
463C22×D4C2418yes—
464C22×D4C2411yescharacteristic
465C22×D4C2414yes—
466C22×D4C2418yes—
467C22×D4C24132yes—
468C22×D4C2418yes—
469C22×D4C2414yes—
470C22×D4C2412yes—
471C22×D4C2414yes—
472C22×D4C2418yes—
473C22×D4C2414yes—
474C22×D4C24116yes—
475C22×D4C2414yes—
476C22×D4C2418yes—
477C22×D4C2418yes—
478C22×D4C2418yes—
479C22×D4C2418yes—
480C22×D4C2418yes—
481C22×D4C24132yes—
482C22×D4C24164yes—
483C22×D4C24164yes—
484C22×D4C2411yescharacteristic
485C23×C4—216no—
486C23×C4—432no—
487C23×C4—88no—
488C23×C4C2412yes—
489C23×C4C2412yes—
490C23×C4C2411yescharacteristic
491C23×C4C2414yes—
492C23×C4C2414yes—
493C23×C4C2414yes—
494C23×C4C2418yes—
495C23×C4C24116yes—
496C23×C4C2414yes—
497C23×C4C2418yes—
498C23×C4C2411yescharacteristic
499C23×C4C2418yes—
500C23×C4C2414yes—
501C23×C4C2414yes—
502C23×C4C24116yes—
503C23×C4C24116yes—
504C23×C4C2418yes—
505C23×C4C2412yes—
506C23×C4C2418yes—
507C23×C4C2418yes—
508C23×C4C24164yes—
509C23×C4C24132yes—
510C23×C4C2411yescharacteristic
511C4⋊Q8C24132yes—
512C4⋊Q8C24132yes—
513C4⋊Q8C24116yes—
514C4⋊Q8C24132yes—
515C4⋊Q8C24132yes—
516C4⋊Q8C24132yes—
517C4⋊Q8C24132yes—
518C4⋊Q8C241128yes—
519#127C24116yes—
520#127C24132yes—
521#127C24132yes—
522#126C24164yes—
523#126C24164yes—
524#126C241128yes—
525#126C241128yes—
526#125C24164yes—
527#125C24164yes—
528#125C24132yes—
529#125C24132yes—
530#125C24164yes—
531#125C24164yes—
532#125C241128yes—
533#124C24132yes—
534#124C24132yes—
535#124C24164yes—
536#124C24164yes—
537#124C24132yes—
538#124C24164yes—
539#124C241128yes—
540#124C241128yes—
541#123C241128yes—
542#123C241128yes—
543#123C24164yes—
544#123C24164yes—
545#123C24164yes—
546#123C24164yes—
547#123C24164yes—
548#123C241128yes—
549#123C241128yes—
550#123C241128yes—
551#123C241128yes—
552C22⋊Q8C24132yes—
553C22⋊Q8C24164yes—
554C22⋊Q8C24164yes—
555C22⋊Q8C24132yes—
556C22⋊Q8C24132yes—
557C22⋊Q8C24164yes—
558C22⋊Q8C241128yes—
559C22⋊Q8C24164yes—
560C22⋊Q8C24164yes—
561C22⋊Q8C241128yes—
562C22⋊Q8C241128yes—
563C22⋊Q8C241128yes—
564C22⋊Q8C241128yes—
565C22⋊Q8C241128yes—
566C22⋊Q8C24132yes—
567C22⋊Q8C24132yes—
568C22⋊Q8C24132yes—
569C22⋊Q8C24164yes—
570C22⋊Q8C24164yes—
571C22⋊Q8C24164yes—
572C22⋊Q8C24164yes—
573C22⋊Q8C24164yes—
574C22⋊Q8C241128yes—
575C22⋊Q8C241128yes—
576C22⋊Q8C241128yes—
577C22⋊Q8C241128yes—
578#121C24132yes—
579#121C24132yes—
580#121C24164yes—
581#121C24164yes—
582#121C241128yes—
583#121C241128yes—
584#121C241128yes—
585#121C24164yes—
586#121C241128yes—
587#121C24164yes—
588#121C24164yes—
589#121C24164yes—
590#121C24132yes—
591#121C24132yes—
592#121C24164yes—
593#121C24164yes—
594#121C24164yes—
595#121C24132yes—
596#121C24132yes—
597#121C24164yes—
598#121C24132yes—
599#121C24132yes—
600#121C24164yes—
601#121C241128yes—
602#121C241128yes—
603#121C241128yes—
604#121C241128yes—
605#120C24164yes—
606#120C24164yes—
607#120C24164yes—
608#120C241128yes—
609C4×Q8C24132yes—
610C4×Q8C24132yes—
611C4×Q8C24116yes—
612C4×Q8C24116yes—
613C4×Q8C24164yes—
614C4×Q8C24132yes—
615C4×Q8C24164yes—
616C4×D4C24116yes—
617C4×D4C24132yes—
618C4×D4C24132yes—
619C4×D4C24132yes—
620C4×D4C24164yes—
621C4×D4C24116yes—
622C4×D4C24132yes—
623C4×D4C24164yes—
624C4×D4C24164yes—
625C4×D4C24132yes—
626C4×D4C24132yes—
627C4×D4C24132yes—
628C4×D4C24116yes—
629C4×D4C24132yes—
630C4×D4C24116yes—
631C4×D4C241128yes—
632C4×D4C241128yes—
633C4×D4C24164yes—
634C4×D4C24164yes—
635C4×D4C241128yes—
636C4×D4C24164yes—
637C4×D4C24164yes—
638C4×D4C24132yes—
639C4×D4C241128yes—
640C4×D4C24132yes—
641C4×D4C24164yes—
642#117C24116yes—
643#117C24132yes—
644#117C24164yes—
645#117C24164yes—
646#117C24164yes—
647#117C24164yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C24116yes—
653C2×C4⋊C4C24116yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C24116yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C24116yes—
660C2×C4⋊C4C24164yes—
661C2×C4⋊C4C24132yes—
662C2×C4⋊C4C24164yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C24116yes—
671C2×C4⋊C4C24132yes—
672C2×C4⋊C4C24116yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C24116yes—
675C2×C4⋊C4C24164yes—
676C2×C4⋊C4C24164yes—
677C2×C4⋊C4C24132yes—
678C2×C4⋊C4C241128yes—
679C2×C4⋊C4C2412yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C24116yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C24116yes—
693C2×C22⋊C4C24116yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C24132yes—
699C2×C22⋊C4C24116yes—
700C2×C22⋊C4C24164yes—
701C2×C22⋊C4C241128yes—
702C2×C22⋊C4C241128yes—
703C2×C22⋊C4C2418yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C24116yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2418yes—
710C2×C22⋊C4C2418yes—
711C2×C42C24116yes—
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2418yes—
720C2×C42C24116yes—
721C2×C42C24132yes—
722C24—28no—
723C24—28no—
724C24—232no—
725C24—44no—
726C24—416no—
727C24—416no—
728C24C2514yes—
729C24C2512yes—
730C24C2518yes—
731C24C2518yes—
732C24C2511yescharacteristic
733C24C2512yes—
734C24C25132yes—
735#41—264no—
736#41—2128no—
737#41—4128no—
738#41—4128no—
739#41—4128no—
740#41—464no—
741#41—464no—
742#41—4128no—
743#41—864no—
744#41—864no—
745C2×Q8—216no—
746C2×Q8—232no—
747C2×Q8—216no—
748C2×Q8—28no—
749C2×Q8—416no—
750C2×Q8—416no—
751C2×Q8—416no—
752C2×Q8—48no—
753C2×Q8—464no—
754C2×Q8—4128no—
755C2×Q8—816no—
756C2×Q8C25116yes—
757C2×Q8C25116yes—
758C2×Q8C2518yes—
759C2×Q8C25116yes—
760C2×Q8C25132yes—
761C2×Q8C25132yes—
762C2×Q8C25132yes—
763C2×D4—216no—
764C2×D4—232no—
765C2×D4—28no—
766C2×D4—232no—
767C2×D4—232no—
768C2×D4—2128no—
769C2×D4—28no—
770C2×D4—216no—
771C2×D4—24no—
772C2×D4—216no—
773C2×D4—464no—
774C2×D4—416no—
775C2×D4—416no—
776C2×D4—416no—
777C2×D4—48no—
778C2×D4—416no—
779C2×D4—432no—
780C2×D4—416no—
781C2×D4—416no—
782C2×D4—48no—
783C2×D4—4128no—
784C2×D4—864no—
785C2×D42−1+418yescomplemented
786C2×D4C2518yes—
787C2×D4C25132yes—
788C2×D4C2514yes—
789C2×D4C25116yes—
790C2×D4C25132yes—
791C2×D4C25116yes—
792C2×D4C2518yes—
793C2×D4C25116yes—
794C2×D4C25132yes—
795C2×D4C25116yes—
796C2×D4C25164yes—
797C2×D4C25116yes—
798C2×D4C25132yes—
799C2×D4C25132yes—
800C2×D4C25132yes—
801C2×D4C25132yes—
802C2×D4C25132yes—
803C2×D4C2514yes—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—216no—
807C22×C4—216no—
808C22×C4—264no—
809C22×C4—216no—
810C22×C4—232no—
811C22×C4—24no—
812C22×C4—216no—
813C22×C4—4128no—
814C22×C4—416no—
815C22×C4—416no—
816C22×C4—416no—
817C22×C4—44no—
818C22×C4—416no—
819C22×C4—48no—
820C22×C4—416no—
821C22×C4—432no—
822C22×C4—42no—
823C22×C4—432no—
824C22×C4—48no—
825C22×C4—832no—
826C22×C4H(5,𝔽2)18yes—
827C22×C4C2514yes—
828C22×C4C2518yes—
829C22×C4C25116yes—
830C22×C4C25116yes—
831C22×C4C2518yes—
832C22×C4C25116yes—
833C22×C4C25116yes—
834C22×C4C25132yes—
835C22×C4C2514yes—
836C22×C4C2511yescharacteristic
837C22×C4C2512yes—
838C22×C4C2518yes—
839C22×C4C2514yes—
840C22×C4C2518yes—
841C22×C4C2514yes—
842C22×C4C2514yes—
843C22×C4C2514yes—
844C22×C4C2514yes—
845C22×C4C2514yes—
846C22×C4C25116yes—
847C22×C4C2518yes—
848C22×C4C25132yes—
849C22×C4C25132yes—
850C22×C4C25116yes—
851C22×C4C25164yes—
852C22×C4C25164yes—
853C22×C4C25132yes—
854C22×C4C25132yes—
855C22×C4C25132yes—
856C22×C4C2514yes—
857C22×C4C2512yes—
858C22×C4C2511yescharacteristic
859C4⋊C4C25116yes—
860C4⋊C4C25132yes—
861C4⋊C4C2518yes—
862C4⋊C4C2518yes—
863C4⋊C4C25164yes—
864C4⋊C4C25164yes—
865C4⋊C4C25132yes—
866C4⋊C4C25116yes—
867C4⋊C4C25164yes—
868C4⋊C4C25132yes—
869C4⋊C4C25116yes—
870C4⋊C4C25116yes—
871C4⋊C4C25132yes—
872C4⋊C4C2518yes—
873C4⋊C4C25132yes—
874C4⋊C4C25116yes—
875C4⋊C4C25164yes—
876C4⋊C4C25132yes—
877C4⋊C4C2518yes—
878C4⋊C4C25116yes—
879C4⋊C4C25132yes—
880C4⋊C4C25132yes—
881C4⋊C4C25116yes—
882C4⋊C4C25116yes—
883C4⋊C4C25116yes—
884C22⋊C4C25116yes—
885C22⋊C4C25132yes—
886C22⋊C4C25132yes—
887C22⋊C4C25132yes—
888C22⋊C4C25164yes—
889C22⋊C4C25132yes—
890C22⋊C4C25164yes—
891C22⋊C4C25164yes—
892C22⋊C4C25132yes—
893C22⋊C4C25116yes—
894C22⋊C4C25132yes—
895C22⋊C4C25132yes—
896C22⋊C4C25132yes—
897C22⋊C4C25116yes—
898C22⋊C4C25116yes—
899C22⋊C4C25116yes—
900C22⋊C4C25164yes—
901C22⋊C4C25132yes—
902C22⋊C4C25132yes—
903C22⋊C4C25132yes—
904C42C2518yes—
905C42C25116yes—
906C42C2518yes—
907C42C25116yes—
908C42C25116yes—
909C42C25116yes—
910C42C25116yes—
911C42C25164yes—
912C23—24no—
913C23—22no—
914C23—22no—
915C23—24no—
916C23—216no—
917C23—24no—
918C23—216no—
919C23—28no—
920C23—28no—
921C23—216no—
922C23—24no—
923C23—216no—
924C23—24no—
925C23—216no—
926C23—28no—
927C23—264no—
928C23—48no—
929C23—432no—
930C23—432no—
931C23—432no—
932C23—864no—
933C23C2×H(5,𝔽2)14yes—
934C23C2×2−1+418yes—
935C23C2618yes—
936C23C2614yes—
937C23C26116yes—
938C23C2612yes—
939C23C2614yes—
940C23C2611yescharacteristic
941Q8—232no—
942Q8—232no—
943Q8—216no—
944Q8—432no—
945Q8—432no—
946Q8—432no—
947Q8—416no—
948D4—232no—
949D4—264no—
950D4—216no—
951D4—264no—
952D4—216no—
953D4—232no—
954D4—28no—
955D4—232no—
956D4—432no—
957D4—432no—
958D4—432no—
959D4—416no—
960D4—432no—
961D4—464no—
962D4—432no—
963D4—432no—
964D4—416no—
965D4C2×2−1+4116yescomplemented
966C2×C4—28no—
967C2×C4—216no—
968C2×C4—28no—
969C2×C4—216no—
970C2×C4—28no—
971C2×C4—216no—
972C2×C4—22no—
973C2×C4—28no—
974C2×C4—28no—
975C2×C4—216no—
976C2×C4—28no—
977C2×C4—24no—
978C2×C4—232no—
979C2×C4—232no—
980C2×C4—232no—
981C2×C4—264no—
982C2×C4—28no—
983C2×C4—232no—
984C2×C4—432no—
985C2×C4—432no—
986C2×C4—432no—
987C2×C4—48no—
988C2×C4—432no—
989C2×C4—416no—
990C2×C4—432no—
991C2×C4—464no—
992C2×C4—44no—
993C2×C4—464no—
994C2×C4—416no—
995C2×C4C2×H(5,𝔽2)18yes—
996C2×C4C2×H(5,𝔽2)116yes—
997C2×C4C2×2−1+414yes—
998C2×C4C2618yes—
999C2×C4C2612yes—
1000C2×C4C2614yes—
1001C2×C4C2618yes—
1002C2×C4C26116yes—
1003C2×C4C26116yes—
1004C2×C4C2618yes—
1005C2×C4C2618yes—
1006C2×C4C2618yes—
1007C2×C4C2618yes—
1008C2×C4C2614yes—
1009C2×C4C2612yes—
1010C22—24no—
1011C22—22no—
1012C22—22no—
1013C22—24no—
1014C22—28no—
1015C22—216no—
1016C22—24no—
1017C22—216no—
1018C22—28no—
1019C22—28no—
1020C22—24no—
1021C22—216no—
1022C22—24no—
1023C22—216no—
1024C22—28no—
1025C22—432no—
1026C22—48no—
1027C22—432no—
1028C22—416no—
1029C22—864no—
1030C22C22×H(5,𝔽2)14yes—
1031C22C22×H(5,𝔽2)12yes—
1032C22C22×2−1+418yes—
1033C22C22×2−1+412yes—
1034C22H(7,𝔽2)12yes—
1035C22C2711yescharacteristic
1036C4—28no—
1037C4—28no—
1038C4—216no—
1039C4—28no—
1040C4—22no—
1041C4—28no—
1042C4—28no—
1043C4—216no—
1044C4—28no—
1045C4—24no—
1046C4C22×H(5,𝔽2)18yes—
1047C4C22×2−1+414yes—
1048C2—24no—
1049C2—28no—
1050C2—44no—
1051C2—416no—
1052C2—48no—
1053C2#6294414yesdirect product factor
1054C2C23×H(5,𝔽2)11yescharacteristic
1055C2C23×2−1+411yescharacteristic
1056C2C2×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. #62944C2direct (N × H)
2. C2×#3489C2semidirect
3. C2×#3511C2semidirect
4. C2×#3497C2semidirect
5. C2×#3519C2semidirect
6. C2×#3519C2semidirect
7. C2×#3492C2semidirect
8. C2×#3501C2semidirect
9. C2×#3548C2semidirect
10. C2×#3547C2semidirect
11. C2×#3559C2semidirect
12. C2×#3536C2semidirect
13. C2×#3536C2semidirect
14. C2×#3541C2semidirect
15. C22×#554C2semidirect
16. C2×D4×#41C2semidirect
17. C2×#3461C2semidirect
18. C22×#537C2semidirect
19. C22×2−1+4C22semidirect
20. C23×#41C22semidirect
21. #3559C22semidirect
22. #3548C22semidirect
23. #3547C22semidirect
24. #3541C22semidirect
25. #3536C22semidirect
26. #3536C22semidirect
27. C2×#563C22semidirect
28. C2×#562C22semidirect
29. C2×#562C22semidirect
30. C2×#562C22semidirect
31. #3519C22semidirect
32. #3519C22semidirect
33. #3511C22semidirect
34. #3501C22semidirect
35. #3497C22semidirect
36. #3492C22semidirect
37. #3489C22semidirect
38. C2×#556C22semidirect
39. C2×#555C22semidirect
40. C2×#555C22semidirect
43. C2×#554C22semidirect
44. C2×#554C22semidirect
45. C2×#554C22semidirect
46. C2×#554C22semidirect
47. C2×#554C22semidirect
48. C2×#554C22semidirect
49. C2×#554C22semidirect
50. C2×#553C22semidirect
51. C2×#553C22semidirect
52. C2×#553C22semidirect
53. C2×#553C22semidirect
54. C2×#552C22semidirect
55. D4×#41C22semidirect
56. C2×#550C22semidirect
57. C2×#550C22semidirect
58. C2×#550C22semidirect
60. C2×D4×Q8C22semidirect
61. C2×D4×Q8C22semidirect
62. C2×#548C22semidirect
63. C2×#548C22semidirect
64. C2×#548C22semidirect
65. C2×#548C22semidirect
66. C2×#547C22semidirect
67. C2×#547C22semidirect
68. C2×#547C22semidirect
69. C2×#547C22semidirect
70. C2×#547C22semidirect
71. C2×#547C22semidirect
72. C2×#546C22semidirect
73. C2×#546C22semidirect
74. C2×#546C22semidirect
75. C2×#546C22semidirect
76. C2×#546C22semidirect
77. C2×#546C22semidirect
81. #3461C22semidirect
82. C2×#544C22semidirect
83. C2×#544C22semidirect
84. C2×#543C22semidirect
85. C2×#542C22semidirect
86. C2×#542C22semidirect
87. C2×#542C22semidirect
88. C2×#541C22semidirect
89. C2×#540C22semidirect
90. C2×#540C22semidirect
91. C2×#539C22semidirect
92. C2×#539C22semidirect
93. C2×#539C22semidirect
94. C2×#538C22semidirect
95. C2×#538C22semidirect
97. C2×#537C22semidirect
98. C2×#537C22semidirect
99. C2×#537C22semidirect
100. C2×#537C22semidirect
101. C2×#537C22semidirect
102. C2×#537C22semidirect
103. C2×#537C22semidirect
104. C2×#537C22semidirect
105. C2×#537C22semidirect
106. C2×#536C22semidirect
107. C2×#536C22semidirect
108. C2×#533C22semidirect
109. C2×#533C22semidirect
110. C2×#532C22semidirect
111. C2×#532C22semidirect
112. C2×#532C22semidirect
113. C2×#532C22semidirect
114. C22×C4⋊Q8C22semidirect
115. C2×#529C22semidirect
116. C2×#529C22semidirect
117. C22×#125C22semidirect
118. C2×#525C22semidirect
119. C2×#525C22semidirect
120. C2×#525C22semidirect
121. C2×#525C22semidirect
122. C22×C22⋊Q8C22semidirect
123. C22×C22⋊Q8C22semidirect
124. C22×C22⋊Q8C22semidirect
125. C22×C22⋊Q8C22semidirect
126. C22×#121C22semidirect
127. C22×#121C22semidirect
128. C2×#520C22semidirect
130. C2×C4×#41C22semidirect
131. C22×C4×Q8C22semidirect
135. C23×C4⋊C4C22semidirect
137. C2×2−1+4C23semidirect
149. C22×#41C23semidirect
162. #563C23semidirect
163. #562C23semidirect
164. #562C23semidirect
165. #562C23semidirect
166. #556C23semidirect
167. #555C23semidirect
168. #555C23semidirect
171. #554C23semidirect
172. #554C23semidirect
173. #554C23semidirect
174. #554C23semidirect
175. #554C23semidirect
176. #554C23semidirect
177. #553C23semidirect
178. #553C23semidirect
179. #553C23semidirect
180. #553C23semidirect
181. #552C23semidirect
182. #550C23semidirect
183. #550C23semidirect
184. #550C23semidirect
186. D4×Q8C23semidirect
187. D4×Q8C23semidirect
188. #548C23semidirect
189. #548C23semidirect
190. #548C23semidirect
191. #548C23semidirect
192. #547C23semidirect
193. #547C23semidirect
194. #547C23semidirect
195. #547C23semidirect
196. #547C23semidirect
197. #547C23semidirect
198. #546C23semidirect
199. #546C23semidirect
200. #546C23semidirect
201. #546C23semidirect
202. #546C23semidirect
203. #546C23semidirect
207. #544C23semidirect
208. #544C23semidirect
209. #543C23semidirect
210. #542C23semidirect
211. #542C23semidirect
212. #542C23semidirect
213. #541C23semidirect
214. #540C23semidirect
215. #540C23semidirect
216. #539C23semidirect
217. #539C23semidirect
218. #539C23semidirect
219. #538C23semidirect
220. #538C23semidirect
222. #537C23semidirect
223. #537C23semidirect
224. #537C23semidirect
225. #537C23semidirect
226. #537C23semidirect
227. #537C23semidirect
228. #537C23semidirect
229. #537C23semidirect
230. #536C23semidirect
231. #536C23semidirect
232. #533C23semidirect
233. #533C23semidirect
234. #532C23semidirect
235. #532C23semidirect
236. #532C23semidirect
237. #532C23semidirect
246. C2×C4⋊Q8C23semidirect
250. #529C23semidirect
251. #529C23semidirect
263. C2×#125C23semidirect
272. #525C23semidirect
273. #525C23semidirect
274. #525C23semidirect
275. #525C23semidirect
313. C2×C22⋊Q8C23semidirect
314. C2×C22⋊Q8C23semidirect
315. C2×C22⋊Q8C23semidirect
316. C2×C22⋊Q8C23semidirect
344. C2×#121C23semidirect
345. C2×#121C23semidirect
350. #520C23semidirect
352. C4×#41C23semidirect
360. C2×C4×Q8C23semidirect
409. C22×C4⋊C4C23semidirect
785. C2×D42−1+4semidirect
965. D4C2×2−1+4semidirect
1053. C2#62944direct (N × H)

Maximal subgroups

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

subgroupindex
#629442
C2×#34892
C2×#35112
C2×#34972
C2×#35192
C2×#34922
C2×#35012
C2×#35482
C2×#35472
C2×#35592
C2×#35362
C2×#35412
C22×#5542
C2×D4×#412
C2×#34612
C22×#5372