Finite Group Databasebeta

← #10578628

Subgroups — #10578628

Order 512.

6310 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62788C211yesmaximal, characteristic, complemented
2C22×#556C211yesmaximal, characteristic, complemented
3#61905C218yesmaximal, complemented
4#61899C218yesmaximal, complemented
5#61894C218yesmaximal, complemented
6#61889C212yesmaximal, complemented
7#61888C212yesmaximal, complemented
8#61882C214yesmaximal, complemented
9#61403C218yesmaximal, complemented
10#61323C218yesmaximal, complemented
11#60800C212yesmaximal, complemented
12#60799C214yesmaximal, complemented
13#60560C214yesmaximal, complemented
14#60558C212yesmaximal, complemented
15#60248C211yesmaximal, characteristic, complemented
16#3523C2214yescomplemented
17#3522C2214yescomplemented
18#3516—24no—
19#3507C2212yescomplemented
20#3507C2214yescomplemented
21#3502C2211yescharacteristic, complemented
22#3497C2211yescharacteristic, complemented
23#3492—21no—
24#3492—22no—
25#3486—21no—
26#3482—24no—
27#3480C2214yescomplemented
28Q8×#41C2214yescomplemented
29C2×#556—21no—
30C2×#556—21no—
31C2×#556—22no—
32C2×#556—24no—
33C2×#556—24no—
34C2×#556C2218yes—
35C2×#556C2212yes—
36C2×#556C2212yes—
37C2×#556C2214yes—
38C2×#556C2218yes—
39#3461—21no—
40#3461—22no—
41#3444C2214yes—
42#3444C2212yes—
43C22×C4⋊Q8C2211yescharacteristic
44C22×#126—22no—
45C22×#124C2212yes—
46C22×C22⋊Q8—21no—
47C4×2−1+4—21no—
48C22×C4×Q8C2212yes—
49C22×C4×Q8C2211yescharacteristic
50C22×C4×D4C2211yescharacteristic
51C22×#117—21no—
52#3402C22132yescomplemented
53#3401C22132yescomplemented
54#3398C22116yescomplemented
55#3397C22116yescomplemented
56#3394C22116yescomplemented
57#3393C22116yescomplemented
58#3377C22132yescomplemented
59#3376C22132yescomplemented
60#3369C22116yescomplemented
61#3367C22116yescomplemented
62#3364C22116yescomplemented
63#3360C22116yescomplemented
64#3218C2218yescomplemented
65#3218C2218yescomplemented
66#3215C2218yes—
67#3215C2218yes—
68#3213C2218yes—
69#3213C2218yes—
70#3211C22116yes—
71#3211C22116yes—
72#3209C2214yescomplemented
73#3209C2214yescomplemented
74#3206C2214yescomplemented
75#3206C2214yescomplemented
76#3153C2218yes—
77#3152C2214yescomplemented
78#3140C2218yes—
79#3139C2214yescomplemented
80#3117C22116yescomplemented
81#3114C2218yes—
82#3113C2218yescomplemented
83#3112C2218yescomplemented
84#3110C2214yes—
85#3109C2214yes—
86#3108C22116yescomplemented
87#3105C2218yes—
88#3104C2218yescomplemented
89#3103C2218yescomplemented
90#3101C2214yes—
91#3100C2214yes—
92#3092C2214yes—
93#3078C2218yescomplemented
94#3077C2214yes—
95#3040C22116yes—
96#3039C2218yescomplemented
97#3037C2218yescomplemented
98#3036C2214yes—
99#3004C2218yes—
100#3003C2214yes—
101#2984C2218yescomplemented
102#2983C2212yescomplemented
103#2983C2214yescomplemented
104#2982C2212yescomplemented
105Q8×M16C2218yescomplemented
106C4×#137C22116yescomplemented
107C4×AGL(1,ℤ/8)C2218yes—
108#2920C2214yes—
109#2920C2212yes—
110C2×2−1+4—21no—
111C23×Q8D411yescharacteristic
112C23×Q8C2312yes—
113C23×D4C2311yescharacteristic
114C24×C4—21no—
115C2×#137C23116yes—
116C2×AGL(1,ℤ/8)C2318yes—
117#559C2314yescomplemented
118#559C2318yescomplemented
119Q82C2314yescomplemented
120#557—24no—
121#557C2314yescomplemented
122#557C2314yescomplemented
123#557C2318yescomplemented
124#556—28no—
125#556—28no—
126#556—28no—
127#556—216no—
128#556—28no—
129#556—216no—
130#556—28no—
131#556—28no—
132#556—216no—
133#556—24no—
134#556—28no—
135#556C23116yes—
136#556C23116yes—
137#556C23132yes—
138#556C2314yescomplemented
139#556C2318yescomplemented
140#554—24no—
141#554—28no—
142#554C2314yescomplemented
143#554C2318yescomplemented
144#553—24no—
145#553—28no—
146#552—24no—
147#552—28no—
148#552—24no—
149#552—28no—
150#550C2314yescomplemented
151D4×Q8—24no—
152D4×Q8—24no—
153D4×Q8C2314yescomplemented
154#548—24no—
155#548—24no—
156#548—24no—
157#547—24no—
158#547—28no—
159#544—21no—
160#544—22no—
161#542—24no—
162#542—28no—
163#541—24no—
164#541—28no—
165#539—24no—
166#539—24no—
167#539—24no—
168#537—21no—
169#537—22no—
170#536—22no—
171#536—24no—
172#533—24no—
173#533—28no—
174#533C2312yes—
175#533C2314yes—
176#533C2312yes—
177#533C2314yes—
178#533C2312yes—
179#533C2314yes—
180#532C2312yes—
181#532C2314yes—
182#532C2312yes—
183#532C2314yes—
184#532C2312yes—
185#532C2314yes—
186C2×C4⋊Q8—21no—
187C2×C4⋊Q8—22no—
188C2×C4⋊Q8—21no—
189C2×C4⋊Q8—22no—
190C2×C4⋊Q8C2314yes—
191C2×C4⋊Q8C2312yes—
192C2×C4⋊Q8C2314yes—
193C2×C4⋊Q8C2312yes—
194#529—24no—
195#529—28no—
196#529—22no—
197#529—24no—
198#529—22no—
199#529—24no—
200#529—22no—
201#529—22no—
202#529—24no—
203#529—24no—
204#529C2314yes—
205#529C2318yes—
206#529C2314yes—
207#529C2318yes—
208C2×#126—24no—
209C2×#126—24no—
210C2×#126—24no—
211C2×#126—24no—
212C2×#126—216no—
213C2×#126—216no—
214C2×#124—22no—
215C2×#124—24no—
216C2×#124—22no—
217C2×#124—24no—
218C2×#124C2318yes—
219C2×#124C2314yes—
220C2×#124C2318yes—
221C2×#124C2314yes—
222#525—22no—
223#525—24no—
224#525—22no—
225#525—24no—
226#525C2314yes—
227C2×C22⋊Q8—22no—
228C2×C22⋊Q8—22no—
229C2×C22⋊Q8—24no—
230C2×C22⋊Q8—28no—
231C2×C22⋊Q8—28no—
232#520—24no—
233#520—22no—
234#520—24no—
235#519—21no—
236#519—24no—
237C4×#41—24no—
238C4×#41—22no—
239C4×#41—24no—
240C4×#41—22no—
241C4×#41—24no—
242C4×#41C2314yes—
243C4×#41C2318yes—
244C2×C4×Q8—24no—
245C2×C4×Q8—22no—
246C2×C4×Q8—24no—
247C2×C4×Q8—24no—
248C2×C4×Q8—22no—
249C2×C4×Q8D411yescharacteristic
250C2×C4×Q8D411yescharacteristic
251C2×C4×Q8D412yes—
252C2×C4×Q8D414yes—
253C2×C4×Q8D414yes—
254C2×C4×Q8C2318yes—
255C2×C4×Q8C2318yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2314yes—
263C2×C4×D4—21no—
264C2×C4×D4—22no—
265C2×C4×D4—21no—
266C2×C4×D4—22no—
267C2×C4×D4C2314yes—
268C2×C4×D4C2312yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×#117—22no—
272C2×#117—22no—
273C2×#117—24no—
274C2×#117—28no—
275C2×#117—28no—
276C22×C4⋊C4—21no—
277C22×C4⋊C4—22no—
278C22×C4⋊C4—21no—
279C22×C4⋊C4D411yescharacteristic
280C22×C4⋊C4D412yes—
281C22×C4⋊C4C2311yescharacteristic
282C22×C22⋊C4—22no—
283C22×C22⋊C4—21no—
284C22×C22⋊C4—22no—
285C22×C42—22no—
286C22×C42C2311yescharacteristic
287C22×C42C2312yes—
288#497C23116yes—
289#497C23116yescomplemented
290#496C23116yes—
291#495C23132yes—
292#494C2318yescomplemented
293#492C2318yescomplemented
294#491C23116yescomplemented
295#489C23116yes—
296#489C23116yes—
297#488C23132yes—
298#487C2318yescomplemented
299#487C2318yescomplemented
300#484C2318yes—
301#483C2318yes—
302#481C2318yes—
303#480C2318yes—
304#479C23132yescomplemented
305#478C23116yes—
306#477C23116yescomplemented
307#476C2318yes—
308#475C23116yescomplemented
309#474C2318yes—
310#464C23132yes—
311#464C23132yes—
312#464C23132yescomplemented
313#463C23132yes—
314#463C23116yes—
315#463C23132yes—
316#462C23116yescomplemented
317#462C23116yescomplemented
318#462C23116yescomplemented
319#461C2318yes—
320#461C23116yescomplemented
321#461C23116yescomplemented
322#460C23116yescomplemented
323#459C2318yes—
324#451C23116yes—
325#451C23116yes—
326#450C2318yes—
327#450C2318yes—
328#448C23116yes—
329#448C23116yes—
330#447C2318yes—
331#447C2318yes—
332#446C23116yescomplemented
333#446C23132yescomplemented
334C8×Q8C23116yescomplemented
335#442C23116yes—
336#441C23132yescomplemented
337#440C23116yes—
338#440C23132yescomplemented
339C4×Q16C23132yescomplemented
340C4×SD16C23116yes—
341C4×SD16C23132yescomplemented
342C4×D8C23116yes—
343#432C2314yes—
344#432C2318yes—
345#432C2314yes—
346#432C2318yes—
347#431C2314yes—
348#431C2318yes—
349#431C2314yes—
350#431C2318yes—
351#428C2318yes—
352#423C2314yes—
353#423C2318yes—
354#419C23116yes—
355#418C2318yes—
356#417C2318yes—
357#407C2314yes—
358C4×M16C2314yes—
359C4×M16C2318yes—
360C25—21no—
3612−1+4—48no—
362C2×#41—24no—
363C2×#41—24no—
364C2×#41—22no—
365C2×#41—24no—
366C2×#41—22no—
367C2×#41C2414yes—
368C22×Q8—24no—
369C22×Q8—22no—
370C22×Q8—22no—
371C22×Q8—22no—
372C22×Q8—44no—
373C22×Q8—48no—
374C22×Q8C2×D411yescharacteristic
375C22×Q8C2×D411yescharacteristic
376C22×Q8C2×D412yes—
377C22×Q8C2×D414yes—
378C22×Q8C2×D414yes—
379C22×Q8C2414yes—
380C22×Q8C2414yes—
381C22×Q8C2414yes—
382C22×D4—21no—
383C22×D4—21no—
384C22×D4—21no—
385C22×D4—44no—
386C22×D4C2412yes—
387C22×D4C2412yes—
388C22×D4C2412yes—
389C23×C4—22no—
390C23×C4—21no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—48no—
396C23×C4C2×D411yescharacteristic
397C23×C4C2×D411yescharacteristic
398C23×C4C2×D412yes—
399C23×C4C2×D412yes—
400C23×C4C2411yescharacteristic
401#137—432no—
402AGL(1,ℤ/8)—416no—
403C2×Q16C24132yes—
404C2×SD16C24116yes—
405C2×SD16C24132yes—
406C2×D8C24116yes—
407C2×M16C2418yes—
408C4⋊Q8—24no—
409C4⋊Q8—28no—
410C4⋊Q8—24no—
411C4⋊Q8—28no—
412C4⋊Q8—24no—
413C4⋊Q8—24no—
414C4⋊Q8—24no—
415C4⋊Q8—24no—
416C4⋊Q8—24no—
417C4⋊Q8—24no—
418C4⋊Q8C2418yes—
419C4⋊Q8C2418yes—
420C4⋊Q8C2412yes—
421C4⋊Q8C2414yes—
422C4⋊Q8C2412yes—
423C4⋊Q8C2414yes—
424C4⋊Q8C2414yes—
425C4⋊Q8C2412yes—
426#127C2412yes—
427#127C2414yes—
428#126—232no—
429#126—232no—
430#126—232no—
431#126—232no—
432#126—28no—
433#126—28no—
434#126—28no—
435#126—24no—
436#126—28no—
437#126—24no—
438#126—28no—
439#125—24no—
440#125—28no—
441#125—28no—
442#125—28no—
443#125—28no—
444#125—22no—
445#125—24no—
446#125—22no—
447#125—24no—
448#125C2414yes—
449#125C2418yes—
450#124—24no—
451#124—28no—
452#124—28no—
453#124—28no—
454#124—28no—
455#124—28no—
456#124—28no—
457#124—28no—
458#124—22no—
459#124—24no—
460#124—22no—
461#124—24no—
462#124C24116yes—
463#124C24116yes—
464#124C2414yes—
465#124C2418yes—
466#123—28no—
467#123—24no—
468#123—28no—
469#123—24no—
470#123—24no—
471#123—28no—
472#123—28no—
473#123—28no—
474C22⋊Q8—216no—
475C22⋊Q8—216no—
476C22⋊Q8—232no—
477C22⋊Q8—24no—
478C22⋊Q8—28no—
479C22⋊Q8—24no—
480C22⋊Q8—28no—
481C22⋊Q8—24no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8—24no—
485C22⋊Q8—22no—
486C22⋊Q8—24no—
487C22⋊Q8—24no—
488C22⋊Q8—22no—
489C22⋊Q8—24no—
490C22⋊Q8—28no—
491C22⋊Q8—28no—
492C22⋊Q8—28no—
493C22⋊Q8—28no—
494C22⋊Q8C2414yes—
495C22⋊Q8C2414yes—
496#121—24no—
497#121—22no—
498#121—22no—
499#121—24no—
500#121—22no—
501#121—24no—
502#121—24no—
503#121—22no—
504#121—24no—
505#121—28no—
506#121C2414yes—
507#121C2414yes—
508#120—24no—
509C4×Q8—24no—
510C4×Q8—24no—
511C4×Q8—24no—
512C4×Q8—28no—
513C4×Q8—28no—
514C4×Q8—28no—
515C4×Q8—28no—
516C4×Q8—28no—
517C4×Q8—28no—
518C4×Q8—28no—
519C4×Q8—22no—
520C4×Q8—24no—
521C4×Q8—22no—
522C4×Q8—24no—
523C4×Q8—22no—
524C4×Q8—24no—
525C4×Q8—22no—
526C4×Q8—24no—
527C4×Q8C2×D414yes—
528C4×Q8C2×D414yes—
529C4×Q8C2×D414yes—
530C4×Q8C2×D418yes—
531C4×Q8C2×D414yes—
532C4×Q8C2×D418yes—
533C4×Q8C2×D414yes—
534C4×Q8C2×D418yes—
535C4×Q8C2×D414yes—
536C4×Q8C24116yes—
537C4×Q8C24116yes—
538C4×Q8C2418yes—
539C4×Q8C2414yes—
540C4×Q8C2414yes—
541C4×Q8C2418yes—
542C4×Q8C2414yes—
543C4×Q8C2414yes—
544C4×Q8C2418yes—
545C4×D4—24no—
546C4×D4—24no—
547C4×D4—28no—
548C4×D4—24no—
549C4×D4—24no—
550C4×D4—28no—
551C4×D4—24no—
552C4×D4—28no—
553C4×D4—28no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4—28no—
557C4×D4—24no—
558C4×D4—24no—
559C4×D4—24no—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—24no—
563C4×D4—22no—
564C4×D4—24no—
565C4×D4—22no—
566C4×D4—24no—
567C4×D4—22no—
568C4×D4—24no—
569C4×D4—22no—
570C4×D4—24no—
571C4×D4C2418yes—
572C4×D4C2418yes—
573C4×D4C2414yes—
574C4×D4C2418yes—
575C4×D4C2418yes—
576C4×D4C2414yes—
577#117—24no—
578#117—22no—
579#117—24no—
580#117—22no—
581#117—216no—
582#117—216no—
583#117—232no—
584#117—24no—
585#117—28no—
586#117—24no—
587#117—28no—
588#117—24no—
589#117—28no—
590#117—24no—
591#117—28no—
592#117C2414yes—
593C2×C4⋊C4—24no—
594C2×C4⋊C4—24no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—24no—
598C2×C4⋊C4—24no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—24no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—28no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D412yes—
613C2×C4⋊C4C2×D414yes—
614C2×C4⋊C4C2×D414yes—
615C2×C4⋊C4C2×D412yes—
616C2×C4⋊C4C2×D412yes—
617C2×C4⋊C4C2×D412yes—
618C2×C4⋊C4C2×D412yes—
619C2×C4⋊C4C2×D418yes—
620C2×C4⋊C4C2×D418yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C22⋊C4—28no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—28no—
627C2×C22⋊C4—24no—
628C2×C22⋊C4—24no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—28no—
635C2×C22⋊C4—28no—
636C2×C42—28no—
637C2×C42—24no—
638C2×C42—28no—
639C2×C42—24no—
640C2×C42—24no—
641C2×C42—28no—
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D412yes—
644C2×C42C2×D411yescharacteristic
645C2×C42C2×D412yes—
646C2×C42C2×D412yes—
647C2×C42C2×D414yes—
648C2×C42C2×D412yes—
649C2×C42C2×D414yes—
650C2×C42C2412yes—
651C2×C42C2411yescharacteristic
652C2×C42C2412yes—
653C2×C42C2411yescharacteristic
654C2×C42C2414yes—
655C2×C42C2412yes—
656C2×C42C2414yes—
657C2×C42C2412yes—
658#107C24116yes—
659#106C24116yes—
660C4⋊C8C2418yes—
661C4⋊C8C24116yes—
662C4⋊C8C24116yes—
663C4⋊C8C2418yes—
664#103C24116yes—
665#103C24132yes—
666#103C24132yes—
667#102C24116yes—
668#102C24116yes—
669#102C24116yes—
670C22⋊C8C2418yes—
671C22⋊C8C2418yes—
672#97C2418yes—
673#97C24116yes—
674C4×C8C2418yes—
675C4×C8C24116yes—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24C22×D411yescharacteristic
683#41—216no—
684#41—416no—
685#41—416no—
686#41—48no—
687#41—88no—
688#41—84no—
689C2×Q8—24no—
690C2×Q8—24no—
691C2×Q8—24no—
692C2×Q8—22no—
693C2×Q8—24no—
694C2×Q8—24no—
695C2×Q8—24no—
696C2×Q8—24no—
697C2×Q8—22no—
698C2×Q8—216no—
699C2×Q8—44no—
700C2×Q8—48no—
701C2×Q8—48no—
702C2×Q8—48no—
703C2×Q8—48no—
704C2×Q8—48no—
705C2×Q8—48no—
706C2×Q8—48no—
707C2×Q8—416no—
708C2×Q8C22×D414yes—
709C2×Q8C22×D414yes—
710C2×Q8C22×D418yes—
711C2×Q8C2518yes—
712C2×Q8C2514yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—24no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—28no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4C2514yes—
730C2×D4C2514yes—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—24no—
737C22×C4—24no—
738C22×C4—24no—
739C22×C4—24no—
740C22×C4—28no—
741C22×C4—24no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—24no—
746C22×C4—42no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—48no—
750C22×C4—416no—
751C22×C4—416no—
752C22×C4—44no—
753C22×C4—48no—
754C22×C4—48no—
755C22×C4C22×D414yes—
756C22×C4C22×D411yescharacteristic
757C22×C4C22×D411yescharacteristic
758C22×C4C22×D411yescharacteristic
759C22×C4C22×D412yes—
760C22×C4C22×D412yes—
761C22×C4C22×D412yes—
762C22×C4C22×D412yes—
763C22×C4C22×D412yes—
764C22×C4C22×D411yescharacteristic
765C22×C4C22×D412yes—
766C22×C4C22×D414yes—
767C22×C4C22×D412yes—
768C22×C4C22×D411yescharacteristic
769C22×C4C22×D412yes—
770C22×C4C22×D411yescharacteristic
771C22×C4C22×D414yes—
772C22×C4C22×D414yes—
773C22×C4C22×D411yescharacteristic
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2511yescharacteristic
777Q16—432no—
778SD16—416no—
779SD16—432no—
780D8—416no—
781M16—216no—
782C2×C8C25116yes—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—216no—
786C4⋊C4—216no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—24no—
793C4⋊C4—22no—
794C4⋊C4—28no—
795C4⋊C4—24no—
796C4⋊C4—24no—
797C4⋊C4—22no—
798C4⋊C4—24no—
799C4⋊C4—24no—
800C4⋊C4—24no—
801C4⋊C4—22no—
802C4⋊C4—24no—
803C4⋊C4—22no—
804C4⋊C4—28no—
805C4⋊C4—24no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—24no—
810C4⋊C4C22×D414yes—
811C4⋊C4C22×D418yes—
812C4⋊C4C22×D414yes—
813C4⋊C4C22×D418yes—
814C4⋊C4C22×D418yes—
815C4⋊C4C22×D418yes—
816C4⋊C4C22×D418yes—
817C4⋊C4C2514yes—
818C4⋊C4C2514yes—
819C4⋊C4C2514yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—216no—
824C22⋊C4—216no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—216no—
828C22⋊C4—216no—
829C22⋊C4—28no—
830C22⋊C4—24no—
831C22⋊C4—24no—
832C22⋊C4—24no—
833C22⋊C4—28no—
834C22⋊C4—24no—
835C22⋊C4—28no—
836C22⋊C4—24no—
837C22⋊C4—28no—
838C22⋊C4—24no—
839C42—216no—
840C42—216no—
841C42—24no—
842C42—28no—
843C42—24no—
844C42—28no—
845C42—24no—
846C42C22×D412yes—
847C42C22×D414yes—
848C42C22×D412yes—
849C42C22×D412yes—
850C42C22×D412yes—
851C42C22×D414yes—
852C42C22×D414yes—
853C42C22×D414yes—
854C42C22×D412yes—
855C42C22×D412yes—
856C42C22×D414yes—
857C42C22×D414yes—
858C42C2512yes—
859C42C2514yes—
860C42C2512yes—
861C42C2514yes—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—24no—
866C23—24no—
867C23—44no—
868C23—44no—
869C23—44no—
870C23—44no—
871C23—44no—
872C23—44no—
873C23—44no—
874C23—44no—
875C23—44no—
876C23—816no—
877C23C23×D411yescharacteristic
878C23C23×D411yescharacteristic
879C23C23×D411yescharacteristic
880Q8—28no—
881Q8—28no—
882Q8—28no—
883Q8—216no—
884Q8—48no—
885Q8—48no—
886Q8—48no—
887Q8—48no—
888Q8—48no—
889Q8—44no—
890Q8—84no—
891Q8—82no—
892D4—28no—
893D4—28no—
894D4—44no—
895D4—44no—
896D4—48no—
897D4—48no—
898D4—48no—
899D4—48no—
900D4—44no—
901D4—44no—
902D4—84no—
903D4—82no—
904C2×C4—28no—
905C2×C4—24no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—44no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—41no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—416no—
930C2×C4—416no—
931C2×C4—44no—
932C2×C4—44no—
933C2×C4—48no—
934C2×C4—48no—
935C2×C4—48no—
936C2×C4—44no—
937C2×C4—48no—
938C2×C4—416no—
939C2×C4—48no—
940C2×C4—88no—
941C2×C4—84no—
942C2×C4#57514yes—
943C2×C4C23×D414yes—
944C2×C4C23×D414yes—
945C2×C4C23×D412yes—
946C2×C4C23×D414yes—
947C2×C4C23×D411yescharacteristic
948C2×C4C23×D411yescharacteristic
949C2×C4C23×D414yes—
950C2×C4C23×D412yes—
951C2×C4C23×D412yes—
952C2×C4C23×D411yescharacteristic
953C2×C4C23×D412yes—
954C2×C4#58514yes—
955C2×C4C2611yescharacteristic
956C8—216no—
957C22—28no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—88no—
971C22—88no—
972C22—88no—
973C22#348712yes—
974C22C2×#57512yes—
975C22#358612yes—
976C22C24×D411yescharacteristic
977C4—21no—
978C4—21no—
979C4—22no—
980C4—24no—
981C4—24no—
982C4—24no—
983C4—22no—
984C4—24no—
985C4—22no—
986C4—48no—
987C4—44no—
988C4—44no—
989C4—44no—
990C4—44no—
991C4#348712yes—
992C4C2×#57514yes—
993C4C2×#58512yes—
994C2—22no—
995C2—22no—
996C2—22no—
997C2—84no—
998C2—84no—
999C2C2×#348711yescharacteristic
1000C2C22×#57511yescharacteristic
1001C2C2×#358611yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62788C2semidirect
2. C22×#556C2semidirect
3. #61905C2semidirect
4. #61899C2semidirect
5. #61894C2semidirect
6. #61889C2semidirect
7. #61888C2semidirect
8. #61882C2semidirect
9. #61403C2semidirect
10. #61323C2semidirect
11. #60800C2semidirect
12. #60799C2semidirect
13. #60560C2semidirect
14. #60558C2semidirect
15. #60248C2semidirect
16. #3523C22semidirect
17. #3522C22semidirect
19. #3507C22semidirect
20. #3507C22semidirect
21. #3502C22semidirect
22. #3497C22semidirect
27. #3480C22semidirect
28. Q8×#41C22semidirect
52. #3402C22semidirect
53. #3401C22semidirect
54. #3398C22semidirect
55. #3397C22semidirect
56. #3394C22semidirect
57. #3393C22semidirect
58. #3377C22semidirect
59. #3376C22semidirect
60. #3369C22semidirect
61. #3367C22semidirect
62. #3364C22semidirect
63. #3360C22semidirect
64. #3218C22semidirect
65. #3218C22semidirect
72. #3209C22semidirect
73. #3209C22semidirect
74. #3206C22semidirect
75. #3206C22semidirect
77. #3152C22semidirect
79. #3139C22semidirect
80. #3117C22semidirect
82. #3113C22semidirect
83. #3112C22semidirect
86. #3108C22semidirect
88. #3104C22semidirect
89. #3103C22semidirect
93. #3078C22semidirect
96. #3039C22semidirect
97. #3037C22semidirect
101. #2984C22semidirect
102. #2983C22semidirect
103. #2983C22semidirect
104. #2982C22semidirect
105. Q8×M16C22semidirect
106. C4×#137C22semidirect
117. #559C23semidirect
118. #559C23semidirect
119. Q82C23semidirect
121. #557C23semidirect
122. #557C23semidirect
123. #557C23semidirect
138. #556C23semidirect
139. #556C23semidirect
142. #554C23semidirect
143. #554C23semidirect
150. #550C23semidirect
153. D4×Q8C23semidirect
289. #497C23semidirect
292. #494C23semidirect
293. #492C23semidirect
294. #491C23semidirect
298. #487C23semidirect
299. #487C23semidirect
304. #479C23semidirect
306. #477C23semidirect
308. #475C23semidirect
312. #464C23semidirect
316. #462C23semidirect
317. #462C23semidirect
318. #462C23semidirect
320. #461C23semidirect
321. #461C23semidirect
322. #460C23semidirect
332. #446C23semidirect
333. #446C23semidirect
334. C8×Q8C23semidirect
336. #441C23semidirect
338. #440C23semidirect
339. C4×Q16C23semidirect
341. C4×SD16C23semidirect

Maximal subgroups

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

subgroupindex
#627882
C22×#5562
#619052
#618992
#618942
#618892
#618882
#618822
#614032
#613232
#608002
#607992
#605602
#605582
#602482