Finite Group Databasebeta

← #10580909

Subgroups — #10580909

Order 512.

6310 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62781C212yesmaximal, complemented
2#62533C218yesmaximal, complemented
3#62475C214yesmaximal, complemented
4#62419C214yesmaximal, complemented
5#62361C212yesmaximal, complemented
6#62358C212yesmaximal, complemented
7#62247C214yesmaximal, complemented
8#62246C211yesmaximal, characteristic, complemented
9#62245C211yesmaximal, characteristic, complemented
10#62244C214yesmaximal, complemented
11#62243C212yesmaximal, complemented
12#61433C214yesmaximal, complemented
13#61432C218yesmaximal, complemented
14#61431C214yesmaximal, complemented
15#60948C212yesmaximal, complemented
16#60945C214yesmaximal, complemented
17#60673C212yesmaximal, complemented
18C2×#3168C214yesmaximal, complemented
19C2×C8×#41C211yesmaximal, characteristic, complemented
20#3521—28no—
21#3515C2218yescomplemented
22#3514C2218yescomplemented
23#3507C2214yescomplemented
24#3505C2218yescomplemented
25#3501C2212yes—
26#3496C2212yes—
27#3493—22no—
28#3491—24no—
29#3485—22no—
30#3482C2218yescomplemented
31#3481C2218yescomplemented
32#3475—28no—
33#3461—22no—
34#3459—24no—
35#3444C2214yescomplemented
36C2×#529C2218yescomplemented
37C4×H(5,𝔽2)—22no—
38C2×C4×#41C2211yescharacteristic
39#3396C2214yescomplemented
40#3394C2218yescomplemented
41#3393C2214yescomplemented
42#3383C2214yescomplemented
43#3381C2218yescomplemented
44#3380C2214yescomplemented
45#3365C2218yescomplemented
46#3364C2218yescomplemented
47#3361C2218yescomplemented
48#3360C2218yescomplemented
49#3339C2218yescomplemented
50#3338C2214yescomplemented
51#3337C22116yescomplemented
52#3336C2218yescomplemented
53#3335C2218yescomplemented
54#3334C2214yescomplemented
55#3301C22116yescomplemented
56#3300C22116yescomplemented
57#3299C2218yescomplemented
58#3298C2218yescomplemented
59#3297C22116yescomplemented
60#3296C22116yescomplemented
61#3295C2218yescomplemented
62#3294C2218yescomplemented
63D4×Q16C2214yescomplemented
64#3285C2218yescomplemented
65#3282C22116yescomplemented
66D4×SD16C2218yescomplemented
67#3280C2218yescomplemented
68D4×D8C2214yescomplemented
69#3250C2218yescomplemented
70#3250C2218yescomplemented
71#3249C2212yescomplemented
72#3246C2214yescomplemented
73#3245C2212yes—
74#3233C2218yescomplemented
75#3232C22116yescomplemented
76#3212C2218yescomplemented
77#3211C22116yescomplemented
78#3191C2218yescomplemented
79#3189C2214yescomplemented
80#3187C2218yescomplemented
81#3186C2214yes—
82#3170C2212yescomplemented
83#3170C2212yescomplemented
84#3169C2212yes—
85#3169C2212yescomplemented
86#3168C2214yescomplemented
87#3168C2214yescomplemented
88#3168C2214yescomplemented
89#3168C2214yescomplemented
90#3168C2218yescomplemented
91#3168C2218yescomplemented
92#3168C2218yescomplemented
93#3168C2218yescomplemented
94#3168C2218yescomplemented
95#3168C2218yescomplemented
96#3168C2218yescomplemented
97#3167C2214yescomplemented
98#3167C2214yescomplemented
99#3160C2212yescomplemented
100C2×#499C2214yescomplemented
101#3147C2212yescomplemented
102C2×#495C2214yescomplemented
103#3131C2214yescomplemented
104C2×#488C2218yescomplemented
105#3108C22116yescomplemented
106#3107C2218yescomplemented
107#3106C2218yescomplemented
108#3105C22116yescomplemented
109#3050C2214yescomplemented
110#3050C2214yescomplemented
111C2×#467C2214yescomplemented
112C2×#466C2214yes—
113C2×#465C2218yescomplemented
114C8×#41C2214yescomplemented
115C8×#41C2214yescomplemented
116C8×#41C2214yescomplemented
117C8×#41C2214yescomplemented
118C2×C8×Q8C2211yescharacteristic, complemented
119C2×C8×Q8C2211yescharacteristic, complemented
120C4×#135C2214yescomplemented
121C4×#135C2214yescomplemented
122C2×C4×Q16C2214yescomplemented
123C2×C4×SD16C2218yescomplemented
124C2×C4×D8C2214yescomplemented
125C2×C8×D4C2211yescharacteristic
126C2×C8×D4C2211yescharacteristic
127C2×C8×D4C2212yescomplemented
128C2×C8×D4C2212yescomplemented
129C2×#431C2212yescomplemented
130C2×#431C2211yescharacteristic, complemented
131C22×C4×C8C2211yescharacteristic, complemented
132C22×C4×C8C2212yescomplemented
133C2×H(5,𝔽2)—22no—
134C22×#41D411yescharacteristic
135C2×#135C2314yes—
136C2×#135C2314yes—
137C22×Q16C2314yes—
138C22×SD16C2318yes—
139C22×D8C2314yes—
140C23×C8C2312yes—
141C23×C8C2312yes—
142C23×C8C2311yescharacteristic
143C23×C8C2311yescharacteristic
144#559C2318yes—
145#557C2318yes—
146#556—28no—
147#556—28no—
148#556C2318yes—
149#555—28no—
150#554—28no—
151#554C2318yes—
152#554C2318yes—
153#553—216no—
154#553—28no—
155#553C23116yes—
156#552—28no—
157#552—216no—
158#552—28no—
159#552—216no—
160#552C23116yes—
161#551—216no—
162#551—216no—
163#551—216no—
164D4×Q8C2318yes—
165#548C23116yes—
166#547—28no—
167#547—28no—
168#547C2318yes—
169#546—28no—
170#546—28no—
171#546—28no—
172#546C23116yes—
173D42C2318yes—
174#544—22no—
175#543—24no—
176#542—28no—
177#541—28no—
178#539—216no—
179#539—28no—
180#539—28no—
181#538—216no—
182#538—28no—
183#537—22no—
184#536—24no—
185#534—28no—
186#534—24no—
187#533—28no—
188#533C2314yes—
189#533C2314yes—
190#533C2314yes—
191#532C2314yes—
192#532C2314yes—
193#532C2314yes—
194#529—28no—
195#529—216no—
196#529—28no—
197#529—28no—
198#529—28no—
199#529—28no—
200#529—24no—
201#529—24no—
202#529—24no—
203#529—24no—
204#529C23116yes—
205#529C2318yes—
206#529C23116yes—
207#529C23116yes—
208#529C2318yes—
209C2×#126—28no—
210C2×#125C2318yes—
211C2×#124C2318yes—
212#525—24no—
213#525—24no—
214#525—216no—
215#525C2318yes—
216C2×#123—28no—
217C2×C22⋊Q8C2318yes—
218C2×#121C2318yes—
219#520—28no—
220#520—24no—
221#518—22no—
222#518—28no—
223#518—28no—
224C4×#41—28no—
225C4×#41—24no—
226C4×#41—24no—
227C4×#41D414yes—
228C4×#41D414yes—
229C4×#41C2318yes—
230C4×#41C2314yes—
231C4×#41C2314yes—
232C2×C4×Q8D411yescharacteristic
233C2×C4×Q8C2318yes—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—28no—
236C2×C4×D4—28no—
237C2×C4×D4D411yescharacteristic
238C2×C4×D4D412yes—
239C2×C4×D4C2318yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×#117—28no—
243C2×#117D412yes—
244C2×#117D411yescharacteristic
245C22×C42C2312yes—
246C22×C42C2311yescharacteristic
247#500C2312yes—
248#500C2312yes—
249#499C2318yes—
250#499C2318yes—
251#499C2314yes—
252#499C2318yes—
253#499C2314yes—
254#498C2314yes—
255#495C2318yes—
256#495C2318yes—
257#495C2314yes—
258#495C2318yes—
259#495C2314yes—
260#494C2312yes—
261#493C2312yes—
262#492C2314yes—
263#488C23116yes—
264#488C23116yes—
265#488C2318yes—
266#488C23116yes—
267#488C2318yes—
268#487C2314yes—
269#487C2314yes—
270#486C2314yes—
271#486C2314yes—
272#485C23116yes—
273#484C23116yes—
274#483C23116yes—
275#482C23116yes—
276#481C23116yes—
277#480C23116yes—
278#479C23116yes—
279#479C23116yes—
280#478C23116yes—
281#478C23116yes—
282#477C2318yes—
283#476C2318yes—
284#475C2318yes—
285#474C2318yes—
286#467C2314yes—
287#467C2318yes—
288#467C2314yes—
289#467C2318yes—
290#467C2318yes—
291#467C2314yes—
292#467C2314yes—
293#466C2318yes—
294#466C2314yes—
295#466C2314yes—
296#466C2318yes—
297#466C2318yes—
298#466C2314yes—
299#466C2314yes—
300#465C23116yes—
301#465C2318yes—
302#465C2318yes—
303#465C2318yes—
304#465C2318yes—
305#465C23116yes—
306#465C23116yes—
307#464C23116yes—
308#464C23116yes—
309#463C23116yes—
310#463C23116yes—
311#462C2318yes—
312#461C2318yes—
313#460C2318yes—
314#459C2318yes—
315#452C23116yes—
316#451C23116yes—
317#450C23116yes—
318#449C23116yes—
319#448C23116yes—
320#447C23116yes—
321C8×Q8C2314yes—
322C8×Q8C2314yes—
323C8×Q8C2314yes—
324C8×Q8C2314yes—
325C4×Q16C2318yes—
326C4×Q16C2314yes—
327C4×Q16C2318yes—
328C4×Q16C2314yes—
329C4×Q16C2318yes—
330C4×Q16C2314yes—
331C4×Q16C2314yes—
332C4×SD16C2318yes—
333C4×SD16C23116yes—
334C4×SD16C23116yes—
335C4×SD16C2318yes—
336C4×SD16C23116yes—
337C4×SD16C2318yes—
338C4×SD16C2318yes—
339C4×D8C2314yes—
340C4×D8C2318yes—
341C4×D8C2314yes—
342C4×D8C2314yes—
343C4×D8C2318yes—
344C4×D8C2318yes—
345C4×D8C2314yes—
346C8×D4C2314yes—
347C8×D4C2314yes—
348C8×D4C2318yes—
349C8×D4C2318yes—
350C8×D4C2314yes—
351C8×D4C2314yes—
352C8×D4C2318yes—
353C8×D4C2318yes—
354#431C2318yes—
355#431C2314yes—
356#431C2318yes—
357#431C2314yes—
358#427C2314yes—
359#427C2314yes—
360C2×#107C2314yes—
361C2×#107C2314yes—
362C2×#106C2318yes—
363C2×C4⋊C8C2311yescharacteristic
364C2×C4⋊C8C2311yescharacteristic
365C2×C4⋊C8C2312yes—
366C2×C4⋊C8C2312yes—
367#416C2318yes—
368#416C2318yes—
369C2×#103C2318yes—
370C2×#103C2318yes—
371C2×#102C2318yes—
372C2×#102C2318yes—
373C2×C22⋊C8C2312yes—
374C2×C22⋊C8C2312yes—
375C2×C22⋊C8C2312yes—
376C2×C4×C8C2311yescharacteristic
377C2×C4×C8C2314yes—
378C2×C4×C8C2312yes—
379C2×C4×C8C2314yes—
380C2×C4×C8C2312yes—
381C2×C4×C8C2311yescharacteristic
382C2×C4×C8C2312yes—
383C2×C4×C8C2311yescharacteristic
384C2×C4×C8C2312yes—
385C2×C4×C8C2312yes—
386C2×C4×C8C2312yes—
387C2×C4×C8C2314yes—
388C2×C4×C8C2314yes—
389C2×C4×C8C2311yescharacteristic
390C2×C4×C8C2312yes—
391H(5,𝔽2)—416no—
392C2×#41—28no—
393C2×#41—28no—
394C2×#41—24no—
395C2×#41—24no—
396C2×#41C2×D414yes—
397C2×#41C2×D414yes—
398C2×#41C2418yes—
399C22×Q8C2×D411yescharacteristic
400C22×Q8C2418yes—
401C22×D4—28no—
402C22×D4—28no—
403C22×D4C2×D412yes—
404C22×D4C2×D411yescharacteristic
405C22×D4C2418yes—
406C23×C4—28no—
407C23×C4C2×D412yes—
408C23×C4C2×D411yescharacteristic
409C23×C4C2×D412yes—
410C23×C4C2×D411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413#135—48no—
414#135—48no—
415C2×Q16—48no—
416C2×Q16C2414yes—
417C2×Q16C2418yes—
418C2×Q16C2414yes—
419C2×SD16—416no—
420C2×SD16C2418yes—
421C2×SD16C24116yes—
422C2×SD16C2418yes—
423C2×D8—48no—
424C2×D8C2414yes—
425C2×D8C2418yes—
426C2×D8C2414yes—
427C22×C8—44no—
428C22×C8—44no—
429C22×C8—42no—
430C22×C8—42no—
431C22×C8C2411yescharacteristic
432C22×C8C2411yescharacteristic
433C22×C8C2414yes—
434C22×C8C2414yes—
435C22×C8C2412yes—
436C22×C8C2412yes—
437C22×C8C2412yes—
438C22×C8C2411yescharacteristic
439C22×C8C2412yes—
440C22×C8C2411yescharacteristic
441C22×C8C2414yes—
442C22×C8C2414yes—
443C22×C8C2412yes—
444C22×C8C2412yes—
445C4⋊Q8—28no—
446C4⋊Q8—28no—
447C4⋊Q8C2414yes—
448C4⋊Q8C2414yes—
449C4⋊Q8C2414yes—
450#127C2414yes—
451#126—216no—
452#126—216no—
453#126—216no—
454#126—28no—
455#126—216no—
456#126—216no—
457#126—216no—
458#126—28no—
459#125—216no—
460#125—28no—
461#125—216no—
462#125—28no—
463#125—28no—
464#125—24no—
465#125—24no—
466#125C2418yes—
467#125C24116yes—
468#124—28no—
469#124—216no—
470#124—28no—
471#124—28no—
472#124—24no—
473#124—24no—
474#124C2418yes—
475#124C24116yes—
476#123—216no—
477#123—28no—
478#123—216no—
479#123—216no—
480#123—216no—
481#123—28no—
482#123—28no—
483#123—216no—
484#123—216no—
485#123—216no—
486#123—216no—
487C22⋊Q8—28no—
488C22⋊Q8—28no—
489C22⋊Q8—28no—
490C22⋊Q8—28no—
491C22⋊Q8—24no—
492C22⋊Q8—24no—
493C22⋊Q8—24no—
494C22⋊Q8—24no—
495C22⋊Q8—216no—
496C22⋊Q8—28no—
497C22⋊Q8—216no—
498C22⋊Q8—216no—
499C22⋊Q8—216no—
500C22⋊Q8C2418yes—
501C22⋊Q8C24116yes—
502C22⋊Q8C2418yes—
503#121—216no—
504#121—216no—
505#121—28no—
506#121—28no—
507#121—24no—
508#121—24no—
509#121—24no—
510#121—24no—
511#121—28no—
512#121—216no—
513#121C2418yes—
514#121C24116yes—
515#121C2418yes—
516#120—28no—
517#120—216no—
518#120—216no—
519C4×Q8—28no—
520C4×Q8—28no—
521C4×Q8—28no—
522C4×Q8—24no—
523C4×Q8—24no—
524C4×Q8—24no—
525C4×Q8—24no—
526C4×Q8C2×D414yes—
527C4×Q8C2×D414yes—
528C4×Q8C2×D414yes—
529C4×Q8C2418yes—
530C4×Q8C24116yes—
531C4×Q8C2418yes—
532C4×Q8C2414yes—
533C4×D4—28no—
534C4×D4—28no—
535C4×D4—216no—
536C4×D4—28no—
537C4×D4—216no—
538C4×D4—216no—
539C4×D4—28no—
540C4×D4—28no—
541C4×D4—28no—
542C4×D4—28no—
543C4×D4—28no—
544C4×D4—28no—
545C4×D4—216no—
546C4×D4—216no—
547C4×D4—24no—
548C4×D4—28no—
549C4×D4—28no—
550C4×D4—24no—
551C4×D4—24no—
552C4×D4—24no—
553C4×D4C2×D414yes—
554C4×D4C2×D414yes—
555C4×D4C2×D418yes—
556C4×D4C2×D418yes—
557C4×D4C2×D414yes—
558C4×D4C2×D418yes—
559C4×D4C2418yes—
560C4×D4C24116yes—
561C4×D4C2418yes—
562C4×D4C2414yes—
563C4×D4C2418yes—
564#117—24no—
565#117—24no—
566#117—28no—
567#117—216no—
568#117—28no—
569#117—216no—
570#117—216no—
571#117—216no—
572#117—28no—
573#117—28no—
574#117C2×D418yes—
575#117C2×D418yes—
576#117C2×D414yes—
577#117C2×D414yes—
578#117C2418yes—
579C2×C4⋊C4—28no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—28no—
583C2×C4⋊C4—28no—
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D412yes—
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D412yes—
588C2×C4⋊C4C2418yes—
589C2×C4⋊C4C2418yes—
590C2×C22⋊C4—28no—
591C2×C22⋊C4—28no—
592C2×C22⋊C4—28no—
593C2×C22⋊C4—28no—
594C2×C22⋊C4—28no—
595C2×C22⋊C4—216no—
596C2×C22⋊C4C2×D412yes—
597C2×C22⋊C4C2×D412yes—
598C2×C22⋊C4C2×D412yes—
599C2×C42—28no—
600C2×C42—28no—
601C2×C42C2×D414yes—
602C2×C42C2×D411yescharacteristic
603C2×C42C2×D412yes—
604C2×C42C2×D411yescharacteristic
605C2×C42C2×D412yes—
606C2×C42C2×D412yes—
607C2×C42C2×D414yes—
608C2×C42C2×D412yes—
609C2×C42C2414yes—
610C2×C42C2412yes—
611C2×C42C2411yescharacteristic
612C2×C42C2412yes—
613C2×C42C2414yes—
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616#107C2414yes—
617#107C2414yes—
618#107C2418yes—
619#107C2418yes—
620#107C2414yes—
621#107C2414yes—
622#106C2418yes—
623#106C24116yes—
624#106C2418yes—
625C4⋊C8C2414yes—
626C4⋊C8C2414yes—
627C4⋊C8C2418yes—
628C4⋊C8C2418yes—
629#103C2418yes—
630#103C2418yes—
631#103C24116yes—
632#103C24116yes—
633#103C2418yes—
634#103C2418yes—
635#102C2418yes—
636#102C2418yes—
637#102C24116yes—
638#102C24116yes—
639#102C2418yes—
640#102C2418yes—
641C22⋊C8C2418yes—
642C22⋊C8C2418yes—
643C22⋊C8C2418yes—
644C4×C8C2411yescharacteristic
645C4×C8C2411yescharacteristic
646C4×C8C2411yescharacteristic
647C4×C8C2411yescharacteristic
648C4×C8C2412yes—
649C4×C8C2414yes—
650C4×C8C2414yes—
651C4×C8C2412yes—
652C4×C8C2412yes—
653C4×C8C2414yes—
654C4×C8C2412yes—
655C4×C8C2414yes—
656C4×C8C2412yes—
657C4×C8C2414yes—
658C4×C8C2412yes—
659C4×C8C2414yes—
660C24—28no—
661C24C22×D411yescharacteristic
662C24C22×D412yes—
663#41—216no—
664#41—216no—
665#41—48no—
666#41—48no—
667#41—432no—
668#41—416no—
669#41—88no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—48no—
675C2×Q8—48no—
676C2×Q8C22×D414yes—
677C2×Q8C2518yes—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—216no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—24no—
684C2×D4—24no—
685C2×D4—28no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—432no—
689C2×D4—432no—
690C2×D4#13518yescomplemented
691C2×D4C22×D418yes—
692C2×D4C22×D414yes—
693C2×D4C2518yes—
694C22×C4—28no—
695C22×C4—24no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—216no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—44no—
708C22×C4—42no—
709C22×C4—816no—
710C22×C4C22×D411yescharacteristic
711C22×C4C22×D414yes—
712C22×C4C22×D414yes—
713C22×C4C22×D412yes—
714C22×C4C22×D412yes—
715C22×C4C22×D412yes—
716C22×C4C22×D414yes—
717C22×C4C22×D411yescharacteristic
718C22×C4C22×D412yes—
719C22×C4C22×D414yes—
720C22×C4C22×D411yescharacteristic
721C22×C4C22×D412yes—
722C22×C4C22×D412yes—
723C22×C4C22×D414yes—
724C22×C4C22×D412yes—
725C22×C4C22×D411yescharacteristic
726C22×C4C22×D412yes—
727C22×C4C22×D411yescharacteristic
728C22×C4C2514yes—
729C22×C4C2512yes—
730C22×C4C2511yescharacteristic
731Q16—28no—
732Q16—48no—
733Q16—44no—
734SD16—216no—
735SD16—416no—
736SD16—48no—
737D8—28no—
738D8—48no—
739D8—44no—
740C2×C8—22no—
741C2×C8—22no—
742C2×C8—28no—
743C2×C8—28no—
744C2×C8—24no—
745C2×C8—24no—
746C2×C8—44no—
747C2×C8—42no—
748C2×C8—44no—
749C2×C8—42no—
750C2×C8—42no—
751C2×C8—41no—
752C2×C8—42no—
753C2×C8—41no—
754C2×C8C2511yescharacteristic
755C2×C8C2511yescharacteristic
756C2×C8C2514yes—
757C2×C8C2512yes—
758C2×C8C2512yes—
759C2×C8C2514yes—
760C2×C8C2511yescharacteristic
761C2×C8C2511yescharacteristic
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—24no—
765C4⋊C4—216no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—216no—
769C4⋊C4—216no—
770C4⋊C4—216no—
771C4⋊C4—28no—
772C4⋊C4—28no—
773C4⋊C4—24no—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—24no—
777C4⋊C4—28no—
778C4⋊C4C22×D414yes—
779C4⋊C4C22×D418yes—
780C4⋊C4C22×D414yes—
781C4⋊C4C22×D418yes—
782C4⋊C4C2518yes—
783C4⋊C4C2518yes—
784C22⋊C4—28no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—216no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—216no—
795C22⋊C4—216no—
796C22⋊C4—216no—
797C22⋊C4—28no—
798C22⋊C4C22×D418yes—
799C22⋊C4C22×D418yes—
800C22⋊C4C22×D418yes—
801C42—216no—
802C42—28no—
803C42—28no—
804C42—28no—
805C42C22×D411yescharacteristic
806C42C22×D412yes—
807C42C22×D414yes—
808C42C22×D412yes—
809C42C22×D414yes—
810C42C22×D412yes—
811C42C22×D414yes—
812C42C22×D412yes—
813C42C22×D414yes—
814C42C22×D412yes—
815C42C22×D411yescharacteristic
816C42C22×D414yes—
817C42C2511yescharacteristic
818C42C2514yes—
819C42C2512yes—
820C42C2511yescharacteristic
821C23—22no—
822C23—28no—
823C23—42no—
824C23—41no—
825C23—42no—
826C23—41no—
827C23—416no—
828C23—88no—
829C23—88no—
830C23C2×#13518yes—
831C23C23×D412yes—
832C23C23×D411yescharacteristic
833C23C23×D414yes—
834Q8—28no—
835Q8—28no—
836Q8—28no—
837Q8—48no—
838Q8—88no—
839Q8—84no—
840D4—216no—
841D4—28no—
842D4—28no—
843D4—416no—
844D4—432no—
845D4—48no—
846D4—88no—
847D4—84no—
848D4—88no—
849D4—88no—
850D4C2×#135116yes—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—28no—
854C2×C4—28no—
855C2×C4—22no—
856C2×C4—28no—
857C2×C4—24no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—28no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—42no—
870C2×C4—44no—
871C2×C4—41no—
872C2×C4—42no—
873C2×C4—44no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—416no—
880C2×C4—816no—
881C2×C4—88no—
882C2×C4—88no—
883C2×C4—88no—
884C2×C4C2×#13514yes—
885C2×C4C23×D412yes—
886C2×C4C23×D414yes—
887C2×C4C23×D411yescharacteristic
888C2×C4C23×D411yescharacteristic
889C2×C4C23×D411yescharacteristic
890C2×C4C23×D411yescharacteristic
891C2×C4C23×D414yes—
892C2×C4C23×D414yes—
893C2×C4C23×D412yes—
894C2×C4C23×D412yes—
895C2×C4C23×D411yescharacteristic
896C2×C4C2611yescharacteristic
897C8—21no—
898C8—21no—
899C8—24no—
900C8—22no—
901C8—24no—
902C8—22no—
903C8#58512yes—
904C8#58512yes—
905C22—21no—
906C22—24no—
907C22—21no—
908C22—24no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—48no—
913C22—44no—
914C22—48no—
915C22—48no—
916C22—48no—
917C22—1616no—
918C22C22×#13512yes—
919C22C22×#13518yes—
920C22C24×D411yescharacteristic
921C4—21no—
922C4—22no—
923C4—24no—
924C4—21no—
925C4—21no—
926C4—24no—
927C4—21no—
928C4—24no—
929C4—22no—
930C4—48no—
931C4—48no—
932C4—48no—
933C4C22×#13514yes—
934C4#358412yes—
935C4C2×#58511yescharacteristic
936C4C2×#58511yescharacteristic
937C2—22no—
938C2—28no—
939C2—42no—
940C2—88no—
941C2#6281211yescharacteristic
942C2C23×#13511yescharacteristic
943C2C2×#358411yescharacteristic
subgroupG/H
centerC2×C4C23×D4
commutator, Frattini, cosocleC2×C4C26
socleC22C24×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62781C2semidirect
2. #62533C2semidirect
3. #62475C2semidirect
4. #62419C2semidirect
5. #62361C2semidirect
6. #62358C2semidirect
7. #62247C2semidirect
8. #62246C2semidirect
9. #62245C2semidirect
10. #62244C2semidirect
11. #62243C2semidirect
12. #61433C2semidirect
13. #61432C2semidirect
14. #61431C2semidirect
15. #60948C2semidirect
16. #60945C2semidirect
17. #60673C2semidirect
18. C2×#3168C2semidirect
19. C2×C8×#41C2semidirect
21. #3515C22semidirect
22. #3514C22semidirect
23. #3507C22semidirect
24. #3505C22semidirect
30. #3482C22semidirect
31. #3481C22semidirect
35. #3444C22semidirect
36. C2×#529C22semidirect
39. #3396C22semidirect
40. #3394C22semidirect
41. #3393C22semidirect
42. #3383C22semidirect
43. #3381C22semidirect
44. #3380C22semidirect
45. #3365C22semidirect
46. #3364C22semidirect
47. #3361C22semidirect
48. #3360C22semidirect
49. #3339C22semidirect
50. #3338C22semidirect
51. #3337C22semidirect
52. #3336C22semidirect
53. #3335C22semidirect
54. #3334C22semidirect
55. #3301C22semidirect
56. #3300C22semidirect
57. #3299C22semidirect
58. #3298C22semidirect
59. #3297C22semidirect
60. #3296C22semidirect
61. #3295C22semidirect
62. #3294C22semidirect
63. D4×Q16C22semidirect
64. #3285C22semidirect
65. #3282C22semidirect
66. D4×SD16C22semidirect
67. #3280C22semidirect
68. D4×D8C22semidirect
69. #3250C22semidirect
70. #3250C22semidirect
71. #3249C22semidirect
72. #3246C22semidirect
74. #3233C22semidirect
75. #3232C22semidirect
76. #3212C22semidirect
77. #3211C22semidirect
78. #3191C22semidirect
79. #3189C22semidirect
80. #3187C22semidirect
82. #3170C22semidirect
83. #3170C22semidirect
85. #3169C22semidirect
86. #3168C22semidirect
87. #3168C22semidirect
88. #3168C22semidirect
89. #3168C22semidirect
90. #3168C22semidirect
91. #3168C22semidirect
92. #3168C22semidirect
93. #3168C22semidirect
94. #3168C22semidirect
95. #3168C22semidirect
96. #3168C22semidirect
97. #3167C22semidirect
98. #3167C22semidirect
99. #3160C22semidirect
100. C2×#499C22semidirect
101. #3147C22semidirect
102. C2×#495C22semidirect
103. #3131C22semidirect
104. C2×#488C22semidirect
105. #3108C22semidirect
106. #3107C22semidirect
107. #3106C22semidirect
108. #3105C22semidirect
109. #3050C22semidirect
110. #3050C22semidirect
111. C2×#467C22semidirect
113. C2×#465C22semidirect
114. C8×#41C22semidirect
115. C8×#41C22semidirect
116. C8×#41C22semidirect
117. C8×#41C22semidirect
118. C2×C8×Q8C22semidirect
119. C2×C8×Q8C22semidirect
120. C4×#135C22semidirect
121. C4×#135C22semidirect
122. C2×C4×Q16C22semidirect
123. C2×C4×SD16C22semidirect
124. C2×C4×D8C22semidirect
127. C2×C8×D4C22semidirect
128. C2×C8×D4C22semidirect
129. C2×#431C22semidirect
130. C2×#431C22semidirect
131. C22×C4×C8C22semidirect
132. C22×C4×C8C22semidirect
690. C2×D4#135semidirect

Maximal subgroups

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

subgroupindex
#627812
#625332
#624752
#624192
#623612
#623582
#622472
#622462
#622452
#622442
#622432
#614332
#614322
#614312
#609482
#609452
#606732
C2×#31682
C2×C8×#412