Finite Group Databasebeta

← #10575159

Subgroups — #10575159

Order 512.

7344 conjugacy classes of subgroups.

The subgroup lattice has 1207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62860C211yesmaximal, characteristic, complemented
2#62653C211yesmaximal, characteristic, complemented
3#60595C218yesmaximal, complemented
4#60594C218yesmaximal, complemented
5#60583C218yesmaximal, complemented
6#60581C218yesmaximal, complemented
7#60577C218yesmaximal, complemented
8#60573C218yesmaximal, complemented
9#60519C211yesmaximal, characteristic, complemented
10#60516C211yesmaximal, characteristic, complemented
11#60491C211yesmaximal, characteristic, complemented
12#60489C211yesmaximal, characteristic, complemented
13#60427C211yesmaximal, characteristic, complemented
14C2×#3044C211yesmaximal, characteristic, complemented
15#60368C211yesmaximal, characteristic
16C2×#3011C211yesmaximal, characteristic, complemented
17#60169C211yesmaximal, characteristic, complemented
18#60169C211yesmaximal, characteristic, complemented
19C2×#2950C211yesmaximal, characteristic, complemented
20#60161C211yesmaximal, characteristic, complemented
21#60126C211yesmaximal, characteristic, complemented
22C22×2−1+4C2211yescharacteristic
23C2×#575C2211yescharacteristic
24C22×#137C2211yescharacteristic
25C22×#137C2211yescharacteristic
26C23×Q16C2211yescharacteristic
27#3510—22no—
28#3510C2214yescomplemented
29#3509—22no—
30#3509C2214yescomplemented
31#3507—24no—
32#3495—24no—
33#3495C2218yes—
34#3491—24no—
35#3461C2218yescomplemented
36#3458C2211yescharacteristic
37#3449C2211yescharacteristic
38C2×#536C2211yescharacteristic
39C2×#536C2211yescharacteristic
40C4×2−1+4—24no—
41C4×2−1+4—24no—
42C4×2−1+4C2218yes—
43C4×2−1+4C2218yescomplemented
44#3428—22no—
45#3428—24no—
46#3428C2211yescharacteristic
47#3428C2211yescharacteristic
48#3428C2211yescharacteristic
49#3428C2211yescharacteristic
50#3428C2211yescharacteristic
51#3428C2214yescomplemented
52C2×#519—22no—
53C2×#519C2211yescharacteristic
54C2×#519C2211yescharacteristic
55C2×#519C2211yescharacteristic
56C2×#519C2214yescomplemented
57#3127C22116yescomplemented
58#3127C22116yescomplemented
59#3125C22116yescomplemented
60#3124C22116yescomplemented
61#3121C22116yescomplemented
62#3121C22116yescomplemented
63#3120C22116yescomplemented
64#3120C22116yescomplemented
65#3117C22116yescomplemented
66#3116C22116yescomplemented
67#3113C22116yescomplemented
68#3111C22116yescomplemented
69#3108C22116yescomplemented
70#3107C22116yescomplemented
71#3104C22116yescomplemented
72#3102C22116yescomplemented
73#3099C2214yescomplemented
74#3098C2214yescomplemented
75#3097C2214yescomplemented
76#3097C2218yescomplemented
77#3097C2218yescomplemented
78#3096C2214yescomplemented
79#3095C2218yescomplemented
80#3091C2218yes—
81#3084C2214yescomplemented
82#3083C2214yescomplemented
83#3082C2214yescomplemented
84#3082C2218yescomplemented
85#3082C2218yescomplemented
86#3081C2214yescomplemented
87#3078C2218yescomplemented
88#3076C2218yescomplemented
89#3046C2218yescomplemented
90#3044C2218yes—
91#3044C2214yes—
92#3044C2214yescomplemented
93#3044C2214yescomplemented
94#3042C2214yes—
95#3040C2214yescomplemented
96#3039C2214yescomplemented
97C2×#464C2214yescomplemented
98C2×#462C2214yescomplemented
99#3013C2218yes—
100#3011C2214yes—
101#3011C2218yes—
102#3011C2214yescomplemented
103#3011C2214yescomplemented
104#3010C2214yes—
105#3005C2214yes—
106#3004C2214yes—
107C2×#452C2214yescomplemented
108C2×#451C2214yescomplemented
109#2950C2218yescomplemented
110#2950C2218yescomplemented
111#2950C2214yescomplemented
112#2950C2214yescomplemented
113#2949C2214yescomplemented
114#2949C2214yescomplemented
115#2947C2214yes—
116#2947C2218yes—
117#2947C2214yescomplemented
118#2947C2218yescomplemented
119#2946C2214yes—
120#2946C2214yescomplemented
121C4×#137C2218yescomplemented
122C4×#137C2218yescomplemented
123#2943C2214yescomplemented
124C2×#441C2214yescomplemented
125C4×#135C2214yescomplemented
126C2×C4×Q16C2214yescomplemented
127#2925C2218yescomplemented
128#2924C2218yescomplemented
129#2923C2214yescomplemented
130#2922C2214yescomplemented
131#2911C2211yescharacteristic
132#2911C2211yescharacteristic
133#2911C2211yescharacteristic
134C2×#427C2211yescharacteristic
135#2905C2211yescharacteristic
136C2×#424C2211yescharacteristic
137#2896C2211yescharacteristic
138#2896C2211yescharacteristic
139C2×#419C2211yescharacteristic
140C2×#419C2211yescharacteristic
141C2×#419C2211yescharacteristic
142C2×#419C2211yescharacteristic
143C2×#416C2211yescharacteristic
144C2×#416C2211yescharacteristic
145#2879C2211yescharacteristic
146C2×#408C2211yescharacteristic
147#2873C2211yescharacteristic
148C2×#405C2211yescharacteristic
149C2×2−1+4—22no—
150C2×2−1+4—22no—
151C2×2−1+4—28no—
152C2×2−1+4—28no—
153C2×2−1+4C2314yes—
154C2×2−1+4C2314yes—
155C22×#41—22no—
156C22×#41—21no—
157C22×#41C2312yes—
158C22×#41C2311yescharacteristic
159C22×#41C2311yescharacteristic
160C22×#41C2311yescharacteristic
161C23×Q8—21no—
162C23×Q8C2312yes—
163C23×Q8C2311yescharacteristic
164C23×Q8C2311yescharacteristic
165#575—28no—
166C2×#137—28no—
167C2×#137—28no—
168C2×#137C2314yes—
169C2×#137C2314yes—
170C2×#137C2312yes—
171C2×#137C2314yes—
172C2×#137C2312yes—
173C2×#137C2314yes—
174C2×AGL(1,ℤ/8)C2312yes—
175C2×AGL(1,ℤ/8)C2312yes—
176C2×#135C2314yes—
177C22×Q16—28no—
178C22×Q16C2312yes—
179C22×Q16C2312yes—
180C22×Q16C2312yes—
181C22×Q16C2314yes—
182C22×Q16C2312yes—
183C22×Q16C2314yes—
184C22×SD16C2312yes—
185C22×SD16C2312yes—
186C22×M16C2311yescharacteristic
187C22×M16C2311yescharacteristic
188C22×M16C2311yescharacteristic
189C23×C8C2311yescharacteristic
190#559—28no—
191#557—28no—
192#556—28no—
193#556—28no—
194#556—28no—
195#554—28no—
196#552—216no—
197#552—216no—
198#552—28no—
199#552—28no—
200#551—216no—
201#551—216no—
202#544—22no—
203#544C2314yes—
204#544C2314yes—
205#543—22no—
206#542—28no—
207#542C23116yes—
208#541—28no—
209#541C23116yes—
210#539—216no—
211#537C2314yes—
212#536—22no—
213#536—22no—
214#536—21no—
215#536—22no—
216#536—22no—
217#536C2314yes—
218#536C2314yes—
219#536C2314yes—
220#536C2314yes—
221#536C2312yes—
222#535—21no—
223#535C2312yes—
224#534—22no—
225#533—28no—
226#533—22no—
227#533—22no—
228#533C23116yes—
229#533C2314yes—
230#532—22no—
231C2×C4⋊Q8—21no—
232C2×C4⋊Q8C2312yes—
233#529—216no—
234#529—28no—
235#529C23116yes—
236C2×#124—21no—
237C2×#124C2312yes—
238#525—22no—
239#525C2314yes—
240C2×#123—22no—
241C2×#123—22no—
242C2×C22⋊Q8—22no—
243C2×C22⋊Q8C2314yes—
244#520—216no—
245#520—28no—
246#520—216no—
247#520—28no—
248#520—22no—
249#520—22no—
250#520—22no—
251#520—28no—
252#520D414yes—
253#520D414yes—
254#520C2314yes—
255#520C23116yes—
256#520C2314yes—
257#520C2314yes—
258#520C2314yes—
259#520C2314yes—
260#519—21no—
261#519—28no—
262#519—28no—
263#519—22no—
264#519—22no—
265#519—28no—
266#519—22no—
267#519—22no—
268#519—22no—
269#519—22no—
270#519—28no—
271#519D412yes—
272#519C2314yes—
273#519C2314yes—
274#519C2312yes—
275#519C23116yes—
276#519C2314yes—
277#519C2314yes—
278#519C2314yes—
279#519C2314yes—
280#519C2312yes—
281#519C2312yes—
282#518—22no—
283#518—21no—
284#518—22no—
285#518—22no—
286#518—28no—
287#518—22no—
288#518D414yes—
289#518D412yes—
290#518C2312yes—
291#518C2312yes—
292#518C2312yes—
293C4×#41—22no—
294C4×#41—22no—
295C4×#41—216no—
296C4×#41—28no—
297C4×#41—216no—
298C4×#41—28no—
299C4×#41—22no—
300C4×#41—22no—
301C4×#41—22no—
302C4×#41—28no—
303C4×#41C2314yes—
304C4×#41C23116yes—
305C4×#41C2314yes—
306C4×#41C2314yes—
307C4×#41C2314yes—
308C4×#41C2314yes—
309C2×C4×Q8—28no—
310C2×C4×Q8—28no—
311C2×C4×Q8—22no—
312C2×C4×Q8—22no—
313C2×C4×Q8—22no—
314C2×C4×Q8—28no—
315C2×C4×Q8C2314yes—
316C2×C4×Q8C23116yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2314yes—
319C2×#117—22no—
320C2×#117—22no—
321C2×#117—28no—
322C2×#117—22no—
323C2×#117—22no—
324C2×#117—22no—
325C2×#117—22no—
326C2×#117—28no—
327C2×#117C2314yes—
328C2×#117C2311yescharacteristic
329C2×#117C2311yescharacteristic
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2314yes—
335#485C2318yes—
336#485C2318yes—
337#485C23116yes—
338#485C23116yes—
339#484C2318yes—
340#484C23116yes—
341#483C2318yes—
342#483C23116yes—
343#482C2318yes—
344#482C2318yes—
345#481C2318yes—
346#480C2318yes—
347#479C2318yes—
348#479C2318yes—
349#479C23116yes—
350#479C23116yes—
351#478C2318yes—
352#478C2318yes—
353#477C2318yes—
354#477C23116yes—
355#476C2318yes—
356#475C2318yes—
357#475C23116yes—
358#474C2318yes—
359#464C23116yes—
360#464C23116yes—
361#464C23116yes—
362#463C23116yes—
363#462C23116yes—
364#462C23116yes—
365#462C23116yes—
366#461C23116yes—
367#452C23116yes—
368#452C23116yes—
369#452C23116yes—
370#451C23116yes—
371#451C23116yes—
372#451C23116yes—
373#449C23116yes—
374#448C23116yes—
375#442C2318yes—
376#441C23116yes—
377#441C2318yes—
378#441C23116yes—
379#441C23116yes—
380#441C23116yes—
381#440C23116yes—
382#440C23116yes—
383#440C2318yes—
384#440C2318yes—
385C4×Q16C23116yes—
386C4×Q16C2318yes—
387C4×Q16C23116yes—
388C4×Q16C23116yes—
389C4×Q16C23116yes—
390C4×SD16C23116yes—
391C4×SD16C23116yes—
392C4×SD16C2318yes—
393C4×SD16C2318yes—
394C4×D8C2318yes—
395#433C23116yes—
396#433C23116yes—
397#432C23116yes—
398#431C23116yes—
399#428C2314yes—
400#428C2314yes—
401#428C2314yes—
402#428C2314yes—
403#428C2314yes—
404#428C2314yes—
405#427C2314yes—
406#427C2314yes—
407#427C2314yes—
408#427C2314yes—
409#427C2314yes—
410C2×#107C2312yes—
411C2×#106C2312yes—
412#424C2314yes—
413#424C2314yes—
414#424C2314yes—
415#424C2312yes—
416#424C2312yes—
417#423C2314yes—
418C2×C4⋊C8C2314yes—
419#419C2314yes—
420#419C2314yes—
421#419C2314yes—
422#419C2314yes—
423#419C2312yes—
424#419C2314yes—
425#419C2314yes—
426#419C2314yes—
427#419C2314yes—
428#419C2312yes—
429#418C2312yes—
430#418C2312yes—
431#417C2314yes—
432#417C2314yes—
433#416C2314yes—
434#416C2314yes—
435#416C2312yes—
436#416C2312yes—
437#416C2314yes—
438#416C2314yes—
439#416C2312yes—
440#416C2312yes—
441C2×#103C2312yes—
442C2×#103C2314yes—
443C2×#103C2314yes—
444C2×#103C2312yes—
445C2×#103C2314yes—
446C2×#103C2314yes—
447C2×#102C2312yes—
448C2×#102C2312yes—
449#408C2314yes—
450#408C2314yes—
451#408C2314yes—
452#408C2312yes—
453#408C2312yes—
454#407C2314yes—
455C2×C22⋊C8C2314yes—
456#405C2314yes—
457#405C2314yes—
458#405C2314yes—
459#405C2314yes—
460C4×M16C2314yes—
461C2×#97C2312yes—
462C2×C4×C8C2312yes—
4632−1+4—232no—
4642−1+4—232no—
4652−1+4—216no—
4662−1+4—216no—
4672−1+4—216no—
4682−1+4—216no—
469C2×#41—232no—
470C2×#41—216no—
471C2×#41—28no—
472C2×#41—28no—
473C2×#41—28no—
474C2×#41—24no—
475C2×#41—24no—
476C2×#41—28no—
477C2×#41—24no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—24no—
483C2×#41—24no—
484C2×#41—24no—
485C2×#41—24no—
486C2×#41—24no—
487C2×#41C2×D412yes—
488C2×#41C2×D412yes—
489C2×#41#4118yes—
490C2×#41C2418yes—
491C2×#41C2412yes—
492C2×#41C2412yes—
493C2×#41C2412yes—
494C2×#41C2412yes—
495C2×#41C2412yes—
496C2×#41C2412yes—
497C22×Q8—216no—
498C22×Q8—24no—
499C22×Q8—24no—
500C22×Q8—28no—
501C22×Q8—28no—
502C22×Q8—24no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—22no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×Q8—21no—
510C22×Q8—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8C2×D411yescharacteristic
514C22×Q8#4118yes—
515C22×Q8C2418yes—
516C22×Q8C2412yes—
517C22×Q8C2412yes—
518C22×Q8C2412yes—
519C22×Q8C2411yescharacteristic
520C22×Q8C2412yes—
521C22×Q8C2412yes—
522C22×Q8C2411yescharacteristic
523C22×Q8C2412yes—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4C2×D412yes—
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—22no—
532C23×C4—21no—
533C23×C4—22no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2412yes—
538C23×C4C2411yescharacteristic
539#137—216no—
540#137—216no—
541#137—28no—
542#137—216no—
543#137—216no—
544#137—28no—
545AGL(1,ℤ/8)—28no—
546AGL(1,ℤ/8)—28no—
547#135—216no—
548C2×Q16—216no—
549C2×Q16—216no—
550C2×Q16—28no—
551C2×Q16—28no—
552C2×Q16—28no—
553C2×Q16—28no—
554C2×Q16C2418yes—
555C2×Q16C2418yes—
556C2×Q16C2418yes—
557C2×Q16C2418yes—
558C2×Q16C2414yes—
559C2×SD16—28no—
560C2×SD16—28no—
561C2×SD16C2418yes—
562C2×SD16C2418yes—
563C2×SD16C2414yes—
564C2×SD16C2414yes—
565C2×D8C2414yes—
566C2×M16—24no—
567C2×M16—24no—
568C2×M16—24no—
569C2×M16C2412yes—
570C2×M16C2412yes—
571C2×M16C2412yes—
572C2×M16C2412yes—
573C2×M16C2412yes—
574C2×M16C2412yes—
575C22×C8—24no—
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2412yes—
579C22×C8C2412yes—
580C22×C8C2412yes—
581C22×C8C2412yes—
582C22×C8C2412yes—
583C4⋊Q8—24no—
584C4⋊Q8—24no—
585C4⋊Q8—22no—
586C4⋊Q8—24no—
587C4⋊Q8—24no—
588C4⋊Q8—24no—
589C4⋊Q8C2418yes—
590C4⋊Q8C2418yes—
591#127—22no—
592#126—216no—
593#126—216no—
594#126—216no—
595#126—216no—
596#125—24no—
597#125—216no—
598#125—216no—
599#125—24no—
600#125—216no—
601#125C2418yes—
602#124—22no—
603#124—24no—
604#124—24no—
605#124—22no—
606#124—216no—
607#124—24no—
608#124C2418yes—
609#123—28no—
610#123—28no—
611#123—24no—
612#123—24no—
613#123—216no—
614#123—28no—
615#123—28no—
616#123—216no—
617C22⋊Q8—24no—
618C22⋊Q8—28no—
619C22⋊Q8—216no—
620C22⋊Q8—28no—
621C22⋊Q8—28no—
622C22⋊Q8—28no—
623C22⋊Q8—216no—
624C22⋊Q8—28no—
625C22⋊Q8—28no—
626C22⋊Q8C24116yes—
627C22⋊Q8C2418yes—
628#121—24no—
629#121—28no—
630#121C2418yes—
631#120—24no—
632#120—24no—
633C4×Q8—24no—
634C4×Q8—24no—
635C4×Q8—28no—
636C4×Q8—24no—
637C4×Q8—28no—
638C4×Q8—28no—
639C4×Q8—216no—
640C4×Q8—216no—
641C4×Q8—28no—
642C4×Q8—24no—
643C4×Q8—28no—
644C4×Q8—28no—
645C4×Q8—24no—
646C4×Q8—28no—
647C4×Q8—216no—
648C4×Q8—216no—
649C4×Q8—28no—
650C4×Q8—28no—
651C4×Q8—216no—
652C4×Q8—28no—
653C4×Q8C2×D418yes—
654C4×Q8C2×D418yes—
655C4×Q8C2418yes—
656C4×Q8C24116yes—
657C4×Q8C24116yes—
658C4×Q8C2418yes—
659C4×Q8C24116yes—
660C4×Q8C2418yes—
661C4×D4—28no—
662C4×D4—28no—
663C4×D4—24no—
664C4×D4—24no—
665C4×D4—28no—
666C4×D4—28no—
667C4×D4—216no—
668C4×D4—216no—
669C4×D4—28no—
670C4×D4—28no—
671C4×D4—216no—
672C4×D4—24no—
673C4×D4—24no—
674C4×D4—24no—
675C4×D4—28no—
676C4×D4—28no—
677C4×D4—216no—
678C4×D4—216no—
679C4×D4—28no—
680C4×D4C2×D4116yes—
681C4×D4C2×D418yes—
682C4×D4C2×D4116yes—
683C4×D4C2×D418yes—
684C4×D4C2418yes—
685C4×D4C2418yes—
686C4×D4C2418yes—
687#117—24no—
688#117—21no—
689#117—21no—
690#117—21no—
691#117—24no—
692#117—21no—
693#117—21no—
694#117—21no—
695#117—21no—
696#117—21no—
697#117—216no—
698#117—24no—
699#117—24no—
700#117—216no—
701#117—24no—
702#117—24no—
703#117—28no—
704#117—24no—
705#117—28no—
706#117—28no—
707#117—28no—
708#117—216no—
709#117—216no—
710#117—24no—
711#117—28no—
712#117—28no—
713#117—24no—
714#117—216no—
715#117—24no—
716#117—24no—
717#117—216no—
718#117C2×D412yes—
719#117C2×D412yes—
720#117C2×D412yes—
721#117C2×D418yes—
722#117C2×D412yes—
723#117C2×D418yes—
724#117C2412yes—
725#117C2412yes—
726#117C2412yes—
727#117C2412yes—
728#117C2418yes—
729#117C2412yes—
730#117C2412yes—
731#117C2412yes—
732#117C2412yes—
733#117C2412yes—
734#117C2412yes—
735#117C2412yes—
736#117C2412yes—
737#117C2418yes—
738C2×C4⋊C4—24no—
739C2×C4⋊C4—24no—
740C2×C4⋊C4—216no—
741C2×C4⋊C4—24no—
742C2×C4⋊C4—24no—
743C2×C4⋊C4—24no—
744C2×C4⋊C4—24no—
745C2×C4⋊C4—24no—
746C2×C4⋊C4—216no—
747C2×C4⋊C4—24no—
748C2×C4⋊C4C2×D412yes—
749C2×C4⋊C4C2×D412yes—
750C2×C4⋊C4C2×D418yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2418yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C22⋊C4—24no—
757C2×C22⋊C4—21no—
758C2×C22⋊C4—21no—
759C2×C22⋊C4—21no—
760C2×C22⋊C4—21no—
761C2×C22⋊C4—24no—
762C2×C22⋊C4—24no—
763C2×C22⋊C4—24no—
764C2×C22⋊C4—24no—
765C2×C22⋊C4—24no—
766C2×C22⋊C4C2×D412yes—
767C2×C22⋊C4C2×D412yes—
768C2×C22⋊C4C2×D418yes—
769C2×C42—24no—
770C2×C42—24no—
771C2×C42—216no—
772C2×C42—24no—
773C2×C42—24no—
774C2×C42—21no—
775C2×C42—21no—
776C2×C42—21no—
777C2×C42—21no—
778C2×C42—24no—
779C2×C42—216no—
780C2×C42—24no—
781C2×C42—24no—
782C2×C42C2412yes—
783C2×C42C2412yes—
784C2×C42C2418yes—
785#107C2414yes—
786#107C2414yes—
787#107C2418yes—
788#107C2418yes—
789#107C2418yes—
790#106C2414yes—
791#106C2414yes—
792#106C2418yes—
793#106C2418yes—
794#106C2418yes—
795C4⋊C8C2418yes—
796C4⋊C8C2418yes—
797C4⋊C8C24116yes—
798#103C2414yes—
799#103C2414yes—
800#103C2414yes—
801#103C2414yes—
802#103C24116yes—
803#103C24116yes—
804#103C24116yes—
805#103C24116yes—
806#103C2418yes—
807#103C2418yes—
808#102C2414yes—
809#102C2414yes—
810#102C2414yes—
811#102C2414yes—
812#102C2418yes—
813#102C2418yes—
814C22⋊C8C2418yes—
815C22⋊C8C2418yes—
816C22⋊C8C24116yes—
817#97C2418yes—
818#97C2418yes—
819C4×C8C2418yes—
820C4×C8C2418yes—
821C24—21no—
822C24—21no—
823C24C22×D412yes—
824C24C22×D411yescharacteristic
825#41—264no—
826#41—264no—
827#41—232no—
828#41—232no—
829#41—232no—
830#41—216no—
831#41—216no—
832#41—28no—
833#41—28no—
834#41—28no—
835#41—28no—
836#41—24no—
837#41—24no—
838#41—24no—
839#41—24no—
840#41—24no—
841#41—24no—
842#41—24no—
843#41—24no—
844#41—24no—
845#41—24no—
846#41—44no—
847#41—44no—
848#41C2×#4118yes—
849#41C2×#4118yes—
850C2×Q8—216no—
851C2×Q8—232no—
852C2×Q8—232no—
853C2×Q8—232no—
854C2×Q8—216no—
855C2×Q8—216no—
856C2×Q8—24no—
857C2×Q8—28no—
858C2×Q8—28no—
859C2×Q8—28no—
860C2×Q8—28no—
861C2×Q8—22no—
862C2×Q8—21no—
863C2×Q8—22no—
864C2×Q8—22no—
865C2×Q8—22no—
866C2×Q8—22no—
867C2×Q8—22no—
868C2×Q8—21no—
869C2×Q8—28no—
870C2×Q8—22no—
871C2×Q8—24no—
872C2×Q8—24no—
873C2×Q8—24no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—22no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—22no—
882C2×Q8—44no—
883C2×Q8—44no—
884C2×Q8—44no—
885C2×Q8C22×D412yes—
886C2×Q8C22×D412yes—
887C2×Q8C2×#4118yes—
888C2×Q8C2×#4114yes—
889C2×Q8C2×#4118yes—
890C2×Q8C2×#4118yes—
891C2×Q8C2514yes—
892C2×Q8C2512yes—
893C2×Q8C2512yes—
894C2×Q8C2514yes—
895C2×D4—216no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—22no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—22no—
903C2×D4—28no—
904C2×D4—24no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—22no—
908C2×D4—22no—
909C2×D4—22no—
910C2×D4—44no—
911C2×D4C22×D414yes—
912C2×D4C22×D414yes—
913C2×D4C22×D412yes—
914C2×D4C22×D412yes—
915C2×D4C2×#4114yes—
916C2×D4C2512yes—
917C2×D4C2512yes—
918C22×C4—216no—
919C22×C4—216no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—21no—
926C22×C4—28no—
927C22×C4—28no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—24no—
931C22×C4—24no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—22no—
935C22×C4—21no—
936C22×C4—28no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—28no—
944C22×C4—28no—
945C22×C4—28no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4C22×D414yes—
949C22×C4C22×D412yes—
950C22×C4C22×D414yes—
951C22×C4C22×D414yes—
952C22×C4C22×D4116yes—
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C2×#4114yes—
957C22×C4C2×#4114yes—
958C22×C4C2514yes—
959C22×C4C2511yescharacteristic
960C22×C4C2511yescharacteristic
961C22×C4C2511yescharacteristic
962Q16—216no—
963Q16—216no—
964Q16—216no—
965Q16—216no—
966Q16—28no—
967SD16—216no—
968SD16—28no—
969SD16—216no—
970SD16—28no—
971D8—28no—
972M16—24no—
973M16—24no—
974M16—24no—
975M16—24no—
976M16—24no—
977M16—24no—
978C2×C8—24no—
979C2×C8—24no—
980C2×C8—22no—
981C2×C8—22no—
982C2×C8—24no—
983C2×C8—24no—
984C2×C8—24no—
985C2×C8C2512yes—
986C2×C8C2514yes—
987C2×C8C2514yes—
988C2×C8C2514yes—
989C2×C8C2512yes—
990C4⋊C4—216no—
991C4⋊C4—28no—
992C4⋊C4—216no—
993C4⋊C4—28no—
994C4⋊C4—28no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—28no—
999C4⋊C4—216no—
1000C4⋊C4—216no—
1001C4⋊C4—216no—
1002C4⋊C4—22no—
1003C4⋊C4—28no—
1004C4⋊C4—28no—
1005C4⋊C4—28no—
1006C4⋊C4—28no—
1007C4⋊C4C22×D414yes—
1008C4⋊C4C22×D414yes—
1009C4⋊C4C22×D414yes—
1010C4⋊C4C22×D4116yes—
1011C4⋊C4C22×D414yes—
1012C4⋊C4C2514yes—
1013C4⋊C4C2514yes—
1014C4⋊C4C2514yes—
1015C4⋊C4C2514yes—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—22no—
1019C22⋊C4—28no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—216no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—28no—
1029C22⋊C4—28no—
1030C22⋊C4—216no—
1031C22⋊C4—28no—
1032C22⋊C4C22×D414yes—
1033C22⋊C4C22×D414yes—
1034C22⋊C4C22×D414yes—
1035C22⋊C4C22×D414yes—
1036C22⋊C4C22×D4116yes—
1037C42—216no—
1038C42—28no—
1039C42—216no—
1040C42—28no—
1041C42—28no—
1042C42—22no—
1043C42—22no—
1044C42—22no—
1045C42—22no—
1046C42—22no—
1047C42—28no—
1048C42—216no—
1049C42—22no—
1050C42—22no—
1051C42—22no—
1052C42C22×D414yes—
1053C42C22×D4116yes—
1054C42C22×D414yes—
1055C42C2514yes—
1056C42C2514yes—
1057C23—22no—
1058C23—24no—
1059C23—24no—
1060C23—22no—
1061C23—42no—
1062C23—44no—
1063C23—42no—
1064C23—82no—
1065C23—82no—
1066C23#52514yes—
1067C23C23×D414yes—
1068C23C23×D411yescharacteristic
1069C23C23×D411yescharacteristic
1070C23C23×D411yescharacteristic
1071Q8—232no—
1072Q8—22no—
1073Q8—24no—
1074Q8—24no—
1075Q8—24no—
1076Q8—24no—
1077Q8—28no—
1078Q8—28no—
1079Q8—28no—
1080Q8—24no—
1081Q8—22no—
1082Q8—24no—
1083Q8—22no—
1084Q8—44no—
1085Q8—44no—
1086Q8—44no—
1087Q8—42no—
1088Q8—88no—
1089Q8C22×#4114yes—
1090Q8C22×#4118yes—
1091D4—232no—
1092D4—28no—
1093D4—28no—
1094D4—28no—
1095D4—28no—
1096D4—22no—
1097D4—22no—
1098D4—22no—
1099D4—24no—
1100D4—24no—
1101D4—24no—
1102D4—44no—
1103D4—44no—
1104D4—42no—
1105D4—88no—
1106D4C22×#4114yes—
1107C2×C4—232no—
1108C2×C4—232no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—28no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—28no—
1115C2×C4—28no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—28no—
1119C2×C4—28no—
1120C2×C4—28no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—24no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—44no—
1128C2×C4—416no—
1129C2×C4—44no—
1130C2×C4—42no—
1131C2×C4—44no—
1132C2×C4—44no—
1133C2×C4—44no—
1134C2×C4—44no—
1135C2×C4—44no—
1136C2×C4—88no—
1137C2×C4—88no—
1138C2×C4—88no—
1139C2×C4—82no—
1140C2×C4—82no—
1141C2×C4—88no—
1142C2×C4—82no—
1143C2×C4—82no—
1144C2×C4#52514yes—
1145C2×C4#52514yes—
1146C2×C4#52514yes—
1147C2×C4C23×D418yes—
1148C2×C4C23×D418yes—
1149C2×C4C23×D414yes—
1150C2×C4C23×D411yescharacteristic
1151C2×C4C23×D411yescharacteristic
1152C2×C4C23×D411yescharacteristic
1153C2×C4C22×#4112yes—
1154C2×C4C22×#4112yes—
1155C2×C4C22×#4112yes—
1156C2×C4C22×#4112yes—
1157C2×C4C22×#4112yes—
1158C2×C4C22×#4112yes—
1159C2×C4C2611yescharacteristic
1160C8—22no—
1161C8—22no—
1162C8—24no—
1163C8—24no—
1164C8—24no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—28no—
1169C22—24no—
1170C22—24no—
1171C22—44no—
1172C22—44no—
1173C22—44no—
1174C22—42no—
1175C22—84no—
1176C22—84no—
1177C22—162no—
1178C22C2×#52512yes—
1179C22C2×#52512yes—
1180C22C2×#52512yes—
1181C22C24×D411yescharacteristic
1182C4—28no—
1183C4—28no—
1184C4—28no—
1185C4—24no—
1186C4—24no—
1187C4—44no—
1188C4—44no—
1189C4—44no—
1190C4—44no—
1191C4—42no—
1192C4—44no—
1193C4C2×#52512yes—
1194C4C2×#52512yes—
1195C4C2×#52512yes—
1196C4C23×#4111yescharacteristic
1197C4C23×#4111yescharacteristic
1198C2—22no—
1199C2—22no—
1200C2—22no—
1201C2—44no—
1202C2—44no—
1203C2—82no—
1204C2C22×#52511yescharacteristic
1205C2#6309312yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
prime radical#60368C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #3428 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62860C2semidirect
2. #62653C2semidirect
3. #60595C2semidirect
4. #60594C2semidirect
5. #60583C2semidirect
6. #60581C2semidirect
7. #60577C2semidirect
8. #60573C2semidirect
9. #60519C2semidirect
10. #60516C2semidirect
11. #60491C2semidirect
12. #60489C2semidirect
13. #60427C2semidirect
14. C2×#3044C2semidirect
16. C2×#3011C2semidirect
17. #60169C2semidirect
18. #60169C2semidirect
19. C2×#2950C2semidirect
20. #60161C2semidirect
21. #60126C2semidirect
28. #3510C22semidirect
30. #3509C22semidirect
35. #3461C22semidirect
43. C4×2−1+4C22semidirect
51. #3428C22semidirect
56. C2×#519C22semidirect
57. #3127C22semidirect
58. #3127C22semidirect
59. #3125C22semidirect
60. #3124C22semidirect
61. #3121C22semidirect
62. #3121C22semidirect
63. #3120C22semidirect
64. #3120C22semidirect
65. #3117C22semidirect
66. #3116C22semidirect
67. #3113C22semidirect
68. #3111C22semidirect
69. #3108C22semidirect
70. #3107C22semidirect
71. #3104C22semidirect
72. #3102C22semidirect
73. #3099C22semidirect
74. #3098C22semidirect
75. #3097C22semidirect
76. #3097C22semidirect
77. #3097C22semidirect
78. #3096C22semidirect
79. #3095C22semidirect
81. #3084C22semidirect
82. #3083C22semidirect
83. #3082C22semidirect
84. #3082C22semidirect
85. #3082C22semidirect
86. #3081C22semidirect
87. #3078C22semidirect
88. #3076C22semidirect
89. #3046C22semidirect
92. #3044C22semidirect
93. #3044C22semidirect
95. #3040C22semidirect
96. #3039C22semidirect
97. C2×#464C22semidirect
98. C2×#462C22semidirect
102. #3011C22semidirect
103. #3011C22semidirect
107. C2×#452C22semidirect
108. C2×#451C22semidirect
109. #2950C22semidirect
110. #2950C22semidirect
111. #2950C22semidirect
112. #2950C22semidirect
113. #2949C22semidirect
114. #2949C22semidirect
117. #2947C22semidirect
118. #2947C22semidirect
120. #2946C22semidirect
121. C4×#137C22semidirect
122. C4×#137C22semidirect
123. #2943C22semidirect
124. C2×#441C22semidirect
125. C4×#135C22semidirect
126. C2×C4×Q16C22semidirect
127. #2925C22semidirect
128. #2924C22semidirect
129. #2923C22semidirect
130. #2922C22semidirect

Maximal subgroups

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

subgroupindex
#628602
#626532
#605952
#605942
#605832
#605812
#605772
#605732
#605192
#605162
#604912
#604892
#604272
C2×#30442
#603682
C2×#30112
#601692
C2×#29502
#601612
#601262