Finite Group Databasebeta

← #10576380

Subgroups — #10576380

Order 512.

7552 conjugacy classes of subgroups.

The subgroup lattice has 1438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62814C211yesmaximal, characteristic, complemented
2C2×#3486C211yesmaximal, characteristic, complemented
3#61186C218yesmaximal, complemented
4#61185C218yesmaximal, complemented
5#61176C218yesmaximal, complemented
6#61168C218yesmaximal, complemented
7#61158C218yesmaximal, complemented
8#61157C218yesmaximal, complemented
9#60620C211yesmaximal, characteristic, complemented
10#60519C211yesmaximal, characteristic, complemented
11#60511C211yesmaximal, characteristic, complemented
12#60491C211yesmaximal, characteristic, complemented
13#60455C211yesmaximal, characteristic, complemented
14#60444C211yesmaximal, characteristic, complemented
15#60427C211yesmaximal, characteristic, complemented
16#60368C211yesmaximal, characteristic, complemented
17C2×#3004C211yesmaximal, characteristic, complemented
18#60169C211yesmaximal, characteristic, complemented
19#60141C211yesmaximal, characteristic, complemented
20#60088C211yesmaximal, characteristic, complemented
21C22×#419C211yesmaximal, characteristic, complemented
22C22×2−1+4C2211yescharacteristic
23C24×Q8C2211yescharacteristic
24C2×#575C2211yescharacteristic
25C22×#137C2211yescharacteristic
26C22×#137C2211yescharacteristic
27C2×#568C2211yescharacteristic
28C23×M16C2211yescharacteristic
29#3495—22no—
30#3495C2214yescomplemented
31#3494—22no—
32#3494C2214yescomplemented
33#3493C2214yescomplemented
34#3492C2214yescomplemented
35#3491—22no—
36#3490—22no—
37#3486—24no—
38#3486—22no—
39#3486—22no—
40#3486C2218yes—
41#3486C2214yescomplemented
42#3486C2214yescomplemented
43#3475—24no—
44#3475C2218yes—
45C2×D4×Q8—22no—
46C2×D4×Q8C2214yescomplemented
47C2×#548—22no—
48C2×#548C2214yescomplemented
49#3458C2211yescharacteristic
50#3455—22no—
51#3449C2211yescharacteristic
52C2×#536—22no—
53C2×#536C2211yescharacteristic
54C2×#536C2211yescharacteristic
55#3444—22no—
56C2×#525—22no—
57C2×#525C2211yescharacteristic
58C2×#525C2211yescharacteristic
59C2×#525C2211yescharacteristic
60#3428C2211yescharacteristic
61#3428C2211yescharacteristic
62C2×#519C2211yescharacteristic
63C22×#117C2211yescharacteristic
64#3329C22116yescomplemented
65#3328C22116yescomplemented
66#3327C22116yescomplemented
67#3326C22116yescomplemented
68#3321C22116yescomplemented
69#3320C22116yescomplemented
70#3320C22116yescomplemented
71#3316C22116yescomplemented
72#3313C22116yescomplemented
73#3312C22116yescomplemented
74#3312C22116yescomplemented
75#3308C22116yescomplemented
76#3301C22116yescomplemented
77#3300C22116yescomplemented
78#3299C22116yescomplemented
79#3298C22116yescomplemented
80#3140C2214yescomplemented
81#3139C2214yescomplemented
82#3137C2218yescomplemented
83#3137C2218yescomplemented
84#3097C2218yescomplemented
85#3097C2218yescomplemented
86#3095C2214yescomplemented
87#3095C2218yescomplemented
88#3094C2214yescomplemented
89#3093C2214yescomplemented
90#3092C2214yescomplemented
91#3091C2218yescomplemented
92#3082C2218yescomplemented
93#3082C2218yescomplemented
94#3078C2218yescomplemented
95#3063C2218yescomplemented
96#3059C2214yescomplemented
97#3057C2214yescomplemented
98#3056C2214yes—
99#3056C2214yescomplemented
100#3056C2218yescomplemented
101#3055C2214yes—
102#3055C2214yescomplemented
103#3054C2214yescomplemented
104#3050C2214yescomplemented
105#3046C2218yescomplemented
106#3044C2214yescomplemented
107#3042C2214yescomplemented
108#3040C2214yescomplemented
109#3039C2214yescomplemented
110#3013C2218yescomplemented
111#3011C2214yescomplemented
112#3010C2214yescomplemented
113#3005C2214yescomplemented
114#3004C2218yes—
115#3004C2214yescomplemented
116#3004C2214yescomplemented
117#3004C2214yescomplemented
118C2×#451C2214yescomplemented
119C2×#448C2214yescomplemented
120#2950C2214yescomplemented
121#2949C2214yescomplemented
122#2947C2218yescomplemented
123C4×#137C2218yescomplemented
124D4×M16C2218yescomplemented
125#2933C2218yescomplemented
126#2930C2214yescomplemented
127#2929C2214yescomplemented
128#2911C2211yescharacteristic
129#2911C2211yescharacteristic
130#2911C2211yescharacteristic
131#2905C2211yescharacteristic
132#2898C2218yescomplemented
133#2898C2218yescomplemented
134#2896C2211yescharacteristic
135#2896C2211yescharacteristic
136#2896C2211yescharacteristic
137#2896C2211yescharacteristic
138#2896C2214yescomplemented
139C2×#419C2211yescharacteristic
140C2×#419C2211yescharacteristic
141C2×#419C2211yescharacteristic
142C2×#419C2211yescharacteristic
143C2×#419C2211yescharacteristic
144C2×#419C2211yescharacteristic
145C2×#419C2218yescomplemented
146C2×#419C2218yescomplemented
147C2×#419C2214yescomplemented
148C2×#419C2214yescomplemented
149C22×#103C2214yescomplemented
150#2879C2211yescharacteristic
151C2×#407C2211yescharacteristic
152#2873C2211yescharacteristic
153C2×2−1+4—22no—
154C2×2−1+4—22no—
155C2×2−1+4—28no—
156C2×2−1+4—44no—
157C2×2−1+4C2314yes—
158C2×2−1+4C2314yes—
159C22×#41—22no—
160C22×#41—21no—
161C22×#41C2311yescharacteristic
162C22×#41C2311yescharacteristic
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C23×Q8—21no—
166C23×Q8—21no—
167C23×Q8—22no—
168C23×Q8—22no—
169C23×Q8—21no—
170C23×Q8—21no—
171C23×Q8—28no—
172C23×Q8—44no—
173C23×Q8C2311yescharacteristic
174C23×Q8C2312yes—
175C23×Q8C2314yes—
176C23×Q8C2314yes—
177C23×Q8C2312yes—
178C23×Q8C2312yes—
179C23×Q8C2311yescharacteristic
180C24×C4—21no—
181C24×C4C2311yescharacteristic
182#575—44no—
183C2×#137—28no—
184C2×#137—44no—
185C2×#137C2314yes—
186C2×#137C2314yes—
187C2×#137C2314yes—
188C2×#137C2312yes—
189C2×#137C2314yes—
190C2×#137C2312yes—
191C2×AGL(1,ℤ/8)C2312yes—
192C2×AGL(1,ℤ/8)C2312yes—
193C2×#135C2314yes—
194C22×Q16C2312yes—
195C22×Q16C2312yes—
196C22×SD16C2312yes—
197C22×SD16C2312yes—
198#568—44no—
199C2×#131C2314yes—
200C2×#131C2314yes—
201C22×M16—44no—
202C22×M16C2311yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2312yes—
207C22×M16C2314yes—
208C22×M16C2314yes—
209C22×M16C2314yes—
210C23×C8C2312yes—
211#556—24no—
212#556C2318yes—
213#555—24no—
214#555C2318yes—
215#554—24no—
216#554C2318yes—
217#553—24no—
218#553—24no—
219#553C2318yes—
220#553C2318yes—
221#552—28no—
222#552—24no—
223#552—24no—
224#552—28no—
225#552C2318yes—
226#552C2318yes—
227#551—28no—
228#551—28no—
229#551—28no—
230#551—28no—
231D4×Q8—28no—
232D4×Q8—28no—
233D4×Q8—28no—
234D4×Q8—28no—
235D4×Q8—28no—
236D4×Q8—28no—
237D4×Q8C23116yes—
238D4×Q8C23116yes—
239#548—28no—
240#548—28no—
241#548—28no—
242#548—28no—
243#548—28no—
244#548—28no—
245#548C23116yes—
246#548C23116yes—
247#547—24no—
248#547C2318yes—
249#546—28no—
250#546—28no—
251#544—22no—
252#544C2314yes—
253#544C2314yes—
254#543—22no—
255#542—24no—
256#542—24no—
257#541—24no—
258#540—24no—
259#539—28no—
260#538—28no—
261#537C2314yes—
262#536—22no—
263#536—22no—
264#536—21no—
265#536—216no—
266#536—28no—
267#536—28no—
268#536—22no—
269#536—22no—
270#536C2314yes—
271#536C2314yes—
272#536C2314yes—
273#536C2314yes—
274#536C2312yes—
275#535—21no—
276#535C2312yes—
277#534—22no—
278#533—24no—
279#533—22no—
280#533—22no—
281#533C2314yes—
282#532—22no—
283#532—24no—
284C2×C4⋊Q8—21no—
285C2×C4⋊Q8—24no—
286C2×C4⋊Q8C2312yes—
287#529—28no—
288#529—24no—
289#529—24no—
290#529—28no—
291#529—28no—
292#529—28no—
293C2×#124—21no—
294C2×#124—24no—
295C2×#124C2312yes—
296#525—22no—
297#525—21no—
298#525—21no—
299#525—22no—
300#525—21no—
301#525—21no—
302#525—22no—
303#525—216no—
304#525—28no—
305#525—28no—
306#525—28no—
307#525D412yes—
308#525D412yes—
309#525D414yes—
310#525C2314yes—
311#525C2312yes—
312#525C2312yes—
313#525C2314yes—
314#525C2312yes—
315#525C2312yes—
316#525C2314yes—
317#525C2312yes—
318#525C2312yes—
319#525C2314yes—
320C2×#123—22no—
321C2×#123—21no—
322C2×#123—21no—
323C2×#123—22no—
324C2×#123D412yes—
325C2×C22⋊Q8—24no—
326C2×C22⋊Q8—22no—
327C2×C22⋊Q8—24no—
328C2×C22⋊Q8—24no—
329C2×C22⋊Q8D412yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2312yes—
333C2×#121—24no—
334C2×#121D412yes—
335C2×#121C2312yes—
336C2×#121C2312yes—
337C2×#120—21no—
338C2×#120—21no—
339C2×#120D412yes—
340#520—22no—
341#520C2314yes—
342#520C2314yes—
343#520C2314yes—
344#519—21no—
345#519—22no—
346#519—22no—
347#519C2314yes—
348#519C2314yes—
349#519C2312yes—
350#518—22no—
351#518—21no—
352#518—22no—
353#518C2312yes—
354C4×#41—22no—
355C4×#41—22no—
356C4×#41—28no—
357C4×#41—22no—
358C4×#41C2314yes—
359C2×C4×Q8—22no—
360C2×C4×Q8C2314yes—
361C2×C4×D4—24no—
362C2×C4×D4—22no—
363C2×C4×D4—22no—
364C2×C4×D4—24no—
365C2×C4×D4C2314yes—
366C2×#117—21no—
367C2×#117—22no—
368C2×#117—21no—
369C2×#117—22no—
370C2×#117—22no—
371C2×#117—22no—
372C2×#117C2314yes—
373C2×#117C2312yes—
374C2×#117C2314yes—
375C2×#117C2314yes—
376C2×#117C2311yescharacteristic
377C2×#117C2311yescharacteristic
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2311yescharacteristic
381C22×C4⋊C4C2312yes—
382C22×C22⋊C4—21no—
383C22×C42—21no—
384#491C23116yescomplemented
385#489C23116yescomplemented
386#488C23116yescomplemented
387#487C23116yescomplemented
388#485C2318yes—
389#485C2318yes—
390#485C23116yescomplemented
391#485C23116yescomplemented
392#484C2318yes—
393#484C23116yescomplemented
394#483C2318yes—
395#483C23116yescomplemented
396#482C2318yes—
397#482C2318yes—
398#481C2318yes—
399#480C2318yes—
400#479C23116yescomplemented
401#479C23116yescomplemented
402#477C23116yescomplemented
403#475C23116yescomplemented
404#470C2318yes—
405#470C23116yescomplemented
406#469C2318yes—
407#468C2318yes—
408#468C2318yes—
409#468C23116yescomplemented
410#467C2318yes—
411#467C23116yescomplemented
412#466C2318yes—
413#465C2318yes—
414#465C2318yes—
415#465C23116yescomplemented
416#464C23116yescomplemented
417#463C23116yescomplemented
418#462C23116yescomplemented
419#461C23116yescomplemented
420#452C23116yescomplemented
421#451C23116yes—
422#451C23116yes—
423#451C23116yescomplemented
424#449C23116yescomplemented
425#448C23116yes—
426#448C23116yes—
427#448C23116yescomplemented
428#441C23116yescomplemented
429#440C23116yescomplemented
430C4×Q16C23116yescomplemented
431C4×SD16C23116yescomplemented
432#436C23116yes—
433#435C23116yes—
434#435C23116yes—
435C8×D4C23116yes—
436#428C2314yes—
437#428C2314yes—
438#428C2314yes—
439#428C2314yes—
440#428C2314yes—
441#428C2314yes—
442#427C2314yes—
443#427C2314yes—
444#427C2314yes—
445#424C2314yes—
446#424C2314yes—
447#423C2314yes—
448#419C23116yes—
449#419C23116yes—
450#419C2314yes—
451#419C2314yes—
452#419C2314yes—
453#419C2314yes—
454#419C2312yes—
455#419C2314yes—
456#419C2314yes—
457#419C2312yes—
458#419C2314yes—
459#419C2314yes—
460#419C2314yes—
461#419C2312yes—
462#419C2314yes—
463#419C2314yes—
464#419C2314yes—
465#419C2312yes—
466#419C23116yescomplemented
467#418C2312yes—
468#418C2312yes—
469#418C2312yes—
470#418C2312yes—
471#417C2314yes—
472#417C2314yes—
473#417C2314yes—
474#417C2314yes—
475#417C23116yescomplemented
476#416C2314yes—
477#416C2314yes—
478#416C2314yes—
479#416C2314yes—
480#416C23116yescomplemented
481C2×#103C2314yes—
482C2×#103C2314yes—
483C2×#103C2314yes—
484C2×#103C2314yes—
485C2×#103C2314yes—
486C2×#103C2314yes—
487C2×#103C23116yes—
488C2×#103C23116yes—
489C2×#103C23116yescomplemented
490#408C2314yes—
491#408C2314yes—
492#407C2312yes—
493#407C2312yes—
494#407C2314yes—
495#407C2314yes—
496C2×C22⋊C8C2314yes—
497#405C2314yes—
498#405C2314yes—
499C4×M16C2314yes—
500C25C2×D411yescharacteristic
5012−1+4—216no—
5022−1+4—216no—
5032−1+4—48no—
5042−1+4—48no—
5052−1+4—416no—
5062−1+4—416no—
507C2×#41—28no—
508C2×#41—28no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—28no—
512C2×#41—21no—
513C2×#41—21no—
514C2×#41—21no—
515C2×#41—21no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—28no—
520C2×#41—24no—
521C2×#41—24no—
522C2×#41—24no—
523C2×#41—24no—
524C2×#41—44no—
525C2×#41—416no—
526C2×#41—48no—
527C2×#41C2×D412yes—
528C2×#41C2×D412yes—
529C2×#41C2412yes—
530C2×#41C2412yes—
531C2×#41C2412yes—
532C2×#41C2412yes—
533C2×#41C2418yes—
534C2×#41C2412yes—
535C2×#41C2412yes—
536C22×Q8—24no—
537C22×Q8—24no—
538C22×Q8—21no—
539C22×Q8—21no—
540C22×Q8—21no—
541C22×Q8—24no—
542C22×Q8—21no—
543C22×Q8—22no—
544C22×Q8—22no—
545C22×Q8—24no—
546C22×Q8—22no—
547C22×Q8—21no—
548C22×Q8—21no—
549C22×Q8—24no—
550C22×Q8—24no—
551C22×Q8—24no—
552C22×Q8—24no—
553C22×Q8—24no—
554C22×Q8—24no—
555C22×Q8—24no—
556C22×Q8—24no—
557C22×Q8—216no—
558C22×Q8—216no—
559C22×Q8—28no—
560C22×Q8—28no—
561C22×Q8—28no—
562C22×Q8—24no—
563C22×Q8—24no—
564C22×Q8—48no—
565C22×Q8—44no—
566C22×Q8—48no—
567C22×Q8—48no—
568C22×Q8—44no—
569C22×Q8—44no—
570C22×Q8—416no—
571C22×Q8—416no—
572C22×Q8—48no—
573C22×Q8—48no—
574C22×Q8—48no—
575C22×Q8C2×D411yescharacteristic
576C22×Q8#4118yescomplemented
577C22×Q8C2411yescharacteristic
578C22×Q8C2412yes—
579C22×Q8C2411yescharacteristic
580C22×Q8C2412yes—
581C22×Q8C2412yes—
582C22×Q8C2418yes—
583C22×Q8C2418yes—
584C22×Q8C2418yes—
585C22×Q8C2412yes—
586C22×Q8C2412yes—
587C22×Q8C2412yes—
588C22×D4—22no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4C2×D412yes—
594C22×D4C2×D411yescharacteristic
595C22×D4C2×D414yes—
596C22×D4C2411yescharacteristic
597C22×D4C2411yescharacteristic
598C23×C4—21no—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—24no—
602C23×C4—22no—
603C23×C4—21no—
604C23×C4—22no—
605C23×C4—24no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—21no—
609C23×C4—22no—
610C23×C4—21no—
611C23×C4—48no—
612C23×C4C2×D412yes—
613C23×C4C2×D412yes—
614C23×C4C2×D411yescharacteristic
615C23×C4C2×D411yescharacteristic
616C23×C4C2×D411yescharacteristic
617C23×C4C2411yescharacteristic
618C23×C4C2412yes—
619C23×C4C2412yes—
620C23×C4C2412yes—
621C23×C4C2411yescharacteristic
622C23×C4C2411yescharacteristic
623#137—216no—
624#137—216no—
625#137—48no—
626#137—48no—
627#137—44no—
628#137—44no—
629AGL(1,ℤ/8)—44no—
630AGL(1,ℤ/8)—44no—
631#135—48no—
632C2×Q16—28no—
633C2×Q16—44no—
634C2×Q16C2418yes—
635C2×Q16C2418yes—
636C2×Q16C2414yes—
637C2×SD16—28no—
638C2×SD16—44no—
639C2×SD16C2418yes—
640C2×SD16C2418yes—
641C2×SD16C2414yes—
642C2×SD16C2414yes—
643C2×D8C2414yes—
644#131—48no—
645#131—48no—
646C2×M16—24no—
647C2×M16—24no—
648C2×M16—24no—
649C2×M16—24no—
650C2×M16—44no—
651C2×M16—48no—
652C2×M16—48no—
653C2×M16—48no—
654C2×M16C2412yes—
655C2×M16C2412yes—
656C2×M16C2412yes—
657C2×M16C2412yes—
658C2×M16C2412yes—
659C2×M16C2412yes—
660C2×M16C2412yes—
661C2×M16C2412yes—
662C2×M16C2418yes—
663C2×M16C2418yes—
664C22×C8—44no—
665C22×C8C2412yes—
666C22×C8C2412yes—
667C22×C8C2412yes—
668C22×C8C2412yes—
669C22×C8C2418yes—
670C22×C8C2418yes—
671C4⋊Q8—24no—
672C4⋊Q8—24no—
673C4⋊Q8—22no—
674C4⋊Q8—216no—
675C4⋊Q8—216no—
676C4⋊Q8—24no—
677C4⋊Q8—24no—
678C4⋊Q8—24no—
679C4⋊Q8C2418yes—
680C4⋊Q8C2418yes—
681#127—22no—
682#126—28no—
683#126—28no—
684#126—28no—
685#126—28no—
686#126—28no—
687#126—28no—
688#125—24no—
689#125—28no—
690#125—28no—
691#125—28no—
692#125—24no—
693#125C2418yes—
694#124—22no—
695#124—24no—
696#124—24no—
697#124—22no—
698#124—28no—
699#124—216no—
700#124—216no—
701#124—28no—
702#124—28no—
703#124—24no—
704#124C2418yes—
705#123—28no—
706#123—28no—
707#123—28no—
708#123—24no—
709#123—28no—
710#123—22no—
711#123—22no—
712#123—24no—
713#123—22no—
714#123—22no—
715#123—24no—
716#123—24no—
717#123—28no—
718#123—28no—
719#123—28no—
720#123—28no—
721#123—28no—
722#123—28no—
723#123C2×D414yes—
724#123C2×D414yes—
725#123C2×D418yes—
726C22⋊Q8—24no—
727C22⋊Q8—22no—
728C22⋊Q8—22no—
729C22⋊Q8—22no—
730C22⋊Q8—22no—
731C22⋊Q8—28no—
732C22⋊Q8—28no—
733C22⋊Q8—216no—
734C22⋊Q8—216no—
735C22⋊Q8—28no—
736C22⋊Q8—28no—
737C22⋊Q8—28no—
738C22⋊Q8—216no—
739C22⋊Q8—216no—
740C22⋊Q8—216no—
741C22⋊Q8—216no—
742C22⋊Q8—28no—
743C22⋊Q8—28no—
744C22⋊Q8—28no—
745C22⋊Q8—28no—
746C22⋊Q8C2×D414yes—
747C22⋊Q8C2×D414yes—
748C22⋊Q8C2×D414yes—
749C22⋊Q8C2×D414yes—
750C22⋊Q8C2414yes—
751C22⋊Q8C2414yes—
752C22⋊Q8C2414yes—
753C22⋊Q8C2414yes—
754C22⋊Q8C24116yes—
755C22⋊Q8C2418yes—
756#121—216no—
757#121—216no—
758#121—28no—
759#121—28no—
760#121—24no—
761#121—28no—
762#121—28no—
763#121—22no—
764#121—22no—
765#121—22no—
766#121—22no—
767#121C2×D414yes—
768#121C2×D414yes—
769#121C2×D414yes—
770#121C2×D414yes—
771#121C2414yes—
772#121C2414yes—
773#121C2414yes—
774#121C2414yes—
775#121C2418yes—
776#120—22no—
777#120—24no—
778#120—22no—
779#120—22no—
780#120—22no—
781#120—24no—
782#120—24no—
783#120—24no—
784#120C2×D414yes—
785#120C2×D414yes—
786#120C2×D418yes—
787C4×Q8—24no—
788C4×Q8—24no—
789C4×Q8—28no—
790C4×Q8—28no—
791C4×Q8—24no—
792C4×Q8—28no—
793C4×Q8—28no—
794C4×Q8—28no—
795C4×Q8C24116yes—
796C4×Q8C2418yes—
797C4×D4—216no—
798C4×D4—216no—
799C4×D4—28no—
800C4×D4—24no—
801C4×D4—28no—
802C4×D4—24no—
803C4×D4—28no—
804C4×D4—24no—
805C4×D4—24no—
806C4×D4—24no—
807C4×D4—24no—
808C4×D4—24no—
809C4×D4—24no—
810C4×D4—24no—
811C4×D4—24no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—24no—
815C4×D4—216no—
816C4×D4—216no—
817C4×D4—28no—
818C4×D4—28no—
819C4×D4—28no—
820C4×D4C2×D418yes—
821C4×D4C2×D418yes—
822C4×D4C2418yes—
823C4×D4C2418yes—
824C4×D4C2418yes—
825#117—21no—
826#117—21no—
827#117—21no—
828#117—24no—
829#117—21no—
830#117—24no—
831#117—24no—
832#117—24no—
833#117—22no—
834#117—22no—
835#117—21no—
836#117—24no—
837#117—21no—
838#117—24no—
839#117—21no—
840#117—21no—
841#117—24no—
842#117—28no—
843#117—24no—
844#117—28no—
845#117—28no—
846#117—28no—
847#117—28no—
848#117—24no—
849#117C2×D412yes—
850#117C2×D412yes—
851#117C2412yes—
852#117C2412yes—
853#117C2412yes—
854#117C2412yes—
855#117C2412yes—
856#117C2414yes—
857#117C2414yes—
858#117C2412yes—
859#117C2412yes—
860#117C2412yes—
861#117C2418yes—
862#117C2412yes—
863#117C2412yes—
864C2×C4⋊C4—22no—
865C2×C4⋊C4—22no—
866C2×C4⋊C4—22no—
867C2×C4⋊C4—24no—
868C2×C4⋊C4—24no—
869C2×C4⋊C4—24no—
870C2×C4⋊C4—22no—
871C2×C4⋊C4—22no—
872C2×C4⋊C4—24no—
873C2×C4⋊C4C2×D412yes—
874C2×C4⋊C4C2×D414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2418yes—
882C2×C22⋊C4—21no—
883C2×C22⋊C4—21no—
884C2×C22⋊C4—22no—
885C2×C22⋊C4—24no—
886C2×C22⋊C4—24no—
887C2×C22⋊C4—21no—
888C2×C22⋊C4—21no—
889C2×C22⋊C4—24no—
890C2×C22⋊C4—22no—
891C2×C22⋊C4—22no—
892C2×C22⋊C4—24no—
893C2×C22⋊C4—24no—
894C2×C22⋊C4—22no—
895C2×C22⋊C4—22no—
896C2×C22⋊C4—24no—
897C2×C22⋊C4C2×D412yes—
898C2×C22⋊C4C2×D414yes—
899C2×C22⋊C4C2×D414yes—
900C2×C42—21no—
901C2×C42—24no—
902C2×C42—22no—
903C2×C42—24no—
904C2×C42—21no—
905C2×C42—24no—
906C2×C42—21no—
907C2×C42—21no—
908C2×C42—24no—
909C2×C42—24no—
910C2×C42C2412yes—
911#107C2418yes—
912#107C2418yes—
913#107C2418yes—
914#106C2418yes—
915#106C2418yes—
916#106C2418yes—
917C4⋊C8C24116yes—
918#103C24116yes—
919#103C24116yes—
920#103C24116yes—
921#103C24116yes—
922#103C24116yes—
923#103C24116yes—
924#103C2418yes—
925#103C2418yes—
926#103C2418yes—
927#103C2418yes—
928#102C2418yes—
929#102C2418yes—
930#102C2418yes—
931#102C2418yes—
932C22⋊C8C2418yes—
933C22⋊C8C2418yes—
934C22⋊C8C24116yes—
935#97C2418yes—
936C4×C8C2418yes—
937C24—24no—
938C24—21no—
939C24—21no—
940C24—44no—
941C24C22×D411yescharacteristic
942C24C22×D412yes—
943C24C22×D412yes—
944C24C22×D412yes—
945C24C22×D411yescharacteristic
946C24C22×D411yescharacteristic
947#41—28no—
948#41—28no—
949#41—24no—
950#41—24no—
951#41—24no—
952#41—24no—
953#41—216no—
954#41—24no—
955#41—24no—
956#41—24no—
957#41—24no—
958#41—24no—
959#41—24no—
960#41—24no—
961#41—24no—
962#41—48no—
963#41—432no—
964#41—432no—
965#41—416no—
966#41—416no—
967#41—416no—
968#41—44no—
969#41—44no—
970#41—44no—
971#41—44no—
972#41—816no—
973C2×Q8—28no—
974C2×Q8—28no—
975C2×Q8—28no—
976C2×Q8—24no—
977C2×Q8—22no—
978C2×Q8—22no—
979C2×Q8—22no—
980C2×Q8—21no—
981C2×Q8—28no—
982C2×Q8—28no—
983C2×Q8—22no—
984C2×Q8—22no—
985C2×Q8—22no—
986C2×Q8—28no—
987C2×Q8—21no—
988C2×Q8—28no—
989C2×Q8—24no—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—216no—
993C2×Q8—216no—
994C2×Q8—216no—
995C2×Q8—22no—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—24no—
999C2×Q8—22no—
1000C2×Q8—24no—
1001C2×Q8—22no—
1002C2×Q8—24no—
1003C2×Q8—24no—
1004C2×Q8—22no—
1005C2×Q8—416no—
1006C2×Q8—416no—
1007C2×Q8—48no—
1008C2×Q8—48no—
1009C2×Q8—48no—
1010C2×Q8—48no—
1011C2×Q8—48no—
1012C2×Q8—48no—
1013C2×Q8—416no—
1014C2×Q8—416no—
1015C2×Q8—416no—
1016C2×Q8—416no—
1017C2×Q8—416no—
1018C2×Q8—416no—
1019C2×Q8—416no—
1020C2×Q8—416no—
1021C2×Q8—416no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8C22×D412yes—
1026C2×Q8C22×D412yes—
1027C2×Q8C2×#4118yes—
1028C2×Q8C2×#4118yes—
1029C2×Q8C2×#4118yes—
1030C2×Q8C2514yes—
1031C2×Q8C2512yes—
1032C2×Q8C2512yes—
1033C2×Q8C2514yes—
1034C2×D4—28no—
1035C2×D4—24no—
1036C2×D4—24no—
1037C2×D4—22no—
1038C2×D4—22no—
1039C2×D4—24no—
1040C2×D4—22no—
1041C2×D4—22no—
1042C2×D4—28no—
1043C2×D4—24no—
1044C2×D4—28no—
1045C2×D4—24no—
1046C2×D4—21no—
1047C2×D4—21no—
1048C2×D4—22no—
1049C2×D4—22no—
1050C2×D4—22no—
1051C2×D4—22no—
1052C2×D4—48no—
1053C2×D4—48no—
1054C2×D4—48no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—84no—
1058C2×D4C22×D418yes—
1059C2×D4C22×D414yes—
1060C2×D4C22×D414yes—
1061C2×D4C22×D412yes—
1062C2×D4C22×D412yes—
1063C2×D4C22×D418yes—
1064C2×D4C2512yes—
1065C2×D4C2512yes—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—28no—
1072C22×C4—28no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—24no—
1080C22×C4—22no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—22no—
1084C22×C4—24no—
1085C22×C4—22no—
1086C22×C4—24no—
1087C22×C4—22no—
1088C22×C4—21no—
1089C22×C4—21no—
1090C22×C4—28no—
1091C22×C4—28no—
1092C22×C4—28no—
1093C22×C4—22no—
1094C22×C4—22no—
1095C22×C4—22no—
1096C22×C4—24no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—28no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—28no—
1103C22×C4—22no—
1104C22×C4—22no—
1105C22×C4—28no—
1106C22×C4—48no—
1107C22×C4—416no—
1108C22×C4—48no—
1109C22×C4—416no—
1110C22×C4—48no—
1111C22×C4—48no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—84no—
1116C22×C4C22×D412yes—
1117C22×C4C22×D412yes—
1118C22×C4C22×D411yescharacteristic
1119C22×C4C22×D414yes—
1120C22×C4C22×D412yes—
1121C22×C4C22×D412yes—
1122C22×C4C22×D412yes—
1123C22×C4C22×D412yes—
1124C22×C4C22×D411yescharacteristic
1125C22×C4C22×D412yes—
1126C22×C4C22×D412yes—
1127C22×C4C22×D412yes—
1128C22×C4C22×D414yes—
1129C22×C4C22×D411yescharacteristic
1130C22×C4C22×D411yescharacteristic
1131C22×C4C22×D411yescharacteristic
1132C22×C4C2×#4114yes—
1133C22×C4H(5,𝔽2)14yes—
1134C22×C4C2512yes—
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140Q16—216no—
1141Q16—48no—
1142Q16—44no—
1143SD16—216no—
1144SD16—48no—
1145SD16—44no—
1146SD16—44no—
1147D8—44no—
1148M16—24no—
1149M16—24no—
1150M16—24no—
1151M16—24no—
1152M16—24no—
1153M16—24no—
1154M16—24no—
1155M16—24no—
1156M16—48no—
1157M16—48no—
1158C2×C8—24no—
1159C2×C8—24no—
1160C2×C8—24no—
1161C2×C8—24no—
1162C2×C8—48no—
1163C2×C8—48no—
1164C2×C8C2514yes—
1165C2×C8C2514yes—
1166C2×C8C2514yes—
1167C2×C8C2514yes—
1168C4⋊C4—22no—
1169C4⋊C4—22no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—216no—
1175C4⋊C4—216no—
1176C4⋊C4—216no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—22no—
1181C4⋊C4—28no—
1182C4⋊C4—22no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4C22×D414yes—
1188C4⋊C4C22×D418yes—
1189C4⋊C4C22×D414yes—
1190C4⋊C4C22×D418yes—
1191C4⋊C4C2514yes—
1192C4⋊C4C2514yes—
1193C4⋊C4C2514yes—
1194C4⋊C4C2514yes—
1195C22⋊C4—22no—
1196C22⋊C4—22no—
1197C22⋊C4—22no—
1198C22⋊C4—22no—
1199C22⋊C4—22no—
1200C22⋊C4—24no—
1201C22⋊C4—24no—
1202C22⋊C4—22no—
1203C22⋊C4—22no—
1204C22⋊C4—24no—
1205C22⋊C4—22no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—216no—
1211C22⋊C4—28no—
1212C22⋊C4—24no—
1213C22⋊C4—28no—
1214C22⋊C4—216no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—24no—
1218C22⋊C4—28no—
1219C22⋊C4C22×D414yes—
1220C22⋊C4C22×D414yes—
1221C22⋊C4C22×D418yes—
1222C22⋊C4C22×D418yes—
1223C22⋊C4C22×D418yes—
1224C22⋊C4C22×D418yes—
1225C42—22no—
1226C42—24no—
1227C42—22no—
1228C42—22no—
1229C42—22no—
1230C42—24no—
1231C42—22no—
1232C42—28no—
1233C42—28no—
1234C42—216no—
1235C42—22no—
1236C42—22no—
1237C42—22no—
1238C42C22×D414yes—
1239C42C2514yes—
1240C23—24no—
1241C23—22no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23—24no—
1246C23—22no—
1247C23—24no—
1248C23—22no—
1249C23—22no—
1250C23—42no—
1251C23—42no—
1252C23—42no—
1253C23—42no—
1254C23—44no—
1255C23—416no—
1256C23—44no—
1257C23—42no—
1258C23—42no—
1259C23—82no—
1260C23#54614yes—
1261C23C23×D412yes—
1262C23C23×D414yes—
1263C23C23×D412yes—
1264C23C23×D411yescharacteristic
1265C23C23×D411yescharacteristic
1266C23C23×D411yescharacteristic
1267Q8—24no—
1268Q8—28no—
1269Q8—28no—
1270Q8—28no—
1271Q8—24no—
1272Q8—24no—
1273Q8—22no—
1274Q8—24no—
1275Q8—22no—
1276Q8—22no—
1277Q8—24no—
1278Q8—22no—
1279Q8—416no—
1280Q8—416no—
1281Q8—416no—
1282Q8—44no—
1283Q8—44no—
1284Q8—44no—
1285Q8—42no—
1286Q8—42no—
1287Q8—88no—
1288Q8C22×#4118yes—
1289D4—216no—
1290D4—28no—
1291D4—28no—
1292D4—22no—
1293D4—22no—
1294D4—22no—
1295D4—22no—
1296D4—24no—
1297D4—24no—
1298D4—48no—
1299D4—416no—
1300D4—48no—
1301D4—48no—
1302D4—48no—
1303D4—44no—
1304D4—44no—
1305D4—44no—
1306D4—44no—
1307D4—42no—
1308D4—42no—
1309D4—84no—
1310D4—88no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—28no—
1317C2×C4—28no—
1318C2×C4—28no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—28no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—44no—
1341C2×C4—416no—
1342C2×C4—416no—
1343C2×C4—416no—
1344C2×C4—416no—
1345C2×C4—44no—
1346C2×C4—48no—
1347C2×C4—42no—
1348C2×C4—44no—
1349C2×C4—44no—
1350C2×C4—44no—
1351C2×C4—42no—
1352C2×C4—44no—
1353C2×C4—44no—
1354C2×C4—44no—
1355C2×C4—44no—
1356C2×C4—88no—
1357C2×C4—82no—
1358C2×C4—84no—
1359C2×C4—82no—
1360C2×C4—82no—
1361C2×C4—88no—
1362C2×C4#54614yes—
1363C2×C4#54614yes—
1364C2×C4#54614yes—
1365C2×C4C23×D412yes—
1366C2×C4C23×D418yes—
1367C2×C4C23×D414yes—
1368C2×C4C23×D412yes—
1369C2×C4C23×D411yescharacteristic
1370C2×C4C23×D411yescharacteristic
1371C2×C4C23×D411yescharacteristic
1372C2×C4C22×#4112yes—
1373C2×C4C22×#4112yes—
1374C2×C4C22×#4112yes—
1375C2×C4C2×H(5,𝔽2)12yes—
1376C2×C4C2×H(5,𝔽2)12yes—
1377C2×C4C2×H(5,𝔽2)12yes—
1378C2×C4C2611yescharacteristic
1379C8—24no—
1380C8—24no—
1381C8—24no—
1382C8—24no—
1383C22—28no—
1384C22—22no—
1385C22—22no—
1386C22—22no—
1387C22—22no—
1388C22—22no—
1389C22—28no—
1390C22—22no—
1391C22—22no—
1392C22—22no—
1393C22—24no—
1394C22—44no—
1395C22—48no—
1396C22—48no—
1397C22—44no—
1398C22—44no—
1399C22—44no—
1400C22—42no—
1401C22—42no—
1402C22—84no—
1403C22—84no—
1404C22—162no—
1405C22C2×#54612yes—
1406C22C2×#54612yes—
1407C22C2×#54612yes—
1408C22#358614yes—
1409C22C24×D411yescharacteristic
1410C4—28no—
1411C4—22no—
1412C4—22no—
1413C4—28no—
1414C4—24no—
1415C4—44no—
1416C4—44no—
1417C4—44no—
1418C4—44no—
1419C4—42no—
1420C4—44no—
1421C4—42no—
1422C4C2×#54612yes—
1423C4C2×#54612yes—
1424C4C2×#54612yes—
1425C4C23×#4111yescharacteristic
1426C4C22×H(5,𝔽2)11yescharacteristic
1427C2—24no—
1428C2—22no—
1429C2—22no—
1430C2—22no—
1431C2—42no—
1432C2—44no—
1433C2—82no—
1434C2—82no—
1435C2C22×#54611yescharacteristic
1436C2C2×#358612yes—
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62814C2semidirect
2. C2×#3486C2semidirect
3. #61186C2semidirect
4. #61185C2semidirect
5. #61176C2semidirect
6. #61168C2semidirect
7. #61158C2semidirect
8. #61157C2semidirect
9. #60620C2semidirect
10. #60519C2semidirect
11. #60511C2semidirect
12. #60491C2semidirect
13. #60455C2semidirect
14. #60444C2semidirect
15. #60427C2semidirect
16. #60368C2semidirect
17. C2×#3004C2semidirect
18. #60169C2semidirect
19. #60141C2semidirect
20. #60088C2semidirect
21. C22×#419C2semidirect
30. #3495C22semidirect
32. #3494C22semidirect
33. #3493C22semidirect
34. #3492C22semidirect
41. #3486C22semidirect
42. #3486C22semidirect
46. C2×D4×Q8C22semidirect
48. C2×#548C22semidirect
64. #3329C22semidirect
65. #3328C22semidirect
66. #3327C22semidirect
67. #3326C22semidirect
68. #3321C22semidirect
69. #3320C22semidirect
70. #3320C22semidirect
71. #3316C22semidirect
72. #3313C22semidirect
73. #3312C22semidirect
74. #3312C22semidirect
75. #3308C22semidirect
76. #3301C22semidirect
77. #3300C22semidirect
78. #3299C22semidirect
79. #3298C22semidirect
80. #3140C22semidirect
81. #3139C22semidirect
82. #3137C22semidirect
83. #3137C22semidirect
84. #3097C22semidirect
85. #3097C22semidirect
86. #3095C22semidirect
87. #3095C22semidirect
88. #3094C22semidirect
89. #3093C22semidirect
90. #3092C22semidirect
91. #3091C22semidirect
92. #3082C22semidirect
93. #3082C22semidirect
94. #3078C22semidirect
95. #3063C22semidirect
96. #3059C22semidirect
97. #3057C22semidirect
99. #3056C22semidirect
100. #3056C22semidirect
102. #3055C22semidirect
103. #3054C22semidirect
104. #3050C22semidirect
105. #3046C22semidirect
106. #3044C22semidirect
107. #3042C22semidirect
108. #3040C22semidirect
109. #3039C22semidirect
110. #3013C22semidirect
111. #3011C22semidirect
112. #3010C22semidirect
113. #3005C22semidirect
115. #3004C22semidirect
116. #3004C22semidirect
117. #3004C22semidirect
118. C2×#451C22semidirect
119. C2×#448C22semidirect
120. #2950C22semidirect
121. #2949C22semidirect
122. #2947C22semidirect
123. C4×#137C22semidirect
124. D4×M16C22semidirect
125. #2933C22semidirect
126. #2930C22semidirect
127. #2929C22semidirect
132. #2898C22semidirect
133. #2898C22semidirect
138. #2896C22semidirect
145. C2×#419C22semidirect
146. C2×#419C22semidirect
147. C2×#419C22semidirect
148. C2×#419C22semidirect
149. C22×#103C22semidirect
384. #491C23semidirect
385. #489C23semidirect
386. #488C23semidirect
387. #487C23semidirect
390. #485C23semidirect
391. #485C23semidirect
393. #484C23semidirect
395. #483C23semidirect
400. #479C23semidirect
401. #479C23semidirect
402. #477C23semidirect
403. #475C23semidirect
405. #470C23semidirect
409. #468C23semidirect
411. #467C23semidirect
415. #465C23semidirect
416. #464C23semidirect
417. #463C23semidirect
418. #462C23semidirect
419. #461C23semidirect
420. #452C23semidirect
423. #451C23semidirect
424. #449C23semidirect
427. #448C23semidirect
428. #441C23semidirect
429. #440C23semidirect
430. C4×Q16C23semidirect
431. C4×SD16C23semidirect
466. #419C23semidirect
475. #417C23semidirect
480. #416C23semidirect
489. C2×#103C23semidirect
576. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#628142
C2×#34862
#611862
#611852
#611762
#611682
#611582
#611572
#606202
#605192
#605112
#604912
#604552
#604442
#604272
#603682
C2×#30042
#601692
#601412
#600882
C22×#4192