Finite Group Databasebeta

← #10575650

Subgroups — #10575650

Order 512.

6431 conjugacy classes of subgroups.

The subgroup lattice has 1513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62815C211yesmaximal, characteristic, complemented
2C2×#3461C211yesmaximal, characteristic, complemented
3#60932C218yesmaximal, complemented
4#60931C214yesmaximal, complemented
5#60930C214yesmaximal, complemented
6#60927C218yesmaximal, complemented
7#60925C214yesmaximal, complemented
8#60924C214yesmaximal, complemented
9#60921C214yesmaximal, complemented
10#60919C214yesmaximal, complemented
11#60918C214yesmaximal, complemented
12#60917C214yesmaximal, complemented
13#60493C212yesmaximal, complemented
14#60484C211yesmaximal, characteristic, complemented
15C2×#3078C211yesmaximal, characteristic, complemented
16#60456C212yesmaximal, complemented
17#60455C212yesmaximal, complemented
18#60427C212yesmaximal, complemented
19#60415C211yesmaximal, characteristic, complemented
20C2×#3037C211yesmaximal, characteristic, complemented
21#60099C211yesmaximal, characteristic, complemented
22C2×#575C2212yes—
23C22×#137C2212yes—
24C2×#568C2212yes—
25#3512C2214yescomplemented
26#3511C2212yescomplemented
27#3511C2212yescomplemented
28#3510C2214yescomplemented
29#3509C2212yescomplemented
30#3508C2212yescomplemented
31#3507—21no—
32#3507—21no—
33#3506—21no—
34#3506—21no—
35#3505—22no—
36#3505—22no—
37#3480—22no—
38#3480—22no—
39#3475—22no—
40#3475—22no—
41#3461—22no—
42#3461—22no—
43#3461—22no—
44#3461—22no—
45#3461C2214yes—
46#3461C2214yes—
47#3461C2214yescomplemented
48#3461C2214yescomplemented
49C2×#544C2211yescharacteristic
50#3455C2214yes—
51C2×#542—21no—
52C2×#542C2212yescomplemented
53C2×#541—21no—
54C2×#541C2212yescomplemented
55C2×#539—22no—
56#3449C2212yes—
57C2×#537C2211yescharacteristic
58C2×#536C2211yescharacteristic
59C2×#536C2211yescharacteristic
60#3444C2214yes—
61C2×#533—21no—
62C2×#533C2211yescharacteristic
63C2×#533C2212yescomplemented
64C2×#532C2211yescharacteristic
65C2×#529—21no—
66C2×#529—22no—
67C2×#529C2212yescomplemented
68#3428C2212yes—
69C2×C4×#41C2211yescharacteristic
70C2×C4×#41C2211yescharacteristic
71C22×C4×Q8C2211yescharacteristic
72#3263C22116yescomplemented
73#3262C22116yescomplemented
74#3261C22116yescomplemented
75#3260C22116yescomplemented
76#3258C22116yescomplemented
77#3258C22116yescomplemented
78#3258C22116yescomplemented
79#3257C22116yescomplemented
80#3256C22116yescomplemented
81#3255C2218yescomplemented
82#3254C2218yescomplemented
83#3252C2218yescomplemented
84#3252C22116yescomplemented
85#3251C2218yescomplemented
86#3250C22116yescomplemented
87#3249C2218yescomplemented
88#3248C2218yescomplemented
89#3248C22116yescomplemented
90#3247C2218yescomplemented
91#3246C2218yescomplemented
92#3084C2218yescomplemented
93#3083C2218yescomplemented
94#3082C2218yescomplemented
95#3081C2218yescomplemented
96#3080C2214yescomplemented
97#3080C2218yescomplemented
98#3079C2212yescomplemented
99#3079C2212yescomplemented
100#3079C2218yescomplemented
101#3078C2214yescomplemented
102#3078C2214yescomplemented
103#3078C2214yescomplemented
104#3078C2214yescomplemented
105#3078C2212yescomplemented
106#3078C2212yescomplemented
107#3077C2212yescomplemented
108#3077C2212yescomplemented
109#3076C2214yescomplemented
110#3076C2214yescomplemented
111C2×#479C2214yescomplemented
112C2×#477C2212yescomplemented
113C2×#475C2212yescomplemented
114#3063C2218yes—
115#3063C2218yescomplemented
116#3063C2218yescomplemented
117#3062C2218yes—
118#3061C2218yescomplemented
119#3060C2218yescomplemented
120#3059C2218yescomplemented
121#3057C2218yescomplemented
122#3056C2218yescomplemented
123#3056C2218yescomplemented
124#3056C2218yescomplemented
125#3055C2218yescomplemented
126#3046C2218yescomplemented
127#3046C2218yescomplemented
128#3044C2218yescomplemented
129#3042C2218yescomplemented
130#3040C2218yescomplemented
131#3040C2214yescomplemented
132#3039C2218yescomplemented
133#3039C2212yescomplemented
134#3038C2212yescomplemented
135#3037C2214yes—
136#3037C2212yes—
137#3037C2214yes—
138#3037C2212yes—
139#3037C2214yescomplemented
140#3037C2214yescomplemented
141#3036C2212yes—
142#3036C2212yes—
143#3035C2214yescomplemented
144#3035C2214yescomplemented
145C2×#464C2214yescomplemented
146C2×#462C2212yescomplemented
147C2×#460C2212yescomplemented
148#2911C2212yes—
149C2×#428C2212yes—
150#2906C2214yescomplemented
151#2906C2214yescomplemented
152#2906C2214yescomplemented
153#2906C2214yescomplemented
154#2905C2212yes—
155#2905C2214yescomplemented
156C2×#423C2211yescharacteristic
157C2×#423C2211yescharacteristic
158C2×#423C2214yescomplemented
159#2896C2212yes—
160#2896C2212yes—
161C2×#417C2212yes—
162C2×#419C2212yes—
163C22×#41C2312yes—
164C22×#41C2311yescharacteristic
165C22×#41C2311yescharacteristic
166C23×Q8C2311yescharacteristic
167#575—48no—
168C2×#137—48no—
169C2×#137C2314yes—
170C2×#137C2318yes—
171C2×#137C2318yes—
172C2×#137C2314yes—
173C2×AGL(1,ℤ/8)C2314yes—
174C2×AGL(1,ℤ/8)C2314yes—
175C2×#135C2318yes—
176C22×Q16C2314yes—
177C22×SD16C2314yes—
178#568—48no—
179C2×#131C2318yes—
180C2×#131C2318yes—
181C22×M16C2312yes—
182C22×M16C2312yes—
183C22×M16C2318yes—
184#559—22no—
185#559—22no—
186#559—24no—
187#559—24no—
188#557—22no—
189#557—22no—
190#556—22no—
191#556—22no—
192#556—24no—
193#556—24no—
194#556—22no—
195#556—22no—
196#555—22no—
197#555—22no—
198#554—22no—
199#554—22no—
200#553—24no—
201#553—24no—
202#553—24no—
203#553—24no—
204#553—28no—
205#553—28no—
206#552—24no—
207#552—24no—
208#552—24no—
209#552—24no—
210#551—28no—
211#551—28no—
212#550—22no—
213#550—22no—
214#548—24no—
215#548—24no—
216#547—22no—
217#547—22no—
218#546—24no—
219#546—24no—
220#544—22no—
221#544—22no—
222#544C2314yes—
223#544C2314yes—
224#542—24no—
225#542—24no—
226#542—24no—
227#542—24no—
228#542—24no—
229#542—24no—
230#542C2318yes—
231#542C2318yes—
232#542C2318yes—
233#542C2318yes—
234#541—24no—
235#541—24no—
236#541—24no—
237#541—24no—
238#541—24no—
239#541—24no—
240#541C2318yes—
241#541C2318yes—
242#541C2318yes—
243#540C2318yes—
244#539—28no—
245#539—28no—
246#539—28no—
247#539—28no—
248#539—24no—
249#539—24no—
250#538—24no—
251#538—24no—
252#537—22no—
253#537—22no—
254#537C2314yes—
255#537C2314yes—
256#537C2314yes—
257#537C2314yes—
258#536—22no—
259#536—22no—
260#536—22no—
261#536—22no—
262#536—22no—
263#536C2314yes—
264#536C2314yes—
265#536C2314yes—
266#536C2314yes—
267#536C2314yes—
268#535—22no—
269#535C2314yes—
270#534—24no—
271#533—24no—
272#533—24no—
273#533—24no—
274#533—24no—
275#533—21no—
276#533—21no—
277#533—21no—
278#533—21no—
279#533—24no—
280#533—24no—
281#533C2318yes—
282#533C2318yes—
283#533C2314yes—
284#533C2314yes—
285#533C2312yes—
286#533C2312yes—
287#533C2312yes—
288#533C2312yes—
289#532—24no—
290#532—21no—
291#532—21no—
292#532—21no—
293#532—21no—
294#532C2312yes—
295#532C2312yes—
296#532C2312yes—
297#532C2312yes—
298#532C2314yes—
299#532C2314yes—
300C2×C4⋊Q8—21no—
301C2×C4⋊Q8—21no—
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2312yes—
304C2×C4⋊Q8C2311yescharacteristic
305C2×C4⋊Q8C2311yescharacteristic
306C2×C4⋊Q8C2312yes—
307C2×#127C2311yescharacteristic
308#529—28no—
309#529—28no—
310#529—24no—
311#529—24no—
312#529—28no—
313#529—28no—
314#529—24no—
315#529—24no—
316#529—28no—
317#529—28no—
318#529—24no—
319#529—24no—
320#529—24no—
321#529—24no—
322#529—24no—
323#529—24no—
324#529C2318yes—
325#529C2318yes—
326#529C2318yes—
327#529C2318yes—
328C2×#126—22no—
329C2×#126—22no—
330C2×#126—22no—
331C2×#126—22no—
332C2×#125—22no—
333C2×#125—21no—
334C2×#125—22no—
335C2×#125—22no—
336C2×#125C2312yes—
337C2×#125C2312yes—
338C2×#124—21no—
339C2×#124—22no—
340C2×#124C2312yes—
341C2×#124C2312yes—
342#525—24no—
343#525—24no—
344#525—24no—
345#525C2318yes—
346C2×#123—22no—
347C2×#123—22no—
348C2×#123—22no—
349C2×#123—22no—
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8—21no—
352C2×C22⋊Q8—21no—
353C2×C22⋊Q8—22no—
354C2×C22⋊Q8—21no—
355C2×C22⋊Q8—21no—
356C2×C22⋊Q8—22no—
357C2×C22⋊Q8—22no—
358C2×C22⋊Q8C2312yes—
359C2×C22⋊Q8C2312yes—
360C2×C22⋊Q8C2312yes—
361C2×#121—22no—
362C2×#121—21no—
363C2×#121—21no—
364C2×#121—21no—
365C2×#121C2312yes—
366#520—22no—
367#520—22no—
368#520C2314yes—
369#520C2314yes—
370#519C2314yes—
371#518—24no—
372#518C2314yes—
373C4×#41—24no—
374C4×#41—21no—
375C4×#41—21no—
376C4×#41—21no—
377C4×#41—21no—
378C4×#41—24no—
379C4×#41—24no—
380C4×#41D412yes—
381C4×#41D412yes—
382C4×#41D412yes—
383C4×#41D412yes—
384C4×#41C2312yes—
385C4×#41C2312yes—
386C4×#41C2312yes—
387C4×#41C2318yes—
388C4×#41C2312yes—
389C4×#41C2312yes—
390C4×#41C2312yes—
391C4×#41C2312yes—
392C4×#41C2312yes—
393C2×C4×Q8—21no—
394C2×C4×Q8—21no—
395C2×C4×Q8—21no—
396C2×C4×Q8—21no—
397C2×C4×Q8—21no—
398C2×C4×Q8—21no—
399C2×C4×Q8—22no—
400C2×C4×Q8—21no—
401C2×C4×Q8—21no—
402C2×C4×Q8D411yescharacteristic
403C2×C4×Q8D411yescharacteristic
404C2×C4×Q8C2312yes—
405C2×C4×Q8C2312yes—
406C2×C4×Q8C2312yes—
407C2×C4×Q8C2312yes—
408C2×C4×Q8C2312yes—
409C2×C4×Q8C2312yes—
410C2×C4×Q8C2311yescharacteristic
411C2×C4×Q8C2311yescharacteristic
412C2×C4×D4—21no—
413C2×C4×D4—21no—
414C2×C4×D4—22no—
415C2×C4×D4—21no—
416C2×C4×D4—21no—
417C2×C4×D4D412yes—
418C2×C4×D4D411yescharacteristic
419C2×C4×D4D412yes—
420C2×C4×D4D411yescharacteristic
421C2×C4×D4C2311yescharacteristic
422C2×C4×D4C2311yescharacteristic
423C2×#117—22no—
424C2×#117—24no—
425C2×#117—21no—
426C2×#117—22no—
427C2×#117C2312yes—
428C2×#117C2311yescharacteristic
429C2×#117C2311yescharacteristic
430C2×#117C2312yes—
431C22×C4⋊C4—21no—
432C22×C4⋊C4C2311yescharacteristic
433C22×C42—21no—
434C22×C42—21no—
435C22×C42C2311yescharacteristic
436C22×C42C2312yes—
437#479C23116yes—
438#479C23116yes—
439#479C2318yes—
440#479C2318yes—
441#479C23116yes—
442#479C23116yes—
443#478C2318yes—
444#478C2318yes—
445#478C23116yes—
446#478C23116yes—
447#477C2318yes—
448#477C2318yes—
449#477C2314yes—
450#477C2314yes—
451#477C23116yes—
452#476C2314yes—
453#476C2314yes—
454#476C23116yes—
455#475C2318yes—
456#475C2318yes—
457#475C2314yes—
458#475C2314yes—
459#475C23116yes—
460#474C2314yes—
461#474C2314yes—
462#474C23116yes—
463#470C23116yes—
464#470C23116yes—
465#470C23116yes—
466#469C23116yes—
467#468C23116yes—
468#468C23116yes—
469#468C23116yes—
470#468C23116yes—
471#467C23116yes—
472#467C23116yes—
473#467C23116yes—
474#466C23116yes—
475#465C23116yes—
476#465C23116yes—
477#465C23116yes—
478#465C23116yes—
479#464C2318yes—
480#464C23116yes—
481#464C23116yes—
482#464C23116yes—
483#464C2318yes—
484#464C23116yes—
485#463C23116yes—
486#463C2318yes—
487#463C23116yes—
488#463C2318yes—
489#462C2318yes—
490#462C23116yes—
491#462C2314yes—
492#462C23116yes—
493#462C2318yes—
494#462C2314yes—
495#461C23116yes—
496#461C2314yes—
497#461C23116yes—
498#461C2314yes—
499#460C2314yes—
500#460C2318yes—
501#460C2318yes—
502#460C2314yes—
503#459C2314yes—
504#459C2314yes—
505#428C2314yes—
506#428C2314yes—
507#428C2318yes—
508#428C2318yes—
509#428C2314yes—
510#428C2314yes—
511#427C2318yes—
512C2×#107C2314yes—
513C2×#106C2314yes—
514#424C2318yes—
515#424C2318yes—
516#424C23116yes—
517#424C23116yes—
518#423C2312yes—
519#423C2312yes—
520#423C2312yes—
521#423C2312yes—
522#423C2312yes—
523#423C2312yes—
524#423C2312yes—
525#423C2318yes—
526#423C2312yes—
527#423C2318yes—
528#423C2318yes—
529C2×C4⋊C8C2312yes—
530C2×C4⋊C8C2312yes—
531C2×C4⋊C8C2312yes—
532C2×C4⋊C8C2312yes—
533C2×C4⋊C8C2318yes—
534C2×C4⋊C8C2318yes—
535#419C2318yes—
536#419C2318yes—
537#419C2314yes—
538#419C2314yes—
539#418C2314yes—
540#418C2314yes—
541#417C2314yes—
542#417C2318yes—
543#417C2314yes—
544#417C2314yes—
545#417C2314yes—
546#417C2318yes—
547#416C2318yes—
548#416C2318yes—
549C2×#103C2314yes—
550C2×#103C2314yes—
551C2×#103C2314yes—
552C2×#102C2314yes—
553C2×#41—22no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—22no—
557C2×#41—24no—
558C2×#41—24no—
559C2×#41—24no—
560C2×#41—24no—
561C2×#41—28no—
562C2×#41—24no—
563C2×#41—28no—
564C2×#41—24no—
565C2×#41C2×D412yes—
566C2×#41C2×D412yes—
567C2×#41C2414yes—
568C2×#41C2412yes—
569C2×#41C2412yes—
570C2×#41C2414yes—
571C2×#41C2412yes—
572C2×#41C2412yes—
573C22×Q8—21no—
574C22×Q8—21no—
575C22×Q8—21no—
576C22×Q8—22no—
577C22×Q8—21no—
578C22×Q8—21no—
579C22×Q8—24no—
580C22×Q8—24no—
581C22×Q8C2×D411yescharacteristic
582C22×Q8C2412yes—
583C22×Q8C2411yescharacteristic
584C22×Q8C2412yes—
585C22×Q8C2412yes—
586C22×Q8C2412yes—
587C22×D4—21no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4C2×D412yes—
593C22×D4C2×D411yescharacteristic
594C22×D4C2411yescharacteristic
595C22×D4C2412yes—
596C23×C4—21no—
597C23×C4—21no—
598C23×C4—21no—
599C23×C4—22no—
600C23×C4—21no—
601C23×C4—21no—
602C23×C4C2×D412yes—
603C23×C4C2×D411yescharacteristic
604C23×C4C2×D411yescharacteristic
605C23×C4C2×D412yes—
606C23×C4C2412yes—
607C23×C4C2411yescharacteristic
608#137—416no—
609#137—416no—
610#137—48no—
611#137—48no—
612AGL(1,ℤ/8)—48no—
613AGL(1,ℤ/8)—48no—
614#135—416no—
615C2×Q16—48no—
616C2×Q16C24116yes—
617C2×Q16C2418yes—
618C2×SD16—48no—
619C2×SD16C24116yes—
620C2×SD16C2418yes—
621C2×SD16C2418yes—
622C2×D8C2418yes—
623#131—416no—
624#131—416no—
625C2×M16—28no—
626C2×M16—28no—
627C2×M16—416no—
628C2×M16C2414yes—
629C2×M16C2414yes—
630C2×M16C2414yes—
631C2×M16C2414yes—
632C2×M16C24116yes—
633C22×C8C2414yes—
634C22×C8C2414yes—
635C22×C8C24116yes—
636C4⋊Q8—24no—
637C4⋊Q8—24no—
638C4⋊Q8—24no—
639C4⋊Q8—24no—
640C4⋊Q8—24no—
641C4⋊Q8—21no—
642C4⋊Q8—21no—
643C4⋊Q8—24no—
644C4⋊Q8—24no—
645C4⋊Q8—21no—
646C4⋊Q8—21no—
647C4⋊Q8—21no—
648C4⋊Q8—21no—
649C4⋊Q8C2412yes—
650C4⋊Q8C2412yes—
651C4⋊Q8C2418yes—
652C4⋊Q8C2412yes—
653C4⋊Q8C2412yes—
654C4⋊Q8C2412yes—
655C4⋊Q8C2412yes—
656C4⋊Q8C2418yes—
657#127—24no—
658#127—21no—
659#127—21no—
660#127C2412yes—
661#127C2412yes—
662#126—28no—
663#126—28no—
664#126—28no—
665#126—28no—
666#126—28no—
667#126—28no—
668#126—28no—
669#126—28no—
670#126—28no—
671#126—28no—
672#126—28no—
673#126—28no—
674#126—28no—
675#126—28no—
676#125—28no—
677#125—28no—
678#125—24no—
679#125—24no—
680#125—28no—
681#125—28no—
682#125—28no—
683#125—28no—
684#125—28no—
685#125—28no—
686#125—24no—
687#125—22no—
688#125—22no—
689#125—24no—
690#125—24no—
691#125C2414yes—
692#125C2418yes—
693#125C2414yes—
694#124—24no—
695#124—24no—
696#124—24no—
697#124—24no—
698#124—28no—
699#124—28no—
700#124—28no—
701#124—28no—
702#124—24no—
703#124—22no—
704#124—22no—
705#124—24no—
706#124—24no—
707#124C2414yes—
708#124C2418yes—
709#124C2414yes—
710#123—28no—
711#123—28no—
712#123—28no—
713#123—28no—
714#123—28no—
715#123—28no—
716#123—28no—
717#123—28no—
718#123—28no—
719#123—28no—
720#123—28no—
721#123—28no—
722#123—28no—
723#123—28no—
724#123—28no—
725#123—28no—
726C22⋊Q8—24no—
727C22⋊Q8—24no—
728C22⋊Q8—24no—
729C22⋊Q8—24no—
730C22⋊Q8—22no—
731C22⋊Q8—22no—
732C22⋊Q8—22no—
733C22⋊Q8—22no—
734C22⋊Q8—28no—
735C22⋊Q8—28no—
736C22⋊Q8—22no—
737C22⋊Q8—22no—
738C22⋊Q8—22no—
739C22⋊Q8—22no—
740C22⋊Q8—24no—
741C22⋊Q8—24no—
742C22⋊Q8—24no—
743C22⋊Q8—24no—
744C22⋊Q8—24no—
745C22⋊Q8—24no—
746C22⋊Q8—24no—
747C22⋊Q8—24no—
748C22⋊Q8—24no—
749C22⋊Q8—28no—
750C22⋊Q8—28no—
751C22⋊Q8—28no—
752C22⋊Q8—28no—
753C22⋊Q8—28no—
754C22⋊Q8—28no—
755C22⋊Q8C2418yes—
756C22⋊Q8C2418yes—
757C22⋊Q8C2418yes—
758C22⋊Q8C2418yes—
759C22⋊Q8C2418yes—
760#121—28no—
761#121—28no—
762#121—24no—
763#121—24no—
764#121—24no—
765#121—24no—
766#121—28no—
767#121—28no—
768#121—22no—
769#121—22no—
770#121—22no—
771#121—22no—
772#121—22no—
773#121—22no—
774#121—22no—
775#121—22no—
776#121—24no—
777#121—24no—
778#121—24no—
779#121—28no—
780#121—28no—
781#121C2418yes—
782#121C2418yes—
783#121C2418yes—
784#120—28no—
785#120—28no—
786C4×Q8—24no—
787C4×Q8—24no—
788C4×Q8—22no—
789C4×Q8—22no—
790C4×Q8—22no—
791C4×Q8—22no—
792C4×Q8—22no—
793C4×Q8—22no—
794C4×Q8—22no—
795C4×Q8—22no—
796C4×Q8—22no—
797C4×Q8—22no—
798C4×Q8—22no—
799C4×Q8—22no—
800C4×Q8—22no—
801C4×Q8—22no—
802C4×Q8—22no—
803C4×Q8—22no—
804C4×Q8—28no—
805C4×Q8—28no—
806C4×Q8—22no—
807C4×Q8—22no—
808C4×Q8—22no—
809C4×Q8—22no—
810C4×Q8—21no—
811C4×Q8—21no—
812C4×Q8—21no—
813C4×Q8—21no—
814C4×Q8—24no—
815C4×Q8—24no—
816C4×Q8C2×D412yes—
817C4×Q8C2×D412yes—
818C4×Q8C2×D412yes—
819C4×Q8C2×D412yes—
820C4×Q8C2×D412yes—
821C4×Q8C2×D412yes—
822C4×Q8C2×D412yes—
823C4×Q8C2×D412yes—
824C4×Q8C2414yes—
825C4×Q8C2414yes—
826C4×Q8C2414yes—
827C4×Q8C2414yes—
828C4×Q8C2412yes—
829C4×Q8C2412yes—
830C4×Q8C2412yes—
831C4×Q8C2412yes—
832C4×Q8C2418yes—
833C4×Q8C2418yes—
834C4×D4—22no—
835C4×D4—22no—
836C4×D4—22no—
837C4×D4—22no—
838C4×D4—22no—
839C4×D4—22no—
840C4×D4—22no—
841C4×D4—22no—
842C4×D4—28no—
843C4×D4—28no—
844C4×D4—28no—
845C4×D4—28no—
846C4×D4—28no—
847C4×D4—28no—
848C4×D4—28no—
849C4×D4—28no—
850C4×D4—24no—
851C4×D4—24no—
852C4×D4—28no—
853C4×D4—28no—
854C4×D4—22no—
855C4×D4—22no—
856C4×D4—22no—
857C4×D4—22no—
858C4×D4—22no—
859C4×D4—22no—
860C4×D4—22no—
861C4×D4—22no—
862C4×D4—21no—
863C4×D4—21no—
864C4×D4—21no—
865C4×D4—21no—
866C4×D4—24no—
867C4×D4—24no—
868C4×D4C2×D414yes—
869C4×D4C2×D412yes—
870C4×D4C2×D414yes—
871C4×D4C2×D412yes—
872C4×D4C2×D414yes—
873C4×D4C2×D412yes—
874C4×D4C2×D414yes—
875C4×D4C2×D412yes—
876C4×D4C2×D414yes—
877C4×D4C2×D414yes—
878C4×D4C2×D414yes—
879C4×D4C2×D414yes—
880C4×D4C2×D412yes—
881C4×D4C2×D412yes—
882C4×D4C2×D412yes—
883C4×D4C2×D412yes—
884C4×D4C2412yes—
885C4×D4C2412yes—
886C4×D4C2412yes—
887C4×D4C2412yes—
888C4×D4C2418yes—
889C4×D4C2418yes—
890#117—22no—
891#117—28no—
892#117—28no—
893#117—21no—
894#117—21no—
895#117—22no—
896#117—24no—
897#117—24no—
898#117—24no—
899#117—24no—
900#117—28no—
901#117—28no—
902#117—22no—
903#117—22no—
904#117—22no—
905#117—22no—
906#117—28no—
907#117—28no—
908#117—28no—
909#117—28no—
910#117C2×D412yes—
911#117C2×D412yes—
912#117C2×D414yes—
913#117C2×D414yes—
914#117C2414yes—
915#117C2412yes—
916#117C2412yes—
917#117C2414yes—
918#117C2412yes—
919#117C2412yes—
920#117C2414yes—
921#117C2414yes—
922C2×C4⋊C4—22no—
923C2×C4⋊C4—22no—
924C2×C4⋊C4—22no—
925C2×C4⋊C4—22no—
926C2×C4⋊C4—22no—
927C2×C4⋊C4—22no—
928C2×C4⋊C4—21no—
929C2×C4⋊C4—21no—
930C2×C4⋊C4—21no—
931C2×C4⋊C4—21no—
932C2×C4⋊C4—21no—
933C2×C4⋊C4—22no—
934C2×C4⋊C4—22no—
935C2×C4⋊C4—22no—
936C2×C4⋊C4—22no—
937C2×C4⋊C4—21no—
938C2×C4⋊C4—21no—
939C2×C4⋊C4—22no—
940C2×C4⋊C4—22no—
941C2×C4⋊C4—22no—
942C2×C4⋊C4—22no—
943C2×C4⋊C4—22no—
944C2×C4⋊C4—22no—
945C2×C4⋊C4—21no—
946C2×C4⋊C4—21no—
947C2×C4⋊C4—24no—
948C2×C4⋊C4—24no—
949C2×C4⋊C4C2×D411yescharacteristic
950C2×C4⋊C4C2×D411yescharacteristic
951C2×C4⋊C4C2×D412yes—
952C2×C4⋊C4C2×D412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2412yes—
955C2×C4⋊C4C2412yes—
956C2×C4⋊C4C2411yescharacteristic
957C2×C4⋊C4C2411yescharacteristic
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C22⋊C4—22no—
961C2×C22⋊C4—22no—
962C2×C22⋊C4—21no—
963C2×C22⋊C4—22no—
964C2×C22⋊C4—22no—
965C2×C22⋊C4—21no—
966C2×C22⋊C4—21no—
967C2×C22⋊C4—22no—
968C2×C22⋊C4—22no—
969C2×C22⋊C4—22no—
970C2×C22⋊C4—22no—
971C2×C22⋊C4—22no—
972C2×C22⋊C4—28no—
973C2×C22⋊C4C2×D412yes—
974C2×C22⋊C4C2×D412yes—
975C2×C22⋊C4C2×D412yes—
976C2×C42—22no—
977C2×C42—21no—
978C2×C42—21no—
979C2×C42—22no—
980C2×C42—21no—
981C2×C42—22no—
982C2×C42—22no—
983C2×C42—22no—
984C2×C42—22no—
985C2×C42—22no—
986C2×C42—28no—
987C2×C42—22no—
988C2×C42—22no—
989C2×C42—22no—
990C2×C42—22no—
991C2×C42C2×D412yes—
992C2×C42C2×D411yescharacteristic
993C2×C42C2×D411yescharacteristic
994C2×C42C2×D411yescharacteristic
995C2×C42C2×D411yescharacteristic
996C2×C42C2×D412yes—
997C2×C42C2×D411yescharacteristic
998C2×C42C2×D411yescharacteristic
999C2×C42C2×D414yes—
1000C2×C42C2×D414yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2412yes—
1003C2×C42C2411yescharacteristic
1004C2×C42C2411yescharacteristic
1005C2×C42C2411yescharacteristic
1006C2×C42C2411yescharacteristic
1007C2×C42C2411yescharacteristic
1008C2×C42C2414yes—
1009C2×C42C2414yes—
1010#107C24116yes—
1011#107C2418yes—
1012#107C2418yes—
1013#106C24116yes—
1014#106C2418yes—
1015#106C2418yes—
1016C4⋊C8C2414yes—
1017C4⋊C8C2414yes—
1018C4⋊C8C2414yes—
1019C4⋊C8C2414yes—
1020C4⋊C8C2414yes—
1021C4⋊C8C2414yes—
1022C4⋊C8C24116yes—
1023C4⋊C8C24116yes—
1024C4⋊C8C2414yes—
1025C4⋊C8C2414yes—
1026#103C24116yes—
1027#103C24116yes—
1028#103C24116yes—
1029#103C2418yes—
1030#103C2418yes—
1031#103C2418yes—
1032#103C2418yes—
1033#102C24116yes—
1034#102C2418yes—
1035#102C2418yes—
1036#102C2418yes—
1037#102C2418yes—
1038C24—21no—
1039C24—22no—
1040C24C22×D412yes—
1041C24C22×D411yescharacteristic
1042#41—28no—
1043#41—28no—
1044#41—24no—
1045#41—24no—
1046#41—24no—
1047#41—24no—
1048#41—24no—
1049#41—28no—
1050#41—24no—
1051#41—28no—
1052#41—28no—
1053#41—24no—
1054#41—24no—
1055#41—28no—
1056#41—44no—
1057#41—48no—
1058#41—48no—
1059#41—44no—
1060#41—88no—
1061#41—88no—
1062C2×Q8—24no—
1063C2×Q8—22no—
1064C2×Q8—22no—
1065C2×Q8—22no—
1066C2×Q8—22no—
1067C2×Q8—22no—
1068C2×Q8—21no—
1069C2×Q8—22no—
1070C2×Q8—22no—
1071C2×Q8—22no—
1072C2×Q8—28no—
1073C2×Q8—24no—
1074C2×Q8—24no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—22no—
1078C2×Q8—24no—
1079C2×Q8—24no—
1080C2×Q8—24no—
1081C2×Q8—22no—
1082C2×Q8—24no—
1083C2×Q8—44no—
1084C2×Q8—44no—
1085C2×Q8—44no—
1086C2×Q8—82no—
1087C2×Q8—84no—
1088C2×Q8—82no—
1089C2×Q8C22×D412yes—
1090C2×Q8C22×D412yes—
1091C2×Q8C2514yes—
1092C2×Q8C2514yes—
1093C2×Q8C2512yes—
1094C2×D4—28no—
1095C2×D4—24no—
1096C2×D4—24no—
1097C2×D4—22no—
1098C2×D4—22no—
1099C2×D4—28no—
1100C2×D4—28no—
1101C2×D4—28no—
1102C2×D4—24no—
1103C2×D4—21no—
1104C2×D4—22no—
1105C2×D4—22no—
1106C2×D4—22no—
1107C2×D4—22no—
1108C2×D4—22no—
1109C2×D4—24no—
1110C2×D4—22no—
1111C2×D4—22no—
1112C2×D4—24no—
1113C2×D4—44no—
1114C2×D4—48no—
1115C2×D4—82no—
1116C2×D4—82no—
1117C2×D4—84no—
1118C2×D4C22×D414yes—
1119C2×D4C22×D414yes—
1120C2×D4C22×D412yes—
1121C2×D4C22×D412yes—
1122C2×D4C2512yes—
1123C2×D4C2514yes—
1124C22×C4—24no—
1125C22×C4—24no—
1126C22×C4—21no—
1127C22×C4—22no—
1128C22×C4—21no—
1129C22×C4—21no—
1130C22×C4—22no—
1131C22×C4—22no—
1132C22×C4—22no—
1133C22×C4—22no—
1134C22×C4—22no—
1135C22×C4—22no—
1136C22×C4—22no—
1137C22×C4—22no—
1138C22×C4—22no—
1139C22×C4—22no—
1140C22×C4—24no—
1141C22×C4—22no—
1142C22×C4—22no—
1143C22×C4—24no—
1144C22×C4—22no—
1145C22×C4—22no—
1146C22×C4—28no—
1147C22×C4—28no—
1148C22×C4—42no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—48no—
1153C22×C4—44no—
1154C22×C4—81no—
1155C22×C4—82no—
1156C22×C4—82no—
1157C22×C4—82no—
1158C22×C4C22×D411yescharacteristic
1159C22×C4C22×D411yescharacteristic
1160C22×C4C22×D411yescharacteristic
1161C22×C4C22×D412yes—
1162C22×C4C22×D414yes—
1163C22×C4C22×D414yes—
1164C22×C4C22×D411yescharacteristic
1165C22×C4C22×D411yescharacteristic
1166C22×C4C22×D411yescharacteristic
1167C22×C4C22×D411yescharacteristic
1168C22×C4C22×D411yescharacteristic
1169C22×C4C22×D411yescharacteristic
1170C22×C4C22×D412yes—
1171C22×C4C22×D412yes—
1172C22×C4C22×D411yescharacteristic
1173C22×C4C22×D411yescharacteristic
1174C22×C4C22×D411yescharacteristic
1175C22×C4C22×D414yes—
1176C22×C4C22×D414yes—
1177C22×C4C22×D414yes—
1178C22×C4C22×D411yescharacteristic
1179C22×C4C22×D411yescharacteristic
1180C22×C4C22×D411yescharacteristic
1181C22×C4H(5,𝔽2)14yes—
1182C22×C42−1+414yes—
1183C22×C4C2514yes—
1184C22×C4C2511yescharacteristic
1185C22×C4C2511yescharacteristic
1186C22×C4C2511yescharacteristic
1187Q16—416no—
1188Q16—48no—
1189SD16—416no—
1190SD16—48no—
1191SD16—48no—
1192D8—48no—
1193M16—28no—
1194M16—28no—
1195M16—28no—
1196M16—28no—
1197M16—416no—
1198C2×C8—28no—
1199C2×C8—28no—
1200C2×C8—416no—
1201C2×C8C2518yes—
1202C2×C8C2518yes—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—22no—
1210C4⋊C4—22no—
1211C4⋊C4—22no—
1212C4⋊C4—22no—
1213C4⋊C4—22no—
1214C4⋊C4—22no—
1215C4⋊C4—22no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—22no—
1219C4⋊C4—22no—
1220C4⋊C4—28no—
1221C4⋊C4—28no—
1222C4⋊C4—22no—
1223C4⋊C4—22no—
1224C4⋊C4—28no—
1225C4⋊C4—28no—
1226C4⋊C4—28no—
1227C4⋊C4—28no—
1228C4⋊C4—22no—
1229C4⋊C4—22no—
1230C4⋊C4—28no—
1231C4⋊C4—28no—
1232C4⋊C4—24no—
1233C4⋊C4—24no—
1234C4⋊C4—28no—
1235C4⋊C4—28no—
1236C4⋊C4—22no—
1237C4⋊C4—22no—
1238C4⋊C4—21no—
1239C4⋊C4—21no—
1240C4⋊C4—28no—
1241C4⋊C4—28no—
1242C4⋊C4C22×D412yes—
1243C4⋊C4C22×D412yes—
1244C4⋊C4C22×D412yes—
1245C4⋊C4C22×D412yes—
1246C4⋊C4C22×D414yes—
1247C4⋊C4C22×D414yes—
1248C4⋊C4C22×D414yes—
1249C4⋊C4C22×D414yes—
1250C4⋊C4C2514yes—
1251C4⋊C4C2512yes—
1252C4⋊C4C2512yes—
1253C4⋊C4C2514yes—
1254C4⋊C4C2514yes—
1255C22⋊C4—24no—
1256C22⋊C4—28no—
1257C22⋊C4—28no—
1258C22⋊C4—24no—
1259C22⋊C4—22no—
1260C22⋊C4—22no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—24no—
1265C22⋊C4—24no—
1266C22⋊C4—28no—
1267C22⋊C4—28no—
1268C22⋊C4—22no—
1269C22⋊C4—22no—
1270C22⋊C4—22no—
1271C22⋊C4—22no—
1272C22⋊C4—28no—
1273C22⋊C4—28no—
1274C22⋊C4—24no—
1275C22⋊C4—24no—
1276C22⋊C4—28no—
1277C22⋊C4—28no—
1278C22⋊C4—28no—
1279C22⋊C4C22×D414yes—
1280C22⋊C4C22×D414yes—
1281C22⋊C4C22×D414yes—
1282C22⋊C4C22×D414yes—
1283C22⋊C4C22×D414yes—
1284C22⋊C4C22×D414yes—
1285C42—24no—
1286C42—24no—
1287C42—22no—
1288C42—22no—
1289C42—24no—
1290C42—22no—
1291C42—22no—
1292C42—22no—
1293C42—22no—
1294C42—24no—
1295C42—24no—
1296C42—28no—
1297C42—28no—
1298C42—24no—
1299C42C22×D414yes—
1300C42C22×D411yescharacteristic
1301C42C22×D411yescharacteristic
1302C42C22×D411yescharacteristic
1303C42C22×D411yescharacteristic
1304C42C22×D411yescharacteristic
1305C42C22×D411yescharacteristic
1306C42C22×D414yes—
1307C42C22×D411yescharacteristic
1308C42C22×D411yescharacteristic
1309C42C22×D414yes—
1310C42C22×D411yescharacteristic
1311C42C22×D411yescharacteristic
1312C42C22×D414yes—
1313C42C22×D411yescharacteristic
1314C42C22×D411yescharacteristic
1315C42C22×D414yes—
1316C42C2511yescharacteristic
1317C42C2511yescharacteristic
1318C42C2514yes—
1319C42C2511yescharacteristic
1320C42C2511yescharacteristic
1321C23—24no—
1322C23—22no—
1323C23—24no—
1324C23—41no—
1325C23—41no—
1326C23—42no—
1327C23—42no—
1328C23—42no—
1329C23—42no—
1330C23—42no—
1331C23—44no—
1332C23—82no—
1333C23—82no—
1334C23#53714yes—
1335C23C23×D414yes—
1336C23C23×D411yescharacteristic
1337C23C23×D411yescharacteristic
1338C23C23×D411yescharacteristic
1339Q8—24no—
1340Q8—24no—
1341Q8—24no—
1342Q8—22no—
1343Q8—24no—
1344Q8—24no—
1345Q8—24no—
1346Q8—22no—
1347Q8—44no—
1348Q8—44no—
1349Q8—44no—
1350Q8—44no—
1351Q8—44no—
1352Q8—42no—
1353Q8—44no—
1354Q8—82no—
1355Q8—88no—
1356Q8—82no—
1357D4—28no—
1358D4—28no—
1359D4—22no—
1360D4—24no—
1361D4—22no—
1362D4—24no—
1363D4—24no—
1364D4—24no—
1365D4—44no—
1366D4—48no—
1367D4—44no—
1368D4—48no—
1369D4—44no—
1370D4—44no—
1371D4—42no—
1372D4—44no—
1373D4—82no—
1374D4—82no—
1375D4—88no—
1376D4—88no—
1377D4—88no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—28no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—28no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—44no—
1395C2×C4—41no—
1396C2×C4—41no—
1397C2×C4—42no—
1398C2×C4—41no—
1399C2×C4—41no—
1400C2×C4—41no—
1401C2×C4—41no—
1402C2×C4—41no—
1403C2×C4—44no—
1404C2×C4—41no—
1405C2×C4—41no—
1406C2×C4—42no—
1407C2×C4—44no—
1408C2×C4—44no—
1409C2×C4—42no—
1410C2×C4—44no—
1411C2×C4—42no—
1412C2×C4—42no—
1413C2×C4—44no—
1414C2×C4—44no—
1415C2×C4—44no—
1416C2×C4—44no—
1417C2×C4—44no—
1418C2×C4—48no—
1419C2×C4—44no—
1420C2×C4—48no—
1421C2×C4—44no—
1422C2×C4—82no—
1423C2×C4—82no—
1424C2×C4—88no—
1425C2×C4—88no—
1426C2×C4—82no—
1427C2×C4—82no—
1428C2×C4—82no—
1429C2×C4—82no—
1430C2×C4#53714yes—
1431C2×C4#53714yes—
1432C2×C4#53714yes—
1433C2×C4C23×D411yescharacteristic
1434C2×C4C23×D411yescharacteristic
1435C2×C4C23×D411yescharacteristic
1436C2×C4C23×D414yes—
1437C2×C4C23×D411yescharacteristic
1438C2×C4C23×D414yes—
1439C2×C4C23×D411yescharacteristic
1440C2×C4C23×D411yescharacteristic
1441C2×C4C23×D411yescharacteristic
1442C2×C4C23×D414yes—
1443C2×C4C23×D411yescharacteristic
1444C2×C4C23×D411yescharacteristic
1445C2×C4C23×D411yescharacteristic
1446C2×C4C23×D411yescharacteristic
1447C2×C4C2×H(5,𝔽2)12yes—
1448C2×C4C2×H(5,𝔽2)12yes—
1449C2×C4C2×H(5,𝔽2)12yes—
1450C2×C4C2×2−1+412yes—
1451C2×C4C2×2−1+412yes—
1452C2×C4C2×2−1+412yes—
1453C2×C4C2611yescharacteristic
1454C8—28no—
1455C8—28no—
1456C22—21no—
1457C22—21no—
1458C22—21no—
1459C22—21no—
1460C22—21no—
1461C22—21no—
1462C22—24no—
1463C22—24no—
1464C22—24no—
1465C22—44no—
1466C22—42no—
1467C22—44no—
1468C22—44no—
1469C22—42no—
1470C22—42no—
1471C22—44no—
1472C22—84no—
1473C22—84no—
1474C22—164no—
1475C22C2×#53712yes—
1476C22C2×#53712yes—
1477C22C2×#53712yes—
1478C22C24×D411yescharacteristic
1479C4—21no—
1480C4—24no—
1481C4—21no—
1482C4—21no—
1483C4—21no—
1484C4—21no—
1485C4—21no—
1486C4—21no—
1487C4—24no—
1488C4—24no—
1489C4—42no—
1490C4—44no—
1491C4—44no—
1492C4—42no—
1493C4—44no—
1494C4—44no—
1495C4—42no—
1496C4—44no—
1497C4C2×#53712yes—
1498C4C2×#53712yes—
1499C4C2×#53712yes—
1500C4#358612yes—
1501C4C22×H(5,𝔽2)11yescharacteristic
1502C4C22×2−1+411yescharacteristic
1503C2—22no—
1504C2—22no—
1505C2—22no—
1506C2—44no—
1507C2—82no—
1508C2—84no—
1509C2C22×#53711yescharacteristic
1510C2C2×#358611yescharacteristic
1511C2#6309011yescharacteristic
subgroupG/H
center, socleC22C24×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #62815C2semidirect
2. C2×#3461C2semidirect
3. #60932C2semidirect
4. #60931C2semidirect
5. #60930C2semidirect
6. #60927C2semidirect
7. #60925C2semidirect
8. #60924C2semidirect
9. #60921C2semidirect
10. #60919C2semidirect
11. #60918C2semidirect
12. #60917C2semidirect
13. #60493C2semidirect
14. #60484C2semidirect
15. C2×#3078C2semidirect
16. #60456C2semidirect
17. #60455C2semidirect
18. #60427C2semidirect
19. #60415C2semidirect
20. C2×#3037C2semidirect
21. #60099C2semidirect
25. #3512C22semidirect
26. #3511C22semidirect
27. #3511C22semidirect
28. #3510C22semidirect
29. #3509C22semidirect
30. #3508C22semidirect
47. #3461C22semidirect
48. #3461C22semidirect
52. C2×#542C22semidirect
54. C2×#541C22semidirect
63. C2×#533C22semidirect
67. C2×#529C22semidirect
72. #3263C22semidirect
73. #3262C22semidirect
74. #3261C22semidirect
75. #3260C22semidirect
76. #3258C22semidirect
77. #3258C22semidirect
78. #3258C22semidirect
79. #3257C22semidirect
80. #3256C22semidirect
81. #3255C22semidirect
82. #3254C22semidirect
83. #3252C22semidirect
84. #3252C22semidirect
85. #3251C22semidirect
86. #3250C22semidirect
87. #3249C22semidirect
88. #3248C22semidirect
89. #3248C22semidirect
90. #3247C22semidirect
91. #3246C22semidirect
92. #3084C22semidirect
93. #3083C22semidirect
94. #3082C22semidirect
95. #3081C22semidirect
96. #3080C22semidirect
97. #3080C22semidirect
98. #3079C22semidirect
99. #3079C22semidirect
100. #3079C22semidirect
101. #3078C22semidirect
102. #3078C22semidirect
103. #3078C22semidirect
104. #3078C22semidirect
105. #3078C22semidirect
106. #3078C22semidirect
107. #3077C22semidirect
108. #3077C22semidirect
109. #3076C22semidirect
110. #3076C22semidirect
111. C2×#479C22semidirect
112. C2×#477C22semidirect
113. C2×#475C22semidirect
115. #3063C22semidirect
116. #3063C22semidirect
118. #3061C22semidirect
119. #3060C22semidirect
120. #3059C22semidirect
121. #3057C22semidirect
122. #3056C22semidirect
123. #3056C22semidirect
124. #3056C22semidirect
125. #3055C22semidirect
126. #3046C22semidirect
127. #3046C22semidirect
128. #3044C22semidirect
129. #3042C22semidirect
130. #3040C22semidirect
131. #3040C22semidirect
132. #3039C22semidirect
133. #3039C22semidirect
134. #3038C22semidirect
139. #3037C22semidirect
140. #3037C22semidirect
143. #3035C22semidirect
144. #3035C22semidirect
145. C2×#464C22semidirect
146. C2×#462C22semidirect
147. C2×#460C22semidirect
150. #2906C22semidirect
151. #2906C22semidirect
152. #2906C22semidirect
153. #2906C22semidirect
155. #2905C22semidirect
158. C2×#423C22semidirect

Maximal subgroups

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

subgroupindex
#628152
C2×#34612
#609322
#609312
#609302
#609272
#609252
#609242
#609212
#609192
#609182
#609172
#604932
#604842
C2×#30782
#604562
#604552
#604272
#604152
C2×#30372
#600992