Finite Group Databasebeta

← #10574600

Subgroups — #10574600

Order 512.

6007 conjugacy classes of subgroups.

The subgroup lattice has 861 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62694C211yesmaximal, characteristic
2#60346C218yesmaximal, complemented
3#60338C214yesmaximal, complemented
4#60327C218yesmaximal, complemented
5#60318C214yesmaximal, complemented
6#60315C218yesmaximal, complemented
7#60281C211yesmaximal, characteristic, complemented
8#60281C212yesmaximal, complemented
9#60280C214yesmaximal, complemented
10#60279C218yesmaximal, complemented
11#60210C218yesmaximal, complemented
12#60205C214yesmaximal, complemented
13#60204C211yesmaximal, characteristic, complemented
14#60204C212yesmaximal, complemented
15#3531C414yes—
16#3531C414yes—
17#3531C414yes—
18#3531C2212yes—
19#3531C2214yes—
20#3529C418yes—
21#3529C414yes—
22#3529C414yes—
23#3529C414yes—
24#3529C2214yes—
25#3529C2212yes—
26#3529C2214yes—
27#3444C2212yes—
28#3444C2211yescharacteristic
29#3444C2214yes—
30#3444C2218yes—
31#2995C2218yescomplemented
32#2995C2218yescomplemented
33#2995C2218yescomplemented
34#2994C22116yescomplemented
35#2994C22116yescomplemented
36#2993C22116yescomplemented
37#2993C22116yescomplemented
38#2992C22116yescomplemented
39#2992C22116yescomplemented
40#2987C2212yescomplemented
41#2987C2214yescomplemented
42#2986C2218yescomplemented
43#2985C22116yescomplemented
44#2981C22116yes—
45#2980C2212yes—
46#2980C2214yes—
47#2979C2218yes—
48#2978C2214yescomplemented
49#2978C2218yescomplemented
50#2977C2218yescomplemented
51#2977C2218yescomplemented
52#2976C22116yescomplemented
53#2976C22116yescomplemented
54#2969C22116yescomplemented
55#2969C22116yescomplemented
56#2968C22116yescomplemented
57#2968C22116yescomplemented
58#2967C22116yescomplemented
59#2967C22116yescomplemented
60#2966C2218yescomplemented
61#2966C2218yescomplemented
62#2966C2218yescomplemented
63#2965C2214yescomplemented
64#2965C2214yescomplemented
65#2965C2214yescomplemented
66#2965C2218yescomplemented
67#2965C2218yescomplemented
68#2965C2218yescomplemented
69#2965C2218yescomplemented
70#2965C2218yescomplemented
71#2965C2218yescomplemented
72C8×#41C2214yescomplemented
73C8×#41C2214yescomplemented
74C8×#41C2214yescomplemented
75C8×#41C2218yescomplemented
76#2962C22116yescomplemented
77#2961C2218yescomplemented
78#2960C2212yescomplemented
79#2960C2214yescomplemented
80#2935C22116yes—
81#2933C22116yescomplemented
82#2933C22116yescomplemented
83#2932C2218yes—
84#2931C2212yes—
85#2931C2214yes—
86#2930C2218yescomplemented
87#2930C2218yescomplemented
88#2929C2214yescomplemented
89#2929C2218yescomplemented
90#2922C2214yescomplemented
91#2922C2212yescomplemented
92#2922C2214yescomplemented
93#2922C2214yescomplemented
94#2922C2218yescomplemented
95#2922C2218yescomplemented
96#2920C2211yescharacteristic, complemented
97#2920C2212yescomplemented
98#2920C2214yescomplemented
99C2×#431C2218yescomplemented
100C4×#131C2212yescomplemented
101C4×#131C2214yescomplemented
102C4×#131C2214yescomplemented
103C2×C4×M16C2214yescomplemented
104C22×C4×C8C2211yescharacteristic, complemented
105C2×#131C2314yes—
106C2×#131C2318yes—
107C2×#131C2318yes—
108C22×M16C2318yes—
109C23×C8C2312yes—
110#564C2×C412yes—
111#564C2×C414yes—
112#563C2×C418yes—
113#563C2×C414yes—
114#563C2×C418yes—
115#563C2×C418yes—
116#563C2×C418yes—
117#563C2×C414yes—
118#563C2×C418yes—
119#563C2×C418yes—
120#563C2×C414yes—
121#563C2×C418yes—
122#563C2×C414yes—
123#563C2×C414yes—
124#563C2×C412yes—
125#563C2×C414yes—
126#563C2×C418yes—
127#562C2×C418yes—
128#562C2×C412yes—
129#562C2×C418yes—
130#562C2×C418yes—
131#562C2×C414yes—
132#562C2×C418yes—
133#562C2×C418yes—
134#562C2×C418yes—
135#562C2×C418yes—
136#562C2×C414yes—
137#562C2×C418yes—
138#562C2×C418yes—
139#562C2×C414yes—
140#562C2×C414yes—
141H(3,𝔽4)C2×C414yes—
142H(3,𝔽4)C2×C412yes—
143H(3,𝔽4)C2×C414yes—
144#560C2×C418yes—
145#560C2×C414yes—
146#560C2×C418yes—
147#560C2×C414yes—
148#560C2×C418yes—
149#560C2×C414yes—
150#560C2×C418yes—
151#560C2×C418yes—
152#560C2×C418yes—
153#533C2×C412yes—
154#533C2×C412yes—
155#533C2×C412yes—
156#533C2×C418yes—
157#533C2×C418yes—
158#533C2×C418yes—
159#533C2311yescharacteristic
160#533C2312yes—
161#533C2314yes—
162#533C2318yes—
163#532C2×C412yes—
164#532C2×C412yes—
165#532C2×C412yes—
166#532C2×C418yes—
167#532C2×C418yes—
168#532C2×C418yes—
169#532C2311yescharacteristic
170#532C2312yes—
171#532C2314yes—
172#532C2318yes—
173#529C2×C414yes—
174#529C2×C414yes—
175#529C2×C414yes—
176#529C2×C418yes—
177#529C2×C418yes—
178#529C2×C418yes—
179#529C2×C418yes—
180#529C2×C418yes—
181#529C2×C418yes—
182#529C2×C414yes—
183#529C2×C414yes—
184#529C2×C414yes—
185#529C2×C418yes—
186#529C2×C418yes—
187#529C2×C418yes—
188#529C2×C418yes—
189#529C2×C418yes—
190#529C2×C418yes—
191#529C2314yes—
192#529C2314yes—
193#529C2314yes—
194#529C2318yes—
195#529C2318yes—
196#529C2318yes—
197#529C2318yes—
198#529C2318yes—
199#529C2318yes—
200#525C2×C414yes—
201#525C2×C414yes—
202#525C2×C414yes—
203#525C2×C418yes—
204#525C2×C418yes—
205#525C2×C418yes—
206#525C2×C418yes—
207#525C2×C418yes—
208#525C2×C418yes—
209#525C2312yes—
210#525C2314yes—
211#525C2314yes—
212#525C2314yes—
213#525C2318yes—
214#525C2318yes—
215C4×#41C2314yes—
216C4×#41C2314yes—
217C4×#41C2314yes—
218C4×#41C2318yes—
219C4×#41C2312yes—
220C4×#41C2314yes—
221C4×#41C2314yes—
222C22×C42C2311yescharacteristic
223C22×C42C2314yes—
224#446C2318yes—
225#446C2318yes—
226#446C2318yes—
227#446C23116yes—
228#446C23116yes—
229#446C23116yes—
230#446C23116yes—
231#446C23116yes—
232#446C23116yes—
233C8×Q8C2318yes—
234C8×Q8C2318yes—
235C8×Q8C2318yes—
236C8×Q8C23116yes—
237#436C2318yes—
238#436C23116yes—
239#436C23116yes—
240#436C23116yes—
241#436C2318yes—
242#436C2318yes—
243#436C23116yes—
244#436C23116yes—
245#436C23116yes—
246#435C23116yes—
247#435C23116yes—
248#435C23116yes—
249#435C23116yes—
250#435C23116yes—
251#435C23116yes—
252#435C23116yes—
253#435C23116yes—
254#435C23116yes—
255#435C23116yes—
256#435C23116yes—
257#435C23116yes—
258#435C23116yes—
259#435C23116yes—
260#435C23116yes—
261C8×D4C23116yes—
262C8×D4C23116yes—
263C8×D4C23116yes—
264C8×D4C2318yes—
265C8×D4C2318yes—
266C8×D4C2318yes—
267C8×D4C23116yes—
268C8×D4C23116yes—
269C8×D4C23116yes—
270#433C23116yes—
271#433C2318yes—
272#433C23116yes—
273#433C2318yes—
274#433C2318yes—
275#433C23116yes—
276#433C23116yes—
277#433C23116yes—
278#433C23116yes—
279#432C2314yes—
280#432C2314yes—
281#432C2314yes—
282#432C23116yes—
283#431C2318yes—
284#431C2318yes—
285#431C2318yes—
286#431C2318yes—
287#431C23116yes—
288#431C23116yes—
289#431C2314yes—
290#431C2314yes—
291#431C2314yes—
292#431C2318yes—
293#431C2318yes—
294#424C2318yes—
295#424C2314yes—
296#424C2318yes—
297#424C2318yes—
298#424C23116yes—
299#424C23116yes—
300#423C2312yes—
301#423C2314yes—
302#423C2318yes—
303C2×C4⋊C8C23116yes—
304#408C2318yes—
305#408C2314yes—
306#408C2318yes—
307#408C2318yes—
308#408C23116yes—
309#408C23116yes—
310#407C2314yes—
311#407C2312yes—
312#407C2318yes—
313C2×C22⋊C8C23116yes—
314#405C2314yes—
315#405C2318yes—
316#405C2318yes—
317#405C2318yes—
318#405C23116yes—
319#405C23116yes—
320C4×M16C2318yes—
321C4×M16C2318yes—
322C4×M16C23116yes—
323C4×M16C2312yes—
324C4×M16C2314yes—
325C4×M16C2314yes—
326C4×M16C2314yes—
327C2×#97C2318yes—
328C2×C4×C8C2312yes—
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2312yes—
332C2×C4×C8C2312yes—
333C2×C4×C8C2314yes—
334C2×C4×C8C2314yes—
335C2×C4×C8C2314yes—
336C2×C4×C8C2318yes—
337C2×C4×C8C2318yes—
338C2×#41C22×C414yes—
339C2×#41C22×C414yes—
340C2×#41C22×C414yes—
341C2×#41C22×C418yes—
342C2×#41C2412yes—
343C2×#41C2414yes—
344C2×#41C2414yes—
345C23×C4C22×C412yes—
346C23×C4C22×C418yes—
347C23×C4C2411yescharacteristic
348C23×C4C2414yes—
349#131—48no—
350#131—416no—
351#131—416no—
352C2×M16—416no—
353C2×M16C24116yes—
354C2×M16C24116yes—
355C2×M16C2414yes—
356C2×M16C2418yes—
357C2×M16C2418yes—
358C2×M16C2418yes—
359C22×C8—44no—
360C22×C8C2414yes—
361C22×C8C2412yes—
362C22×C8C2418yes—
363C22×C8C2412yes—
364C22×C8C2414yes—
365C22×C8C2418yes—
366C22×C8C24116yes—
367C22×C8C24116yes—
368C4⋊Q8C22×C412yes—
369C4⋊Q8C22×C412yes—
370C4⋊Q8C22×C412yes—
371C4⋊Q8C22×C418yes—
372C4⋊Q8C22×C418yes—
373C4⋊Q8C22×C418yes—
374C4⋊Q8C22×C411yescharacteristic
375C4⋊Q8C22×C412yes—
376C4⋊Q8C22×C414yes—
377C4⋊Q8C22×C418yes—
378#127C22×C411yescharacteristic
379#127C22×C412yes—
380#127C22×C414yes—
381#127C22×C418yes—
382#126C22×C418yes—
383#126C22×C418yes—
384#126C22×C418yes—
385#126C22×C418yes—
386#126C22×C418yes—
387#126C22×C418yes—
388#126C22×C418yes—
389#126C22×C418yes—
390#126C22×C418yes—
391#126C22×C418yes—
392#126C22×C418yes—
393#126C22×C418yes—
394#126C22×C418yes—
395#126C22×C418yes—
396#126C22×C418yes—
397#125C22×C412yes—
398#125C22×C414yes—
399#125C22×C418yes—
400#125C22×C418yes—
401#125C22×C418yes—
402#125C22×C414yes—
403#125C22×C414yes—
404#125C22×C414yes—
405#125C22×C418yes—
406#125C22×C418yes—
407#125C22×C418yes—
408#125C22×C418yes—
409#125C22×C418yes—
410#125C22×C418yes—
411#124C22×C412yes—
412#124C22×C414yes—
413#124C22×C414yes—
414#124C22×C414yes—
415#124C22×C418yes—
416#124C22×C418yes—
417#124C22×C414yes—
418#124C22×C414yes—
419#124C22×C414yes—
420#124C22×C418yes—
421#124C22×C418yes—
422#124C22×C418yes—
423#124C22×C418yes—
424#124C22×C418yes—
425#124C22×C418yes—
426#123C22×C418yes—
427#123C22×C418yes—
428#123C22×C418yes—
429#123C22×C418yes—
430#123C22×C418yes—
431#123C22×C418yes—
432#123C22×C418yes—
433#123C22×C418yes—
434#123C22×C418yes—
435#123C22×C418yes—
436#123C22×C418yes—
437#123C22×C418yes—
438#123C22×C418yes—
439#123C22×C418yes—
440#123C22×C418yes—
441#123C22×C418yes—
442#123C22×C414yes—
443#123C22×C414yes—
444#123C22×C414yes—
445#123C22×C418yes—
446#123C22×C418yes—
447#123C22×C418yes—
448#123C22×C418yes—
449#123C22×C418yes—
450C22⋊Q8C22×C414yes—
451C22⋊Q8C22×C414yes—
452C22⋊Q8C22×C414yes—
453C22⋊Q8C22×C418yes—
454C22⋊Q8C22×C418yes—
455C22⋊Q8C22×C418yes—
456C22⋊Q8C22×C418yes—
457C22⋊Q8C22×C418yes—
458C22⋊Q8C22×C418yes—
459C22⋊Q8C22×C414yes—
460C22⋊Q8C22×C414yes—
461C22⋊Q8C22×C414yes—
462C22⋊Q8C22×C418yes—
463C22⋊Q8C22×C418yes—
464C22⋊Q8C22×C418yes—
465C22⋊Q8C22×C418yes—
466C22⋊Q8C22×C418yes—
467C22⋊Q8C22×C418yes—
468C22⋊Q8C22×C414yes—
469C22⋊Q8C22×C414yes—
470C22⋊Q8C22×C414yes—
471C22⋊Q8C22×C418yes—
472C22⋊Q8C22×C418yes—
473C22⋊Q8C22×C418yes—
474C22⋊Q8C22×C418yes—
475C22⋊Q8C22×C418yes—
476C22⋊Q8C22×C418yes—
477#121C22×C414yes—
478#121C22×C414yes—
479#121C22×C414yes—
480#121C22×C418yes—
481#121C22×C418yes—
482#121C22×C418yes—
483#121C22×C418yes—
484#121C22×C418yes—
485#121C22×C418yes—
486#121C22×C414yes—
487#121C22×C414yes—
488#121C22×C414yes—
489#121C22×C418yes—
490#121C22×C418yes—
491#121C22×C418yes—
492#121C22×C418yes—
493#121C22×C418yes—
494#121C22×C418yes—
495#121C22×C414yes—
496#121C22×C414yes—
497#121C22×C414yes—
498#121C22×C418yes—
499#121C22×C418yes—
500#121C22×C418yes—
501#121C22×C418yes—
502#121C22×C418yes—
503#121C22×C418yes—
504#120C22×C418yes—
505#120C22×C414yes—
506#120C22×C414yes—
507#120C22×C414yes—
508#120C22×C418yes—
509#120C22×C418yes—
510#120C22×C418yes—
511#120C22×C418yes—
512#120C22×C418yes—
513C4×Q8C22×C414yes—
514C4×Q8C22×C414yes—
515C4×Q8C22×C414yes—
516C4×Q8C22×C418yes—
517C4×Q8C22×C414yes—
518C4×Q8C22×C414yes—
519C4×Q8C22×C414yes—
520C4×Q8C22×C418yes—
521C4×Q8C2414yes—
522C4×Q8C2414yes—
523C4×Q8C2414yes—
524C4×Q8C2418yes—
525C4×D4C22×C418yes—
526C4×D4C22×C414yes—
527C4×D4C22×C418yes—
528C4×D4C22×C414yes—
529C4×D4C22×C418yes—
530C4×D4C22×C414yes—
531C4×D4C22×C418yes—
532C4×D4C22×C418yes—
533C4×D4C22×C418yes—
534C4×D4C22×C418yes—
535C4×D4C22×C414yes—
536C4×D4C22×C418yes—
537C4×D4C22×C418yes—
538C4×D4C22×C414yes—
539C4×D4C22×C414yes—
540C4×D4C22×C418yes—
541C4×D4C22×C418yes—
542C4×D4C22×C418yes—
543C4×D4C2418yes—
544C4×D4C2418yes—
545C4×D4C2418yes—
546C4×D4C2414yes—
547C4×D4C2418yes—
548C4×D4C2418yes—
549C4×D4C2414yes—
550C4×D4C2414yes—
551C4×D4C2418yes—
552#117C22×C414yes—
553#117C22×C418yes—
554#117C22×C414yes—
555#117C22×C418yes—
556#117C22×C414yes—
557#117C22×C418yes—
558#117C22×C418yes—
559#117C22×C418yes—
560#117C22×C418yes—
561#117C2412yes—
562#117C2414yes—
563#117C2414yes—
564#117C2414yes—
565#117C2418yes—
566#117C2418yes—
567C2×C42C22×C412yes—
568C2×C42C22×C412yes—
569C2×C42C22×C412yes—
570C2×C42C22×C418yes—
571C2×C42C22×C418yes—
572C2×C42C22×C418yes—
573C2×C42C2411yescharacteristic
574C2×C42C2412yes—
575C2×C42C2414yes—
576C2×C42C2418yes—
577C2×C42C2412yes—
578C2×C42C2411yescharacteristic
579C2×C42C2414yes—
580C2×C42C2418yes—
581C4⋊C8C24116yes—
582C4⋊C8C24116yes—
583C4⋊C8C24116yes—
584C4⋊C8C24116yes—
585C4⋊C8C2418yes—
586C4⋊C8C2418yes—
587C4⋊C8C2418yes—
588C4⋊C8C24116yes—
589C4⋊C8C24116yes—
590C22⋊C8C24116yes—
591C22⋊C8C24116yes—
592C22⋊C8C24116yes—
593C22⋊C8C24116yes—
594C22⋊C8C2418yes—
595C22⋊C8C2418yes—
596C22⋊C8C2418yes—
597C22⋊C8C24116yes—
598C22⋊C8C24116yes—
599#97C24116yes—
600#97C24116yes—
601#97C2418yes—
602#97C2414yes—
603#97C2418yes—
604#97C2418yes—
605C4×C8C2414yes—
606C4×C8C2412yes—
607C4×C8C2412yes—
608C4×C8C2414yes—
609C4×C8C2418yes—
610C4×C8C2418yes—
611C4×C8C24116yes—
612C4×C8C24116yes—
613C4×C8C2411yescharacteristic
614C4×C8C2412yes—
615C4×C8C2411yescharacteristic
616C4×C8C2414yes—
617C4×C8C2418yes—
618C24C23×C411yescharacteristic
619C24C23×C414yes—
620#41—44no—
621#41—48no—
622#41—48no—
623#41—48no—
624#41—48no—
625#41—48no—
626#41—416no—
627C2×Q8C23×C412yes—
628C2×Q8C23×C414yes—
629C2×Q8C23×C414yes—
630C2×Q8C23×C414yes—
631C2×Q8C23×C414yes—
632C2×Q8C23×C414yes—
633C2×Q8C23×C418yes—
634C2×D4C23×C414yes—
635C2×D4C23×C418yes—
636C2×D4C23×C412yes—
637C2×D4C23×C418yes—
638C2×D4C23×C414yes—
639C2×D4C23×C414yes—
640C2×D4C23×C418yes—
641C2×D4C23×C418yes—
642C2×D4C23×C418yes—
643C2×D4C23×C414yes—
644C2×D4C23×C418yes—
645C2×D4C23×C418yes—
646C2×D4C23×C414yes—
647C2×D4C23×C414yes—
648C2×D4C23×C418yes—
649C22×C4—42no—
650C22×C4—48no—
651C22×C4—44no—
652C22×C4—416no—
653C22×C4C23×C412yes—
654C22×C4C23×C412yes—
655C22×C4C23×C412yes—
656C22×C4C23×C418yes—
657C22×C4C23×C418yes—
658C22×C4C23×C418yes—
659C22×C4C23×C411yescharacteristic
660C22×C4C23×C412yes—
661C22×C4C23×C418yes—
662C22×C4C23×C414yes—
663C22×C4C23×C412yes—
664C22×C4C23×C412yes—
665C22×C4C23×C412yes—
666C22×C4C23×C418yes—
667C22×C4C23×C418yes—
668C22×C4C23×C418yes—
669C22×C4C2514yes—
670C22×C4C2512yes—
671C22×C4C2511yescharacteristic
672C22×C4C2518yes—
673M16—232no—
674M16—416no—
675M16—48no—
676M16—44no—
677M16—48no—
678M16—48no—
679C2×C8—28no—
680C2×C8—24no—
681C2×C8—216no—
682C2×C8—42no—
683C2×C8—44no—
684C2×C8—48no—
685C2×C8—416no—
686C2×C8—416no—
687C2×C8C2514yes—
688C2×C8C2512yes—
689C2×C8C2518yes—
690C2×C8C25116yes—
691C2×C8C2512yes—
692C4⋊C4C23×C414yes—
693C4⋊C4C23×C418yes—
694C4⋊C4C23×C414yes—
695C4⋊C4C23×C418yes—
696C4⋊C4C23×C414yes—
697C4⋊C4C23×C418yes—
698C4⋊C4C23×C418yes—
699C4⋊C4C23×C418yes—
700C4⋊C4C23×C418yes—
701C4⋊C4C23×C418yes—
702C4⋊C4C23×C418yes—
703C4⋊C4C23×C418yes—
704C4⋊C4C23×C414yes—
705C4⋊C4C23×C418yes—
706C4⋊C4C23×C418yes—
707C4⋊C4C23×C414yes—
708C4⋊C4C23×C414yes—
709C4⋊C4C23×C418yes—
710C4⋊C4C23×C414yes—
711C4⋊C4C23×C414yes—
712C4⋊C4C23×C414yes—
713C4⋊C4C23×C418yes—
714C4⋊C4C23×C418yes—
715C4⋊C4C23×C418yes—
716C4⋊C4C23×C418yes—
717C4⋊C4C23×C418yes—
718C4⋊C4C23×C418yes—
719C22⋊C4C23×C418yes—
720C22⋊C4C23×C418yes—
721C22⋊C4C23×C418yes—
722C22⋊C4C23×C418yes—
723C22⋊C4C23×C418yes—
724C22⋊C4C23×C418yes—
725C22⋊C4C23×C418yes—
726C22⋊C4C23×C418yes—
727C22⋊C4C23×C418yes—
728C22⋊C4C23×C418yes—
729C22⋊C4C23×C418yes—
730C22⋊C4C23×C418yes—
731C22⋊C4C23×C418yes—
732C22⋊C4C23×C418yes—
733C22⋊C4C23×C418yes—
734C22⋊C4C23×C414yes—
735C22⋊C4C23×C418yes—
736C22⋊C4C23×C418yes—
737C22⋊C4C23×C414yes—
738C22⋊C4C23×C414yes—
739C22⋊C4C23×C418yes—
740C22⋊C4C23×C418yes—
741C22⋊C4C23×C418yes—
742C22⋊C4C23×C418yes—
743C42C23×C412yes—
744C42C23×C412yes—
745C42C23×C412yes—
746C42C23×C418yes—
747C42C23×C418yes—
748C42C23×C418yes—
749C42C23×C412yes—
750C42C23×C411yescharacteristic
751C42C23×C414yes—
752C42C23×C418yes—
753C42C23×C412yes—
754C42C23×C411yescharacteristic
755C42C23×C414yes—
756C42C23×C418yes—
757C42C2512yes—
758C42C2511yescharacteristic
759C42C2514yes—
760C42C2518yes—
761C42C2511yescharacteristic
762C23—42no—
763C23—41no—
764C23—48no—
765C23—44no—
766C23C24×C412yes—
767C23C24×C411yescharacteristic
768C23C24×C414yes—
769C23C24×C418yes—
770Q8—44no—
771Q8—44no—
772Q8—44no—
773Q8—48no—
774Q8—42no—
775Q8—44no—
776Q8—44no—
777D4—48no—
778D4—48no—
779D4—48no—
780D4—44no—
781D4—48no—
782D4—48no—
783D4—44no—
784D4—44no—
785D4—48no—
786D4—44no—
787D4—42no—
788D4—44no—
789D4—44no—
790D4—48no—
791D4—48no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—28no—
795C2×C4—216no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—216no—
801C2×C4—216no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—48no—
806C2×C4—48no—
807C2×C4—48no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—48no—
811C2×C4—44no—
812C2×C4C24×C412yes—
813C2×C4C24×C411yescharacteristic
814C2×C4C24×C414yes—
815C2×C4C24×C418yes—
816C2×C4C24×C412yes—
817C2×C4C24×C412yes—
818C2×C4C24×C412yes—
819C2×C4C24×C418yes—
820C2×C4C24×C418yes—
821C2×C4C24×C418yes—
822C2×C4C24×C412yes—
823C2×C4C2611yescharacteristic
824C8—24no—
825C8—22no—
826C8—28no—
827C8—216no—
828C8#58514yes—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—28no—
833C22—28no—
834C22—28no—
835C22—22no—
836C22—21no—
837C22—24no—
838C22—28no—
839C22—44no—
840C22—88no—
841C22C25×C411yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—28no—
846C4—28no—
847C4—28no—
848C4—22no—
849C4—21no—
850C4—24no—
851C4—28no—
852C4#357314yes—
853C4C2×#58512yes—
854C2—42no—
855C2—41no—
856C2—44no—
857C2—48no—
858C2C4×#58511yescharacteristic
859C2C2×#357312yes—
subgroupG/H
centerC42C25
commutator, socleC22C25×C4
Frattini, cosocleC2×C4C26
prime radical#62694C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C42 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60346C2semidirect
3. #60338C2semidirect
4. #60327C2semidirect
5. #60318C2semidirect
6. #60315C2semidirect
7. #60281C2semidirect
8. #60281C2semidirect
9. #60280C2semidirect
10. #60279C2semidirect
11. #60210C2semidirect
12. #60205C2semidirect
13. #60204C2semidirect
14. #60204C2semidirect
31. #2995C22semidirect
32. #2995C22semidirect
33. #2995C22semidirect
34. #2994C22semidirect
35. #2994C22semidirect
36. #2993C22semidirect
37. #2993C22semidirect
38. #2992C22semidirect
39. #2992C22semidirect
40. #2987C22semidirect
41. #2987C22semidirect
42. #2986C22semidirect
43. #2985C22semidirect
48. #2978C22semidirect
49. #2978C22semidirect
50. #2977C22semidirect
51. #2977C22semidirect
52. #2976C22semidirect
53. #2976C22semidirect
54. #2969C22semidirect
55. #2969C22semidirect
56. #2968C22semidirect
57. #2968C22semidirect
58. #2967C22semidirect
59. #2967C22semidirect
60. #2966C22semidirect
61. #2966C22semidirect
62. #2966C22semidirect
63. #2965C22semidirect
64. #2965C22semidirect
65. #2965C22semidirect
66. #2965C22semidirect
67. #2965C22semidirect
68. #2965C22semidirect
69. #2965C22semidirect
70. #2965C22semidirect
71. #2965C22semidirect
72. C8×#41C22semidirect
73. C8×#41C22semidirect
74. C8×#41C22semidirect
75. C8×#41C22semidirect
76. #2962C22semidirect
77. #2961C22semidirect
78. #2960C22semidirect
79. #2960C22semidirect
81. #2933C22semidirect
82. #2933C22semidirect
86. #2930C22semidirect
87. #2930C22semidirect
88. #2929C22semidirect
89. #2929C22semidirect
90. #2922C22semidirect
91. #2922C22semidirect
92. #2922C22semidirect
93. #2922C22semidirect
94. #2922C22semidirect
95. #2922C22semidirect
96. #2920C22semidirect
97. #2920C22semidirect
98. #2920C22semidirect
99. C2×#431C22semidirect
100. C4×#131C22semidirect
101. C4×#131C22semidirect
102. C4×#131C22semidirect
103. C2×C4×M16C22semidirect
104. C22×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#626942
#603462
#603382
#603272
#603182
#603152
#602812
#602802
#602792
#602102
#602052
#602042