Finite Group Databasebeta

← #10574606

Subgroups — #10574606

Order 512.

6007 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62762C211yesmaximal, characteristic
2#60344C214yesmaximal, complemented
3#60337C212yesmaximal, complemented
4#60331C212yesmaximal, complemented
5#60330C214yesmaximal, complemented
6#60326C214yesmaximal, complemented
7#60320C211yesmaximal, characteristic, complemented
8#60317C211yesmaximal, characteristic, complemented
9#60315C214yesmaximal, complemented
10#60308C211yesmaximal, characteristic, complemented
11#60307C214yesmaximal, complemented
12#60306C214yesmaximal, complemented
13#60305C211yesmaximal, characteristic, complemented
14#60302C214yesmaximal, complemented
15#60300C214yesmaximal, complemented
16#60296C214yesmaximal, complemented
17#60295C212yesmaximal, complemented
18#60287C211yesmaximal, characteristic, complemented
19#60218C214yesmaximal, complemented
20#60215C214yesmaximal, complemented
21#60206C214yesmaximal, complemented
22#60204C212yesmaximal, complemented
23#60204C211yesmaximal, characteristic, complemented
24#3566C418yes—
25#3565C414yes—
26#3562C414yes—
27#3555C412yes—
28#3554C412yes—
29#3547C412yes—
30#3546C412yes—
31#3540C414yes—
32#3539C414yes—
33#3529C2214yes—
34#3483C2211yescharacteristic
35#3482C2212yes—
36#3481C2211yescharacteristic
37#3480C2214yes—
38#3475C2214yes—
39#3461C2214yes—
40#3460C2214yes—
41#3455C2214yes—
42#3444C2211yescharacteristic
43#3444C2212yes—
44#2995C2218yescomplemented
45#2995C2218yescomplemented
46#2995C2218yescomplemented
47#2994C2218yescomplemented
48#2994C2214yescomplemented
49#2994C2214yescomplemented
50#2993C2214yescomplemented
51#2993C2214yescomplemented
52#2993C2218yescomplemented
53#2993C2214yescomplemented
54#2993C2218yescomplemented
55#2993C2214yescomplemented
56#2992C2218yescomplemented
57#2992C2218yescomplemented
58#2991C2212yes—
59#2991C2212yescomplemented
60#2991C2214yescomplemented
61#2990C2212yes—
62#2990C2212yescomplemented
63#2990C2214yescomplemented
64#2989C2214yescomplemented
65#2989C2214yescomplemented
66#2989C2214yescomplemented
67#2989C2214yescomplemented
68#2986C2212yescomplemented
69#2986C2214yescomplemented
70#2985C2214yescomplemented
71#2985C2218yescomplemented
72#2985C2214yescomplemented
73#2984C2214yescomplemented
74#2983C2214yescomplemented
75#2981C2214yes—
76#2981C2218yescomplemented
77#2981C2214yescomplemented
78#2980C2214yescomplemented
79#2980C2218yescomplemented
80#2979C2211yescharacteristic
81#2979C2211yescharacteristic
82#2979C2214yescomplemented
83#2979C2214yescomplemented
84#2978C2214yes—
85#2978C2214yescomplemented
86#2978C2218yescomplemented
87#2978C2218yescomplemented
88#2977C2214yes—
89#2976C2218yescomplemented
90#2976C2218yescomplemented
91#2975C2214yescomplemented
92#2974C2214yescomplemented
93#2971C2214yescomplemented
94#2971C2214yescomplemented
95#2970C2214yescomplemented
96#2970C2214yescomplemented
97#2969C2214yes—
98#2969C2214yescomplemented
99#2969C2214yescomplemented
100#2969C2218yescomplemented
101#2969C2218yescomplemented
102#2969C2214yescomplemented
103#2968C2218yescomplemented
104#2968C2218yescomplemented
105#2967C2218yescomplemented
106#2967C2218yescomplemented
107#2967C2218yescomplemented
108#2967C2218yescomplemented
109#2966C2212yes—
110#2966C2212yes—
111#2966C2214yescomplemented
112#2966C2212yescomplemented
113#2966C2214yescomplemented
114#2966C2212yescomplemented
115#2966C2214yescomplemented
116#2966C2214yescomplemented
117#2966C2218yescomplemented
118#2966C2218yescomplemented
119#2966C2218yescomplemented
120#2966C2214yescomplemented
121#2966C2218yescomplemented
122#2966C2214yescomplemented
123#2966C2218yescomplemented
124#2965C2212yes—
125#2965C2214yescomplemented
126#2965C2212yescomplemented
127#2965C2214yescomplemented
128C8×#41C2212yes—
129C8×#41C2214yescomplemented
130C8×#41C2214yescomplemented
131C8×#41C2212yescomplemented
132C8×#41C2214yescomplemented
133C8×#41C2214yescomplemented
134Q8×M16C2214yescomplemented
135#2962C2214yescomplemented
136#2961C2214yescomplemented
137#2960C2212yescomplemented
138#2960C2211yescharacteristic, complemented
139#2960C2211yescharacteristic, complemented
140#2960C2212yescomplemented
141#2960C2214yescomplemented
142#2960C2214yescomplemented
143C2×C8×Q8C2214yescomplemented
144#2935C2218yescomplemented
145#2935C2214yescomplemented
146D4×M16C2214yescomplemented
147#2933C2218yescomplemented
148#2932C2214yescomplemented
149#2931C2211yescharacteristic
150#2931C2212yes—
151#2931C2211yescharacteristic
152#2931C2212yes—
153#2931C2214yescomplemented
154#2931C2218yescomplemented
155#2931C2214yescomplemented
156#2930C2214yes—
157#2930C2214yescomplemented
158#2929C2214yes—
159#2929C2212yescomplemented
160#2929C2214yescomplemented
161#2929C2212yescomplemented
162#2929C2214yescomplemented
163#2929C2214yescomplemented
164#2929C2218yescomplemented
165C2×C8×D4C2214yescomplemented
166#2925C2214yescomplemented
167#2925C2214yescomplemented
168#2925C2218yescomplemented
169#2924C2218yescomplemented
170#2923C2214yescomplemented
171#2923C2214yescomplemented
172#2922C2212yescomplemented
173#2922C2214yescomplemented
174#2921C2214yescomplemented
175#2920C2212yescomplemented
176#2920C2211yescharacteristic, complemented
177C4×#131C2212yescomplemented
178C4×#131C2214yescomplemented
179C4×#131C2214yescomplemented
180C2×#405C2214yescomplemented
181C22×C4×C8C2211yescharacteristic, complemented
182C2×#131C2312yes—
183C2×#131C2314yes—
184C2×#131C2312yes—
185C2×#131C2314yes—
186C2×#131C2314yes—
187C2×#131C2314yes—
188C22×M16C2314yes—
189C23×C8C2311yescharacteristic
190C23×C8C2311yescharacteristic
191C23×C8C2314yes—
192#563C2×C418yes—
193#563C2×C414yes—
194#562C2×C418yes—
195#562C2×C418yes—
196#562C2×C418yes—
197H(3,𝔽4)C2×C414yes—
198#560C2×C414yes—
199#560C2×C418yes—
200#560C2×C418yes—
201#560C2×C414yes—
202#559C2×C418yes—
203#559C2×C414yes—
204#559C2×C411yescharacteristic
205Q82C2×C411yescharacteristic
206#557C2×C414yes—
207#557C2×C412yes—
208#556C2×C414yes—
209#556C2×C414yes—
210#556C2×C418yes—
211#556C2×C414yes—
212#556C2×C412yes—
213#555C2×C414yes—
214#555C2×C414yes—
215#555C2×C411yescharacteristic
216#555C2×C414yes—
217#554C2×C414yes—
218#554C2×C412yes—
219#553C2×C418yes—
220#553C2×C414yes—
221#553C2×C418yes—
222#553C2×C414yes—
223#553C2×C418yes—
224#553C2×C414yes—
225#552C2×C414yes—
226#552C2×C414yes—
227#552C2×C418yes—
228#552C2×C414yes—
229#552C2×C418yes—
230#551C2×C418yes—
231#551C2×C418yes—
232#551C2×C414yes—
233#550C2×C414yes—
234#550C2×C414yes—
235#550C2×C412yes—
236D4×Q8C2×C412yes—
237#548C2×C414yes—
238#548C2×C414yes—
239#548C2×C414yes—
240#547C2×C414yes—
241#547C2×C414yes—
242#547C2×C412yes—
243#546C2×C414yes—
244#546C2×C414yes—
245#546C2×C414yes—
246D42C2×C411yescharacteristic
247#544C2×C414yes—
248#544C2×C414yes—
249#542C2×C418yes—
250#542C2×C418yes—
251#542C2×C414yes—
252#542C2×C414yes—
253#542C2×C418yes—
254#542C2×C414yes—
255#542C2×C418yes—
256#542C2×C414yes—
257#541C2×C418yes—
258#541C2×C414yes—
259#541C2×C414yes—
260#541C2×C418yes—
261#540C2×C418yes—
262#540C2×C414yes—
263#540C2×C418yes—
264#540C2×C414yes—
265#539C2×C418yes—
266#539C2×C418yes—
267#539C2×C418yes—
268#539C2×C418yes—
269#538C2×C418yes—
270#538C2×C418yes—
271#538C2×C418yes—
272#538C2×C418yes—
273#537C2×C414yes—
274#537C2×C414yes—
275#536C2×C414yes—
276#536C2×C414yes—
277#535C2×C414yes—
278#535C2×C414yes—
279#533C2×C412yes—
280#533C2×C412yes—
281#533C2×C412yes—
282#533C2312yes—
283#533C2311yescharacteristic
284#533C2314yes—
285#533C2314yes—
286#532C2×C412yes—
287#532C2×C412yes—
288#532C2×C412yes—
289#532C2312yes—
290#532C2311yescharacteristic
291#532C2314yes—
292#532C2314yes—
293#532C2318yes—
294#529C2×C412yes—
295#529C2×C412yes—
296#529C2×C414yes—
297#529C2×C414yes—
298#529C2×C414yes—
299#529C2×C414yes—
300#529C2×C414yes—
301#529C2314yes—
302#529C2314yes—
303#529C2312yes—
304#529C2312yes—
305#529C2318yes—
306#529C2318yes—
307#529C2318yes—
308#529C2314yes—
309#529C2318yes—
310#529C2314yes—
311#529C2318yes—
312#525C2×C412yes—
313#525C2×C414yes—
314#525C2×C414yes—
315#525C2×C412yes—
316#525C2314yes—
317#525C2314yes—
318#525C2312yes—
319#525C2314yes—
320#525C2318yes—
321C4×#41C2314yes—
322C4×#41C2314yes—
323C4×#41C2312yes—
324C4×#41C2312yes—
325C4×#41C2314yes—
326C4×#41C2314yes—
327C4×#41C2312yes—
328C4×#41C2314yes—
329C4×#41C2314yes—
330C2×C4×Q8C2314yes—
331C2×C4×D4C2314yes—
332C2×#117C2314yes—
333C22×C42C2311yescharacteristic
334#446C2314yes—
335#446C2312yes—
336#446C2312yes—
337#446C2312yes—
338#446C2312yes—
339#446C2314yes—
340#446C2314yes—
341#446C2314yes—
342#446C2318yes—
343#446C2318yes—
344#446C2318yes—
345#446C2314yes—
346#446C2314yes—
347#446C2318yes—
348#446C2318yes—
349#446C2318yes—
350#446C2318yes—
351#446C2314yes—
352#446C2314yes—
353#446C2318yes—
354C8×Q8C2312yes—
355C8×Q8C2314yes—
356C8×Q8C2318yes—
357C8×Q8C2314yes—
358C8×Q8C2318yes—
359C8×Q8C2314yes—
360C8×Q8C2312yes—
361C8×Q8C2314yes—
362C8×Q8C2314yes—
363C8×Q8C2312yes—
364C8×Q8C2312yes—
365C8×Q8C2314yes—
366C8×Q8C2314yes—
367C8×Q8C2314yes—
368#436C2318yes—
369#436C2318yes—
370#436C2314yes—
371#436C2318yes—
372#436C2312yes—
373#436C2312yes—
374#436C2312yes—
375#436C2314yes—
376#436C2314yes—
377#436C2314yes—
378#436C2312yes—
379#436C2318yes—
380#436C2318yes—
381#436C2318yes—
382#436C2318yes—
383#436C2318yes—
384#436C2314yes—
385#436C2318yes—
386#436C2318yes—
387#436C2314yes—
388#436C2318yes—
389#436C2314yes—
390#436C2314yes—
391#436C2318yes—
392#435C2318yes—
393#435C2318yes—
394#435C2314yes—
395#435C2314yes—
396#435C2314yes—
397#435C2314yes—
398#435C2314yes—
399#435C2314yes—
400#435C2318yes—
401#435C2318yes—
402#435C2314yes—
403#435C2314yes—
404#435C2318yes—
405#435C2318yes—
406#435C2318yes—
407#435C2318yes—
408#435C2318yes—
409#435C2318yes—
410#435C2318yes—
411#435C2318yes—
412#435C2318yes—
413#435C2318yes—
414#435C2318yes—
415#435C2318yes—
416#435C2318yes—
417#435C2318yes—
418#435C2318yes—
419#435C2318yes—
420#435C2318yes—
421#435C2318yes—
422C8×D4C2312yes—
423C8×D4C2318yes—
424C8×D4C2314yes—
425C8×D4C2318yes—
426C8×D4C2314yes—
427C8×D4C2314yes—
428C8×D4C2314yes—
429C8×D4C2314yes—
430C8×D4C2314yes—
431C8×D4C2318yes—
432C8×D4C2318yes—
433C8×D4C2314yes—
434C8×D4C2314yes—
435C8×D4C2318yes—
436C8×D4C2318yes—
437C8×D4C2314yes—
438C8×D4C2314yes—
439C8×D4C2314yes—
440C8×D4C2314yes—
441C8×D4C2312yes—
442C8×D4C2314yes—
443C8×D4C2312yes—
444C8×D4C2314yes—
445C8×D4C2312yes—
446C8×D4C2318yes—
447C8×D4C2314yes—
448C8×D4C2318yes—
449C8×D4C2314yes—
450#433C2314yes—
451#433C2318yes—
452#433C2318yes—
453#433C2318yes—
454#433C2314yes—
455#433C2314yes—
456#433C2314yes—
457#433C2318yes—
458#433C2318yes—
459#433C2318yes—
460#433C2318yes—
461#433C2318yes—
462#433C2318yes—
463#433C2318yes—
464#433C2318yes—
465#433C2318yes—
466#433C2318yes—
467#432C2314yes—
468#432C2312yes—
469#432C2312yes—
470#432C2314yes—
471#432C2318yes—
472#432C2318yes—
473#432C2318yes—
474#432C2318yes—
475#432C2314yes—
476#432C2314yes—
477#432C2318yes—
478#431C2314yes—
479#431C2312yes—
480#431C2312yes—
481#431C2314yes—
482#431C2318yes—
483#431C2314yes—
484#431C2314yes—
485#431C2314yes—
486#431C2314yes—
487#431C2318yes—
488#431C2314yes—
489#431C2314yes—
490#431C2318yes—
491#424C2314yes—
492#424C2312yes—
493#424C2314yes—
494#424C2312yes—
495#424C2314yes—
496#424C2314yes—
497#424C2314yes—
498#424C2314yes—
499#424C2318yes—
500#424C2318yes—
501#423C2312yes—
502#423C2312yes—
503#423C2311yescharacteristic
504#423C2311yescharacteristic
505#423C2314yes—
506#423C2314yes—
507#423C2314yes—
508#423C2318yes—
509#423C2314yes—
510C2×C4⋊C8C2314yes—
511C2×C4⋊C8C2314yes—
512C2×C4⋊C8C2318yes—
513#408C2314yes—
514#408C2312yes—
515#408C2312yes—
516#408C2314yes—
517#408C2314yes—
518#408C2314yes—
519#408C2314yes—
520#408C2314yes—
521#408C2318yes—
522#408C2318yes—
523#408C2318yes—
524#408C2318yes—
525#407C2314yes—
526#407C2312yes—
527#407C2314yes—
528#407C2314yes—
529#407C2318yes—
530C2×C22⋊C8C2318yes—
531#405C2314yes—
532#405C2318yes—
533#405C2318yes—
534#405C2318yes—
535#405C2314yes—
536#405C2314yes—
537#405C2314yes—
538#405C2318yes—
539#405C2314yes—
540#405C2312yes—
541#405C2314yes—
542#405C2314yes—
543#405C2312yes—
544#405C2314yes—
545#405C2314yes—
546#405C2314yes—
547C4×M16C2312yes—
548C4×M16C2314yes—
549C4×M16C2314yes—
550C4×M16C2314yes—
551C4×M16C2314yes—
552C4×M16C2314yes—
553C4×M16C2318yes—
554C2×#97C2314yes—
555C2×#97C2314yes—
556C2×C4×C8C2312yes—
557C2×C4×C8C2311yescharacteristic
558C2×C4×C8C2312yes—
559C2×C4×C8C2311yescharacteristic
560C2×C4×C8C2311yescharacteristic
561C2×C4×C8C2312yes—
562C2×C4×C8C2311yescharacteristic
563C2×C4×C8C2312yes—
564C2×C4×C8C2314yes—
565C2×C4×C8C2314yes—
566C2×C4×C8C2314yes—
567C2×C4×C8C2314yes—
568C2×C4×C8C2318yes—
569C2×#41C22×C414yes—
570C2×#41C22×C412yes—
571C2×#41C22×C414yes—
572C2×#41C22×C412yes—
573C2×#41C22×C414yes—
574C2×#41C22×C414yes—
575C2×#41C2414yes—
576C2×#41C2412yes—
577C2×#41C2414yes—
578C22×Q8C22×C414yes—
579C22×D4C22×C414yes—
580C23×C4C22×C412yes—
581C23×C4C2414yes—
582C23×C4C2411yescharacteristic
583#131—48no—
584#131—44no—
585#131—44no—
586#131—48no—
587#131—48no—
588#131—48no—
589C2×M16—48no—
590C2×M16C2414yes—
591C2×M16C2414yes—
592C2×M16C2418yes—
593C2×M16C2414yes—
594C2×M16C2414yes—
595C2×M16C2412yes—
596C2×M16C2414yes—
597C2×M16C2412yes—
598C2×M16C2414yes—
599C2×M16C2414yes—
600C2×M16C2414yes—
601C2×M16C2414yes—
602C2×M16C2414yes—
603C2×M16C2418yes—
604C22×C8—48no—
605C22×C8—42no—
606C22×C8—42no—
607C22×C8C2412yes—
608C22×C8C2411yescharacteristic
609C22×C8C2414yes—
610C22×C8C2414yes—
611C22×C8C2411yescharacteristic
612C22×C8C2412yes—
613C22×C8C2414yes—
614C22×C8C2414yes—
615C22×C8C2411yescharacteristic
616C22×C8C2412yes—
617C22×C8C2412yes—
618C22×C8C2411yescharacteristic
619C22×C8C2414yes—
620C22×C8C2418yes—
621C22×C8C2414yes—
622C22×C8C2414yes—
623C22×C8C2414yes—
624C22×C8C2418yes—
625C4⋊Q8C22×C412yes—
626C4⋊Q8C22×C412yes—
627C4⋊Q8C22×C412yes—
628C4⋊Q8C22×C412yes—
629C4⋊Q8C22×C411yescharacteristic
630C4⋊Q8C22×C414yes—
631C4⋊Q8C22×C414yes—
632C4⋊Q8C22×C418yes—
633C4⋊Q8C22×C418yes—
634C4⋊Q8C22×C414yes—
635C4⋊Q8C22×C414yes—
636#127C22×C412yes—
637#127C22×C411yescharacteristic
638#127C22×C414yes—
639#127C22×C418yes—
640#127C22×C414yes—
641#126C22×C414yes—
642#126C22×C418yes—
643#126C22×C414yes—
644#126C22×C414yes—
645#126C22×C414yes—
646#126C22×C418yes—
647#126C22×C418yes—
648#126C22×C418yes—
649#126C22×C418yes—
650#126C22×C418yes—
651#126C22×C418yes—
652#126C22×C418yes—
653#126C22×C418yes—
654#126C22×C418yes—
655#126C22×C418yes—
656#126C22×C418yes—
657#126C22×C418yes—
658#125C22×C414yes—
659#125C22×C412yes—
660#125C22×C414yes—
661#125C22×C414yes—
662#125C22×C412yes—
663#125C22×C412yes—
664#125C22×C418yes—
665#125C22×C418yes—
666#125C22×C418yes—
667#125C22×C414yes—
668#125C22×C418yes—
669#125C22×C418yes—
670#125C22×C414yes—
671#125C22×C418yes—
672#125C22×C418yes—
673#124C22×C414yes—
674#124C22×C412yes—
675#124C22×C414yes—
676#124C22×C414yes—
677#124C22×C412yes—
678#124C22×C412yes—
679#124C22×C418yes—
680#124C22×C414yes—
681#124C22×C414yes—
682#124C22×C418yes—
683#124C22×C418yes—
684#124C22×C418yes—
685#124C22×C418yes—
686#124C22×C418yes—
687#124C22×C418yes—
688#124C22×C418yes—
689#124C22×C414yes—
690#124C22×C414yes—
691#123C22×C414yes—
692#123C22×C418yes—
693#123C22×C414yes—
694#123C22×C414yes—
695#123C22×C414yes—
696#123C22×C414yes—
697#123C22×C414yes—
698#123C22×C414yes—
699#123C22×C418yes—
700#123C22×C414yes—
701#123C22×C414yes—
702#123C22×C418yes—
703#123C22×C418yes—
704#123C22×C418yes—
705#123C22×C418yes—
706#123C22×C418yes—
707#123C22×C418yes—
708#123C22×C418yes—
709#123C22×C418yes—
710#123C22×C418yes—
711#123C22×C418yes—
712#123C22×C418yes—
713#123C22×C418yes—
714#123C22×C418yes—
715#123C22×C418yes—
716C22⋊Q8C22×C412yes—
717C22⋊Q8C22×C412yes—
718C22⋊Q8C22×C414yes—
719C22⋊Q8C22×C414yes—
720C22⋊Q8C22×C414yes—
721C22⋊Q8C22×C414yes—
722C22⋊Q8C22×C412yes—
723C22⋊Q8C22×C412yes—
724C22⋊Q8C22×C414yes—
725C22⋊Q8C22×C414yes—
726C22⋊Q8C22×C414yes—
727C22⋊Q8C22×C418yes—
728C22⋊Q8C22×C418yes—
729C22⋊Q8C22×C418yes—
730C22⋊Q8C22×C418yes—
731C22⋊Q8C22×C414yes—
732C22⋊Q8C22×C418yes—
733C22⋊Q8C22×C418yes—
734C22⋊Q8C22×C414yes—
735C22⋊Q8C22×C418yes—
736C22⋊Q8C22×C418yes—
737C22⋊Q8C22×C418yes—
738C22⋊Q8C22×C418yes—
739C22⋊Q8C22×C414yes—
740C22⋊Q8C22×C418yes—
741C22⋊Q8C22×C414yes—
742C22⋊Q8C22×C418yes—
743#121C22×C412yes—
744#121C22×C412yes—
745#121C22×C414yes—
746#121C22×C414yes—
747#121C22×C414yes—
748#121C22×C414yes—
749#121C22×C412yes—
750#121C22×C412yes—
751#121C22×C414yes—
752#121C22×C414yes—
753#121C22×C414yes—
754#121C22×C418yes—
755#121C22×C418yes—
756#121C22×C418yes—
757#121C22×C418yes—
758#121C22×C418yes—
759#121C22×C414yes—
760#121C22×C418yes—
761#121C22×C414yes—
762#121C22×C418yes—
763#121C22×C418yes—
764#121C22×C418yes—
765#121C22×C414yes—
766#121C22×C418yes—
767#121C22×C414yes—
768#121C22×C418yes—
769#121C22×C418yes—
770#121C22×C418yes—
771#121C22×C418yes—
772#121C22×C418yes—
773#121C22×C418yes—
774#120C22×C414yes—
775#120C22×C414yes—
776#120C22×C414yes—
777#120C22×C418yes—
778#120C22×C418yes—
779#120C22×C418yes—
780#120C22×C414yes—
781#120C22×C414yes—
782C4×Q8C22×C414yes—
783C4×Q8C22×C414yes—
784C4×Q8C22×C418yes—
785C4×Q8C22×C414yes—
786C4×Q8C22×C414yes—
787C4×Q8C22×C414yes—
788C4×Q8C22×C412yes—
789C4×Q8C22×C412yes—
790C4×Q8C22×C414yes—
791C4×Q8C22×C414yes—
792C4×Q8C22×C414yes—
793C4×Q8C22×C418yes—
794C4×Q8C22×C414yes—
795C4×Q8C2412yes—
796C4×Q8C2414yes—
797C4×Q8C2418yes—
798C4×Q8C2412yes—
799C4×Q8C2414yes—
800C4×D4C22×C414yes—
801C4×D4C22×C414yes—
802C4×D4C22×C418yes—
803C4×D4C22×C414yes—
804C4×D4C22×C418yes—
805C4×D4C22×C414yes—
806C4×D4C22×C414yes—
807C4×D4C22×C414yes—
808C4×D4C22×C414yes—
809C4×D4C22×C414yes—
810C4×D4C22×C414yes—
811C4×D4C22×C418yes—
812C4×D4C22×C414yes—
813C4×D4C22×C414yes—
814C4×D4C22×C414yes—
815C4×D4C22×C412yes—
816C4×D4C22×C414yes—
817C4×D4C22×C414yes—
818C4×D4C22×C412yes—
819C4×D4C22×C414yes—
820C4×D4C22×C418yes—
821C4×D4C22×C418yes—
822C4×D4C22×C418yes—
823C4×D4C22×C418yes—
824C4×D4C22×C414yes—
825C4×D4C22×C418yes—
826C4×D4C22×C414yes—
827C4×D4C2412yes—
828C4×D4C2414yes—
829C4×D4C2418yes—
830C4×D4C2412yes—
831C4×D4C2414yes—
832C4×D4C2414yes—
833C4×D4C2414yes—
834C4×D4C2418yes—
835C4×D4C2418yes—
836C4×D4C2414yes—
837C4×D4C2414yes—
838C4×D4C2418yes—
839#117C22×C418yes—
840#117C22×C418yes—
841#117C22×C414yes—
842#117C22×C412yes—
843#117C22×C414yes—
844#117C22×C412yes—
845#117C22×C414yes—
846#117C22×C414yes—
847#117C22×C414yes—
848#117C22×C418yes—
849#117C22×C414yes—
850#117C22×C414yes—
851#117C22×C414yes—
852#117C22×C418yes—
853#117C22×C418yes—
854#117C2414yes—
855#117C2418yes—
856#117C2414yes—
857#117C2414yes—
858#117C2414yes—
859#117C2412yes—
860#117C2414yes—
861C2×C4⋊C4C22×C418yes—
862C2×C4⋊C4C22×C414yes—
863C2×C4⋊C4C22×C414yes—
864C2×C4⋊C4C22×C418yes—
865C2×C22⋊C4C22×C418yes—
866C2×C22⋊C4C22×C418yes—
867C2×C42C22×C412yes—
868C2×C42C22×C412yes—
869C2×C42C22×C412yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2414yes—
873C2×C42C2414yes—
874C2×C42C2418yes—
875C2×C42C2412yes—
876C2×C42C2411yescharacteristic
877C2×C42C2411yescharacteristic
878C2×C42C2412yes—
879C4⋊C8C2412yes—
880C4⋊C8C2412yes—
881C4⋊C8C2414yes—
882C4⋊C8C2414yes—
883C4⋊C8C2414yes—
884C4⋊C8C2418yes—
885C4⋊C8C2418yes—
886C4⋊C8C2418yes—
887C4⋊C8C2418yes—
888C4⋊C8C2418yes—
889C4⋊C8C2412yes—
890C4⋊C8C2412yes—
891C4⋊C8C2414yes—
892C4⋊C8C2414yes—
893C4⋊C8C2418yes—
894C4⋊C8C2414yes—
895C4⋊C8C2414yes—
896C4⋊C8C2418yes—
897C4⋊C8C2414yes—
898C4⋊C8C2418yes—
899C4⋊C8C2414yes—
900C4⋊C8C2414yes—
901C4⋊C8C2414yes—
902C4⋊C8C2414yes—
903C22⋊C8C2414yes—
904C22⋊C8C2418yes—
905C22⋊C8C2418yes—
906C22⋊C8C2418yes—
907C22⋊C8C2414yes—
908C22⋊C8C2414yes—
909C22⋊C8C2414yes—
910C22⋊C8C2418yes—
911C22⋊C8C2414yes—
912C22⋊C8C2414yes—
913C22⋊C8C2418yes—
914C22⋊C8C2418yes—
915C22⋊C8C2414yes—
916C22⋊C8C2414yes—
917C22⋊C8C2418yes—
918C22⋊C8C2414yes—
919C22⋊C8C2414yes—
920C22⋊C8C2418yes—
921C22⋊C8C2414yes—
922C22⋊C8C2414yes—
923C22⋊C8C2418yes—
924#97C2414yes—
925#97C2414yes—
926#97C2418yes—
927#97C2418yes—
928#97C2414yes—
929#97C2414yes—
930#97C2414yes—
931#97C2414yes—
932#97C2414yes—
933#97C2414yes—
934#97C2414yes—
935#97C2418yes—
936C4×C8C2411yescharacteristic
937C4×C8C2412yes—
938C4×C8C2412yes—
939C4×C8C2411yescharacteristic
940C4×C8C2412yes—
941C4×C8C2412yes—
942C4×C8C2412yes—
943C4×C8C2414yes—
944C4×C8C2414yes—
945C4×C8C2414yes—
946C4×C8C2414yes—
947C4×C8C2418yes—
948C4×C8C2414yes—
949C4×C8C2414yes—
950C4×C8C2418yes—
951C4×C8C2418yes—
952C4×C8C2411yescharacteristic
953C4×C8C2412yes—
954C4×C8C2411yescharacteristic
955C4×C8C2414yes—
956C4×C8C2414yes—
957C4×C8C2414yes—
958C24C23×C414yes—
959C24C23×C411yescharacteristic
960#41—44no—
961#41—42no—
962#41—42no—
963#41—44no—
964#41—44no—
965#41—44no—
966#41—48no—
967#41—44no—
968#41—48no—
969#41—44no—
970#41—48no—
971#41—48no—
972C2×Q8—48no—
973C2×Q8C23×C412yes—
974C2×Q8C23×C414yes—
975C2×Q8C23×C412yes—
976C2×Q8C23×C414yes—
977C2×Q8C23×C412yes—
978C2×Q8C23×C414yes—
979C2×Q8C23×C418yes—
980C2×Q8C23×C414yes—
981C2×D4—48no—
982C2×D4C23×C412yes—
983C2×D4C23×C414yes—
984C2×D4C23×C412yes—
985C2×D4C23×C414yes—
986C2×D4C23×C414yes—
987C2×D4C23×C414yes—
988C2×D4C23×C412yes—
989C2×D4C23×C414yes—
990C2×D4C23×C418yes—
991C2×D4C23×C414yes—
992C2×D4C23×C414yes—
993C2×D4C23×C414yes—
994C2×D4C23×C414yes—
995C2×D4C23×C418yes—
996C2×D4C23×C418yes—
997C2×D4C23×C418yes—
998C2×D4C23×C414yes—
999C2×D4C23×C414yes—
1000C2×D4C23×C418yes—
1001C22×C4—44no—
1002C22×C4—41no—
1003C22×C4—41no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4C23×C412yes—
1007C22×C4C23×C412yes—
1008C22×C4C23×C412yes—
1009C22×C4C23×C414yes—
1010C22×C4C23×C414yes—
1011C22×C4C23×C412yes—
1012C22×C4C23×C411yescharacteristic
1013C22×C4C23×C412yes—
1014C22×C4C23×C412yes—
1015C22×C4C23×C412yes—
1016C22×C4C23×C414yes—
1017C22×C4C23×C418yes—
1018C22×C4C23×C418yes—
1019C22×C4C23×C414yes—
1020C22×C4C23×C418yes—
1021C22×C4C23×C418yes—
1022C22×C4C23×C418yes—
1023C22×C4C23×C414yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2511yescharacteristic
1027C22×C4C2512yes—
1028C22×C4C2514yes—
1029M16—28no—
1030M16—28no—
1031M16—48no—
1032M16—44no—
1033M16—44no—
1034M16—42no—
1035M16—44no—
1036M16—44no—
1037M16—42no—
1038M16—44no—
1039M16—48no—
1040M16—44no—
1041M16—44no—
1042M16—44no—
1043C2×C8—28no—
1044C2×C8—24no—
1045C2×C8—28no—
1046C2×C8—22no—
1047C2×C8—24no—
1048C2×C8—22no—
1049C2×C8—28no—
1050C2×C8—28no—
1051C2×C8—41no—
1052C2×C8—42no—
1053C2×C8—44no—
1054C2×C8—48no—
1055C2×C8—42no—
1056C2×C8—41no—
1057C2×C8—44no—
1058C2×C8—44no—
1059C2×C8—44no—
1060C2×C8—48no—
1061C2×C8C2512yes—
1062C2×C8C2514yes—
1063C2×C8C2511yescharacteristic
1064C2×C8C2511yescharacteristic
1065C2×C8C2512yes—
1066C2×C8C2514yes—
1067C2×C8C2514yes—
1068C2×C8C2514yes—
1069C2×C8C2514yes—
1070C2×C8C2514yes—
1071C2×C8C2511yescharacteristic
1072C2×C8C2511yescharacteristic
1073C4⋊C4C23×C414yes—
1074C4⋊C4C23×C414yes—
1075C4⋊C4C23×C412yes—
1076C4⋊C4C23×C412yes—
1077C4⋊C4C23×C414yes—
1078C4⋊C4C23×C414yes—
1079C4⋊C4C23×C418yes—
1080C4⋊C4C23×C414yes—
1081C4⋊C4C23×C418yes—
1082C4⋊C4C23×C418yes—
1083C4⋊C4C23×C418yes—
1084C4⋊C4C23×C418yes—
1085C4⋊C4C23×C418yes—
1086C4⋊C4C23×C418yes—
1087C4⋊C4C23×C412yes—
1088C4⋊C4C23×C414yes—
1089C4⋊C4C23×C412yes—
1090C4⋊C4C23×C414yes—
1091C4⋊C4C23×C414yes—
1092C4⋊C4C23×C414yes—
1093C4⋊C4C23×C414yes—
1094C4⋊C4C23×C414yes—
1095C4⋊C4C23×C418yes—
1096C4⋊C4C23×C414yes—
1097C4⋊C4C23×C418yes—
1098C4⋊C4C23×C418yes—
1099C4⋊C4C23×C414yes—
1100C4⋊C4C23×C414yes—
1101C4⋊C4C23×C414yes—
1102C4⋊C4C23×C414yes—
1103C4⋊C4C23×C414yes—
1104C4⋊C4C23×C414yes—
1105C4⋊C4C23×C418yes—
1106C4⋊C4C23×C418yes—
1107C4⋊C4C23×C414yes—
1108C22⋊C4C23×C414yes—
1109C22⋊C4C23×C414yes—
1110C22⋊C4C23×C414yes—
1111C22⋊C4C23×C418yes—
1112C22⋊C4C23×C418yes—
1113C22⋊C4C23×C418yes—
1114C22⋊C4C23×C418yes—
1115C22⋊C4C23×C418yes—
1116C22⋊C4C23×C414yes—
1117C22⋊C4C23×C414yes—
1118C22⋊C4C23×C414yes—
1119C22⋊C4C23×C414yes—
1120C22⋊C4C23×C418yes—
1121C22⋊C4C23×C414yes—
1122C22⋊C4C23×C414yes—
1123C22⋊C4C23×C418yes—
1124C22⋊C4C23×C418yes—
1125C22⋊C4C23×C414yes—
1126C22⋊C4C23×C414yes—
1127C22⋊C4C23×C418yes—
1128C22⋊C4C23×C414yes—
1129C22⋊C4C23×C418yes—
1130C22⋊C4C23×C414yes—
1131C22⋊C4C23×C414yes—
1132C22⋊C4C23×C418yes—
1133C22⋊C4C23×C414yes—
1134C22⋊C4C23×C414yes—
1135C22⋊C4C23×C414yes—
1136C22⋊C4C23×C414yes—
1137C22⋊C4C23×C414yes—
1138C22⋊C4C23×C418yes—
1139C22⋊C4C23×C414yes—
1140C22⋊C4C23×C414yes—
1141C42C23×C411yescharacteristic
1142C42C23×C412yes—
1143C42C23×C412yes—
1144C42C23×C412yes—
1145C42C23×C411yescharacteristic
1146C42C23×C412yes—
1147C42C23×C412yes—
1148C42C23×C414yes—
1149C42C23×C414yes—
1150C42C23×C418yes—
1151C42C23×C414yes—
1152C42C23×C414yes—
1153C42C23×C414yes—
1154C42C23×C414yes—
1155C42C23×C418yes—
1156C42C23×C418yes—
1157C42C2511yescharacteristic
1158C42C2512yes—
1159C42C2514yes—
1160C42C2514yes—
1161C42C2511yescharacteristic
1162C42C2514yes—
1163C23—42no—
1164C23—41no—
1165C23—44no—
1166C23—48no—
1167C23C24×C414yes—
1168C23C24×C411yescharacteristic
1169C23C24×C412yes—
1170C23C24×C414yes—
1171C23C24×C414yes—
1172Q8—24no—
1173Q8—28no—
1174Q8—24no—
1175Q8—48no—
1176Q8—44no—
1177Q8—44no—
1178Q8—42no—
1179Q8—44no—
1180D4—24no—
1181D4—28no—
1182D4—24no—
1183D4—48no—
1184D4—44no—
1185D4—44no—
1186D4—44no—
1187D4—48no—
1188D4—44no—
1189D4—48no—
1190D4—48no—
1191D4—44no—
1192D4—44no—
1193D4—44no—
1194D4—44no—
1195D4—42no—
1196D4—44no—
1197D4—44no—
1198D4—48no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—21no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—24no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—28no—
1213C2×C4—28no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—44no—
1218C2×C4—48no—
1219C2×C4—42no—
1220C2×C4—41no—
1221C2×C4—48no—
1222C2×C4—44no—
1223C2×C4—48no—
1224C2×C4—44no—
1225C2×C4—48no—
1226C2×C4—48no—
1227C2×C4C24×C412yes—
1228C2×C4C24×C412yes—
1229C2×C4C24×C414yes—
1230C2×C4C24×C411yescharacteristic
1231C2×C4C24×C412yes—
1232C2×C4C24×C414yes—
1233C2×C4C24×C414yes—
1234C2×C4C24×C414yes—
1235C2×C4C24×C412yes—
1236C2×C4C24×C418yes—
1237C2×C4C24×C414yes—
1238C2×C4C24×C414yes—
1239C2×C4C24×C414yes—
1240C2×C4C24×C412yes—
1241C2×C4C2611yescharacteristic
1242C8—22no—
1243C8—24no—
1244C8—21no—
1245C8—24no—
1246C8—21no—
1247C8—22no—
1248C8—24no—
1249C8—24no—
1250C8—24no—
1251C8—24no—
1252C8#58512yes—
1253C8#58512yes—
1254C22—24no—
1255C22—22no—
1256C22—22no—
1257C22—22no—
1258C22—24no—
1259C22—24no—
1260C22—28no—
1261C22—24no—
1262C22—24no—
1263C22—22no—
1264C22—21no—
1265C22—24no—
1266C22—24no—
1267C22—44no—
1268C22—88no—
1269C22C25×C411yescharacteristic
1270C4—22no—
1271C4—22no—
1272C4—24no—
1273C4—22no—
1274C4—24no—
1275C4—24no—
1276C4—28no—
1277C4—24no—
1278C4—24no—
1279C4—21no—
1280C4—22no—
1281C4—24no—
1282C4—24no—
1283C4#357314yes—
1284C4C2×#58511yescharacteristic
1285C4C2×#58511yescharacteristic
1286C2—44no—
1287C2—41no—
1288C2—42no—
1289C2—44no—
1290C2—44no—
1291C2C4×#58511yescharacteristic
1292C2C2×#357312yes—
subgroupG/H
centerC2×C8C25
commutator, socleC22C25×C4
Frattini, cosocleC2×C4C26
prime radical#62762C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60344C2semidirect
3. #60337C2semidirect
4. #60331C2semidirect
5. #60330C2semidirect
6. #60326C2semidirect
7. #60320C2semidirect
8. #60317C2semidirect
9. #60315C2semidirect
10. #60308C2semidirect
11. #60307C2semidirect
12. #60306C2semidirect
13. #60305C2semidirect
14. #60302C2semidirect
15. #60300C2semidirect
16. #60296C2semidirect
17. #60295C2semidirect
18. #60287C2semidirect
19. #60218C2semidirect
20. #60215C2semidirect
21. #60206C2semidirect
22. #60204C2semidirect
23. #60204C2semidirect
44. #2995C22semidirect
45. #2995C22semidirect
46. #2995C22semidirect
47. #2994C22semidirect
48. #2994C22semidirect
49. #2994C22semidirect
50. #2993C22semidirect
51. #2993C22semidirect
52. #2993C22semidirect
53. #2993C22semidirect
54. #2993C22semidirect
55. #2993C22semidirect
56. #2992C22semidirect
57. #2992C22semidirect
59. #2991C22semidirect
60. #2991C22semidirect
62. #2990C22semidirect
63. #2990C22semidirect
64. #2989C22semidirect
65. #2989C22semidirect
66. #2989C22semidirect
67. #2989C22semidirect
68. #2986C22semidirect
69. #2986C22semidirect
70. #2985C22semidirect
71. #2985C22semidirect
72. #2985C22semidirect
73. #2984C22semidirect
74. #2983C22semidirect
76. #2981C22semidirect
77. #2981C22semidirect
78. #2980C22semidirect
79. #2980C22semidirect
82. #2979C22semidirect
83. #2979C22semidirect
85. #2978C22semidirect
86. #2978C22semidirect
87. #2978C22semidirect
89. #2976C22semidirect
90. #2976C22semidirect
91. #2975C22semidirect
92. #2974C22semidirect
93. #2971C22semidirect
94. #2971C22semidirect
95. #2970C22semidirect
96. #2970C22semidirect
98. #2969C22semidirect
99. #2969C22semidirect
100. #2969C22semidirect
101. #2969C22semidirect
102. #2969C22semidirect
103. #2968C22semidirect
104. #2968C22semidirect
105. #2967C22semidirect
106. #2967C22semidirect
107. #2967C22semidirect
108. #2967C22semidirect
111. #2966C22semidirect
112. #2966C22semidirect
113. #2966C22semidirect
114. #2966C22semidirect
115. #2966C22semidirect
116. #2966C22semidirect
117. #2966C22semidirect
118. #2966C22semidirect
119. #2966C22semidirect
120. #2966C22semidirect
121. #2966C22semidirect
122. #2966C22semidirect
123. #2966C22semidirect
125. #2965C22semidirect
126. #2965C22semidirect
127. #2965C22semidirect
129. C8×#41C22semidirect
130. C8×#41C22semidirect
131. C8×#41C22semidirect
132. C8×#41C22semidirect
133. C8×#41C22semidirect
134. Q8×M16C22semidirect
135. #2962C22semidirect
136. #2961C22semidirect
137. #2960C22semidirect
138. #2960C22semidirect
139. #2960C22semidirect
140. #2960C22semidirect
141. #2960C22semidirect
142. #2960C22semidirect
143. C2×C8×Q8C22semidirect
144. #2935C22semidirect
145. #2935C22semidirect
146. D4×M16C22semidirect
147. #2933C22semidirect
148. #2932C22semidirect
153. #2931C22semidirect
154. #2931C22semidirect
155. #2931C22semidirect
157. #2930C22semidirect
159. #2929C22semidirect
160. #2929C22semidirect
161. #2929C22semidirect
162. #2929C22semidirect
163. #2929C22semidirect
164. #2929C22semidirect
165. C2×C8×D4C22semidirect
166. #2925C22semidirect
167. #2925C22semidirect
168. #2925C22semidirect
169. #2924C22semidirect
170. #2923C22semidirect
171. #2923C22semidirect
172. #2922C22semidirect
173. #2922C22semidirect
174. #2921C22semidirect
175. #2920C22semidirect
176. #2920C22semidirect
177. C4×#131C22semidirect
178. C4×#131C22semidirect
179. C4×#131C22semidirect
180. C2×#405C22semidirect
181. C22×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#627622
#603442
#603372
#603312
#603302
#603262
#603202
#603172
#603152
#603082
#603072
#603062
#603052
#603022
#603002
#602962
#602952
#602872
#602182
#602152
#602062
#602042