Finite Group Databasebeta

← #10574605

Subgroups — #10574605

Order 512.

6017 conjugacy classes of subgroups.

The subgroup lattice has 1073 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62755C211yesmaximal, characteristic
2#60340C214yesmaximal, complemented
3#60338C212yesmaximal, complemented
4#60332C212yesmaximal, complemented
5#60330C214yesmaximal, complemented
6#60322C214yesmaximal, complemented
7#60318C212yesmaximal, complemented
8#60314C214yesmaximal, complemented
9#60307C212yesmaximal, complemented
10#60305C214yesmaximal, complemented
11#60304C214yesmaximal, complemented
12#60299C218yesmaximal, complemented
13#60296C214yesmaximal, complemented
14#60291C212yesmaximal, complemented
15#60286C211yesmaximal, characteristic, complemented
16#60215C218yesmaximal, complemented
17#60206C214yesmaximal, complemented
18#60204C211yesmaximal, characteristic, complemented
19C2×#2966C212yesmaximal, complemented
20#3566C418yes—
21#3564C414yes—
22#3560C414yes—
23#3553C414yes—
24#3545C414yes—
25#3535C414yes—
26#3534C414yes—
27#3531C2212yes—
28#3529C2212yes—
29#3481C2214yes—
30#3475C2218yes—
31#3461C2214yes—
32#3459C2214yes—
33#3455C2214yes—
34#3444C2211yescharacteristic
35C2×#529C2212yes—
36#2995C2214yescomplemented
37#2995C2214yescomplemented
38#2995C2218yescomplemented
39#2995C2218yescomplemented
40#2995C2218yescomplemented
41#2994C2218yescomplemented
42#2994C2218yescomplemented
43#2993C2218yescomplemented
44#2993C2218yescomplemented
45#2992C2214yescomplemented
46#2992C2214yescomplemented
47#2992C2214yescomplemented
48#2992C2214yescomplemented
49#2992C2218yescomplemented
50#2992C2218yescomplemented
51#2992C2218yescomplemented
52#2990C2218yescomplemented
53#2989C2218yescomplemented
54#2987C2212yescomplemented
55#2987C2218yescomplemented
56#2985C2218yescomplemented
57#2985C2218yescomplemented
58#2983C2214yescomplemented
59#2980C2212yescomplemented
60#2980C2214yescomplemented
61#2979C2214yescomplemented
62#2978C2214yescomplemented
63#2978C2218yescomplemented
64#2977C2214yescomplemented
65#2977C2214yescomplemented
66#2977C2218yescomplemented
67#2976C2218yescomplemented
68#2976C2218yescomplemented
69#2976C2218yescomplemented
70#2974C2218yescomplemented
71#2974C2218yescomplemented
72#2973C2214yescomplemented
73#2973C2218yescomplemented
74#2970C2218yescomplemented
75#2970C2218yescomplemented
76#2969C2218yescomplemented
77#2969C2218yescomplemented
78#2968C2218yescomplemented
79#2968C2218yescomplemented
80#2968C2218yescomplemented
81#2968C2218yescomplemented
82#2967C2218yescomplemented
83#2967C2218yescomplemented
84#2967C2218yescomplemented
85#2967C2218yescomplemented
86#2966C2214yescomplemented
87#2966C2214yescomplemented
88#2966C2214yescomplemented
89#2966C2214yescomplemented
90#2966C2214yescomplemented
91#2966C2214yescomplemented
92#2966C2214yescomplemented
93#2966C2214yescomplemented
94#2966C2214yescomplemented
95#2966C2214yescomplemented
96#2966C2218yescomplemented
97#2966C2218yescomplemented
98#2966C2218yescomplemented
99#2966C2218yescomplemented
100#2966C2218yescomplemented
101#2966C2218yescomplemented
102#2965C2214yescomplemented
103C8×#41C2214yescomplemented
104C8×#41C2218yescomplemented
105#2962C2218yescomplemented
106#2961C2214yescomplemented
107#2960C2211yescharacteristic, complemented
108#2960C2211yescharacteristic, complemented
109#2960C2214yescomplemented
110#2960C2218yescomplemented
111C2×#446C2212yescomplemented
112C2×C8×Q8C2212yescomplemented
113D4×M16C2218yescomplemented
114#2933C2218yescomplemented
115#2933C2218yescomplemented
116#2932C2214yescomplemented
117#2931C2211yescharacteristic, complemented
118#2931C2211yescharacteristic, complemented
119#2931C2214yescomplemented
120#2930C2214yescomplemented
121#2930C2214yescomplemented
122#2929C2212yescomplemented
123#2929C2212yescomplemented
124#2929C2214yescomplemented
125#2929C2214yescomplemented
126#2929C2218yescomplemented
127#2929C2218yescomplemented
128C2×#436C2212yescomplemented
129C2×#435C2214yescomplemented
130C2×C8×D4C2212yescomplemented
131C2×C8×D4C2214yescomplemented
132C2×C8×D4C2218yescomplemented
133#2925C2218yescomplemented
134#2924C2218yescomplemented
135#2924C2218yescomplemented
136#2923C2214yescomplemented
137#2923C2214yescomplemented
138#2922C2212yescomplemented
139#2921C2214yescomplemented
140#2920C2211yescharacteristic, complemented
141C2×#433C2214yescomplemented
142C2×#432C2212yescomplemented
143C4×#131C2212yescomplemented
144C4×#131C2214yescomplemented
145C2×#405C2214yescomplemented
146C2×#405C2214yescomplemented
147C22×C4×C8C2211yescharacteristic, complemented
148C2×#131C2314yes—
149C2×#131C2312yes—
150C2×#131C2312yes—
151C2×#131C2314yes—
152C22×M16C2314yes—
153C22×M16C2314yes—
154C23×C8C2311yescharacteristic
155C23×C8C2311yescharacteristic
156C23×C8C2314yes—
157C23×C8C2314yes—
158#564C2×C412yes—
159#563C2×C412yes—
160#563C2×C414yes—
161#563C2×C418yes—
162#563C2×C414yes—
163#563C2×C418yes—
164#562C2×C418yes—
165#562C2×C414yes—
166#562C2×C418yes—
167#562C2×C412yes—
168H(3,𝔽4)C2×C412yes—
169#560C2×C418yes—
170#560C2×C414yes—
171#559C2×C414yes—
172#556C2×C418yes—
173#555C2×C418yes—
174#554C2×C418yes—
175#554C2×C418yes—
176#553C2×C418yes—
177#553C2×C418yes—
178#553C2×C418yes—
179#553C2×C418yes—
180#552C2×C418yes—
181#552C2×C418yes—
182#552C2×C418yes—
183#552C2×C418yes—
184#551C2×C418yes—
185#551C2×C418yes—
186#551C2×C418yes—
187#551C2×C418yes—
188#551C2×C414yes—
189#551C2×C418yes—
190#551C2×C414yes—
191#547C2×C418yes—
192#546C2×C418yes—
193#546C2×C418yes—
194#546C2×C418yes—
195#546C2×C418yes—
196D42C2×C414yes—
197#544C2×C414yes—
198#543C2×C414yes—
199#542C2×C418yes—
200#542C2×C418yes—
201#542C2×C418yes—
202#542C2×C418yes—
203#541C2×C418yes—
204#541C2×C418yes—
205#541C2×C418yes—
206#540C2×C418yes—
207#539C2×C418yes—
208#539C2×C418yes—
209#539C2×C418yes—
210#539C2×C418yes—
211#539C2×C418yes—
212#539C2×C418yes—
213#539C2×C414yes—
214#539C2×C414yes—
215#538C2×C418yes—
216#538C2×C418yes—
217#538C2×C414yes—
218#538C2×C414yes—
219#538C2×C418yes—
220#538C2×C418yes—
221#537C2×C414yes—
222#536C2×C418yes—
223#534C2×C418yes—
224#534C2×C414yes—
225#533C2×C412yes—
226#533C2311yescharacteristic
227#533C2314yes—
228#533C2318yes—
229#532C2×C412yes—
230#532C2311yescharacteristic
231#532C2314yes—
232#529C2×C414yes—
233#529C2×C414yes—
234#529C2×C414yes—
235#529C2×C414yes—
236#529C2×C414yes—
237#529C2×C414yes—
238#529C2314yes—
239#529C2314yes—
240#529C2314yes—
241#529C2314yes—
242#529C2314yes—
243#529C2318yes—
244#529C2318yes—
245#529C2318yes—
246#529C2318yes—
247#529C2318yes—
248#529C2318yes—
249C2×#126C2×C414yes—
250C2×#125C2×C412yes—
251C2×#124C2×C412yes—
252#525C2×C414yes—
253#525C2312yes—
254#525C2314yes—
255#525C2314yes—
256#525C2318yes—
257#525C2318yes—
258C2×#123C2×C414yes—
259C2×C22⋊Q8C2×C412yes—
260C2×#121C2×C412yes—
261C4×#41C2314yes—
262C4×#41C2318yes—
263C4×#41C2312yes—
264C4×#41C2314yes—
265C2×C4×Q8C2312yes—
266C2×C4×D4C2314yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2318yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C22×C42C2311yescharacteristic
272#446C2314yes—
273#446C2314yes—
274#446C2314yes—
275#446C2314yes—
276#446C2314yes—
277#446C2314yes—
278#446C2318yes—
279#446C2318yes—
280#446C2318yes—
281#446C2318yes—
282#446C2318yes—
283#446C2318yes—
284#446C2318yes—
285#446C2318yes—
286#446C2318yes—
287#446C2318yes—
288#446C2318yes—
289#446C2318yes—
290C8×Q8C2314yes—
291C8×Q8C2314yes—
292C8×Q8C2314yes—
293C8×Q8C2314yes—
294C8×Q8C2318yes—
295C8×Q8C2314yes—
296C8×Q8C2314yes—
297C8×Q8C2318yes—
298#436C2314yes—
299#436C2314yes—
300#436C2314yes—
301#436C2314yes—
302#436C2318yes—
303#436C2318yes—
304#436C2318yes—
305#436C2314yes—
306#436C2314yes—
307#436C2318yes—
308#436C2318yes—
309#436C2318yes—
310#436C2318yes—
311#436C2318yes—
312#435C2318yes—
313#435C2318yes—
314#435C2318yes—
315#435C2318yes—
316#435C2318yes—
317#435C2318yes—
318#435C2318yes—
319#435C2318yes—
320#435C2318yes—
321#435C2318yes—
322#435C2318yes—
323#435C2318yes—
324#435C2318yes—
325#435C2318yes—
326#435C2318yes—
327#435C2318yes—
328#435C2318yes—
329#435C2318yes—
330#435C2318yes—
331#435C2318yes—
332#435C2318yes—
333#435C2318yes—
334#435C2318yes—
335#435C2318yes—
336#435C2318yes—
337#435C2318yes—
338#435C2318yes—
339#435C2318yes—
340#435C2318yes—
341#435C2318yes—
342C8×D4C2318yes—
343C8×D4C2318yes—
344C8×D4C2314yes—
345C8×D4C2314yes—
346C8×D4C2318yes—
347C8×D4C2318yes—
348C8×D4C2318yes—
349C8×D4C2318yes—
350C8×D4C2314yes—
351C8×D4C2314yes—
352C8×D4C2318yes—
353C8×D4C2318yes—
354C8×D4C2318yes—
355C8×D4C2318yes—
356C8×D4C2318yes—
357C8×D4C2318yes—
358C8×D4C2314yes—
359C8×D4C2318yes—
360C8×D4C2314yes—
361C8×D4C2318yes—
362C8×D4C2318yes—
363C8×D4C2318yes—
364#433C2318yes—
365#433C2318yes—
366#433C2318yes—
367#433C2318yes—
368#433C2318yes—
369#433C2318yes—
370#433C2318yes—
371#433C2318yes—
372#433C2318yes—
373#433C2318yes—
374#433C2318yes—
375#433C2318yes—
376#433C2318yes—
377#433C2318yes—
378#433C2318yes—
379#433C2318yes—
380#433C2318yes—
381#432C2314yes—
382#432C2314yes—
383#432C2314yes—
384#432C2314yes—
385#432C2314yes—
386#432C2318yes—
387#432C2318yes—
388#432C2318yes—
389#432C2318yes—
390#432C2318yes—
391#432C2318yes—
392#431C2314yes—
393#431C2318yes—
394#431C2318yes—
395#431C2318yes—
396#431C2318yes—
397#424C2312yes—
398#424C2312yes—
399#424C2314yes—
400#424C2314yes—
401#424C2314yes—
402#424C2314yes—
403#424C2318yes—
404#424C2318yes—
405#424C2318yes—
406#424C2318yes—
407#423C2311yescharacteristic
408#423C2311yescharacteristic
409#423C2314yes—
410#423C2314yes—
411#423C2318yes—
412C2×C4⋊C8C2312yes—
413C2×C4⋊C8C2312yes—
414C2×C4⋊C8C2314yes—
415C2×C4⋊C8C2314yes—
416C2×C4⋊C8C2318yes—
417#408C2312yes—
418#408C2312yes—
419#408C2314yes—
420#408C2314yes—
421#408C2314yes—
422#408C2314yes—
423#408C2318yes—
424#408C2318yes—
425#407C2312yes—
426#407C2314yes—
427#407C2314yes—
428#407C2318yes—
429#407C2318yes—
430C2×C22⋊C8C2314yes—
431C2×C22⋊C8C2314yes—
432C2×C22⋊C8C2314yes—
433C2×C22⋊C8C2318yes—
434C2×C22⋊C8C2318yes—
435#405C2318yes—
436#405C2318yes—
437#405C2318yes—
438#405C2318yes—
439#405C2318yes—
440#405C2318yes—
441#405C2318yes—
442#405C2318yes—
443#405C2312yes—
444#405C2314yes—
445#405C2314yes—
446#405C2312yes—
447#405C2314yes—
448#405C2314yes—
449C4×M16C2312yes—
450C4×M16C2314yes—
451C4×M16C2314yes—
452C4×M16C2318yes—
453C2×#97C2314yes—
454C2×#97C2314yes—
455C2×#97C2314yes—
456C2×#97C2314yes—
457C2×C4×C8C2312yes—
458C2×C4×C8C2311yescharacteristic
459C2×C4×C8C2312yes—
460C2×C4×C8C2311yescharacteristic
461C2×C4×C8C2312yes—
462C2×C4×C8C2312yes—
463C2×C4×C8C2311yescharacteristic
464C2×C4×C8C2311yescharacteristic
465C2×C4×C8C2314yes—
466C2×C4×C8C2314yes—
467C2×C4×C8C2314yes—
468C2×C4×C8C2318yes—
469C2×#41C22×C414yes—
470C2×#41C22×C418yes—
471C2×#41C2414yes—
472C2×#41C2412yes—
473C22×Q8C22×C412yes—
474C22×D4C22×C414yes—
475C22×D4C22×C412yes—
476C22×D4C22×C418yes—
477C23×C4C22×C412yes—
478C23×C4C2414yes—
479C23×C4C2414yes—
480C23×C4C2411yescharacteristic
481#131—48no—
482#131—44no—
483#131—44no—
484#131—48no—
485C2×M16—48no—
486C2×M16—48no—
487C2×M16C2418yes—
488C2×M16C2418yes—
489C2×M16C2418yes—
490C2×M16C2418yes—
491C2×M16C2414yes—
492C2×M16C2412yes—
493C2×M16C2414yes—
494C2×M16C2412yes—
495C2×M16C2414yes—
496C2×M16C2414yes—
497C22×C8—42no—
498C22×C8—48no—
499C22×C8—48no—
500C22×C8—42no—
501C22×C8C2412yes—
502C22×C8C2411yescharacteristic
503C22×C8C2414yes—
504C22×C8C2412yes—
505C22×C8C2418yes—
506C22×C8C2411yescharacteristic
507C22×C8C2414yes—
508C22×C8C2412yes—
509C22×C8C2412yes—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2414yes—
513C22×C8C2414yes—
514C22×C8C2418yes—
515C22×C8C2418yes—
516C22×C8C2414yes—
517C22×C8C2414yes—
518C22×C8C2418yes—
519C4⋊Q8C22×C412yes—
520C4⋊Q8C22×C411yescharacteristic
521C4⋊Q8C22×C414yes—
522C4⋊Q8C22×C418yes—
523C4⋊Q8C22×C418yes—
524C4⋊Q8C22×C418yes—
525#127C22×C411yescharacteristic
526#127C22×C414yes—
527#126C22×C418yes—
528#126C22×C418yes—
529#126C22×C418yes—
530#126C22×C418yes—
531#126C22×C418yes—
532#126C22×C418yes—
533#126C22×C418yes—
534#126C22×C418yes—
535#126C22×C418yes—
536#126C22×C418yes—
537#126C22×C418yes—
538#126C22×C418yes—
539#126C22×C418yes—
540#126C22×C418yes—
541#126C22×C418yes—
542#126C22×C418yes—
543#126C22×C418yes—
544#125C22×C414yes—
545#125C22×C414yes—
546#125C22×C414yes—
547#125C22×C414yes—
548#125C22×C412yes—
549#125C22×C414yes—
550#125C22×C418yes—
551#125C22×C418yes—
552#125C22×C418yes—
553#125C22×C418yes—
554#125C22×C418yes—
555#125C22×C418yes—
556#125C22×C418yes—
557#125C22×C418yes—
558#125C22×C418yes—
559#124C22×C414yes—
560#124C22×C414yes—
561#124C22×C414yes—
562#124C22×C414yes—
563#124C22×C412yes—
564#124C22×C414yes—
565#124C22×C418yes—
566#124C22×C418yes—
567#124C22×C418yes—
568#124C22×C418yes—
569#124C22×C418yes—
570#124C22×C418yes—
571#124C22×C414yes—
572#124C22×C414yes—
573#123C22×C418yes—
574#123C22×C418yes—
575#123C22×C418yes—
576#123C22×C418yes—
577#123C22×C418yes—
578#123C22×C414yes—
579#123C22×C418yes—
580#123C22×C418yes—
581#123C22×C418yes—
582#123C22×C418yes—
583#123C22×C418yes—
584#123C22×C414yes—
585#123C22×C414yes—
586#123C22×C418yes—
587#123C22×C418yes—
588#123C22×C418yes—
589#123C22×C418yes—
590#123C22×C418yes—
591#123C22×C418yes—
592#123C22×C418yes—
593#123C22×C418yes—
594#123C22×C418yes—
595#123C22×C418yes—
596#123C22×C418yes—
597#123C22×C418yes—
598C22⋊Q8C22×C414yes—
599C22⋊Q8C22×C414yes—
600C22⋊Q8C22×C414yes—
601C22⋊Q8C22×C414yes—
602C22⋊Q8C22×C414yes—
603C22⋊Q8C22×C414yes—
604C22⋊Q8C22×C414yes—
605C22⋊Q8C22×C418yes—
606C22⋊Q8C22×C418yes—
607C22⋊Q8C22×C418yes—
608C22⋊Q8C22×C418yes—
609C22⋊Q8C22×C418yes—
610C22⋊Q8C22×C418yes—
611C22⋊Q8C22×C418yes—
612C22⋊Q8C22×C418yes—
613C22⋊Q8C22×C418yes—
614C22⋊Q8C22×C418yes—
615C22⋊Q8C22×C418yes—
616C22⋊Q8C22×C418yes—
617C22⋊Q8C22×C418yes—
618C22⋊Q8C22×C418yes—
619C22⋊Q8C22×C418yes—
620C22⋊Q8C22×C418yes—
621C22⋊Q8C22×C418yes—
622C22⋊Q8C22×C418yes—
623#121C22×C414yes—
624#121C22×C414yes—
625#121C22×C414yes—
626#121C22×C414yes—
627#121C22×C414yes—
628#121C22×C414yes—
629#121C22×C414yes—
630#121C22×C418yes—
631#121C22×C418yes—
632#121C22×C418yes—
633#121C22×C418yes—
634#121C22×C418yes—
635#121C22×C418yes—
636#121C22×C418yes—
637#121C22×C418yes—
638#121C22×C418yes—
639#121C22×C418yes—
640#121C22×C418yes—
641#121C22×C418yes—
642#121C22×C418yes—
643#121C22×C418yes—
644#120C22×C414yes—
645#120C22×C418yes—
646#120C22×C418yes—
647#120C22×C418yes—
648#120C22×C418yes—
649#120C22×C418yes—
650#120C22×C414yes—
651#120C22×C414yes—
652C4×Q8C22×C414yes—
653C4×Q8C22×C414yes—
654C4×Q8C22×C414yes—
655C4×Q8C22×C414yes—
656C4×Q8C22×C418yes—
657C4×Q8C22×C418yes—
658C4×Q8C2414yes—
659C4×Q8C2414yes—
660C4×Q8C2418yes—
661C4×Q8C2414yes—
662C4×D4C22×C414yes—
663C4×D4C22×C414yes—
664C4×D4C22×C418yes—
665C4×D4C22×C418yes—
666C4×D4C22×C418yes—
667C4×D4C22×C418yes—
668C4×D4C22×C418yes—
669C4×D4C22×C418yes—
670C4×D4C22×C418yes—
671C4×D4C22×C418yes—
672C4×D4C22×C414yes—
673C4×D4C22×C414yes—
674C4×D4C22×C418yes—
675C4×D4C22×C418yes—
676C4×D4C22×C418yes—
677C4×D4C22×C418yes—
678C4×D4C22×C418yes—
679C4×D4C22×C418yes—
680C4×D4C2418yes—
681C4×D4C2418yes—
682C4×D4C2414yes—
683C4×D4C2414yes—
684C4×D4C2418yes—
685C4×D4C2418yes—
686C4×D4C2418yes—
687C4×D4C2418yes—
688C4×D4C2414yes—
689#117C22×C418yes—
690#117C22×C418yes—
691#117C22×C418yes—
692#117C22×C418yes—
693#117C22×C414yes—
694#117C22×C418yes—
695#117C22×C418yes—
696#117C22×C418yes—
697#117C22×C418yes—
698#117C2418yes—
699#117C2418yes—
700#117C2418yes—
701#117C2414yes—
702#117C2412yes—
703#117C2414yes—
704C2×C4⋊C4C22×C414yes—
705C2×C4⋊C4C22×C414yes—
706C2×C4⋊C4C22×C418yes—
707C2×C4⋊C4C22×C412yes—
708C2×C4⋊C4C22×C414yes—
709C2×C4⋊C4C22×C418yes—
710C2×C4⋊C4C22×C412yes—
711C2×C4⋊C4C22×C414yes—
712C2×C22⋊C4C22×C414yes—
713C2×C22⋊C4C22×C414yes—
714C2×C22⋊C4C22×C418yes—
715C2×C22⋊C4C22×C414yes—
716C2×C22⋊C4C22×C414yes—
717C2×C22⋊C4C22×C414yes—
718C2×C22⋊C4C22×C418yes—
719C2×C22⋊C4C22×C418yes—
720C2×C42C22×C412yes—
721C2×C42C22×C412yes—
722C2×C42C22×C412yes—
723C2×C42C2412yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2412yes—
728C2×C42C2418yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C4⋊C8C2418yes—
732C4⋊C8C2418yes—
733C4⋊C8C2418yes—
734C4⋊C8C2418yes—
735C4⋊C8C2418yes—
736C4⋊C8C2418yes—
737C4⋊C8C2414yes—
738C4⋊C8C2414yes—
739C4⋊C8C2418yes—
740C4⋊C8C2414yes—
741C4⋊C8C2414yes—
742C4⋊C8C2418yes—
743C4⋊C8C2414yes—
744C4⋊C8C2414yes—
745C4⋊C8C2418yes—
746C4⋊C8C2418yes—
747C4⋊C8C2418yes—
748C4⋊C8C2418yes—
749C22⋊C8C2418yes—
750C22⋊C8C2418yes—
751C22⋊C8C2418yes—
752C22⋊C8C2418yes—
753C22⋊C8C2418yes—
754C22⋊C8C2418yes—
755C22⋊C8C2418yes—
756C22⋊C8C2418yes—
757C22⋊C8C2418yes—
758C22⋊C8C2418yes—
759C22⋊C8C2418yes—
760C22⋊C8C2418yes—
761C22⋊C8C2418yes—
762C22⋊C8C2418yes—
763C22⋊C8C2418yes—
764#97C2418yes—
765#97C2418yes—
766#97C2418yes—
767#97C2418yes—
768#97C2418yes—
769#97C2418yes—
770#97C2414yes—
771#97C2414yes—
772#97C2414yes—
773#97C2418yes—
774C4×C8C2411yescharacteristic
775C4×C8C2412yes—
776C4×C8C2412yes—
777C4×C8C2411yescharacteristic
778C4×C8C2412yes—
779C4×C8C2412yes—
780C4×C8C2412yes—
781C4×C8C2414yes—
782C4×C8C2414yes—
783C4×C8C2418yes—
784C4×C8C2418yes—
785C4×C8C2418yes—
786C4×C8C2418yes—
787C4×C8C2411yescharacteristic
788C4×C8C2412yes—
789C4×C8C2411yescharacteristic
790C4×C8C2414yes—
791C4×C8C2418yes—
792C24C23×C411yescharacteristic
793C24C23×C414yes—
794C24C23×C414yes—
795#41—44no—
796#41—42no—
797#41—42no—
798#41—44no—
799#41—48no—
800#41—416no—
801C2×Q8—44no—
802C2×Q8C23×C414yes—
803C2×Q8C23×C412yes—
804C2×Q8C23×C414yes—
805C2×Q8C23×C414yes—
806C2×Q8C23×C418yes—
807C2×Q8C23×C414yes—
808C2×D4—44no—
809C2×D4—48no—
810C2×D4—416no—
811C2×D4C23×C418yes—
812C2×D4C23×C418yes—
813C2×D4C23×C414yes—
814C2×D4C23×C418yes—
815C2×D4C23×C414yes—
816C2×D4C23×C412yes—
817C2×D4C23×C418yes—
818C2×D4C23×C414yes—
819C2×D4C23×C414yes—
820C2×D4C23×C418yes—
821C2×D4C23×C414yes—
822C2×D4C23×C418yes—
823C2×D4C23×C418yes—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4C23×C412yes—
832C22×C4C23×C412yes—
833C22×C4C23×C414yes—
834C22×C4C23×C412yes—
835C22×C4C23×C411yescharacteristic
836C22×C4C23×C412yes—
837C22×C4C23×C412yes—
838C22×C4C23×C412yes—
839C22×C4C23×C412yes—
840C22×C4C23×C418yes—
841C22×C4C23×C414yes—
842C22×C4C23×C418yes—
843C22×C4C23×C418yes—
844C22×C4C23×C418yes—
845C22×C4C23×C414yes—
846C22×C4C23×C418yes—
847C22×C4C23×C418yes—
848C22×C4C23×C414yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2511yescharacteristic
852C22×C4C2518yes—
853M16—216no—
854M16—48no—
855M16—48no—
856M16—44no—
857M16—48no—
858M16—42no—
859M16—44no—
860M16—44no—
861M16—42no—
862M16—44no—
863C2×C8—24no—
864C2×C8—216no—
865C2×C8—24no—
866C2×C8—22no—
867C2×C8—28no—
868C2×C8—22no—
869C2×C8—28no—
870C2×C8—41no—
871C2×C8—48no—
872C2×C8—42no—
873C2×C8—44no—
874C2×C8—44no—
875C2×C8—48no—
876C2×C8—42no—
877C2×C8—41no—
878C2×C8—44no—
879C2×C8—44no—
880C2×C8—48no—
881C2×C8C2512yes—
882C2×C8C2511yescharacteristic
883C2×C8C2511yescharacteristic
884C2×C8C2512yes—
885C2×C8C2514yes—
886C2×C8C2514yes—
887C2×C8C2518yes—
888C2×C8C2518yes—
889C2×C8C2511yescharacteristic
890C2×C8C2511yescharacteristic
891C4⋊C4C23×C418yes—
892C4⋊C4C23×C418yes—
893C4⋊C4C23×C418yes—
894C4⋊C4C23×C418yes—
895C4⋊C4C23×C418yes—
896C4⋊C4C23×C418yes—
897C4⋊C4C23×C418yes—
898C4⋊C4C23×C418yes—
899C4⋊C4C23×C418yes—
900C4⋊C4C23×C418yes—
901C4⋊C4C23×C414yes—
902C4⋊C4C23×C414yes—
903C4⋊C4C23×C418yes—
904C4⋊C4C23×C414yes—
905C4⋊C4C23×C414yes—
906C4⋊C4C23×C418yes—
907C4⋊C4C23×C418yes—
908C4⋊C4C23×C418yes—
909C4⋊C4C23×C418yes—
910C4⋊C4C23×C414yes—
911C4⋊C4C23×C418yes—
912C4⋊C4C23×C418yes—
913C4⋊C4C23×C414yes—
914C4⋊C4C23×C418yes—
915C4⋊C4C23×C418yes—
916C4⋊C4C23×C418yes—
917C4⋊C4C23×C414yes—
918C22⋊C4C23×C418yes—
919C22⋊C4C23×C418yes—
920C22⋊C4C23×C418yes—
921C22⋊C4C23×C418yes—
922C22⋊C4C23×C418yes—
923C22⋊C4C23×C418yes—
924C22⋊C4C23×C418yes—
925C22⋊C4C23×C418yes—
926C22⋊C4C23×C418yes—
927C22⋊C4C23×C418yes—
928C22⋊C4C23×C418yes—
929C22⋊C4C23×C418yes—
930C22⋊C4C23×C418yes—
931C22⋊C4C23×C418yes—
932C22⋊C4C23×C418yes—
933C22⋊C4C23×C418yes—
934C22⋊C4C23×C418yes—
935C22⋊C4C23×C418yes—
936C22⋊C4C23×C418yes—
937C22⋊C4C23×C418yes—
938C22⋊C4C23×C418yes—
939C22⋊C4C23×C414yes—
940C22⋊C4C23×C414yes—
941C22⋊C4C23×C418yes—
942C22⋊C4C23×C414yes—
943C42C23×C412yes—
944C42C23×C412yes—
945C42C23×C412yes—
946C42C23×C412yes—
947C42C23×C412yes—
948C42C23×C411yescharacteristic
949C42C23×C411yescharacteristic
950C42C23×C414yes—
951C42C23×C418yes—
952C42C23×C418yes—
953C42C23×C418yes—
954C42C23×C414yes—
955C42C23×C418yes—
956C42C2511yescharacteristic
957C42C2518yes—
958C42C2512yes—
959C42C2511yescharacteristic
960C42C2514yes—
961C23—24no—
962C23—28no—
963C23—41no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—48no—
968C23C24×C418yes—
969C23C24×C414yes—
970C23C24×C411yescharacteristic
971C23C24×C412yes—
972Q8—44no—
973Q8—44no—
974Q8—44no—
975Q8—48no—
976Q8—44no—
977Q8—42no—
978D4—216no—
979D4—216no—
980D4—44no—
981D4—44no—
982D4—48no—
983D4—48no—
984D4—48no—
985D4—44no—
986D4—48no—
987D4—48no—
988D4—44no—
989D4—44no—
990D4—42no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—28no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—28no—
997C2×C4—21no—
998C2×C4—24no—
999C2×C4—21no—
1000C2×C4—24no—
1001C2×C4—28no—
1002C2×C4—42no—
1003C2×C4—42no—
1004C2×C4—42no—
1005C2×C4—42no—
1006C2×C4—41no—
1007C2×C4—48no—
1008C2×C4—42no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—48no—
1012C2×C4—44no—
1013C2×C4—48no—
1014C2×C4—48no—
1015C2×C4—48no—
1016C2×C4—48no—
1017C2×C4C24×C412yes—
1018C2×C4C24×C412yes—
1019C2×C4C24×C411yescharacteristic
1020C2×C4C24×C414yes—
1021C2×C4C24×C418yes—
1022C2×C4C24×C412yes—
1023C2×C4C24×C412yes—
1024C2×C4C24×C412yes—
1025C2×C4C24×C418yes—
1026C2×C4C24×C418yes—
1027C2×C4C24×C418yes—
1028C2×C4C2611yescharacteristic
1029C8—22no—
1030C8—28no—
1031C8—22no—
1032C8—21no—
1033C8—24no—
1034C8—21no—
1035C8—24no—
1036C8—28no—
1037C8#58512yes—
1038C8#58512yes—
1039C22—22no—
1040C22—22no—
1041C22—28no—
1042C22—22no—
1043C22—28no—
1044C22—28no—
1045C22—28no—
1046C22—21no—
1047C22—24no—
1048C22—44no—
1049C22—88no—
1050C22—88no—
1051C22#357314yes—
1052C22C25×C411yescharacteristic
1053C4—22no—
1054C4—22no—
1055C4—22no—
1056C4—22no—
1057C4—28no—
1058C4—28no—
1059C4—28no—
1060C4—22no—
1061C4—28no—
1062C4—21no—
1063C4—24no—
1064C4C2×#58511yescharacteristic
1065C4C2×#58511yescharacteristic
1066C2—24no—
1067C2—41no—
1068C2—44no—
1069C2—48no—
1070C2C4×#58511yescharacteristic
1071C2C2×#357312yes—
subgroupG/H
centerC2×C8C25
commutator, socleC22C25×C4
Frattini, cosocleC2×C4C26
prime radical#62755C2
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. #60340C2semidirect
3. #60338C2semidirect
4. #60332C2semidirect
5. #60330C2semidirect
6. #60322C2semidirect
7. #60318C2semidirect
8. #60314C2semidirect
9. #60307C2semidirect
10. #60305C2semidirect
11. #60304C2semidirect
12. #60299C2semidirect
13. #60296C2semidirect
14. #60291C2semidirect
15. #60286C2semidirect
16. #60215C2semidirect
17. #60206C2semidirect
18. #60204C2semidirect
19. C2×#2966C2semidirect
36. #2995C22semidirect
37. #2995C22semidirect
38. #2995C22semidirect
39. #2995C22semidirect
40. #2995C22semidirect
41. #2994C22semidirect
42. #2994C22semidirect
43. #2993C22semidirect
44. #2993C22semidirect
45. #2992C22semidirect
46. #2992C22semidirect
47. #2992C22semidirect
48. #2992C22semidirect
49. #2992C22semidirect
50. #2992C22semidirect
51. #2992C22semidirect
52. #2990C22semidirect
53. #2989C22semidirect
54. #2987C22semidirect
55. #2987C22semidirect
56. #2985C22semidirect
57. #2985C22semidirect
58. #2983C22semidirect
59. #2980C22semidirect
60. #2980C22semidirect
61. #2979C22semidirect
62. #2978C22semidirect
63. #2978C22semidirect
64. #2977C22semidirect
65. #2977C22semidirect
66. #2977C22semidirect
67. #2976C22semidirect
68. #2976C22semidirect
69. #2976C22semidirect
70. #2974C22semidirect
71. #2974C22semidirect
72. #2973C22semidirect
73. #2973C22semidirect
74. #2970C22semidirect
75. #2970C22semidirect
76. #2969C22semidirect
77. #2969C22semidirect
78. #2968C22semidirect
79. #2968C22semidirect
80. #2968C22semidirect
81. #2968C22semidirect
82. #2967C22semidirect
83. #2967C22semidirect
84. #2967C22semidirect
85. #2967C22semidirect
86. #2966C22semidirect
87. #2966C22semidirect
88. #2966C22semidirect
89. #2966C22semidirect
90. #2966C22semidirect
91. #2966C22semidirect
92. #2966C22semidirect
93. #2966C22semidirect
94. #2966C22semidirect
95. #2966C22semidirect
96. #2966C22semidirect
97. #2966C22semidirect
98. #2966C22semidirect
99. #2966C22semidirect
100. #2966C22semidirect
101. #2966C22semidirect
102. #2965C22semidirect
103. C8×#41C22semidirect
104. C8×#41C22semidirect
105. #2962C22semidirect
106. #2961C22semidirect
107. #2960C22semidirect
108. #2960C22semidirect
109. #2960C22semidirect
110. #2960C22semidirect
111. C2×#446C22semidirect
112. C2×C8×Q8C22semidirect
113. D4×M16C22semidirect
114. #2933C22semidirect
115. #2933C22semidirect
116. #2932C22semidirect
117. #2931C22semidirect
118. #2931C22semidirect
119. #2931C22semidirect
120. #2930C22semidirect
121. #2930C22semidirect
122. #2929C22semidirect
123. #2929C22semidirect
124. #2929C22semidirect
125. #2929C22semidirect
126. #2929C22semidirect
127. #2929C22semidirect
128. C2×#436C22semidirect
129. C2×#435C22semidirect
130. C2×C8×D4C22semidirect
131. C2×C8×D4C22semidirect
132. C2×C8×D4C22semidirect
133. #2925C22semidirect
134. #2924C22semidirect
135. #2924C22semidirect
136. #2923C22semidirect
137. #2923C22semidirect
138. #2922C22semidirect
139. #2921C22semidirect
140. #2920C22semidirect
141. C2×#433C22semidirect
142. C2×#432C22semidirect
143. C4×#131C22semidirect
144. C4×#131C22semidirect
145. C2×#405C22semidirect
146. C2×#405C22semidirect
147. C22×C4×C8C22semidirect

Maximal subgroups

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

subgroupindex
#627552
#603402
#603382
#603322
#603302
#603222
#603182
#603142
#603072
#603052
#603042
#602992
#602962
#602912
#602862
#602152
#602062
#602042
C2×#29662