Finite Group Databasebeta

← #11675285

Subgroups — #11675285

Order 768.

1798 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86280C211yesmaximal, characteristic, complemented
2#86224C211yesmaximal, characteristic, complemented
3C3×#3135C211yesmaximal, characteristic, complemented
4#83367C211yesmaximal, characteristic, complemented
5#83297C211yesmaximal, characteristic
6#81732C214yesmaximal, complemented
7#81710C214yesmaximal, complemented
8#81676C214yesmaximal, complemented
9#81670C214yesmaximal, complemented
10#78863C212yesmaximal, complemented
11#78828C212yesmaximal, complemented
12#78823C212yesmaximal, complemented
13#78820C212yesmaximal, complemented
14C2×#4710C211yesmaximal, characteristic, complemented
15#78480C211yesmaximal, characteristic, complemented
16#61333—31nomaximal, Sylow
17C3×#533C2211yescharacteristic
18C3×#532C2211yescharacteristic
19#5827C2212yes—
20#5825C2212yes—
21C2×#949C2212yes—
22C22×#204C2211yescharacteristic
23#5730C2212yes—
24#5727C2212yes—
25#5721C2212yescomplemented
26#5713C2212yescomplemented
27#5690C2214yes—
28#5671C2214yescomplemented
29#5634—22no—
30D3×C22⋊Q8—22no—
31#5602—22no—
32#5600—22no—
33#5579—22no—
34#5579—21no—
35Q8×D12—21no—
36#5543—21no—
37#5542—21no—
38#5541—22no—
39#5521C2212yes—
40#5519C2212yes—
41C2×C4×D12C2211yescharacteristic
42#5470C2211yescharacteristic
43C2×C4×Dic6C2211yescharacteristic
44C3×#491C2212yescomplemented
45C3×#490C2212yescomplemented
46C3×#489C2212yescomplemented
47C3×#489C2212yescomplemented
48C3×#416C2212yes—
49C3×#416C2212yes—
50C2×C3×#97C2211yescharacteristic
51#5232C2212yes—
52C2×#821C2211yescharacteristic
53C2×#818C2211yescharacteristic
54C2×#816C2211yescharacteristic
55#5102C2212yes—
56#5101C2212yes—
57#5094C2212yescomplemented
58#5091C2212yescomplemented
59#5083C2212yes—
60#5072C2212yes—
61#5063C2214yescomplemented
62#5057C2214yes—
63#5004C2212yes—
64#4995C2212yes—
65#4924C2211yescharacteristic
66#4818C2214yes—
67#4818C2214yes—
68#4817C2214yes—
69#4797C2214yescomplemented
70#4796C2214yescomplemented
71#4793C2214yescomplemented
72#4792C2214yescomplemented
73#4788C2214yes—
74#4787C2214yes—
75#4787C2214yes—
76#4785C2214yes—
77#4768C2214yescomplemented
78#4766C2214yescomplemented
79#4765C2214yescomplemented
80#4759C2214yescomplemented
81#4756C2214yes—
82#4710C2214yes—
83#4710C2214yes—
84#4701C2214yescomplemented
85#4701C2214yescomplemented
86#3507—31no—
87#3501—31no—
88#3376—34no—
89#3372—34no—
90#3370—34no—
91#3367—34no—
92#3137—32no—
93#3135D311yescharacteristic, complemented
94#3083—32no—
95#3078—31no—
96#3042—32no—
97#3036—31no—
98#2961—31no—
99#2946—32no—
100C2×#440—31no—
101C2×C3×#41C2312yes—
102C2×D3×Q8—22no—
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×Dic6C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×C4⋊Q8C2311yescharacteristic
109C3×C4⋊Q8C2311yescharacteristic
110C3×C4⋊Q8C2311yescharacteristic
111C3×#127C2311yescharacteristic
112C3×#125C2312yes—
113C3×#124C2312yes—
114C3×C22⋊Q8—21no—
115C3×C22⋊Q8—21no—
116C3×#121—21no—
117C3×#121—21no—
118C3×C4×Q8—21no—
119C3×C4×Q8—21no—
120C3×C4×D4—21no—
121C3×C4×D4—21no—
122C3×#117C2312yes—
123C2×C3×C42C2311yescharacteristic
124#949—28no—
125#946—22no—
126#946—24no—
127Q8×Dic3C2314yes—
128#944C2314yes—
129C2×#215C2314yes—
130#936—22no—
131#936C2314yes—
132#935—24no—
133#935—24no—
134D4×Dic3—24no—
135D4×Dic3—22no—
136D4×Dic3C2314yes—
137C2×#213C2314yes—
138C2×(C2×D3)⋊C4—21no—
139#926—22no—
140#926C2312yes—
141C2×C4⋊Dic3—22no—
142C2×C4⋊Dic3C2311yescharacteristic
143C2×C4⋊Dic3C2311yescharacteristic
144#924—22no—
145#924—22no—
146#924D412yes—
147#924D412yes—
148C2×Dic3⋊C4—21no—
149C2×C4×Dic3—21no—
150C2×#208C2312yes—
151C2×#204—24no—
152C2×#204C2314yes—
153#897—22no—
154#897—24no—
155#896—24no—
156#896—24no—
157#896—24no—
158#893C2314yes—
159#893C2314yes—
160D3×C4⋊C4—22no—
161D3×C4⋊C4—24no—
162#890—22no—
163#890C2314yes—
164#889—24no—
165#888C2314yes—
166#887—22no—
167D3×C22⋊C4—24no—
168#879—24no—
169#879—24no—
170#878—24no—
171#878—24no—
172#877—24no—
173C4×D12—21no—
174C4×D12—21no—
175C4×D12—22no—
176C4×D12—22no—
177C4×D12C2312yes—
178C4×D12C2312yes—
179#870—22no—
180#870D412yes—
181#869—22no—
182#869D411yescharacteristic
183#869D411yescharacteristic
184C4×Dic6—21no—
185C4×Dic6—21no—
186C4×Dic6C2312yes—
187C4×Dic6C2312yes—
188C4×Dic6C2312yes—
189C4×Dic6C2312yes—
190C3×#103C2312yes—
191C3×#103C2312yes—
192C3×#103C2312yes—
193C3×#103C2312yes—
194C3×#102C2312yes—
195C3×#102C2312yes—
196C3×#102C2312yes—
197C3×#102C2312yes—
198C3×#97C2312yes—
199C3×#97C2312yes—
200#835C2314yes—
201#832C2314yes—
202#821C2314yes—
203#818C2314yes—
204#816C2314yes—
205#815C2314yes—
206Dic3⋊C8C2314yes—
207Dic3⋊C8C2314yes—
208C8×Dic3C2314yes—
209#810C2314yes—
210#810C2314yes—
211#808C2314yes—
212#807C2314yes—
213C4⋊(C3⋊C8)C2312yes—
214C4⋊(C3⋊C8)C2312yes—
215C2×AGL(1,ℤ/8)—32no—
216C22×SD16—31no—
217#559—32no—
218#557—32no—
219#556—34no—
220#556—61no—
221#554—32no—
222#554—34no—
223#554—61no—
224#554—62no—
225#554—61no—
226#552—62no—
227D4×Q8—32no—
228D4×Q8—61no—
229#544—32no—
230#543—62no—
231#539—62no—
232#536—32no—
233#533—31no—
234#533C2×D311yescharacteristic
235#532C2×D311yescharacteristic
236#529—62no—
237C2×C22⋊Q8—62no—
238#520—32no—
239#518—32no—
240C2×C4×Q8—31no—
241C2×C4×D4—31no—
242#491—34no—
243#491C2×D312yescomplemented
244#490C2×D312yescomplemented
245#489—34no—
246#489C2×D312yescomplemented
247#489C2×D312yescomplemented
248#488—34no—
249#487—34no—
250#479—34no—
251#479—34no—
252#478—34no—
253#477—32no—
254#477—34no—
255#475—32no—
256#474—34no—
257#463—34no—
258#463—34no—
259#463—34no—
260#461—32no—
261#461—34no—
262#461—34no—
263#459—32no—
264#446—34no—
265#446—34no—
266#442—34no—
267#440—34no—
268#440—34no—
269#440—34no—
270C4×SD16—34no—
271C4×D8—34no—
272#428—32no—
273C2×#107—31no—
274#424—32no—
275#423—31no—
276#419—32no—
277#417—32no—
278#416C2×D312yes—
279#416C2×D312yes—
280C2×#103—31no—
281C2×#102—31no—
282#405—32no—
283C2×#97C2×D311yescharacteristic
284C23×D3—21no—
285C3×#41—24no—
286C3×#41—24no—
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8C2412yes—
290C2×C3×D4—22no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4C2412yes—
294C22×C3×C4—22no—
295C22×C3×C4C2×D411yescharacteristic
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2411yescharacteristic
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—24no—
302D3×Q8—84no—
303C2×D12—21no—
304C2×D12—22no—
305C2×D12#4114yes—
306C2×D12C2412yes—
307C2×C4×D3—22no—
308C2×C4×D3—22no—
309C2×C4×D3—24no—
310C2×C4×D3—24no—
311C2×C4×D3—82no—
312C2×Dic6—22no—
313C2×Dic6—22no—
314C2×Dic6—21no—
315C2×Dic6—24no—
316C2×Dic6C2×D412yes—
317C2×Dic6C2×D412yes—
318C2×Dic6C2412yes—
319C2×C3×C8—22no—
320C2×C3×C8—22no—
321C2×C3×C8C2412yes—
322C2×C3×C8C2412yes—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4C2412yes—
330C3×C4⋊C4C2412yes—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—22no—
333C3×C22⋊C4—22no—
334C3×C42—22no—
335C3×C42C2×D411yescharacteristic
336C3×C42C2×D411yescharacteristic
337C3×C42C2411yescharacteristic
338C3×C42C2411yescharacteristic
339#217—24no—
340#217—24no—
341#217—24no—
342#217C2×D414yes—
343#215—28no—
344#213—28no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—22no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—24no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3—24no—
352C4⋊Dic3—24no—
353C4⋊Dic3C2×D412yes—
354C4⋊Dic3C2×D412yes—
355C4⋊Dic3C2×D412yes—
356C4⋊Dic3C2×D412yes—
357C4⋊Dic3C2412yes—
358C4⋊Dic3C2412yes—
359Dic3⋊C4—22no—
360Dic3⋊C4—22no—
361Dic3⋊C4—24no—
362Dic3⋊C4—24no—
363Dic3⋊C4—24no—
364Dic3⋊C4—24no—
365Dic3⋊C4C2×D414yes—
366Dic3⋊C4C2×D414yes—
367C4×Dic3—22no—
368C4×Dic3—22no—
369C4×Dic3—24no—
370C4×Dic3C2414yes—
371#208—24no—
372C2×C3⋊C8C2414yes—
373#204—28no—
374C2×#41C22×D312yes—
375C22×Q8—31no—
376C22×Q8—62no—
377C22×D4—31no—
378C23×C4—61no—
379AGL(1,ℤ/8)—68no—
380C2×SD16—34no—
381C2×SD16—34no—
382C2×SD16—64no—
383C2×D8—34no—
384C2×M16—32no—
385C22×C8C22×D311yescharacteristic
386C22×C8C22×D311yescharacteristic
387C4⋊Q8—34no—
388C4⋊Q8—34no—
389C4⋊Q8—31no—
390C4⋊Q8—31no—
391C4⋊Q8—62no—
392C4⋊Q8C22×D311yescharacteristic
393C4⋊Q8C22×D311yescharacteristic
394C4⋊Q8C22×D311yescharacteristic
395#127C22×D311yescharacteristic
396#126—64no—
397#126—64no—
398#125—34no—
399#125—32no—
400#125—62no—
401#125—62no—
402#125—64no—
403#125C22×D312yes—
404#124—34no—
405#124—62no—
406#124C22×D312yes—
407#123—64no—
408#123—64no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—32no—
412C22⋊Q8—32no—
413C22⋊Q8—64no—
414C22⋊Q8—64no—
415C22⋊Q8—64no—
416C22⋊Q8—64no—
417C22⋊Q8—64no—
418C22⋊Q8—62no—
419C22⋊Q8—64no—
420C22⋊Q8—62no—
421C22⋊Q8—62no—
422C22⋊Q8—62no—
423C22⋊Q8—64no—
424#121—21no—
425#121—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8—32no—
429C4×Q8—32no—
430C4×Q8—34no—
431C4×Q8—32no—
432C4×Q8—32no—
433C4×Q8—62no—
434C4×Q8—61no—
435C4×Q8—61no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—34no—
439C4×D4—34no—
440C4×D4—34no—
441C4×D4—32no—
442C4×D4—32no—
443C4×D4—62no—
444C4×D4—62no—
445C4×D4—64no—
446C4×D4—62no—
447C4×D4—61no—
448C4×D4—61no—
449#117—32no—
450#117—64no—
451#117—62no—
452#117C22×D312yes—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—31no—
455C2×C4⋊C4—64no—
456C2×C4⋊C4—62no—
457C2×C4⋊C4—62no—
458C2×C4⋊C4—61no—
459C2×C22⋊C4—64no—
460C2×C22⋊C4—61no—
461C2×C42—61no—
462C2×C42C22×D311yescharacteristic
463#107—34no—
464#107—34no—
465#106—34no—
466C4⋊C8—34no—
467C4⋊C8—34no—
468C4⋊C8—32no—
469C4⋊C8—32no—
470#103—34no—
471#103—34no—
472#103—34no—
473#103—34no—
474#103C22×D312yes—
475#103C22×D312yes—
476#103C22×D312yes—
477#103C22×D312yes—
478#102—34no—
479#102—34no—
480#102C22×D312yes—
481#102C22×D312yes—
482#102C22×D312yes—
483#102C22×D312yes—
484#97—34no—
485#97C22×D312yes—
486#97C22×D312yes—
487C4×C8—34no—
488C23×C3—22no—
489C23×C3C22×D411yescharacteristic
490C22×D3—22no—
491C22×D3—24no—
492C22×D3—81no—
493C22×D3—81no—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—42no—
497C3×Q8—81no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—42no—
501C3×D4—44no—
502C3×D4—81no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—44no—
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4C22×D411yescharacteristic
513C2×C3×C4C22×D411yescharacteristic
514C2×C3×C4C2×#4112yes—
515C2×C3×C42−1+412yes—
516C2×C3×C4C2511yescharacteristic
517C2×Dic3—22no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—42no—
521C2×Dic3—84no—
522C2×Dic3—81no—
523C2×Dic3—81no—
524C2×Dic3C22×D414yes—
525C2×Dic3C22×D414yes—
526D12—24no—
527D12—22no—
528D12C2×#4114yes—
529C4×D3—44no—
530C4×D3—84no—
531C4×D3—84no—
532C4×D3—82no—
533Dic6—22no—
534Dic6—22no—
535Dic6—42no—
536Dic6—42no—
537Dic6—42no—
538Dic6—84no—
539C3×C8—22no—
540C3×C8—22no—
541C3⋊C8—24no—
542C24—61no—
543#41—24no—
544#41—24no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—32no—
548C2×Q8—32no—
549C2×Q8—32no—
550C2×Q8—64no—
551C2×Q8—61no—
552C2×Q8—62no—
553C2×Q8—62no—
554C2×Q8—244no—
555C2×Q8C23×D312yes—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—34no—
560C2×D4—32no—
561C2×D4—61no—
562C2×D4—62no—
563C2×D4C23×D312yes—
564C22×C4—22no—
565C22×C4—64no—
566C22×C4—64no—
567C22×C4—64no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—242no—
574C22×C4D3×D411yescharacteristic
575C22×C4D3×D411yescharacteristic
576C22×C4C23×D311yescharacteristic
577SD16—68no—
578SD16—68no—
579D8—68no—
580M16—64no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—34no—
584C2×C8C23×D312yes—
585C2×C8C23×D312yes—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—22no—
591C4⋊C4—21no—
592C4⋊C4—32no—
593C4⋊C4—34no—
594C4⋊C4—32no—
595C4⋊C4—32no—
596C4⋊C4—34no—
597C4⋊C4—32no—
598C4⋊C4—32no—
599C4⋊C4—32no—
600C4⋊C4—64no—
601C4⋊C4—64no—
602C4⋊C4—64no—
603C4⋊C4—64no—
604C4⋊C4—64no—
605C4⋊C4—64no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—62no—
609C4⋊C4—62no—
610C4⋊C4C23×D312yes—
611C4⋊C4C23×D312yes—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—34no—
616C22⋊C4—64no—
617C22⋊C4—64no—
618C22⋊C4—64no—
619C22⋊C4—64no—
620C22⋊C4—64no—
621C22⋊C4—62no—
622C22⋊C4—62no—
623C42—22no—
624C42—34no—
625C42—64no—
626C42—62no—
627C42—62no—
628C42D3×D411yescharacteristic
629C42D3×D411yescharacteristic
630C42C23×D311yescharacteristic
631C42C23×D311yescharacteristic
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—42no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3#54812yes—
638C22×C3C23×D411yescharacteristic
639C2×D3—24no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—84no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4#54812yes—
651C3×C4C22×#4111yescharacteristic
652C3×C4C2×2−1+411yescharacteristic
653Dic3—24no—
654Dic3—24no—
655Dic3—42no—
656Dic3—42no—
657Dic3—42no—
658C23—22no—
659C23—62no—
660C23—64no—
661C23—241no—
662C23—241no—
663C23C2×D3×D411yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—42no—
667Q8—62no—
668Q8—62no—
669Q8—81no—
670Q8—122no—
671Q8—122no—
672Q8—122no—
673Q8—244no—
674D4—22no—
675D4—22no—
676D4—34no—
677D4—42no—
678D4—44no—
679D4—64no—
680D4—62no—
681D4—81no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—34no—
686C2×C4—34no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—44no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—124no—
694C2×C4—122no—
695C2×C4—242no—
696C2×C4—244no—
697C2×C4—244no—
698C2×C4—244no—
699C2×C4—241no—
700C2×C4—241no—
701C2×C4C2×D3×D411yescharacteristic
702C2×C4C2×D3×D411yescharacteristic
703C2×C4C2×D3×D411yescharacteristic
704C2×C4C2×D3×D411yescharacteristic
705C2×C4C2×D3×D411yescharacteristic
706C2×C4D3×#4112yes—
707C2×C4#101012yes—
708C2×C4C24×D311yescharacteristic
709C8—22no—
710C8—22no—
711C8—64no—
712C2×C3—22no—
713C2×C3—82no—
714C2×C3C2×#54811yescharacteristic
715C2×C3#358511yescharacteristic
716C2×C3#358611yescharacteristic
717D3—44no—
718C22—21no—
719C22—21no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—64no—
724C22—122no—
725C22—122no—
726C22—244no—
727C22#567712yes—
728C22C22×D3×D411yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—42no—
734C4—42no—
735C4—42no—
736C4—64no—
737C4—64no—
738C4—122no—
739C4—122no—
740C4—122no—
741C4#567712yes—
742C4C2×D3×#4111yescharacteristic
743C4C2×#101011yescharacteristic
744C3#6133311yescharacteristic, complemented, Sylow
745C2—22no—
746C2—82no—
747C2—124no—
748C2C2×#567711yescharacteristic
749C2#8720011yescharacteristic
750C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3135C2
socleC22×C3C23×D4
prime radical#83297C2
hypercenter#3135D3
hypocenterC3#61333
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3135

Complements

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

NH ≅ G/Ntype
1. #86280C2semidirect
2. #86224C2semidirect
3. C3×#3135C2semidirect
4. #83367C2semidirect
6. #81732C2semidirect
7. #81710C2semidirect
8. #81676C2semidirect
9. #81670C2semidirect
10. #78863C2semidirect
11. #78828C2semidirect
12. #78823C2semidirect
13. #78820C2semidirect
14. C2×#4710C2semidirect
15. #78480C2semidirect
25. #5721C22semidirect
26. #5713C22semidirect
28. #5671C22semidirect
44. C3×#491C22semidirect
45. C3×#490C22semidirect
46. C3×#489C22semidirect
47. C3×#489C22semidirect
57. #5094C22semidirect
58. #5091C22semidirect
61. #5063C22semidirect
69. #4797C22semidirect
70. #4796C22semidirect
71. #4793C22semidirect
72. #4792C22semidirect
77. #4768C22semidirect
78. #4766C22semidirect
79. #4765C22semidirect
80. #4759C22semidirect
84. #4701C22semidirect
85. #4701C22semidirect
93. #3135D3semidirect
243. #491C2×D3semidirect
244. #490C2×D3semidirect
246. #489C2×D3semidirect
247. #489C2×D3semidirect
744. C3#61333semidirect

Maximal subgroups

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

subgroupindex
#862802
#862242
C3×#31352
#833672
#832972
#817322
#817102
#816762
#816702
#788632
#788282
#788232
#788202
C2×#47102
#784802
#613333