Finite Group Databasebeta

← #11675401

Subgroups — #11675401

Order 768.

1792 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86204C211yesmaximal, characteristic, complemented
2#85766C211yesmaximal, characteristic, complemented
3C2×C3×#461C211yesmaximal, characteristic, complemented
4#83848C212yesmaximal
5#83843C212yesmaximal, complemented
6#83198C211yesmaximal, characteristic, complemented
7C4×#932C211yesmaximal, characteristic
8#80419C214yesmaximal, complemented
9#80418C214yesmaximal, complemented
10#80417C212yesmaximal, complemented
11#80416C212yesmaximal, complemented
12#80415C212yesmaximal, complemented
13#80414C212yesmaximal, complemented
14#79025C211yesmaximal, characteristic, complemented
15#79008C211yesmaximal, characteristic, complemented
16#78785C212yesmaximal, complemented
17#78779C212yesmaximal, complemented
18#61340—31nomaximal, Sylow
19C22×C3×SD16C2212yes—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22#5816C2212yes—
23#5812C2212yes—
24#5798C2212yes—
25C2×#932C2211yescharacteristic
26C2×#924—22no—
27#5732C2212yescomplemented
28#5732C2212yescomplemented
29#5731—22no—
30#5728—21no—
31#5728—21no—
32#5721C2212yescomplemented
33#5721C2212yescomplemented
34#5543—21no—
35#5543C2212yes—
36#5539—22no—
37#5539C2214yes—
38D4×Dic6—21no—
39D4×Dic6C2212yes—
40#5513—22no—
41#5513—22no—
42#5500C2212yes—
43#5483—22no—
44C4×#235C2211yescharacteristic
45#5470C2211yescharacteristic
46#5470C2211yescharacteristic
47C3×#461C2212yes—
48C3×#461C2212yes—
49C3×#461C2214yes—
50C2×C3×C4⋊C8C2211yescharacteristic
51C2×C3×#103C2212yes—
52#5225C2212yes—
53#5225C2212yes—
54#5215C2211yescharacteristic
55#5165C2214yes—
56#5165C2214yes—
57#5164C2214yes—
58#5164C2214yes—
59#5162C2214yes—
60#5162C2214yes—
61Dic3×SD16C2214yes—
62Dic3×SD16C2214yes—
63#5113C2212yes—
64#5106C2212yes—
65#5102C2212yes—
66#5101C2212yes—
67#5082C2214yescomplemented
68#5079C2212yescomplemented
69#5079C2212yescomplemented
70#5018C2212yes—
71C4×#214C2212yes—
72#5014C2212yes—
73C4×#213C2212yes—
74#4966C2211yescharacteristic
75#4964C2211yescharacteristic
76C4×#208C2211yescharacteristic
77#4851C2211yescharacteristic, complemented
78#4850C2211yescharacteristic, complemented
79#4847C2212yescomplemented
80#4846C2211yescharacteristic, complemented
81#4842C2211yescharacteristic, complemented
82#4831C2212yescomplemented
83#4830C2212yescomplemented
84#4829C2212yescomplemented
85#4828C2214yescomplemented
86#4800C2214yescomplemented
87#4799C2214yescomplemented
88#4797C2214yescomplemented
89#4796C2214yescomplemented
90#4794C2214yescomplemented
91#4793C2214yescomplemented
92#4792C2214yescomplemented
93#4791C2214yescomplemented
94#3509—31no—
95#3501—31no—
96#3376—34no—
97#3372—32no—
98#3372—34no—
99#3367—32no—
100#3360—32no—
101#3359—32no—
102#3139—31no—
103#3137—32no—
104#3082—32no—
105#3076—31no—
106#3042—32no—
107C2×#461D311yescharacteristic, complemented
108#2962—31no—
109#2949—32no—
110C4×AGL(1,ℤ/8)—31no—
111C22×C3×Q8C2312yes—
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C2×#235C2311yescharacteristic
115C22×Dic6—22no—
116C2×C3×SD16—28no—
117C2×C3×SD16C2314yes—
118C2×C3×SD16C2314yes—
119C22×C3×C8C2312yes—
120C3×C4⋊Q8—21no—
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8C2312yes—
123C3×C4⋊Q8C2312yes—
124C3×C4×D4—21no—
125C3×C4×D4—21no—
126C3×C4×D4C2312yes—
127C3×C4×D4C2312yes—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C22⋊C4—21no—
132C2×C3×C42C2311yescharacteristic
133C2×#217—24no—
134#947C2314yes—
135#946—22no—
136#946—22no—
137Q8×Dic3—22no—
138Q8×Dic3—22no—
139Q8×Dic3C2314yes—
140Q8×Dic3C2314yes—
141#944C2314yes—
142D4×Dic3—22no—
143D4×Dic3—22no—
144D4×Dic3C2314yes—
145D4×Dic3C2314yes—
146C2×#214C2312yes—
147#932—24no—
148C2×#213C2312yes—
149#929—24no—
150C4×#67—21no—
151C4×#67—21no—
152#926—24no—
153#926C2312yes—
154#926C2311yescharacteristic
155#926C2312yes—
156C2×C4⋊Dic3—22no—
157#924—21no—
158#924—21no—
159#924—22no—
160#924—24no—
161#924—22no—
162#924—24no—
163#924D412yes—
164#924D412yes—
165C2×Dic3⋊C4—24no—
166C2×#208C2311yescharacteristic
167C2×#208C2311yescharacteristic
168#898—24no—
169#898—24no—
170#897—22no—
171#897—22no—
172#892—22no—
173#892—22no—
174#890—22no—
175#890—22no—
176#890—22no—
177#890C2314yes—
178#889—24no—
179#889—24no—
180#888—22no—
181#888C2314yes—
182#887—22no—
183#887—22no—
184#878—24no—
185#878—24no—
186#878—24no—
187#878—24no—
188C4×D12C2311yescharacteristic
189C4×D12C2311yescharacteristic
190#872—21no—
191C42×D3—21no—
192#870D412yes—
193#870C2312yes—
194#869D411yescharacteristic
195#869D411yescharacteristic
196#869C2311yescharacteristic
197#869C2311yescharacteristic
198C4×Dic6—21no—
199C4×Dic6—21no—
200C4×Dic6C2311yescharacteristic
201C4×Dic6C2311yescharacteristic
202C4×Dic6C2312yes—
203C4×Dic6C2312yes—
204C3×C4⋊C8C2312yes—
205C3×C4⋊C8C2311yescharacteristic
206C3×C4⋊C8C2311yescharacteristic
207C3×#103C2314yes—
208C3×#103C2314yes—
209#835C2314yes—
210#835C2314yes—
211#835C2314yes—
212#835C2314yes—
213#832C2312yes—
214#832C2312yes—
215#821C2312yes—
216#821C2312yes—
217#818C2312yes—
218#818C2312yes—
219#817C2312yes—
220#817C2312yes—
221#816C2312yes—
222#816C2312yes—
223#815C2314yes—
224Dic3⋊C8C2314yes—
225Dic3⋊C8C2314yes—
226C8×Dic3C2314yes—
227#810C2312yes—
228#809C2312yes—
229#808C2312yes—
230#807C2312yes—
231#803C2312yes—
232C4×C3⋊C8C2312yes—
233C2×AGL(1,ℤ/8)—31no—
234C22×SD16C2×D312yes—
235#557—32no—
236#557—32no—
237#556—32no—
238#556—32no—
239#554—32no—
240#554—34no—
241#554—62no—
242#554—61no—
243#552—62no—
244#552—62no—
245D4×Q8—32no—
246D4×Q8—61no—
247#544—32no—
248#543—62no—
249#541—62no—
250#536—32no—
251#533—31no—
252#533—31no—
253#533—61no—
254#533—61no—
255C2×C4⋊Q8C2×D311yescharacteristic
256C2×C22⋊Q8—62no—
257#519—32no—
258#518—32no—
259C4×#41—31no—
260C2×C4×D4C2×D311yescharacteristic
261#491—34no—
262#491—34no—
263#489—34no—
264#488—34no—
265#487—32no—
266#487—32no—
267#487—34no—
268#479—32no—
269#479—34no—
270#479—34no—
271#478—32no—
272#477—31no—
273#477—34no—
274#476—31no—
275#475—31no—
276#475—34no—
277#474—31no—
278#463—34no—
279#463—34no—
280#461—34no—
281#461—34no—
282#461C2×D312yes—
283#461C2×D312yes—
284#461C2×D314yes—
285#446—32no—
286#446—34no—
287C8×Q8—32no—
288#442—32no—
289#440—34no—
290#440—34no—
291#440—32no—
292C4×SD16—34no—
293C4×SD16—34no—
294C4×SD16—32no—
295C4×D8—32no—
296#428—31no—
297#427—32no—
298#424—32no—
299C2×C4⋊C8C2×D311yescharacteristic
300#419—32no—
301#419—32no—
302#418—31no—
303#417—31no—
304#416—32no—
305C2×#103C2×D312yes—
306#405—32no—
307C4×M16—31no—
308C24×C3—21no—
309C2×C3×Q8—22no—
310C2×C3×Q8—24no—
311C2×C3×Q8—24no—
312C2×C3×Q8C2414yes—
313C2×C3×D4—21no—
314C2×C3×D4—22no—
315C2×C3×D4#4114yes—
316C2×C3×D4C2412yes—
317C22×C3×C4—22no—
318C22×C3×C4—21no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—82no—
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2411yescharacteristic
325C2×#67—21no—
326C22×Dic3—24no—
327C22×Dic3—24no—
328#235—22no—
329#235—22no—
330C2×D12C2411yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×Dic6—21no—
335C2×Dic6—21no—
336C2×Dic6—24no—
337C2×Dic6—84no—
338C2×Dic6C2×D412yes—
339C2×Dic6C2×D412yes—
340C2×Dic6C2411yescharacteristic
341C3×SD16—28no—
342C3×SD16—28no—
343C2×C3×C8—24no—
344C2×C3×C8C2412yes—
345C2×C3×C8C2412yes—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—22no—
350C3×C4⋊C4—22no—
351C3×C4⋊C4C2412yes—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—22no—
354C3×C42C2×D411yescharacteristic
355C3×C42C2×D411yescharacteristic
356C3×C42C2411yescharacteristic
357C3×C42C2411yescharacteristic
358#217—22no—
359#217—21no—
360#217—24no—
361#217—24no—
362#217C2×D414yes—
363#214—24no—
364#213—24no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—24no—
368(C2×D3)⋊C4—24no—
369C4⋊Dic3—21no—
370C4⋊Dic3—21no—
371C4⋊Dic3—24no—
372C4⋊Dic3—24no—
373C4⋊Dic3—24no—
374C4⋊Dic3C2×D412yes—
375C4⋊Dic3C2×D412yes—
376C4⋊Dic3C2×D412yes—
377C4⋊Dic3C2×D412yes—
378C4⋊Dic3C2411yescharacteristic
379C4⋊Dic3C2411yescharacteristic
380C4⋊Dic3C2412yes—
381C4⋊Dic3C2412yes—
382Dic3⋊C4—22no—
383Dic3⋊C4—22no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—24no—
387Dic3⋊C4—24no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4C2×D414yes—
391Dic3⋊C4C2×D414yes—
392C4×Dic3—22no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3—24no—
397C4×Dic3—24no—
398C4×Dic3C2414yes—
399#208—22no—
400#208—22no—
401C2×C3⋊C8C2412yes—
402C2×C3⋊C8C2412yes—
403C2×#41—31no—
404C22×Q8—62no—
405C22×Q8C22×D312yes—
406C22×D4C22×D311yescharacteristic
407C23×C4—21no—
408AGL(1,ℤ/8)—64no—
409C2×SD16—28no—
410C2×SD16—32no—
411C2×SD16C22×D314yes—
412C2×SD16C22×D314yes—
413C2×D8—32no—
414C2×M16—31no—
415C2×M16—31no—
416C22×C8C22×D312yes—
417C4⋊Q8—21no—
418C4⋊Q8—21no—
419C4⋊Q8—34no—
420C4⋊Q8—34no—
421C4⋊Q8—31no—
422C4⋊Q8—31no—
423C4⋊Q8—31no—
424C4⋊Q8—31no—
425C4⋊Q8—62no—
426C4⋊Q8C22×D312yes—
427C4⋊Q8C22×D312yes—
428#126—64no—
429#126—64no—
430#125—34no—
431#125—32no—
432#125—32no—
433#125—62no—
434#125—62no—
435#125—64no—
436#125—64no—
437#125—62no—
438#124—34no—
439#123—64no—
440C22⋊Q8—32no—
441C22⋊Q8—32no—
442C22⋊Q8—64no—
443C22⋊Q8—64no—
444C22⋊Q8—64no—
445C22⋊Q8—64no—
446C22⋊Q8—64no—
447C22⋊Q8—62no—
448C22⋊Q8—62no—
449C22⋊Q8—62no—
450C22⋊Q8—64no—
451C22⋊Q8—62no—
452C22⋊Q8—62no—
453C22⋊Q8—62no—
454C22⋊Q8—61no—
455C22⋊Q8—61no—
456C4×Q8—32no—
457C4×Q8—32no—
458C4×Q8—34no—
459C4×Q8—34no—
460C4×Q8—31no—
461C4×Q8—31no—
462C4×Q8—62no—
463C4×Q8—62no—
464C4×Q8—62no—
465C4×Q8—62no—
466C4×Q8—61no—
467C4×Q8—61no—
468C4×D4—21no—
469C4×D4—21no—
470C4×D4—34no—
471C4×D4—34no—
472C4×D4—31no—
473C4×D4—31no—
474C4×D4—62no—
475C4×D4—62no—
476C4×D4—61no—
477C4×D4—61no—
478C4×D4C22×D312yes—
479C4×D4C22×D312yes—
480#117—32no—
481#117—31no—
482#117—32no—
483#117—64no—
484#117—62no—
485#117—62no—
486#117—61no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—64no—
490C2×C4⋊C4—62no—
491C2×C4⋊C4C22×D311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—64no—
494C2×C42—61no—
495C2×C42C22×D311yescharacteristic
496#107—32no—
497#107—32no—
498#107—32no—
499#106—32no—
500#106—32no—
501#106—32no—
502C4⋊C8—34no—
503C4⋊C8—34no—
504C4⋊C8C22×D311yescharacteristic
505C4⋊C8C22×D311yescharacteristic
506C4⋊C8C22×D312yes—
507#103—34no—
508#103—34no—
509#103—34no—
510#103—34no—
511#103—32no—
512#103—32no—
513#103—32no—
514#103C22×D314yes—
515#103C22×D314yes—
516#102—32no—
517#102—32no—
518#102—32no—
519#102—32no—
520#102—32no—
521#97—34no—
522#97—32no—
523C4×C8—34no—
524C4×C8—32no—
525C23×C3—22no—
526C23×C3—24no—
527C23×C3—81no—
528C23×C3—81no—
529C23×C3C22×D411yescharacteristic
530C22×D3—21no—
531C3×Q8—24no—
532C3×Q8—24no—
533C3×Q8—44no—
534C3×D4—24no—
535C3×D4—22no—
536C3×D4C2×#4114yes—
537C2×C3×C4—22no—
538C2×C3×C4—24no—
539C2×C3×C4—22no—
540C2×C3×C4—41no—
541C2×C3×C4—44no—
542C2×C3×C4—44no—
543C2×C3×C4—82no—
544C2×C3×C4—81no—
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C22×D411yescharacteristic
548C2×C3×C4C22×D411yescharacteristic
549C2×C3×C4C22×D411yescharacteristic
550C2×C3×C4C2×#4112yes—
551C2×C3×C42−1+412yes—
552C2×C3×C4C2511yescharacteristic
553#67—42no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—84no—
560C2×Dic3—84no—
561C2×Dic3C22×D414yes—
562C2×Dic3C22×D414yes—
563D12—21no—
564D12—21no—
565C4×D3—42no—
566C4×D3—42no—
567C4×D3—42no—
568Dic6—24no—
569Dic6—21no—
570Dic6—21no—
571Dic6—42no—
572Dic6—42no—
573Dic6—84no—
574Dic6—81no—
575C3×C8—22no—
576C3×C8—22no—
577C3⋊C8—22no—
578C3⋊C8—22no—
579C24—21no—
580#41—62no—
581#41—62no—
582C2×Q8—22no—
583C2×Q8—24no—
584C2×Q8—24no—
585C2×Q8—32no—
586C2×Q8—32no—
587C2×Q8—31no—
588C2×Q8—64no—
589C2×Q8—61no—
590C2×Q8—61no—
591C2×Q8—244no—
592C2×Q8C23×D314yes—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—31no—
596C2×D4—61no—
597C2×D4#23714yes—
598C2×D4C23×D312yes—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—82no—
609C22×C4D3×D411yescharacteristic
610C22×C4D3×D411yescharacteristic
611C22×C4C23×D311yescharacteristic
612SD16—28no—
613SD16—28no—
614SD16—64no—
615D8—64no—
616M16—62no—
617M16—62no—
618C2×C8—24no—
619C2×C8—32no—
620C2×C8—32no—
621C2×C8C23×D312yes—
622C2×C8C23×D312yes—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—32no—
629C4⋊C4—34no—
630C4⋊C4—32no—
631C4⋊C4—32no—
632C4⋊C4—32no—
633C4⋊C4—34no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—32no—
637C4⋊C4—32no—
638C4⋊C4—64no—
639C4⋊C4—64no—
640C4⋊C4—64no—
641C4⋊C4—64no—
642C4⋊C4—64no—
643C4⋊C4—64no—
644C4⋊C4—64no—
645C4⋊C4—62no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—61no—
649C4⋊C4—62no—
650C4⋊C4—61no—
651C4⋊C4C23×D312yes—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—34no—
655C22⋊C4—64no—
656C22⋊C4—64no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—62no—
660C22⋊C4—61no—
661C22⋊C4—61no—
662C22⋊C4—61no—
663C42—34no—
664C42—64no—
665C42—64no—
666C42—61no—
667C42—61no—
668C42—61no—
669C42—62no—
670C42D3×D411yescharacteristic
671C42D3×D411yescharacteristic
672C42C23×D311yescharacteristic
673C42C23×D311yescharacteristic
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—24no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—84no—
680C22×C3#54812yes—
681C22×C3C23×D411yescharacteristic
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—44no—
689C3×C4—42no—
690C3×C4#54812yes—
691C3×C4#57712yes—
692C3×C4C22×#4111yescharacteristic
693C3×C4C2×2−1+411yescharacteristic
694Dic3—24no—
695Dic3—24no—
696Dic3—42no—
697Dic3—41no—
698Dic3—41no—
699Dic3—42no—
700Dic3—41no—
701C23—22no—
702C23—24no—
703C23—61no—
704C23—81no—
705C23—81no—
706C23C2×D3×D411yescharacteristic
707Q8—24no—
708Q8—24no—
709Q8—44no—
710Q8—64no—
711Q8—61no—
712Q8—61no—
713Q8—122no—
714Q8—122no—
715Q8—241no—
716Q8—244no—
717D4—22no—
718D4—24no—
719D4—61no—
720D4—61no—
721D4—122no—
722D4C2×#23714yes—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—34no—
727C2×C4—34no—
728C2×C4—41no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—82no—
737C2×C4—81no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—244no—
742C2×C4—244no—
743C2×C4C2×D3×D411yescharacteristic
744C2×C4C2×D3×D411yescharacteristic
745C2×C4C2×D3×D411yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4C2×D3×D411yescharacteristic
748C2×C4C2×#23712yes—
749C2×C4#101012yes—
750C2×C4C24×D311yescharacteristic
751C8—22no—
752C8—22no—
753C8—62no—
754C8—62no—
755C2×C3—22no—
756C2×C3—44no—
757C2×C3C2×#54811yescharacteristic
758C2×C3C2×#57711yescharacteristic
759C2×C3#358611yescharacteristic
760D3—81no—
761C22—21no—
762C22—21no—
763C22—24no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22#559812yes—
771C22C22×D3×D411yescharacteristic
772C4—21no—
773C4—21no—
774C4—21no—
775C4—42no—
776C4—44no—
777C4—64no—
778C4—64no—
779C4—121no—
780C4—122no—
781C4—121no—
782C4—122no—
783C4—121no—
784C4#559812yes—
785C4#576212yes—
786C4C22×#23711yescharacteristic
787C4C2×#101011yescharacteristic
788C3#6134011yescharacteristic, complemented, Sylow
789C2—22no—
790C2—44no—
791C2—241no—
792C2C2×#559811yescharacteristic
793C2C2×#576211yescharacteristic
794C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#461C2
socleC22×C3C23×D4
prime radicalC2×#932C22
hypercenterC2×#461D3
hypocenterC3#61340
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. #86204C2semidirect
2. #85766C2semidirect
3. C2×C3×#461C2semidirect
5. #83843C2semidirect
6. #83198C2semidirect
8. #80419C2semidirect
9. #80418C2semidirect
10. #80417C2semidirect
11. #80416C2semidirect
12. #80415C2semidirect
13. #80414C2semidirect
14. #79025C2semidirect
15. #79008C2semidirect
16. #78785C2semidirect
17. #78779C2semidirect
27. #5732C22semidirect
28. #5732C22semidirect
32. #5721C22semidirect
33. #5721C22semidirect
67. #5082C22semidirect
68. #5079C22semidirect
69. #5079C22semidirect
77. #4851C22semidirect
78. #4850C22semidirect
79. #4847C22semidirect
80. #4846C22semidirect
81. #4842C22semidirect
82. #4831C22semidirect
83. #4830C22semidirect
84. #4829C22semidirect
85. #4828C22semidirect
86. #4800C22semidirect
87. #4799C22semidirect
88. #4797C22semidirect
89. #4796C22semidirect
90. #4794C22semidirect
91. #4793C22semidirect
92. #4792C22semidirect
93. #4791C22semidirect
107. C2×#461D3semidirect
788. C3#61340semidirect

Maximal subgroups

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

subgroupindex
#862042
#857662
C2×C3×#4612
#838482
#838432
#831982
C4×#9322
#804192
#804182
#804172
#804162
#804152
#804142
#790252
#790082
#787852
#787792
#613403