Finite Group Databasebeta

← #11675231

Subgroups — #11675231

Order 768.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86204C211yesmaximal, characteristic, complemented
2#85828C211yesmaximal, characteristic, complemented
3C3×#3039C211yesmaximal, characteristic, complemented
4#83971C212yesmaximal
5#83965C212yesmaximal, complemented
6C2×#5079C211yesmaximal, characteristic, complemented
7C4×#950C211yesmaximal, characteristic
8#80465C212yesmaximal, complemented
9#80464C212yesmaximal, complemented
10#80463C212yesmaximal, complemented
11#80462C212yesmaximal, complemented
12#80417C212yesmaximal, complemented
13#80416C212yesmaximal, complemented
14#80415C212yesmaximal, complemented
15#80414C212yesmaximal, complemented
16#79060C211yesmaximal, characteristic, complemented
17#79044C211yesmaximal, characteristic, complemented
18#78952C212yesmaximal, complemented
19#78950C212yesmaximal, complemented
20#61330—31nomaximal, Sylow
21C2×C3×#137C2212yes—
22C2×C3×C4⋊Q8C2211yescharacteristic
23C3×C4×#41C2211yescharacteristic
24#5827C2212yes—
25C2×#950C2211yescharacteristic
26#5816C2212yes—
27#5812C2212yes—
28#5732C2212yes—
29#5732C2212yes—
30#5731—22no—
31#5728—21no—
32#5728—21no—
33#5721C2212yes—
34#5721C2212yes—
35#5570C2212yes—
36Q8×Dic6C2212yes—
37#5543—22no—
38#5543C2212yes—
39D4×Dic6—22no—
40D4×Dic6C2212yes—
41#5519—22no—
42#5519C2212yes—
43#5513—22no—
44#5513—22no—
45C4×#235C2211yescharacteristic
46#5470—21no—
47#5470C2211yescharacteristic
48C2×#869—21no—
49C2×#869C2211yescharacteristic
50C3×#462C2212yes—
51C3×#462C2212yes—
52C3×#461C2212yes—
53C3×#461C2212yes—
54C3×#423C2211yescharacteristic
55C3×#419C2212yes—
56#5233C2211yescharacteristic
57C2×#835C2212yes—
58C2×#835C2212yes—
59#5185C2214yes—
60#5184C2214yes—
61#5182C2214yes—
62Dic3×Q16C2214yes—
63#5165C2214yes—
64#5164C2214yes—
65#5162C2214yes—
66Dic3×SD16C2214yes—
67#5133C2212yes—
68#5122C2212yes—
69#5121C2212yes—
70#5119C2212yes—
71#5079C2212yes—
72#5079C2212yes—
73#5079C2212yes—
74#5079C2212yes—
75C4×#216C2211yescharacteristic
76C4×#216C2211yescharacteristic
77C4×#215C2211yescharacteristic
78C4×#215C2211yescharacteristic
79C4×#214C2211yescharacteristic
80C4×#214C2211yescharacteristic
81C4×#213C2211yescharacteristic
82C4×#213C2211yescharacteristic
83#5002C2211yescharacteristic
84#4998C2211yescharacteristic
85C2×C4×C3⋊C8C2211yescharacteristic
86#4851C2212yes—
87#4850C2212yes—
88#4846C2212yes—
89#4842C2212yes—
90#4831C2212yes—
91#4831C2212yes—
92#4830C2212yes—
93#4830C2212yes—
94#4800C2214yes—
95#4799C2214yes—
96#4797C2214yes—
97#4796C2214yes—
98#4794C2214yes—
99#4793C2214yes—
100#4792C2214yes—
101#4791C2214yes—
102#3509—31no—
103#3503—31no—
104#3374—32no—
105#3372—32no—
106#3369—32no—
107#3367—32no—
108#3364—32no—
109#3363—32no—
110#3360—32no—
111#3359—32no—
112#3137—32no—
113C2×#487—31no—
114#3082—32no—
115#3079—31no—
116#3046—32no—
117#3039D311yescharacteristic, complemented
118#2960—31no—
119#2947—32no—
120C4×#135—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8C2312yes—
123C2×#235C2311yescharacteristic
124C22×Dic6—21no—
125C22×Dic6—22no—
126C3×#137—28no—
127C2×C3×Q16C2314yes—
128C2×C3×SD16C2314yes—
129C2×C3×M16C2312yes—
130C3×C4⋊Q8—21no—
131C3×C4⋊Q8—21no—
132C3×C4⋊Q8C2312yes—
133C3×C4⋊Q8C2312yes—
134C3×C4×Q8C2311yescharacteristic
135C3×C4×Q8C2311yescharacteristic
136C3×C4×D4—21no—
137C3×C4×D4—21no—
138C3×C4×D4C2311yescharacteristic
139C3×C4×D4C2311yescharacteristic
140C3×#117—21no—
141C3×#117C2311yescharacteristic
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C42—21no—
145C2×C3×C42C2311yescharacteristic
146#950—24no—
147#947C2314yes—
148#946—22no—
149#946—22no—
150Q8×Dic3—22no—
151Q8×Dic3—22no—
152Q8×Dic3C2314yes—
153Q8×Dic3C2314yes—
154Q8×Dic3C2314yes—
155#944C2314yes—
156C2×#216C2311yescharacteristic
157C2×#215C2311yescharacteristic
158D4×Dic3—24no—
159D4×Dic3C2314yes—
160C2×#214C2311yescharacteristic
161C2×#213C2311yescharacteristic
162#929—24no—
163C4×#67—21no—
164C4×#67—21no—
165#926—24no—
166#926—22no—
167#926C2311yescharacteristic
168#926C2312yes—
169C2×C4⋊Dic3—21no—
170C2×C4⋊Dic3—22no—
171C2×C4⋊Dic3—22no—
172C2×C4⋊Dic3C2312yes—
173#924—22no—
174#924—22no—
175#924D412yes—
176#924D412yes—
177C22×C3⋊C8C2311yescharacteristic
178C22×C3⋊C8C2311yescharacteristic
179#898—24no—
180#898—24no—
181#897—22no—
182#897—22no—
183#892—22no—
184#892—22no—
185#890—22no—
186#890—22no—
187#890—24no—
188#890C2314yes—
189#889—24no—
190#889—24no—
191#888—24no—
192#888C2314yes—
193#887—22no—
194#887—22no—
195#878—24no—
196#878—24no—
197#878—24no—
198C4×D12C2311yescharacteristic
199C4×D12C2311yescharacteristic
200#872—21no—
201C42×D3—21no—
202#870—22no—
203#870D412yes—
204#869—22no—
205#869—21no—
206#869—21no—
207#869—22no—
208#869—22no—
209#869D411yescharacteristic
210#869D411yescharacteristic
211#869C2312yes—
212#869C2312yes—
213C4×Dic6—22no—
214C4×Dic6—22no—
215C4×Dic6C2311yescharacteristic
216C4×Dic6C2311yescharacteristic
217C4×Dic6C2312yes—
218C4×Dic6C2312yes—
219C3×C4⋊C8C2312yes—
220C3×C4⋊C8C2312yes—
221C3×#103C2314yes—
222C3×#103C2314yes—
223#835C2314yes—
224#835C2314yes—
225#835C2314yes—
226#835C2314yes—
227#835C2311yescharacteristic
228#835C2311yescharacteristic
229#832C2311yescharacteristic
230#832C2311yescharacteristic
231#821C2314yes—
232#818C2314yes—
233#817C2314yes—
234#816C2314yes—
235#815C2314yes—
236Dic3⋊C8C2314yes—
237Dic3⋊C8C2314yes—
238C8×Dic3C2314yes—
239#810C2311yescharacteristic
240#810C2311yescharacteristic
241#809C2311yescharacteristic
242#809C2311yescharacteristic
243#808C2311yescharacteristic
244#808C2311yescharacteristic
245#807C2311yescharacteristic
246#807C2311yescharacteristic
247C4×C3⋊C8C2311yescharacteristic
248C4×C3⋊C8C2311yescharacteristic
249C4×C3⋊C8C2311yescharacteristic
250C4×C3⋊C8C2311yescharacteristic
251C2×#137C2×D312yes—
252C2×#135—31no—
253Q82—32no—
254#557—32no—
255#557—32no—
256#557—32no—
257#556—32no—
258#556—32no—
259#554—32no—
260#554—62no—
261#552—62no—
262#552—62no—
263D4×Q8—32no—
264D4×Q8—62no—
265#544—32no—
266#544—62no—
267#541—62no—
268#536—32no—
269#533—31no—
270#533—61no—
271#533—61no—
272#533—61no—
273C2×C4⋊Q8—31no—
274C2×C4⋊Q8—61no—
275C2×C4⋊Q8C2×D311yescharacteristic
276#520—32no—
277#519—32no—
278C4×#41—31no—
279C4×#41C2×D311yescharacteristic
280#491—34no—
281#489—34no—
282#488—34no—
283#487—32no—
284#487—32no—
285#487—32no—
286#487—32no—
287#487—34no—
288#479—34no—
289#479—34no—
290#477—32no—
291#477—34no—
292#476—32no—
293#475—32no—
294#475—34no—
295#474—32no—
296#464—34no—
297#463—34no—
298#462—34no—
299#462C2×D312yes—
300#462C2×D312yes—
301#461—34no—
302#461C2×D312yes—
303#461C2×D312yes—
304#446—32no—
305#446—32no—
306C8×Q8—32no—
307C8×Q8—32no—
308#441—34no—
309#440—34no—
310C4×Q16—34no—
311C4×Q16—31no—
312C4×Q16—31no—
313C4×SD16—34no—
314C4×SD16—31no—
315C4×SD16—31no—
316C4×SD16—31no—
317C4×SD16—31no—
318C4×D8—31no—
319C4×D8—31no—
320#428—32no—
321#427—31no—
322#424—32no—
323#423C2×D311yescharacteristic
324#419C2×D312yes—
325#417—32no—
326#416—31no—
327#416—31no—
328C2×#103—32no—
329C2×#103—32no—
330#405—32no—
331C2×C4×C8—31no—
332C3×#41—22no—
333C3×#41#4114yes—
334C2×C3×Q8—22no—
335C2×C3×Q8—24no—
336C2×C3×Q8—24no—
337C2×C3×Q8C2414yes—
338C2×C3×Q8C2411yescharacteristic
339C2×C3×D4—21no—
340C2×C3×D4C2411yescharacteristic
341C22×C3×C4—21no—
342C22×C3×C4—22no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4C2×D411yescharacteristic
346C22×C3×C4C2×D411yescharacteristic
347C22×C3×C4C2411yescharacteristic
348C2×#67—21no—
349C22×Dic3—22no—
350C22×Dic3—24no—
351#235—22no—
352#235—22no—
353C2×D12C2411yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—21no—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—24no—
360C2×Dic6—84no—
361C2×Dic6—82no—
362C2×Dic6C2×D412yes—
363C2×Dic6C2×D412yes—
364C2×Dic6C2411yescharacteristic
365C3×Q16—28no—
366C3×SD16—28no—
367C3×M16—24no—
368C2×C3×C8C2414yes—
369C3×C4⋊C4—22no—
370C3×C4⋊C4—22no—
371C3×C4⋊C4—21no—
372C3×C4⋊C4—22no—
373C3×C4⋊C4—22no—
374C3×C4⋊C4—21no—
375C3×C4⋊C4C2411yescharacteristic
376C3×C4⋊C4C2411yescharacteristic
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—21no—
383C3×C42C2×D411yescharacteristic
384C3×C42C2×D411yescharacteristic
385C3×C42C2411yescharacteristic
386C3×C42C2411yescharacteristic
387#217—21no—
388#217—24no—
389#217C2×D414yes—
390#216—22no—
391#215—22no—
392#214—22no—
393#213—22no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—24no—
397(C2×D3)⋊C4—24no—
398C4⋊Dic3—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—22no—
401C4⋊Dic3—24no—
402C4⋊Dic3—24no—
403C4⋊Dic3—24no—
404C4⋊Dic3—24no—
405C4⋊Dic3C2×D412yes—
406C4⋊Dic3C2×D412yes—
407C4⋊Dic3C2×D412yes—
408C4⋊Dic3C2×D412yes—
409C4⋊Dic3C2411yescharacteristic
410C4⋊Dic3C2411yescharacteristic
411C4⋊Dic3C2414yes—
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414Dic3⋊C4—24no—
415Dic3⋊C4—24no—
416Dic3⋊C4—24no—
417Dic3⋊C4—24no—
418Dic3⋊C4C2×D414yes—
419Dic3⋊C4C2×D414yes—
420C4×Dic3—21no—
421C4×Dic3—21no—
422C4×Dic3—21no—
423C4×Dic3—24no—
424C4×Dic3—24no—
425C4×Dic3—24no—
426C4×Dic3C2414yes—
427C2×C3⋊C8—22no—
428C2×C3⋊C8—22no—
429C2×C3⋊C8C2411yescharacteristic
430C2×C3⋊C8C2411yescharacteristic
431C2×C3⋊C8C2411yescharacteristic
432C2×C3⋊C8C2411yescharacteristic
433C2×#41—31no—
434C2×#41C22×D311yescharacteristic
435C22×Q8—62no—
436C22×Q8—61no—
437C22×Q8C22×D312yes—
438#137—28no—
439#135—64no—
440C2×Q16—31no—
441C2×Q16C22×D314yes—
442C2×SD16—31no—
443C2×SD16—31no—
444C2×SD16C22×D314yes—
445C2×D8—31no—
446C2×M16C22×D312yes—
447C22×C8—31no—
448C22×C8—31no—
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—34no—
452C4⋊Q8—34no—
453C4⋊Q8—31no—
454C4⋊Q8—31no—
455C4⋊Q8—32no—
456C4⋊Q8—32no—
457C4⋊Q8—62no—
458C4⋊Q8—62no—
459C4⋊Q8—62no—
460C4⋊Q8—64no—
461C4⋊Q8—61no—
462C4⋊Q8—61no—
463C4⋊Q8C22×D312yes—
464C4⋊Q8C22×D312yes—
465#126—64no—
466#126—64no—
467#125—34no—
468#125—32no—
469#125—62no—
470#125—62no—
471#125—62no—
472#125—64no—
473#125—64no—
474#125—64no—
475#124—34no—
476#123—64no—
477C22⋊Q8—32no—
478C22⋊Q8—32no—
479C22⋊Q8—64no—
480C22⋊Q8—64no—
481C22⋊Q8—64no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C4×Q8—32no—
489C4×Q8—32no—
490C4×Q8—34no—
491C4×Q8—34no—
492C4×Q8—34no—
493C4×Q8—31no—
494C4×Q8—31no—
495C4×Q8—62no—
496C4×Q8—62no—
497C4×Q8—62no—
498C4×Q8—62no—
499C4×Q8—62no—
500C4×Q8—62no—
501C4×Q8C22×D311yescharacteristic
502C4×Q8C22×D311yescharacteristic
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—34no—
506C4×D4—31no—
507C4×D4—31no—
508C4×D4—64no—
509C4×D4—61no—
510C4×D4—61no—
511C4×D4C22×D311yescharacteristic
512C4×D4C22×D311yescharacteristic
513#117—21no—
514#117—32no—
515#117—31no—
516#117—64no—
517#117—62no—
518#117—62no—
519#117—62no—
520#117—61no—
521#117C22×D311yescharacteristic
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—32no—
525C2×C4⋊C4—62no—
526C2×C4⋊C4—62no—
527C2×C4⋊C4—61no—
528C2×C42—21no—
529C2×C42—61no—
530C2×C42C22×D311yescharacteristic
531#107—34no—
532#107—31no—
533#107—31no—
534#106—34no—
535#106—31no—
536#106—31no—
537C4⋊C8—34no—
538C4⋊C8—34no—
539C4⋊C8C22×D312yes—
540C4⋊C8C22×D312yes—
541#103—34no—
542#103—34no—
543#103—34no—
544#103—34no—
545#103—31no—
546#103—31no—
547#103—34no—
548#103—31no—
549#103—31no—
550#103C22×D314yes—
551#103C22×D314yes—
552#102—31no—
553#102—31no—
554#102—34no—
555#102—31no—
556#102—31no—
557#97—34no—
558C4×C8—34no—
559C4×C8—31no—
560C4×C8—31no—
561C4×C8—31no—
562C4×C8—31no—
563C23×C3—21no—
564C23×C3C22×D411yescharacteristic
565C22×D3—21no—
566C3×Q8—21no—
567C3×Q8—24no—
568C3×Q8—24no—
569C3×Q8—44no—
570C3×Q8C2×#4112yes—
571C3×D4—24no—
572C3×D4—21no—
573C3×D4C2×#4112yes—
574C2×C3×C4—21no—
575C2×C3×C4—24no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—24no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—44no—
582C2×C3×C4—42no—
583C2×C3×C4—42no—
584C2×C3×C4C22×D411yescharacteristic
585C2×C3×C4C22×D411yescharacteristic
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C2×C3×C4C22×D411yescharacteristic
589C2×C3×C4C2×#4112yes—
590C2×C3×C42−1+412yes—
591C2×C3×C4C2511yescharacteristic
592#67—42no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—24no—
597C2×Dic3—84no—
598C2×Dic3—82no—
599C2×Dic3C22×D414yes—
600C2×Dic3C22×D414yes—
601D12—21no—
602D12—21no—
603C4×D3—42no—
604C4×D3—42no—
605C4×D3—42no—
606Dic6—24no—
607Dic6—24no—
608Dic6—21no—
609Dic6—21no—
610Dic6—44no—
611Dic6—84no—
612Dic6—82no—
613C3×C8—24no—
614C3⋊C8—21no—
615C3⋊C8—21no—
616C3⋊C8—21no—
617C3⋊C8—21no—
618#41—22no—
619#41—62no—
620#41—62no—
621#41#23714yes—
622C2×Q8—22no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—32no—
626C2×Q8—32no—
627C2×Q8—31no—
628C2×Q8—64no—
629C2×Q8—62no—
630C2×Q8—62no—
631C2×Q8—242no—
632C2×Q8—244no—
633C2×Q8C23×D314yes—
634C2×Q8C23×D311yescharacteristic
635C2×D4—21no—
636C2×D4—31no—
637C2×D4—61no—
638C2×D4C23×D311yescharacteristic
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—64no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4D3×D411yescharacteristic
649C22×C4D3×D411yescharacteristic
650C22×C4C23×D311yescharacteristic
651Q16—28no—
652Q16—62no—
653SD16—28no—
654SD16—62no—
655SD16—62no—
656D8—62no—
657M16—24no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—62no—
663C2×C8—62no—
664C2×C8C23×D314yes—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—32no—
672C4⋊C4—32no—
673C4⋊C4—32no—
674C4⋊C4—32no—
675C4⋊C4—34no—
676C4⋊C4—34no—
677C4⋊C4—34no—
678C4⋊C4—31no—
679C4⋊C4—31no—
680C4⋊C4—64no—
681C4⋊C4—64no—
682C4⋊C4—64no—
683C4⋊C4—64no—
684C4⋊C4—64no—
685C4⋊C4—64no—
686C4⋊C4—64no—
687C4⋊C4—64no—
688C4⋊C4—62no—
689C4⋊C4—62no—
690C4⋊C4—62no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4C23×D311yescharacteristic
694C4⋊C4C23×D311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—34no—
699C22⋊C4—64no—
700C22⋊C4—64no—
701C22⋊C4—64no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C42—21no—
706C42—21no—
707C42—21no—
708C42—34no—
709C42—64no—
710C42—64no—
711C42—64no—
712C42—61no—
713C42—61no—
714C42—61no—
715C42D3×D411yescharacteristic
716C42D3×D411yescharacteristic
717C42C23×D311yescharacteristic
718C42C23×D311yescharacteristic
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—22no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3#54812yes—
725C22×C3C23×D411yescharacteristic
726C2×D3—41no—
727C2×D3—41no—
728C2×D3—41no—
729C3×C4—22no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—44no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4#54812yes—
736C3×C4#57712yes—
737C3×C4#57812yes—
738C3×C4C22×#4111yescharacteristic
739C3×C4C2×2−1+411yescharacteristic
740Dic3—24no—
741Dic3—24no—
742Dic3—41no—
743Dic3—44no—
744Dic3—41no—
745Dic3—41no—
746C23—21no—
747C23—61no—
748C23C2×D3×D411yescharacteristic
749Q8—21no—
750Q8—24no—
751Q8—24no—
752Q8—44no—
753Q8—64no—
754Q8—64no—
755Q8—61no—
756Q8—61no—
757Q8—124no—
758Q8—242no—
759Q8—244no—
760Q8C2×#23712yes—
761D4—24no—
762D4—21no—
763D4—61no—
764D4—61no—
765D4—122no—
766D4C2×#23712yes—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—24no—
774C2×C4—34no—
775C2×C4—34no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—64no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4—122no—
786C2×C4—244no—
787C2×C4—242no—
788C2×C4C2×D3×D411yescharacteristic
789C2×C4C2×D3×D411yescharacteristic
790C2×C4C2×D3×D411yescharacteristic
791C2×C4C2×D3×D411yescharacteristic
792C2×C4C2×D3×D411yescharacteristic
793C2×C4C2×#23712yes—
794C2×C4#101012yes—
795C2×C4C24×D311yescharacteristic
796C8—24no—
797C8—61no—
798C8—61no—
799C8—61no—
800C8—61no—
801C2×C3—22no—
802C2×C3—42no—
803C2×C3C2×#54811yescharacteristic
804C2×C3C2×#57711yescharacteristic
805C2×C3C2×#57811yescharacteristic
806D3—81no—
807C22—21no—
808C22—21no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22#559812yes—
816C22C22×D3×D411yescharacteristic
817C4—21no—
818C4—21no—
819C4—22no—
820C4—41no—
821C4—41no—
822C4—44no—
823C4—64no—
824C4—64no—
825C4—121no—
826C4—124no—
827C4—121no—
828C4—121no—
829C4#559812yes—
830C4#577812yes—
831C4#577912yes—
832C4C22×#23711yescharacteristic
833C4C2×#101011yescharacteristic
834C3#6133011yescharacteristic, complemented, Sylow
835C2—22no—
836C2—42no—
837C2—241no—
838C2C2×#559811yescharacteristic
839C2C2×#577811yescharacteristic
840C2C2×#577911yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3039C2
socleC22×C3C23×D4
prime radicalC2×#950C22
hypercenter#3039D3
hypocenterC3#61330
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

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

NH ≅ G/Ntype
1. #86204C2semidirect
2. #85828C2semidirect
3. C3×#3039C2semidirect
5. #83965C2semidirect
6. C2×#5079C2semidirect
8. #80465C2semidirect
9. #80464C2semidirect
10. #80463C2semidirect
11. #80462C2semidirect
12. #80417C2semidirect
13. #80416C2semidirect
14. #80415C2semidirect
15. #80414C2semidirect
16. #79060C2semidirect
17. #79044C2semidirect
18. #78952C2semidirect
19. #78950C2semidirect
117. #3039D3semidirect
834. C3#61330semidirect

Maximal subgroups

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

subgroupindex
#862042
#858282
C3×#30392
#839712
#839652
C2×#50792
C4×#9502
#804652
#804642
#804632
#804622
#804172
#804162
#804152
#804142
#790602
#790442
#789522
#789502
#613303