Finite Group Databasebeta

← #11664520

Subgroups — #11664520

Order 768.

2078 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86235C211yesmaximal, characteristic
2C2×#5689C211yesmaximal, characteristic, complemented
3C3×#3142C211yesmaximal, characteristic, complemented
4#83283C211yesmaximal, characteristic, complemented
5#83012C211yesmaximal, characteristic, complemented
6#81738C214yesmaximal, complemented
7#81714C214yesmaximal, complemented
8#81639C214yesmaximal, complemented
9#81638C214yesmaximal, complemented
10#78881C212yesmaximal, complemented
11D3×#417C212yesmaximal, complemented
12#78879C212yesmaximal, complemented
13#78878C212yesmaximal, complemented
14#78528C211yesmaximal, characteristic, complemented
15#78514C211yesmaximal, characteristic, complemented
16#60621—31nomaximal, Sylow
17C2×D3×#41C2212yes—
18C3×#532C2211yescharacteristic
19C2×C3×#125C2211yescharacteristic, complemented
20#5832C2212yes—
21C2×D3×M16C2212yes—
22#5724C2212yes—
23#5715C2212yes—
24#5689—22no—
25#5689—22no—
26#5689C2214yescomplemented
27#5689C2214yescomplemented
28#5675C2212yes—
29#5674C2212yes—
30#5605—21no—
31#5605—21no—
32#5597—21no—
33#5597—21no—
34#5547—22no—
35#5547—22no—
36C2×#897—21no—
37C2×#896—21no—
38C2×#892C2211yescharacteristic
39C2×D3×C4⋊C4C2211yescharacteristic
40C2×#890C2211yescharacteristic, complemented
41C2×#889—21no—
42C2×#888—21no—
43C2×#888C2211yescharacteristic, complemented
44#5477C2211yescharacteristic
45C2×#872C2211yescharacteristic
46C2×#869C2211yescharacteristic, complemented
47C3×#491C2212yescomplemented
48C3×#490C2212yescomplemented
49C3×#488C2214yescomplemented
50C3×#417C2212yescomplemented
51C3×#417C2212yescomplemented
52C3×C4×M16C2211yescharacteristic, complemented
53#5232C2212yescomplemented
54#5232C2212yescomplemented
55#5133C2212yescomplemented
56#5133C2212yescomplemented
57Dic3×M16C2212yescomplemented
58#5079C2212yescomplemented
59#5070C2212yescomplemented
60#5069C2212yescomplemented
61#5068C2214yescomplemented
62#5067C2212yescomplemented
63#5055C2214yescomplemented
64#4966C2212yescomplemented
65#4966C2212yescomplemented
66C4×#208C2211yescharacteristic, complemented
67#4804C2214yes—
68#4803C2214yes—
69#4802C2214yescomplemented
70D3×#103C2214yescomplemented
71#4800C2214yescomplemented
72#4797C2214yescomplemented
73#4794C2214yescomplemented
74#4792C2214yescomplemented
75#4772C2214yes—
76#4771C2214yes—
77#4770C2214yescomplemented
78D3×#102C2214yescomplemented
79#4768C2214yescomplemented
80#4765C2214yescomplemented
81#4764C2214yescomplemented
82#4760C2214yescomplemented
83#4714C2214yescomplemented
84#4708C2214yescomplemented
85#4694C2212yescomplemented
86#4689C2214yescomplemented
87#4681C2212yescomplemented
88C2×#544—31no—
89#3449—31no—
90#3142—32no—
91#3142—31no—
92#3142D311yescharacteristic, complemented
93#3141—32no—
94#3141—31no—
95#3141—31no—
96#3137—34no—
97#3137—34no—
98#3136—34no—
99#3136—34no—
100#2896—32no—
101C2×#417—32no—
102#2873—31no—
103C2×C3×#41C2312yes—
104D3×#41—28no—
105D3×#41—28no—
106C2×#239C2312yes—
107C2×D3×Q8C2312yes—
108C2×#237—22no—
109C2×#237C2312yes—
110C2×D3×D4—22no—
111C2×D3×D4C2312yes—
112C2×#235—22no—
113C2×#235C2312yes—
114C22×C4×D3—21no—
115C22×C4×D3—22no—
116C22×C4×D3C2311yescharacteristic
117C22×Dic6—21no—
118C22×Dic6—21no—
119C2×C3×M16C2312yes—
120C3×C4⋊Q8C2311yescharacteristic
121C3×#127C2311yescharacteristic
122C3×#125—21no—
123C3×#125—21no—
124C3×#125C2312yes—
125C3×#125C2312yes—
126C3×#124C2312yes—
127C3×#121—21no—
128C3×#121—21no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136#947C2312yes—
137#944C2312yes—
138#940C2312yes—
139#939—22no—
140#939—22no—
141#939—22no—
142#939—22no—
143#937—22no—
144#937—22no—
145#936C2312yes—
146#930—21no—
147#930—21no—
148C4×#67—22no—
149C4×#67—22no—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4D411yescharacteristic
152C2×(C2×D3)⋊C4D411yescharacteristic
153C2×C4⋊Dic3—21no—
154C2×C4⋊Dic3—21no—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×C4⋊Dic3C2311yescharacteristic
157C2×Dic3⋊C4—21no—
158C2×Dic3⋊C4—21no—
159C2×Dic3⋊C4—21no—
160C2×Dic3⋊C4D411yescharacteristic
161C2×Dic3⋊C4D411yescharacteristic
162C2×C4×Dic3—21no—
163C2×C4×Dic3C2311yescharacteristic
164C2×#208C2312yes—
165D3×M16—28no—
166C2×ΓL(1,𝔽25)C2314yes—
167C2×D3×C8C2314yes—
168#897—24no—
169#897—24no—
170#896—24no—
171#896—24no—
172#896—22no—
173#896—22no—
174#894—22no—
175#894—22no—
176#892—22no—
177#892C2314yes—
178D3×C4⋊C4—22no—
179D3×C4⋊C4C2314yes—
180#890—22no—
181#890C2314yes—
182#889—24no—
183#889—24no—
184#888—24no—
185#888—24no—
186#888—22no—
187#888C2314yes—
188#884—22no—
189#884—22no—
190#883—22no—
191#883—22no—
192#882—22no—
193#882—22no—
194#878—22no—
195#878—22no—
196#875C2312yes—
197#874C2311yescharacteristic
198C4×D12—21no—
199C4×D12—21no—
200#872D412yes—
201#872D412yes—
202#872C2312yes—
203#872C2312yes—
204#869—21no—
205#869—21no—
206#869C2311yescharacteristic
207#869C2312yes—
208#869C2312yes—
209C3×#103C2314yes—
210C3×#103C2314yes—
211C3×#102C2314yes—
212C3×#102C2314yes—
213C3×#97C2312yes—
214C3×C4×C8C2312yes—
215#835C2314yes—
216#835C2314yes—
217#832C2314yes—
218#832C2314yes—
219#821C2314yes—
220#821C2314yes—
221#816C2314yes—
222#816C2314yes—
223#815C2314yes—
224C8×Dic3C2314yes—
225#810C2314yes—
226#810C2314yes—
227#809C2314yes—
228#809C2314yes—
229#803C2312yes—
230C4×C3⋊C8C2312yes—
231C22×#41—32no—
232C22×M16—32no—
233#544—34no—
234#544—34no—
235#544—62no—
236#544—62no—
237#537—61no—
238#537—61no—
239#536—32no—
240#536—32no—
241#535—32no—
242#535—32no—
243#534—61no—
244#534—61no—
245#532—32no—
246#532—31no—
247#532C2×D311yescharacteristic
248C2×C4⋊Q8—31no—
249C2×C4⋊Q8—31no—
250C2×C4⋊Q8—61no—
251C2×#125—31no—
252C2×#125—61no—
253C2×#125C2×D311yescharacteristic, complemented
254#525—62no—
255#525—62no—
256C2×C22⋊Q8—61no—
257C2×C22⋊Q8—61no—
258C2×#117—31no—
259C2×#117—31no—
260C22×C4⋊C4—31no—
261#491—32no—
262#491—34no—
263#491C2×D312yescomplemented
264#490—32no—
265#490—34no—
266#490C2×D312yescomplemented
267#489—34no—
268#489—34no—
269#489—34no—
270#489—34no—
271#488—34no—
272#488—34no—
273#488—34no—
274#488C2×D314yescomplemented
275#487—32no—
276#487—34no—
277#487—32no—
278#486—32no—
279#486—34no—
280#486—32no—
281#419—34no—
282#418—34no—
283#417—32no—
284#417—32no—
285#417—32no—
286#417—32no—
287#417—32no—
288#417—32no—
289#417—34no—
290#417—34no—
291#417C2×D312yescomplemented
292#417C2×D312yescomplemented
293#416—34no—
294#416—34no—
295C2×#103—34no—
296C2×#102—34no—
297#405—34no—
298#405—34no—
299C4×M16—32no—
300C4×M16—31no—
301C4×M16C2×D311yescharacteristic, complemented
302C23×D3—22no—
303C23×D3C2×D411yescharacteristic
304C3×#41—24no—
305C3×#41—24no—
306C2×C3×Q8C2412yes—
307C2×C3×D4—22no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4C2412yes—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—22no—
314C22×C3×C4C2×D411yescharacteristic
315C22×C3×C4C2×D411yescharacteristic
316C22×C3×C4C2411yescharacteristic
317C2×#67—22no—
318C2×#67—22no—
319C2×#67—22no—
320C2×#67—22no—
321C2×#67—22no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—22no—
325C22×Dic3C2×D411yescharacteristic
326C22×Dic3C2×D411yescharacteristic
327C22×Dic3C2×D411yescharacteristic
328#239—24no—
329#239—24no—
330D3×Q8—24no—
331D3×Q8—24no—
332#237—24no—
333#237—24no—
334#237—48no—
335D3×D4—24no—
336D3×D4—24no—
337D3×D4—48no—
338#235—24no—
339#235—24no—
340#235—48no—
341C2×D12—22no—
342C2×D12—21no—
343C2×D12—21no—
344C2×D12C2412yes—
345C2×C4×D3—22no—
346C2×C4×D3—22no—
347C2×C4×D3—22no—
348C2×C4×D3—24no—
349C2×C4×D3—48no—
350C2×C4×D3—82no—
351C2×C4×D3C2×D412yes—
352C2×C4×D3#4118yes—
353C2×C4×D3C2412yes—
354C2×Dic6—22no—
355C2×Dic6—22no—
356C2×Dic6—22no—
357C2×Dic6—24no—
358C2×Dic6—82no—
359C2×Dic6—82no—
360C2×Dic6C2412yes—
361C3×M16—24no—
362C2×C3×C8C2414yes—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—22no—
365C3×C4⋊C4—22no—
366C3×C4⋊C4—22no—
367C3×C4⋊C4—22no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4C2412yes—
372C3×C4⋊C4C2412yes—
373C3×C22⋊C4—22no—
374C3×C22⋊C4—22no—
375C3×C42C2×D411yescharacteristic
376C3×C42C2×D411yescharacteristic
377C3×C42C2411yescharacteristic
378C3×C42C2411yescharacteristic
379#217—22no—
380#217—22no—
381(C2×D3)⋊C4—24no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—22no—
384(C2×D3)⋊C4—22no—
385(C2×D3)⋊C4—22no—
386(C2×D3)⋊C4C2×D412yes—
387(C2×D3)⋊C4C2×D412yes—
388(C2×D3)⋊C4C2×D412yes—
389(C2×D3)⋊C4C2×D412yes—
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—22no—
393C4⋊Dic3—22no—
394C4⋊Dic3—21no—
395C4⋊Dic3—21no—
396C4⋊Dic3—24no—
397C4⋊Dic3C2412yes—
398C4⋊Dic3C2412yes—
399Dic3⋊C4—22no—
400Dic3⋊C4—22no—
401Dic3⋊C4—24no—
402Dic3⋊C4—24no—
403Dic3⋊C4—24no—
404Dic3⋊C4C2×D412yes—
405Dic3⋊C4C2×D412yes—
406Dic3⋊C4C2×D412yes—
407Dic3⋊C4C2×D412yes—
408C4×Dic3—24no—
409C4×Dic3C2×D412yes—
410C4×Dic3C2412yes—
411#208—24no—
412C2×C3⋊C8C2414yes—
413ΓL(1,𝔽25)—28no—
414D3×C8—28no—
415C2×#41—32no—
416C2×#41—32no—
417C2×#41—32no—
418C2×#41—62no—
419C2×#41—62no—
420C2×#41—68no—
421C2×#41—68no—
422C2×#41C22×D312yes—
423C22×Q8—32no—
424C22×Q8—61no—
425C22×Q8—61no—
426C22×D4—32no—
427C22×D4—62no—
428C23×C4—31no—
429C23×C4—62no—
430C23×C4—61no—
431C2×M16—32no—
432C2×M16—34no—
433C2×M16—68no—
434C2×M16C22×D312yes—
435C22×C8—34no—
436C4⋊Q8—34no—
437C4⋊Q8—32no—
438C4⋊Q8—32no—
439C4⋊Q8—32no—
440C4⋊Q8—31no—
441C4⋊Q8—62no—
442C4⋊Q8—64no—
443C4⋊Q8—64no—
444C4⋊Q8—61no—
445C4⋊Q8—61no—
446C4⋊Q8C22×D311yescharacteristic
447#127—32no—
448#127—31no—
449#127C22×D311yescharacteristic
450#125—21no—
451#125—21no—
452#125—34no—
453#125—62no—
454#125—64no—
455#125—64no—
456#125C22×D312yes—
457#125C22×D312yes—
458#124—32no—
459#124—32no—
460#124—32no—
461#124C22×D312yes—
462#123—62no—
463#123—62no—
464#123—62no—
465#123—62no—
466C22⋊Q8—62no—
467C22⋊Q8—62no—
468C22⋊Q8—64no—
469C22⋊Q8—64no—
470C22⋊Q8—64no—
471C22⋊Q8—64no—
472C22⋊Q8—62no—
473C22⋊Q8—62no—
474#121—21no—
475#121—21no—
476#121—62no—
477#121—62no—
478#121—62no—
479#121—62no—
480#121—62no—
481#121—62no—
482#121—61no—
483#121—61no—
484#120—62no—
485#120—62no—
486#120—62no—
487#120—62no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—62no—
491C4×D4—62no—
492C4×D4—61no—
493C4×D4—61no—
494#117—32no—
495#117—32no—
496#117—32no—
497#117—32no—
498#117—34no—
499#117—62no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—31no—
505C2×C4⋊C4—31no—
506C2×C4⋊C4—34no—
507C2×C4⋊C4—62no—
508C2×C4⋊C4—61no—
509C2×C4⋊C4—61no—
510C2×C4⋊C4—61no—
511C2×C4⋊C4—61no—
512C2×C4⋊C4—61no—
513C2×C4⋊C4C22×D311yescharacteristic
514C2×C4⋊C4C22×D311yescharacteristic
515C2×C22⋊C4—31no—
516C2×C22⋊C4—31no—
517C2×C22⋊C4—61no—
518C2×C42—31no—
519C2×C42—61no—
520C2×C42C22×D311yescharacteristic
521#103—34no—
522#103—34no—
523#103—34no—
524#103—34no—
525#103—34no—
526#103—34no—
527#103C22×D314yes—
528#103C22×D314yes—
529#102—34no—
530#102—34no—
531#102—34no—
532#102—34no—
533#102—34no—
534#102—34no—
535#102C22×D314yes—
536#102C22×D314yes—
537#97—34no—
538#97—32no—
539#97C22×D312yes—
540C4×C8—34no—
541C4×C8—32no—
542C4×C8C22×D312yes—
543C23×C3—22no—
544C23×C3C22×D411yescharacteristic
545C22×D3—22no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—44no—
549C22×D3—82no—
550C22×D3—82no—
551C22×D3#12414yes—
552C22×D3C22×D412yes—
553C3×Q8—22no—
554C3×Q8—22no—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—44no—
558C3×D4—81no—
559C3×D4—81no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—41no—
564C2×C3×C4—41no—
565C2×C3×C4—42no—
566C2×C3×C4—42no—
567C2×C3×C4—44no—
568C2×C3×C4C22×D411yescharacteristic
569C2×C3×C4C22×D411yescharacteristic
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4C22×D411yescharacteristic
572C2×C3×C4C22×D411yescharacteristic
573C2×C3×C4C2×#4114yes—
574C2×C3×C4C2511yescharacteristic
575#67—44no—
576#67—44no—
577#67—44no—
578#67—82no—
579#67—82no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—41no—
584C2×Dic3—41no—
585C2×Dic3—42no—
586C2×Dic3—42no—
587C2×Dic3—44no—
588C2×Dic3#12414yes—
589C2×Dic3C22×D412yes—
590C2×Dic3C22×D412yes—
591C2×Dic3C22×D412yes—
592D12—22no—
593D12—22no—
594D12—44no—
595D12—81no—
596D12—81no—
597C4×D3—44no—
598C4×D3—44no—
599C4×D3—44no—
600C4×D3—84no—
601C4×D3#12418yes—
602C4×D3C2×#4114yes—
603C4×D3C2×#4114yes—
604Dic6—22no—
605Dic6—22no—
606Dic6—44no—
607Dic6—84no—
608Dic6—82no—
609Dic6—82no—
610C3×C8—24no—
611C3⋊C8—24no—
612C24—31no—
613C24—62no—
614#41—24no—
615#41—24no—
616#41—64no—
617#41—64no—
618#41—64no—
619#41—64no—
620#41—64no—
621#41—64no—
622#41—128no—
623#41—128no—
624C2×Q8—32no—
625C2×Q8—62no—
626C2×Q8—64no—
627C2×Q8—64no—
628C2×Q8—64no—
629C2×Q8—62no—
630C2×Q8—62no—
631C2×Q8—242no—
632C2×Q8—242no—
633C2×Q8C23×D312yes—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—32no—
638C2×D4—62no—
639C2×D4—64no—
640C2×D4—64no—
641C2×D4—62no—
642C2×D4—62no—
643C2×D4—62no—
644C2×D4—62no—
645C2×D4—62no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—128no—
649C2×D4C23×D312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—31no—
654C22×C4—32no—
655C22×C4—38no—
656C22×C4—32no—
657C22×C4—31no—
658C22×C4—31no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—64no—
662C22×C4—62no—
663C22×C4—61no—
664C22×C4—61no—
665C22×C4—62no—
666C22×C4—128no—
667C22×C4—242no—
668C22×C4D3×D411yescharacteristic
669C22×C4D3×D411yescharacteristic
670C22×C4C23×D311yescharacteristic
671M16—24no—
672M16—68no—
673M16—64no—
674C2×C8—34no—
675C2×C8—68no—
676C2×C8C23×D314yes—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—32no—
688C4⋊C4—32no—
689C4⋊C4—32no—
690C4⋊C4—32no—
691C4⋊C4—64no—
692C4⋊C4—64no—
693C4⋊C4—64no—
694C4⋊C4—64no—
695C4⋊C4—62no—
696C4⋊C4—62no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—62no—
700C4⋊C4—62no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C4⋊C4C23×D312yes—
704C4⋊C4C23×D312yes—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—32no—
708C22⋊C4—32no—
709C22⋊C4—32no—
710C22⋊C4—32no—
711C22⋊C4—62no—
712C22⋊C4—62no—
713C22⋊C4—64no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C42—32no—
719C42—32no—
720C42—64no—
721C42D3×D411yescharacteristic
722C42D3×D411yescharacteristic
723C42C23×D311yescharacteristic
724C42C23×D311yescharacteristic
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3C2×#12412yes—
731C22×C3C23×D411yescharacteristic
732C2×D3—22no—
733C2×D3—22no—
734C2×D3—44no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—88no—
739C2×D3C2×#12414yes—
740C3×C4—21no—
741C3×C4—21no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—42no—
745C3×C4—42no—
746C3×C4—42no—
747C3×C4C2×#12412yes—
748C3×C4C22×#4112yes—
749Dic3—22no—
750Dic3—22no—
751Dic3—42no—
752Dic3—42no—
753Dic3—42no—
754Dic3C2×#12414yes—
755C23—22no—
756C23—32no—
757C23—34no—
758C23—62no—
759C23—121no—
760C23—121no—
761C23—124no—
762C23—242no—
763C23—242no—
764C23C2×D3×D411yescharacteristic
765Q8—22no—
766Q8—22no—
767Q8—62no—
768Q8—62no—
769Q8—124no—
770Q8—242no—
771Q8—242no—
772Q8—244no—
773D4—22no—
774D4—22no—
775D4—44no—
776D4—62no—
777D4—62no—
778D4—81no—
779D4—81no—
780D4—124no—
781D4—124no—
782D4—124no—
783D4—124no—
784D4—241no—
785D4—241no—
786D4—242no—
787D4—242no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—34no—
792C2×C4—32no—
793C2×C4—38no—
794C2×C4—34no—
795C2×C4—34no—
796C2×C4—32no—
797C2×C4—32no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—62no—
806C2×C4—124no—
807C2×C4—124no—
808C2×C4—124no—
809C2×C4—121no—
810C2×C4—121no—
811C2×C4—122no—
812C2×C4—122no—
813C2×C4—124no—
814C2×C4—244no—
815C2×C4C2×D3×D411yescharacteristic
816C2×C4C2×D3×D411yescharacteristic
817C2×C4C2×D3×D411yescharacteristic
818C2×C4C2×D3×D411yescharacteristic
819C2×C4C2×D3×D411yescharacteristic
820C2×C4D3×#4114yes—
821C2×C4C24×D311yescharacteristic
822C8—24no—
823C8—64no—
824C2×C3—22no—
825C2×C3—82no—
826C2×C3C22×#12411yescharacteristic
827C2×C3#358511yescharacteristic
828C2×C3#358611yescharacteristic
829D3—24no—
830D3—82no—
831C22—21no—
832C22—21no—
833C22—34no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—62no—
838C22—62no—
839C22—124no—
840C22—122no—
841C22—122no—
842C22—122no—
843C22—248no—
844C22D3×#12412yes—
845C22C22×D3×D411yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—34no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—62no—
855C4—62no—
856C4—122no—
857C4—122no—
858C4—122no—
859C4D3×#12412yes—
860C4C2×D3×#4112yes—
861C3#6062111yescharacteristic, complemented, Sylow
862C2—22no—
863C2—64no—
864C2—82no—
865C2—242no—
866C2C2×D3×#12411yescharacteristic
867C2#8720011yescharacteristic
868C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3142C2
socleC22×C3C23×D4
prime radical#86235C2
hypercenter#3142D3
hypocenterC3#60621
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
2. C2×#5689C2semidirect
3. C3×#3142C2semidirect
4. #83283C2semidirect
5. #83012C2semidirect
6. #81738C2semidirect
7. #81714C2semidirect
8. #81639C2semidirect
9. #81638C2semidirect
10. #78881C2semidirect
11. D3×#417C2semidirect
12. #78879C2semidirect
13. #78878C2semidirect
14. #78528C2semidirect
15. #78514C2semidirect
19. C2×C3×#125C22semidirect
26. #5689C22semidirect
27. #5689C22semidirect
40. C2×#890C22semidirect
43. C2×#888C22semidirect
46. C2×#869C22semidirect
47. C3×#491C22semidirect
48. C3×#490C22semidirect
49. C3×#488C22semidirect
50. C3×#417C22semidirect
51. C3×#417C22semidirect
52. C3×C4×M16C22semidirect
53. #5232C22semidirect
54. #5232C22semidirect
55. #5133C22semidirect
56. #5133C22semidirect
57. Dic3×M16C22semidirect
58. #5079C22semidirect
59. #5070C22semidirect
60. #5069C22semidirect
61. #5068C22semidirect
62. #5067C22semidirect
63. #5055C22semidirect
64. #4966C22semidirect
65. #4966C22semidirect
66. C4×#208C22semidirect
69. #4802C22semidirect
70. D3×#103C22semidirect
71. #4800C22semidirect
72. #4797C22semidirect
73. #4794C22semidirect
74. #4792C22semidirect
77. #4770C22semidirect
78. D3×#102C22semidirect
79. #4768C22semidirect
80. #4765C22semidirect
81. #4764C22semidirect
82. #4760C22semidirect
83. #4714C22semidirect
84. #4708C22semidirect
85. #4694C22semidirect
86. #4689C22semidirect
87. #4681C22semidirect
92. #3142D3semidirect
253. C2×#125C2×D3semidirect
263. #491C2×D3semidirect
266. #490C2×D3semidirect
274. #488C2×D3semidirect
291. #417C2×D3semidirect
292. #417C2×D3semidirect
301. C4×M16C2×D3semidirect
861. C3#60621semidirect

Maximal subgroups

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

subgroupindex
#862352
C2×#56892
C3×#31422
#832832
#830122
#817382
#817142
#816392
#816382
#788812
D3×#4172
#788792
#788782
#785282
#785142
#606213