Finite Group Databasebeta

← #11659399

Subgroups — #11659399

Order 768.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87260C211yesmaximal, characteristic, complemented
2C2×#5822C211yesmaximal, characteristic
3C2×#5504C211yesmaximal, characteristic, complemented
4C2×C3×#417C211yesmaximal, characteristic, complemented
5#83768C211yesmaximal, characteristic, complemented
6#83747C211yesmaximal, characteristic, complemented
7C2×#4964C211yesmaximal, characteristic, complemented
8#78869C214yesmaximal, complemented
9#78868C214yesmaximal, complemented
10#78867C214yesmaximal, complemented
11#78866C214yesmaximal, complemented
12#78774C214yesmaximal, complemented
13#78726C214yesmaximal, complemented
14#60170—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×#235C2211yescharacteristic
17C22×C3×M16C2211yescharacteristic
18C22×C3×C4⋊C4C2211yescharacteristic
19#5827—21no—
20#5827—21no—
21#5827C2212yescomplemented
22#5827C2212yescomplemented
23Dic3×#41—22no—
24Dic3×#41C2214yes—
25C2×#951C2212yes—
26#5822C4116yescomplemented
27C2×#950C2214yes—
28C2×#949C2212yes—
29#5812C2212yescomplemented
30C2×#942C2212yes—
31#5798—22no—
32#5798C2212yescomplemented
33C2×#932C2212yes—
34C2×C4×#67—22no—
35C2×#926—22no—
36C2×#926C2211yescharacteristic
37C2×#926C2211yescharacteristic
38C22×#208C2211yescharacteristic
39#5504—22no—
40#5504—22no—
41#5504C2214yes—
42#5504C2214yescomplemented
43C2×#893C2212yescomplemented
44C2×#892—21no—
45C2×D3×C4⋊C4—21no—
46C2×#887C2212yescomplemented
47C3×#417C2214yes—
48C3×#417C2214yescomplemented
49C2×C3×#103C2212yescomplemented
50C2×C3×#102C2212yescomplemented
51#5133C2212yescomplemented
52#5133C2212yescomplemented
53#5131C2212yescomplemented
54#5122C2214yescomplemented
55#5120C2212yescomplemented
56Dic3×M16C2214yescomplemented
57#5113C2214yes—
58#5101C2214yescomplemented
59#4964C2214yescomplemented
60#4964C2214yescomplemented
61C2×#808C2212yescomplemented
62C2×#807C2212yescomplemented
63#4817C2218yescomplemented
64#4790C2218yescomplemented
65#4789C2218yescomplemented
66#4788C2218yescomplemented
67#4785C2218yescomplemented
68#4758C2218yescomplemented
69#4757C2218yescomplemented
70#4756C2218yescomplemented
71C2×#575—31no—
72#3428—31no—
73C2×#520—31no—
74#2952—34no—
75#2951—34no—
76#2947—34no—
77#2946—34no—
78C4×#137—34no—
79C4×AGL(1,ℤ/8)—34no—
80C2×#428—31no—
81#2896—31no—
82C2×#417D311yescharacteristic, complemented
83#2873—31no—
84C2×C3×#41—21no—
85C2×C3×#41—21no—
86C2×C3×#41—24no—
87C2×C3×#41C2×C418yescomplemented
88C2×C3×#41C2312yes—
89C2×C3×#41C2312yes—
90C22×C3×Q8C2311yescharacteristic
91C22×C3×D4—21no—
92C22×C3×D4C2311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4—21no—
95C23×C3×C4C2311yescharacteristic
96C22×#67—21no—
97C2×#235—21no—
98C2×#235—21no—
99C2×#235—24no—
100C2×#235C2×C418yescomplemented
101C2×#235C2312yes—
102C2×#235C2312yes—
103C22×D12C2311yescharacteristic
104C22×C4×D3—21no—
105C22×C4×D3—22no—
106C22×Dic6C2311yescharacteristic
107C2×C3×M16—24no—
108C2×C3×M16C2312yes—
109C2×C3×M16C2312yes—
110C22×C3×C8C2312yes—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2312yes—
116C2×C3×C4⋊C4C2312yes—
117C2×#217—21no—
118C2×#217—24no—
119C2×#217D412yes—
120#951C2×C4116yescomplemented
121#950C2×C4132yescomplemented
122#949C2×C4116yescomplemented
123Q8×Dic3—22no—
124Q8×Dic3—22no—
125Q8×Dic3C2314yes—
126Q8×Dic3C2314yes—
127C2×#216C2314yes—
128#942C2×C4116yescomplemented
129C2×#215C2314yes—
130D4×Dic3—24no—
131D4×Dic3—24no—
132D4×Dic3—24no—
133D4×Dic3—24no—
134D4×Dic3—22no—
135D4×Dic3—22no—
136D4×Dic3C2314yes—
137D4×Dic3C2314yes—
138C2×#214C2314yes—
139#932C2×C4116yescomplemented
140C2×#213C2314yes—
141C4×#67—28no—
142C4×#67—28no—
143C2×(C2×D3)⋊C4—22no—
144#926—21no—
145#926—21no—
146#926—24no—
147#926—22no—
148#926—22no—
149#926—24no—
150#926D412yes—
151#926D412yes—
152#926C2312yes—
153#926C2312yes—
154#926C2312yes—
155#926C2312yes—
156C2×C4⋊Dic3—22no—
157C2×C4⋊Dic3—22no—
158C2×C4⋊Dic3D411yescharacteristic
159C2×C4⋊Dic3D411yescharacteristic
160C2×C4⋊Dic3C2311yescharacteristic
161C2×C4⋊Dic3C2311yescharacteristic
162C2×Dic3⋊C4—22no—
163C2×C4×Dic3—21no—
164C2×C4×Dic3—22no—
165C2×C4×Dic3—24no—
166C2×C4×Dic3C2312yes—
167C2×#208C2×C418yescomplemented
168C2×#208C2312yes—
169C2×#208C2312yes—
170C22×C3⋊C8C2312yes—
171#893—24no—
172#893C2318yes—
173#892—24no—
174#892—24no—
175D3×C4⋊C4—24no—
176D3×C4⋊C4—24no—
177#887—24no—
178#887C2318yes—
179C3×#103C2318yes—
180C3×#102C2318yes—
181#821C2314yes—
182#821C2314yes—
183#816C2314yes—
184#816C2314yes—
185#815C2318yes—
186C8×Dic3C2318yes—
187#808C2318yes—
188#807C2318yes—
189C22×#41—31no—
190C22×#41C2×D311yescharacteristic
191#575—316no—
192C2×#137—32no—
193C2×#137—32no—
194C2×AGL(1,ℤ/8)—32no—
195C2×AGL(1,ℤ/8)—32no—
196C2×#135—34no—
197C22×M16—31no—
198C22×M16C2×D311yescharacteristic
199#520—32no—
200#520—32no—
201#520—34no—
202#520—34no—
203#520—62no—
204#520—62no—
205#520—61no—
206#520—61no—
207#519—32no—
208#518—32no—
209#518—62no—
210C4×#41—34no—
211C4×#41—62no—
212C2×C4×Q8—32no—
213C2×C4×D4—32no—
214C2×C4×D4—62no—
215C2×#117—31no—
216C2×#117—31no—
217C2×#117—61no—
218C2×#117—62no—
219C22×C4⋊C4—61no—
220C22×C4⋊C4C2×D311yescharacteristic
221#442—38no—
222#441—38no—
223#440—38no—
224#440—38no—
225C4×Q16—38no—
226C4×SD16—38no—
227C4×SD16—38no—
228C4×D8—38no—
229#428—34no—
230#428—34no—
231C2×#107—32no—
232C2×#106—32no—
233#419—32no—
234#418—32no—
235#417—32no—
236#417—32no—
237#417C2×D314yes—
238#417C2×D314yescomplemented
239#416—34no—
240C2×#103C2×D312yescomplemented
241C2×#102C2×D312yescomplemented
242#405—34no—
243#405—34no—
244C4×M16—34no—
245C24×C3—21no—
246C24×C3C2×D411yescharacteristic
247C23×D3—21no—
248C3×#41—28no—
249C3×#41—28no—
250C3×#41—24no—
251C3×#41—24no—
252C3×#41C22×C418yes—
253C3×#41C22×C418yescomplemented
254C2×C3×Q8—21no—
255C2×C3×Q8—22no—
256C2×C3×Q8C22×C414yescomplemented
257C2×C3×Q8C2412yes—
258C2×C3×D4—28no—
259C2×C3×D4—22no—
260C2×C3×D4—22no—
261C2×C3×D4—21no—
262C2×C3×D4—22no—
263C2×C3×D4C22×C414yescomplemented
264C2×C3×D4C2412yes—
265C22×C3×C4—21no—
266C22×C3×C4—28no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—82no—
273C22×C3×C4C22×C414yes—
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4#4114yes—
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C2×#67—28no—
282C2×#67—22no—
283C2×#67—22no—
284C22×Dic3—21no—
285C22×Dic3—21no—
286C22×Dic3—21no—
287C22×Dic3—24no—
288C22×Dic3—24no—
289C22×Dic3C2×D412yes—
290C22×Dic3C2×D412yes—
291#235—28no—
292#235—28no—
293#235—24no—
294#235—24no—
295#235C22×C418yes—
296#235C22×C418yes—
297C2×D12—21no—
298C2×D12—22no—
299C2×D12C22×C414yes—
300C2×D12C2412yes—
301C2×C4×D3—28no—
302C2×C4×D3—22no—
303C2×C4×D3—22no—
304C2×C4×D3—28no—
305C2×C4×D3—84no—
306C2×Dic6—21no—
307C2×Dic6—22no—
308C2×Dic6C22×C414yes—
309C2×Dic6C2412yes—
310C3×M16—24no—
311C3×M16—24no—
312C2×C3×C8—24no—
313C2×C3×C8C2414yes—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4C2414yes—
318#217—22no—
319#217—22no—
320#217—24no—
321#217—24no—
322#217C2×D414yes—
323#217C2×D414yes—
324#216C22×C4116yescomplemented
325#215C22×C4116yescomplemented
326#214C22×C4116yescomplemented
327#213C22×C4116yescomplemented
328(C2×D3)⋊C4—28no—
329C4⋊Dic3—21no—
330C4⋊Dic3—21no—
331C4⋊Dic3—24no—
332C4⋊Dic3—24no—
333C4⋊Dic3C2×D412yes—
334C4⋊Dic3C2×D412yes—
335C4⋊Dic3C2×D412yes—
336C4⋊Dic3C2×D412yes—
337C4⋊Dic3C2412yes—
338C4⋊Dic3C2412yes—
339Dic3⋊C4—28no—
340C4×Dic3—22no—
341C4×Dic3—22no—
342C4×Dic3—28no—
343C4×Dic3—24no—
344C4×Dic3—24no—
345C4×Dic3C2×D414yes—
346C4×Dic3C2414yes—
347#208C22×C418yes—
348#208C22×C418yescomplemented
349C2×C3⋊C8C22×C418yescomplemented
350C2×C3⋊C8C2414yes—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—24no—
354C2×#41—38no—
355C2×#41—32no—
356C2×#41—32no—
357C2×#41—61no—
358C2×#41—61no—
359C2×#41—64no—
360C2×#41C4×D318yescomplemented
361C2×#41C22×D312yes—
362C2×#41C22×D312yes—
363C22×Q8—31no—
364C22×Q8C22×D311yescharacteristic
365C22×D4—21no—
366C22×D4—31no—
367C22×D4—61no—
368C22×D4C22×D311yescharacteristic
369C23×C4—21no—
370C23×C4—21no—
371C23×C4—62no—
372C23×C4—61no—
373C23×C4C22×D311yescharacteristic
374#137—316no—
375#137—316no—
376AGL(1,ℤ/8)—316no—
377AGL(1,ℤ/8)—316no—
378#135—332no—
379C2×Q16—34no—
380C2×SD16—34no—
381C2×SD16—34no—
382C2×D8—34no—
383C2×M16—24no—
384C2×M16—38no—
385C2×M16—32no—
386C2×M16—32no—
387C2×M16C22×D312yes—
388C2×M16C22×D312yes—
389C22×C8—32no—
390C22×C8C22×D312yes—
391C4×Q8—34no—
392C4×Q8—34no—
393C4×Q8—38no—
394C4×Q8—64no—
395C4×Q8—62no—
396C4×Q8—62no—
397C4×D4—34no—
398C4×D4—34no—
399C4×D4—38no—
400C4×D4—64no—
401C4×D4—68no—
402C4×D4—68no—
403C4×D4—64no—
404C4×D4—64no—
405C4×D4—62no—
406C4×D4—62no—
407C4×D4—64no—
408C4×D4—64no—
409#117—32no—
410#117—32no—
411#117—32no—
412#117—32no—
413#117—32no—
414#117—32no—
415#117—64no—
416#117—64no—
417#117—64no—
418#117—64no—
419#117—62no—
420#117—62no—
421#117—61no—
422#117—61no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—31no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—64no—
431C2×C4⋊C4—64no—
432C2×C4⋊C4—62no—
433C2×C4⋊C4—62no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4C22×D312yes—
436C2×C4⋊C4C22×D312yes—
437C2×C4⋊C4C22×D312yes—
438C2×C22⋊C4—32no—
439C2×C22⋊C4—64no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—61no—
442C2×C42—32no—
443C2×C42—64no—
444C2×C42—62no—
445C2×C42—61no—
446#107—38no—
447#106—38no—
448#103—34no—
449#103—34no—
450#103C22×D318yes—
451#102—34no—
452#102—34no—
453#102C22×D318yes—
454#97—38no—
455C4×C8—38no—
456C23×C3—22no—
457C23×C3—24no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—81no—
461C23×C3—81no—
462C23×C3C4×D414yes—
463C23×C3C22×D411yescharacteristic
464C23×C3C22×D411yescharacteristic
465C23×C3C22×D411yescharacteristic
466C22×D3—24no—
467C22×D3—22no—
468C22×D3—42no—
469C22×D3—42no—
470C3×Q8—24no—
471C3×Q8—22no—
472C3×Q8C23×C414yes—
473C3×D4—28no—
474C3×D4—28no—
475C3×D4—24no—
476C3×D4—22no—
477C3×D4C23×C414yes—
478C2×C3×C4—24no—
479C2×C3×C4—22no—
480C2×C3×C4—28no—
481C2×C3×C4—28no—
482C2×C3×C4—24no—
483C2×C3×C4—44no—
484C2×C3×C4—82no—
485C2×C3×C4—82no—
486C2×C3×C4C4×D414yes—
487C2×C3×C4C4×D414yes—
488C2×C3×C4C4×D414yes—
489C2×C3×C4C23×C412yes—
490C2×C3×C4C23×C412yes—
491C2×C3×C4C23×C412yes—
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C2×#4112yes—
496C2×C3×C4C2×#4112yes—
497C2×C3×C4C2×#4112yes—
498C2×C3×C4C2511yescharacteristic
499#67—28no—
500#67—28no—
501C2×Dic3—24no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—42no—
506C2×Dic3—42no—
507C2×Dic3—84no—
508C2×Dic3—84no—
509C2×Dic3—81no—
510C2×Dic3—81no—
511C2×Dic3C22×D414yes—
512C2×Dic3C22×D414yes—
513D12—24no—
514D12—22no—
515D12C23×C414yes—
516C4×D3—28no—
517C4×D3—28no—
518C4×D3—88no—
519Dic6—24no—
520Dic6—22no—
521Dic6C23×C414yes—
522C3×C8—24no—
523C3⋊C8C23×C418yes—
524C24—21no—
525C24—61no—
526C24D3×D411yescharacteristic
527#41—28no—
528#41—28no—
529#41—24no—
530#41—24no—
531#41—38no—
532#41—38no—
533#41—68no—
534#41—68no—
535#41—64no—
536#41—64no—
537#41C2×C4×D318yes—
538#41C2×C4×D318yescomplemented
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—34no—
542C2×Q8—32no—
543C2×Q8—61no—
544C2×Q8—62no—
545C2×Q8C2×C4×D314yescomplemented
546C2×Q8C23×D312yes—
547C2×D4—28no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—34no—
553C2×D4—32no—
554C2×D4—68no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—61no—
558C2×D4—62no—
559C2×D4C2×C4×D314yescomplemented
560C2×D4C23×D312yes—
561C22×C4—21no—
562C22×C4—28no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—32no—
569C22×C4—32no—
570C22×C4—68no—
571C22×C4—64no—
572C22×C4—64no—
573C22×C4—61no—
574C22×C4—68no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—82no—
580C22×C4—244no—
581C22×C4C2×C4×D314yes—
582C22×C4D3×D411yescharacteristic
583C22×C4D3×D411yescharacteristic
584C22×C4D3×D411yescharacteristic
585C22×C4#23714yes—
586C22×C4C23×D311yescharacteristic
587C22×C4C23×D311yescharacteristic
588C22×C4C23×D311yescharacteristic
589Q16—316no—
590SD16—316no—
591SD16—316no—
592D8—316no—
593M16—24no—
594M16—24no—
595M16—38no—
596M16—38no—
597C2×C8—24no—
598C2×C8—38no—
599C2×C8—34no—
600C2×C8C23×D314yes—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—32no—
605C4⋊C4—32no—
606C4⋊C4—32no—
607C4⋊C4—32no—
608C4⋊C4—32no—
609C4⋊C4—32no—
610C4⋊C4—68no—
611C4⋊C4—64no—
612C4⋊C4—64no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4C23×D314yes—
616C22⋊C4—34no—
617C22⋊C4—34no—
618C22⋊C4—68no—
619C22⋊C4—64no—
620C22⋊C4—64no—
621C22⋊C4—62no—
622C22⋊C4—62no—
623C42—34no—
624C42—34no—
625C42—64no—
626C42—64no—
627C42—68no—
628C42—62no—
629C42—62no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—24no—
637C22×C3—44no—
638C22×C3—42no—
639C22×C3—42no—
640C22×C3—84no—
641C22×C3C2×C4×D412yes—
642C22×C3C2×C4×D412yes—
643C22×C3C2×C4×D412yes—
644C22×C3C23×D411yescharacteristic
645C2×D3—24no—
646C2×D3—48no—
647C2×D3—42no—
648C2×D3—42no—
649C3×C4—24no—
650C3×C4—44no—
651C3×C4C2×C4×D412yes—
652C3×C4C2×C4×D412yes—
653C3×C4C2×C4×D412yes—
654C3×C4C24×C411yescharacteristic
655C3×C4C22×#4111yescharacteristic
656Dic3—24no—
657Dic3—24no—
658Dic3—24no—
659Dic3—42no—
660Dic3—42no—
661C23—22no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—62no—
666C23—64no—
667C23—81no—
668C23—81no—
669C23—122no—
670C23—122no—
671C23#67⋊C414yes—
672C23C2×D3×D411yescharacteristic
673C23C2×D3×D411yescharacteristic
674C23C2×D3×D411yescharacteristic
675Q8—22no—
676Q8—24no—
677Q8—34no—
678Q8—62no—
679Q8—64no—
680Q8C22×C4×D314yes—
681D4—28no—
682D4—28no—
683D4—22no—
684D4—24no—
685D4—34no—
686D4—68no—
687D4—68no—
688D4—62no—
689D4—64no—
690D4C22×C4×D314yes—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—34no—
697C2×C4—34no—
698C2×C4—44no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—68no—
702C2×C4—68no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—248no—
710C2×C4—244no—
711C2×C4—244no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4#67⋊C414yes—
715C2×C4#67⋊C414yes—
716C2×C4#67⋊C414yes—
717C2×C4C22×C4×D312yes—
718C2×C4C22×C4×D312yes—
719C2×C4C22×C4×D312yes—
720C2×C4C2×D3×D411yescharacteristic
721C2×C4C2×D3×D411yescharacteristic
722C2×C4C2×D3×D411yescharacteristic
723C2×C4C2×#23712yes—
724C2×C4C2×#23712yes—
725C2×C4C2×#23712yes—
726C2×C4C24×D311yescharacteristic
727C8—24no—
728C8—38no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—44no—
733C2×C3C22×C4×D411yescharacteristic
734C2×C3#358511yescharacteristic
735C2×C3#358611yescharacteristic
736D3—44no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—24no—
744C22—44no—
745C22—42no—
746C22—42no—
747C22—64no—
748C22—84no—
749C22—128no—
750C22—122no—
751C22—122no—
752C22C2×#67⋊C412yes—
753C22C2×#67⋊C412yes—
754C22C2×#67⋊C412yes—
755C22C22×D3×D411yescharacteristic
756C4—24no—
757C4—44no—
758C4—64no—
759C4—64no—
760C4—64no—
761C4—122no—
762C4—122no—
763C4C2×#67⋊C412yes—
764C4C2×#67⋊C412yes—
765C4C2×#67⋊C412yes—
766C4C23×C4×D311yescharacteristic
767C4C22×#23711yescharacteristic
768C3#6017011yescharacteristic, complemented, Sylow
769C2—22no—
770C2—22no—
771C2—22no—
772C2—44no—
773C2—124no—
774C2C22×#67⋊C411yescharacteristic
775C2#8719211yescharacteristic
776C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC2×C3×#417C2
socleC22×C3C23×D4
prime radicalC2×#5822C2
cosocleC2×C3×C4C25
hypercenterC2×#417D3
hypocenterC3#60170
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. #87260C2semidirect
3. C2×#5504C2semidirect
4. C2×C3×#417C2semidirect
5. #83768C2semidirect
6. #83747C2semidirect
7. C2×#4964C2semidirect
8. #78869C2semidirect
9. #78868C2semidirect
10. #78867C2semidirect
11. #78866C2semidirect
12. #78774C2semidirect
13. #78726C2semidirect
21. #5827C22semidirect
22. #5827C22semidirect
26. #5822C4semidirect
29. #5812C22semidirect
32. #5798C22semidirect
42. #5504C22semidirect
43. C2×#893C22semidirect
46. C2×#887C22semidirect
48. C3×#417C22semidirect
49. C2×C3×#103C22semidirect
50. C2×C3×#102C22semidirect
51. #5133C22semidirect
52. #5133C22semidirect
53. #5131C22semidirect
54. #5122C22semidirect
55. #5120C22semidirect
56. Dic3×M16C22semidirect
58. #5101C22semidirect
59. #4964C22semidirect
60. #4964C22semidirect
61. C2×#808C22semidirect
62. C2×#807C22semidirect
63. #4817C22semidirect
64. #4790C22semidirect
65. #4789C22semidirect
66. #4788C22semidirect
67. #4785C22semidirect
68. #4758C22semidirect
69. #4757C22semidirect
70. #4756C22semidirect
82. C2×#417D3semidirect
87. C2×C3×#41C2×C4semidirect
100. C2×#235C2×C4semidirect
120. #951C2×C4semidirect
121. #950C2×C4semidirect
122. #949C2×C4semidirect
128. #942C2×C4semidirect
139. #932C2×C4semidirect
167. C2×#208C2×C4semidirect
238. #417C2×D3semidirect
240. C2×#103C2×D3semidirect
241. C2×#102C2×D3semidirect
253. C3×#41C22×C4semidirect
256. C2×C3×Q8C22×C4semidirect
263. C2×C3×D4C22×C4semidirect
324. #216C22×C4semidirect
325. #215C22×C4semidirect
326. #214C22×C4semidirect
327. #213C22×C4semidirect
348. #208C22×C4semidirect
349. C2×C3⋊C8C22×C4semidirect
360. C2×#41C4×D3semidirect
538. #41C2×C4×D3semidirect
545. C2×Q8C2×C4×D3semidirect
559. C2×D4C2×C4×D3semidirect
768. C3#60170semidirect

Maximal subgroups

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

subgroupindex
#872602
C2×#58222
C2×#55042
C2×C3×#4172
#837682
#837472
C2×#49642
#788692
#788682
#788672
#788662
#787742
#787262
#601703