Finite Group Databasebeta

← #11659392

Subgroups — #11659392

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
1C3×#3428C211yesmaximal, characteristic, complemented
2C2×#5822C211yesmaximal, characteristic
3C2×#5523C211yesmaximal, characteristic, complemented
4C2×#5232C211yesmaximal, characteristic, complemented
5#82558C214yesmaximal, complemented
6#82557C214yesmaximal, complemented
7#82547C214yesmaximal, complemented
8#82537C214yesmaximal, complemented
9C4×#951C214yesmaximal, complemented
10C4×#949C214yesmaximal, complemented
11#82213C211yesmaximal, characteristic, complemented
12C2×#4995C211yesmaximal, characteristic, complemented
13#82202C211yesmaximal, characteristic, complemented
14#60170—31nomaximal, Sylow
15C22×C3×#41C2211yescharacteristic
16C22×#235C2211yescharacteristic
17C3×#520—21no—
18C3×#520—21no—
19C3×#520C2212yescomplemented
20C3×#520C2212yescomplemented
21C3×#519C2212yescomplemented
22C3×#518—22no—
23C3×#518C2212yescomplemented
24C3×C4×#41—22no—
25C3×C4×#41C2214yes—
26C2×C3×#117—22no—
27C2×C3×#117C2211yescharacteristic
28C2×C3×#117C2211yescharacteristic
29C2×#951C2212yes—
30#5822C4116yescomplemented
31C2×#950C2214yes—
32C2×#949C2212yes—
33C2×#942C2212yes—
34C2×#932C2212yes—
35C22×C4⋊Dic3C2211yescharacteristic
36C22×#208C2211yescharacteristic
37C22×#208C2211yescharacteristic
38#5523—22no—
39#5523—22no—
40#5523C2214yes—
41#5523C2214yescomplemented
42C2×#892—21no—
43C2×D3×C4⋊C4—21no—
44C2×#67⋊C4—22no—
45C2×C4×D12C2212yescomplemented
46C2×C4×Dic6C2212yescomplemented
47#5232C2214yes—
48#5232C2214yescomplemented
49C2×#835C2212yescomplemented
50C2×#832C2212yescomplemented
51#5030C2218yescomplemented
52C4×#216C2218yescomplemented
53#5026C2218yescomplemented
54C4×#215C2218yescomplemented
55#5018C2218yescomplemented
56C4×#214C2218yescomplemented
57#5014C2218yescomplemented
58C4×#213C2218yescomplemented
59#5004C2212yescomplemented
60#5002C2214yes—
61#5001C2212yescomplemented
62#4997C2214yescomplemented
63#4997C2214yescomplemented
64#4995C2214yescomplemented
65#4995C2214yescomplemented
66#4966C2212yescomplemented
67#4966C2212yescomplemented
68C2×#808C2212yescomplemented
69C2×#807C2212yescomplemented
70C4×#208C2214yescomplemented
71C2×#575—31no—
72#3428D311yescharacteristic, complemented
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×#417—31no—
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×C4C2311yescharacteristic
95C22×#67—21no—
96C23×Dic3—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
107C3×C4×Q8—22no—
108C3×C4×Q8—22no—
109C3×C4×Q8C2314yes—
110C3×C4×Q8C2314yes—
111C3×C4×D4—24no—
112C3×C4×D4—24no—
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C3×C4×D4—24no—
116C3×C4×D4—24no—
117C3×C4×D4C2314yes—
118C3×C4×D4C2314yes—
119C3×#117—21no—
120C3×#117—21no—
121C3×#117—22no—
122C3×#117—22no—
123C3×#117—24no—
124C3×#117—24no—
125C3×#117D412yes—
126C3×#117D412yes—
127C3×#117C2312yes—
128C3×#117C2312yes—
129C3×#117C2312yes—
130C3×#117C2312yes—
131C2×C3×C4⋊C4—22no—
132C2×C3×C4⋊C4—22no—
133C2×C3×C4⋊C4D411yescharacteristic
134C2×C3×C4⋊C4D411yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—24no—
139C2×C3×C22⋊C4D412yes—
140C2×C3×C42—21no—
141C2×C3×C42—24no—
142C2×C3×C42C2312yes—
143#951C2×C4116yescomplemented
144#950C2×C4132yescomplemented
145#949C2×C4116yescomplemented
146C2×#216C2314yes—
147#942C2×C4116yescomplemented
148C2×#215C2314yes—
149C2×#214C2314yes—
150#932C2×C4116yescomplemented
151C2×#213C2314yes—
152C2×(C2×D3)⋊C4—22no—
153C2×C4⋊Dic3—21no—
154C2×C4⋊Dic3—21no—
155C2×C4⋊Dic3—21no—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159C2×Dic3⋊C4—22no—
160C2×C4×Dic3—22no—
161C2×#208—24no—
162C2×#208C2×C418yescomplemented
163C2×#208C2312yes—
164C2×#208C2312yes—
165C2×#208C2312yes—
166C2×#208C2312yes—
167C22×C3⋊C8C2312yes—
168C22×C3⋊C8C2312yes—
169#892—24no—
170#892—24no—
171D3×C4⋊C4—24no—
172D3×C4⋊C4—24no—
173#67⋊C4—28no—
174#67⋊C4—28no—
175C4×D12—24no—
176C4×D12C2318yes—
177C4×Dic6—24no—
178C4×Dic6C2318yes—
179#835C2318yes—
180#832C2318yes—
181#810C2314yes—
182#810C2314yes—
183#809C2314yes—
184#809C2314yes—
185#808C2318yes—
186#807C2318yes—
187#803C2318yes—
188C4×C3⋊C8C2318yes—
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×M16—31no—
199#520—21no—
200#520—21no—
201#520—34no—
202#520—34no—
203#520—62no—
204#520—62no—
205#520C2×D312yescomplemented
206#520C2×D312yescomplemented
207#519C2×D312yescomplemented
208#518—22no—
209#518C2×D312yescomplemented
210C4×#41—22no—
211C4×#41C2×D314yes—
212C2×C4×Q8—32no—
213C2×C4×D4—32no—
214C2×C4×D4—62no—
215C2×#117—22no—
216C2×#117—61no—
217C2×#117C2×D311yescharacteristic
218C2×#117C2×D311yescharacteristic
219C22×C4⋊C4—31no—
220C22×C4⋊C4—61no—
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—34no—
236#417—34no—
237#417—32no—
238#417—32no—
239#416—34no—
240C2×#103—32no—
241C2×#102—32no—
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—21no—
270C22×C3×C4—21no—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4C22×C414yes—
274C22×C3×C4C2×D412yes—
275C22×C3×C4C2×D412yes—
276C22×C3×C4C2×D411yescharacteristic
277C22×C3×C4C2×D411yescharacteristic
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4#4114yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C2×#67—28no—
284C2×#67—22no—
285C2×#67—22no—
286C22×Dic3—21no—
287C22×Dic3—22no—
288C22×Dic3—22no—
289C22×Dic3—22no—
290C22×Dic3—82no—
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×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—24no—
313C3×C4⋊C4—24no—
314C3×C4⋊C4C2×D412yes—
315C3×C4⋊C4C2×D412yes—
316C3×C4⋊C4C2×D412yes—
317C3×C4⋊C4C2×D412yes—
318C3×C4⋊C4C2412yes—
319C3×C4⋊C4C2412yes—
320C3×C22⋊C4—22no—
321C3×C22⋊C4—22no—
322C3×C22⋊C4—24no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4C2×D414yes—
325C3×C22⋊C4C2×D414yes—
326C3×C42—22no—
327C3×C42—24no—
328C3×C42—24no—
329C3×C42—22no—
330C3×C42C2×D414yes—
331C3×C42C2414yes—
332#216C22×C4116yescomplemented
333#215C22×C4116yescomplemented
334#214C22×C4116yescomplemented
335#213C22×C4116yescomplemented
336(C2×D3)⋊C4—28no—
337C4⋊Dic3—22no—
338C4⋊Dic3—22no—
339C4⋊Dic3—22no—
340C4⋊Dic3C2414yes—
341Dic3⋊C4—28no—
342C4×Dic3—28no—
343#208—24no—
344#208—24no—
345#208C22×C418yes—
346#208C22×C418yescomplemented
347C2×C3⋊C8—24no—
348C2×C3⋊C8C22×C418yescomplemented
349C2×C3⋊C8C2414yes—
350C2×C3⋊C8C2414yes—
351C2×#41—24no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41—38no—
355C2×#41—32no—
356C2×#41—32no—
357C2×#41—64no—
358C2×#41—61no—
359C2×#41—61no—
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—61no—
371C23×C4—61no—
372C23×C4—62no—
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—38no—
384C2×M16—32no—
385C2×M16—32no—
386C2×M16—32no—
387C2×M16—32no—
388C2×M16—64no—
389C22×C8—32no—
390C22×C8—32no—
391C4×Q8—22no—
392C4×Q8—22no—
393C4×Q8—38no—
394C4×Q8—64no—
395C4×Q8C22×D314yes—
396C4×Q8C22×D314yes—
397C4×D4—24no—
398C4×D4—24no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—24no—
402C4×D4—24no—
403C4×D4—38no—
404C4×D4—68no—
405C4×D4—68no—
406C4×D4—64no—
407C4×D4C22×D314yes—
408C4×D4C22×D314yes—
409#117—21no—
410#117—21no—
411#117—22no—
412#117—22no—
413#117—24no—
414#117—24no—
415#117—64no—
416#117—64no—
417#117#6712yes—
418#117#6712yes—
419#117C22×D312yes—
420#117C22×D312yes—
421#117C22×D312yes—
422#117C22×D312yes—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—32no—
426C2×C4⋊C4—32no—
427C2×C4⋊C4—32no—
428C2×C4⋊C4—61no—
429C2×C4⋊C4—61no—
430C2×C4⋊C4—61no—
431C2×C4⋊C4—62no—
432C2×C4⋊C4—64no—
433C2×C4⋊C4—64no—
434C2×C4⋊C4#6711yescharacteristic
435C2×C4⋊C4#6711yescharacteristic
436C2×C4⋊C4C22×D311yescharacteristic
437C2×C4⋊C4C22×D311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4#6712yes—
442C2×C42—21no—
443C2×C42—24no—
444C2×C42—62no—
445C2×C42C22×D312yes—
446#107—38no—
447#106—38no—
448#103—38no—
449#103—34no—
450#103—34no—
451#102—38no—
452#102—34no—
453#102—34no—
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—22no—
483C2×C3×C4—22no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—84no—
487C2×C3×C4—84no—
488C2×C3×C4—81no—
489C2×C3×C4—81no—
490C2×C3×C4C4×D414yes—
491C2×C3×C4C4×D414yes—
492C2×C3×C4C4×D414yes—
493C2×C3×C4C23×C412yes—
494C2×C3×C4C23×C412yes—
495C2×C3×C4C23×C412yes—
496C2×C3×C4C22×D414yes—
497C2×C3×C4C22×D414yes—
498C2×C3×C4C22×D411yescharacteristic
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C2×#4112yes—
502C2×C3×C4C2×#4112yes—
503C2×C3×C4C2×#4112yes—
504C2×C3×C4C2511yescharacteristic
505#67—28no—
506#67—28no—
507C2×Dic3—24no—
508C2×Dic3—22no—
509C2×Dic3—24no—
510C2×Dic3—44no—
511C2×Dic3—82no—
512C2×Dic3—82no—
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—
526C24C2×#6711yescharacteristic
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—22no—
540C2×Q8—21no—
541C2×Q8—34no—
542C2×Q8—32no—
543C2×Q8—62no—
544C2×Q8—61no—
545C2×Q8C2×C4×D314yescomplemented
546C2×Q8C23×D312yes—
547C2×D4—28no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—34no—
553C2×D4—32no—
554C2×D4—68no—
555C2×D4—62no—
556C2×D4—62no—
557C2×D4—62no—
558C2×D4—61no—
559C2×D4C2×C4×D314yescomplemented
560C2×D4C23×D312yes—
561C22×C4—21no—
562C22×C4—28no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—61no—
570C22×C4—68no—
571C22×C4—62no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—68no—
577C22×C4—244no—
578C22×C4—242no—
579C22×C4C2×C4×D314yes—
580C22×C4#23514yes—
581C22×C4C2×#6712yes—
582C22×C4C2×#6712yes—
583C22×C4C2×#6711yescharacteristic
584C22×C4C2×#6711yescharacteristic
585C22×C4C2×#6711yescharacteristic
586C22×C4C23×D311yescharacteristic
587C22×C4C23×D311yescharacteristic
588C22×C4C23×D311yescharacteristic
589Q16—316no—
590SD16—316no—
591SD16—316no—
592D8—316no—
593M16—38no—
594M16—38no—
595M16—64no—
596M16—64no—
597C2×C8—38no—
598C2×C8—34no—
599C2×C8—34no—
600C2×C8—64no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—34no—
606C4⋊C4—62no—
607C4⋊C4—62no—
608C4⋊C4—62no—
609C4⋊C4—68no—
610C4⋊C4C2×#6712yes—
611C4⋊C4C2×#6712yes—
612C4⋊C4C2×#6712yes—
613C4⋊C4C2×#6712yes—
614C4⋊C4C23×D312yes—
615C4⋊C4C23×D312yes—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—68no—
621C22⋊C4C2×#6714yes—
622C22⋊C4C2×#6714yes—
623C42—22no—
624C42—24no—
625C42—24no—
626C42—22no—
627C42—68no—
628C42C2×#6714yes—
629C42C23×D314yes—
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—24no—
651C3×C4—24no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4C2×C4×D412yes—
655C3×C4C2×C4×D412yes—
656C3×C4C2×C4×D412yes—
657C3×C4C24×C411yescharacteristic
658C3×C4C22×#4111yescharacteristic
659Dic3—24no—
660Dic3—44no—
661C23—22no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—62no—
666C23—64no—
667C23—81no—
668C23—81no—
669C23—122no—
670C23—122no—
671C23C4×#6714yes—
672C23C22×#6711yescharacteristic
673C23C22×#6711yescharacteristic
674C23C22×#6711yescharacteristic
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—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—62no—
700C2×C4—64no—
701C2×C4—68no—
702C2×C4—68no—
703C2×C4—64no—
704C2×C4—84no—
705C2×C4—84no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—124no—
709C2×C4—248no—
710C2×C4—242no—
711C2×C4—242no—
712C2×C4C4×#6714yes—
713C2×C4C4×#6714yes—
714C2×C4C4×#6714yes—
715C2×C4C22×C4×D312yes—
716C2×C4C22×C4×D312yes—
717C2×C4C22×C4×D312yes—
718C2×C4C2×#23512yes—
719C2×C4C2×#23512yes—
720C2×C4C2×#23512yes—
721C2×C4C22×#6714yes—
722C2×C4C22×#6714yes—
723C2×C4C22×#6711yescharacteristic
724C2×C4C22×#6711yescharacteristic
725C2×C4C22×#6711yescharacteristic
726C2×C4C24×D311yescharacteristic
727C8—38no—
728C8—64no—
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×C4×#6712yes—
753C22C2×C4×#6712yes—
754C22C2×C4×#6712yes—
755C22C23×#6711yescharacteristic
756C4—24no—
757C4—24no—
758C4—24no—
759C4—42no—
760C4—42no—
761C4—64no—
762C4—124no—
763C4C2×C4×#6712yes—
764C4C2×C4×#6712yes—
765C4C2×C4×#6712yes—
766C4C23×C4×D311yescharacteristic
767C4C22×#23511yescharacteristic
768C3#6017011yescharacteristic, complemented, Sylow
769C2—22no—
770C2—22no—
771C2—22no—
772C2—44no—
773C2—124no—
774C2C22×C4×#6711yescharacteristic
775C2#8729811yescharacteristic
776C2#8729911yescharacteristic
subgroupG/H
centerC22C23×#67
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC3×#3428C2
socleC22×C3C23×D4
prime radicalC2×#5822C2
cosocleC2×C3×C4C25
hypercenter#3428D3
hypocenterC3#60170
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. C3×#3428C2semidirect
3. C2×#5523C2semidirect
4. C2×#5232C2semidirect
5. #82558C2semidirect
6. #82557C2semidirect
7. #82547C2semidirect
8. #82537C2semidirect
9. C4×#951C2semidirect
10. C4×#949C2semidirect
11. #82213C2semidirect
12. C2×#4995C2semidirect
13. #82202C2semidirect
19. C3×#520C22semidirect
20. C3×#520C22semidirect
21. C3×#519C22semidirect
23. C3×#518C22semidirect
30. #5822C4semidirect
41. #5523C22semidirect
45. C2×C4×D12C22semidirect
46. C2×C4×Dic6C22semidirect
48. #5232C22semidirect
49. C2×#835C22semidirect
50. C2×#832C22semidirect
51. #5030C22semidirect
52. C4×#216C22semidirect
53. #5026C22semidirect
54. C4×#215C22semidirect
55. #5018C22semidirect
56. C4×#214C22semidirect
57. #5014C22semidirect
58. C4×#213C22semidirect
59. #5004C22semidirect
61. #5001C22semidirect
62. #4997C22semidirect
63. #4997C22semidirect
64. #4995C22semidirect
65. #4995C22semidirect
66. #4966C22semidirect
67. #4966C22semidirect
68. C2×#808C22semidirect
69. C2×#807C22semidirect
70. C4×#208C22semidirect
72. #3428D3semidirect
87. C2×C3×#41C2×C4semidirect
100. C2×#235C2×C4semidirect
143. #951C2×C4semidirect
144. #950C2×C4semidirect
145. #949C2×C4semidirect
147. #942C2×C4semidirect
150. #932C2×C4semidirect
162. C2×#208C2×C4semidirect
205. #520C2×D3semidirect
206. #520C2×D3semidirect
207. #519C2×D3semidirect
209. #518C2×D3semidirect
253. C3×#41C22×C4semidirect
256. C2×C3×Q8C22×C4semidirect
263. C2×C3×D4C22×C4semidirect
332. #216C22×C4semidirect
333. #215C22×C4semidirect
334. #214C22×C4semidirect
335. #213C22×C4semidirect
346. #208C22×C4semidirect
348. 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
C3×#34282
C2×#58222
C2×#55232
C2×#52322
#825582
#825572
#825472
#825372
C4×#9512
C4×#9492
#822132
C2×#49952
#822022
#601703