Finite Group Databasebeta

← #11660516

Subgroups — #11660516

Order 768.

1806 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86219C211yesmaximal, characteristic
2C3×#2981C211yesmaximal, characteristic, complemented
3#83280C211yesmaximal, characteristic, complemented
4#79526C212yesmaximal, complemented
5#79517C212yesmaximal, complemented
6#79464C214yesmaximal, complemented
7#79453C214yesmaximal, complemented
8#79408C212yesmaximal, complemented
9C8×#237C212yesmaximal, complemented
10#79331C211yesmaximal, characteristic, complemented
11#79316C211yesmaximal, characteristic, complemented
12D3×#431C211yesmaximal, characteristic, complemented
13#79266C211yesmaximal, characteristic, complemented
14#78664C214yesmaximal, complemented
15#78648C214yesmaximal, complemented
16#60279—31nomaximal, Sylow
17C3×#532C2211yescharacteristic
18#5828C2212yes—
19Dic3×#41C2212yes—
20#5728C411yescharacteristic
21#5728C411yescharacteristic
22#5716C411yescharacteristic
23#5716C411yescharacteristic
24#5680C412yes—
25#5680C412yes—
26#5606C412yes—
27#5606C412yes—
28#5600C412yes—
29#5600C412yes—
30#5557C2212yes—
31#5557C2212yes—
32C4×#237C2212yes—
33C4×#237C2212yes—
34C2×C42×D3C2211yescharacteristic
35#5470C2211yescharacteristic
36C3×#436C2212yescomplemented
37C3×#435C2214yescomplemented
38C3×C8×D4C2212yescomplemented
39C3×#432C2211yescharacteristic
40C3×#431C2211yescharacteristic
41C3×#408C2214yes—
42#5234C2214yes—
43#5128C2214yes—
44#5127C2214yes—
45#5119C2214yescomplemented
46Dic3×M16C2214yescomplemented
47#5111C2214yes—
48C8×#67C2214yes—
49#5102C2214yescomplemented
50C2×C8×Dic3C2214yescomplemented
51#5012C2212yescomplemented
52#5011C2214yescomplemented
53D4×C3⋊C8C2212yescomplemented
54#4926C2211yescharacteristic
55#4925C2211yescharacteristic
56#4837C2212yes—
57#4833C2212yes—
58#4833C2212yes—
59D3×C4⋊C8C2212yes—
60#4831C2212yescomplemented
61#4830C2212yescomplemented
62#4828C2214yescomplemented
63#4730C2214yes—
64#4729C2214yes—
65#4728C2214yes—
66#4726C2212yes—
67#67⋊C8C2214yes—
68D3×C22⋊C8C2212yes—
69#4720C2214yes—
70#4720C2214yes—
71#4720C2214yescomplemented
72#4720C2214yescomplemented
73#4718C2212yes—
74#4718C2212yes—
75#4718C2214yescomplemented
76#4718C2214yescomplemented
77#4707C2212yes—
78#4705C2212yes—
79#4701C2214yescomplemented
80#4685C2211yescharacteristic
81#4685C2211yescharacteristic
82C4×D3×C8C2211yescharacteristic
83C4×D3×C8C2211yescharacteristic
84#4679C2212yescomplemented
85C8×Dic6C2212yescomplemented
86#3444—31no—
87#2993—32no—
88#2993—32no—
89#2992—34no—
90#2985—31no—
91#2985—31no—
92#2981—31no—
93#2981D311yescharacteristic, complemented
94#2976—34no—
95#2965—32no—
96#2965—34no—
97C8×#41—32no—
98#2922—34no—
99#2920—31no—
100C2×#431—31no—
101C2×C3×#41C2312yes—
102C2×#237C2×C412yes—
103C2×#237C2×C412yes—
104C22×C4×D3C2×C411yescharacteristic
105C22×C4×D3C2×C411yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C2×C3×M16C2314yes—
108C22×C3×C8C2314yes—
109C3×C4⋊Q8C2×C411yescharacteristic
110C3×#127C2×C411yescharacteristic
111C3×#124C2×C412yes—
112C3×#121C2×C412yes—
113C3×#121C2×C412yes—
114C3×C4×D4C2312yes—
115C3×C4×D4C2312yes—
116C2×C3×C42C2311yescharacteristic
117#946C2×C412yes—
118#946C2×C412yes—
119Q8×Dic3C2×C412yes—
120Q8×Dic3C2×C412yes—
121#938C2×C412yes—
122#938C2×C412yes—
123#938C2×C412yes—
124#938C2×C412yes—
125#937C2×C414yes—
126#936C2×C412yes—
127#936C2×C412yes—
128#935C2×C414yes—
129D4×Dic3C2×C412yes—
130D4×Dic3C2×C412yes—
131D4×Dic3C2×C412yes—
132D4×Dic3C2×C412yes—
133D4×Dic3C2×C414yes—
134D4×Dic3C2×C414yes—
135C4×#67C2314yes—
136C4×#67C2314yes—
137#926C2312yes—
138#926C2314yes—
139#924C2×C412yes—
140#924C2×C412yes—
141C2×C4×Dic3C2×C411yescharacteristic
142C2×C4×Dic3C2×C411yescharacteristic
143C2×C4×Dic3C2311yescharacteristic
144C2×C4×Dic3C2314yes—
145C2×#208C2314yes—
146C22×C3⋊C8C2314yes—
147C2×ΓL(1,𝔽25)C2314yes—
148C2×D3×C8C2312yes—
149C2×D3×C8C2312yes—
150#897C2×C412yes—
151#897C2×C412yes—
152#892C2×C412yes—
153#892C2×C412yes—
154#890C2×C412yes—
155#890C2×C412yes—
156#887C2×C412yes—
157#887C2×C412yes—
158#883C2×C414yes—
159#883C2×C414yes—
160#67⋊C4C2×C414yes—
161#67⋊C4C2×C414yes—
162#879C2×C414yes—
163#879C2×C414yes—
164#877C2×C414yes—
165#877C2×C414yes—
166C42×D3C2×C411yescharacteristic
167C42×D3C2×C411yescharacteristic
168C42×D3C2×C411yescharacteristic
169C42×D3C2×C411yescharacteristic
170C42×D3C2311yescharacteristic
171C42×D3C2311yescharacteristic
172C42×D3C2311yescharacteristic
173C42×D3C2311yescharacteristic
174#870C2×C412yes—
175#869C2×C411yescharacteristic
176#869C2×C411yescharacteristic
177C4×Dic6C2312yes—
178C4×Dic6C2312yes—
179C3×C4⋊C8C2312yes—
180C3×C4⋊C8C2312yes—
181C3×C22⋊C8C2312yes—
182C3×C22⋊C8C2312yes—
183C3×C22⋊C8C2314yes—
184C3×C22⋊C8C2314yes—
185C3×#97C2312yes—
186C3×C4×C8C2311yescharacteristic
187C3×C4×C8C2311yescharacteristic
188#830C2314yes—
189#830C2314yes—
190#830C2312yes—
191#830C2312yes—
192(C2×D3)⋊C8C2314yes—
193(C2×D3)⋊C8C2312yes—
194(C2×D3)⋊C8C2312yes—
195#815C2314yes—
196#815C2314yes—
197Dic3⋊C8C2314yes—
198Dic3⋊C8C2314yes—
199Dic3⋊C8C2314yes—
200Dic3⋊C8C2312yes—
201Dic3⋊C8C2312yes—
202Dic3⋊C8C2314yes—
203Dic3⋊C8C2314yes—
204C8×Dic3C2314yes—
205C8×Dic3C2314yes—
206C8×Dic3C2312yes—
207C8×Dic3C2312yes—
208C8×Dic3C2314yes—
209C4⋊(C3⋊C8)C2312yes—
210C4⋊(C3⋊C8)C2312yes—
211#803C2312yes—
212C4×C3⋊C8C2311yescharacteristic
213C4×C3⋊C8C2311yescharacteristic
214#533—31no—
215#533—31no—
216#533—31no—
217#532—31no—
218#532—31no—
219#532C2×D311yescharacteristic
220#529—32no—
221#529—32no—
222#529—32no—
223#529—32no—
224#529—32no—
225#529—32no—
226#525—32no—
227#525—32no—
228#525—32no—
229C4×#41—32no—
230C4×#41—32no—
231C4×#41—32no—
232C22×C42—31no—
233#446—34no—
234#446—32no—
235#446—34no—
236#446—32no—
237C8×Q8—32no—
238C8×Q8—32no—
239#436—34no—
240#436—32no—
241#436—34no—
242#436C2×D312yescomplemented
243#435—34no—
244#435—34no—
245#435—34no—
246#435—34no—
247#435—34no—
248#435C2×D314yescomplemented
249C8×D4—34no—
250C8×D4—32no—
251C8×D4—34no—
252C8×D4C2×D312yescomplemented
253#433—34no—
254#433—34no—
255#433—34no—
256#433—34no—
257#432—31no—
258#432—32no—
259#432C2×D311yescharacteristic
260#431—31no—
261#431—32no—
262#431—32no—
263#431—32no—
264#431—32no—
265#431—34no—
266#431—34no—
267#431—31no—
268#431—31no—
269#431C2×D311yescharacteristic
270#424—34no—
271#424—34no—
272#423—32no—
273C2×C4⋊C8—32no—
274#408—34no—
275#408C2×D314yes—
276#407—32no—
277C2×C22⋊C8—32no—
278C4×M16—34no—
279C4×M16—32no—
280C2×C4×C8—34no—
281C2×C4×C8—31no—
282C2×C4×C8—31no—
283C23×D3C22×C411yescharacteristic
284C3×#41—44no—
285C2×C3×Q8C22×C412yes—
286C2×C3×D4C22×C412yes—
287C2×C3×D4C22×C414yes—
288C2×C3×D4C22×C412yes—
289C2×C3×D4C22×C412yes—
290C22×C3×C4C22×C411yescharacteristic
291C22×C3×C4C22×C411yescharacteristic
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2414yes—
294C2×#67C22×C414yes—
295C2×#67C22×C414yes—
296C22×Dic3C22×C414yes—
297C22×Dic3C22×C414yes—
298C22×Dic3C22×C411yescharacteristic
299C22×Dic3C22×C411yescharacteristic
300C22×Dic3C22×C411yescharacteristic
301#237—28no—
302#237—44no—
303C2×C4×D3—24no—
304C2×C4×D3—42no—
305C2×C4×D3—42no—
306C2×C4×D3C22×C411yescharacteristic
307C2×C4×D3C22×C411yescharacteristic
308C2×C4×D3C22×C411yescharacteristic
309C2×C4×D3C22×C411yescharacteristic
310C2×C4×D3C22×C411yescharacteristic
311C2×C4×D3C22×C411yescharacteristic
312C2×C4×D3C22×C411yescharacteristic
313C2×C4×D3C22×C411yescharacteristic
314C2×C4×D3C22×C411yescharacteristic
315C2×C4×D3C22×C411yescharacteristic
316C2×C4×D3C2411yescharacteristic
317C2×C4×D3C2411yescharacteristic
318C2×Dic6C22×C412yes—
319C2×Dic6C22×C412yes—
320C3×M16—44no—
321C2×C3×C8—44no—
322C2×C3×C8C2412yes—
323C2×C3×C8C2414yes—
324C2×C3×C8C2412yes—
325C3×C4⋊C4C22×C412yes—
326C3×C4⋊C4C22×C412yes—
327C3×C22⋊C4C22×C414yes—
328C3×C22⋊C4C22×C414yes—
329C3×C42C22×C411yescharacteristic
330C3×C42C22×C411yescharacteristic
331C3×C42C2411yescharacteristic
332C3×C42C2411yescharacteristic
333#217C22×C414yes—
334#217C22×C414yes—
335#217C22×C414yes—
336#217C22×C414yes—
337#217C22×C414yes—
338(C2×D3)⋊C4C22×C414yes—
339(C2×D3)⋊C4C22×C414yes—
340C4⋊Dic3C22×C412yes—
341C4⋊Dic3C22×C412yes—
342C4⋊Dic3C22×C412yes—
343C4⋊Dic3C22×C412yes—
344C4⋊Dic3C22×C414yes—
345C4⋊Dic3C22×C414yes—
346Dic3⋊C4C22×C414yes—
347Dic3⋊C4C22×C414yes—
348Dic3⋊C4C22×C414yes—
349Dic3⋊C4C22×C414yes—
350C4×Dic3C22×C411yescharacteristic
351C4×Dic3C22×C411yescharacteristic
352C4×Dic3C22×C411yescharacteristic
353C4×Dic3C22×C411yescharacteristic
354C4×Dic3C22×C411yescharacteristic
355C4×Dic3C22×C411yescharacteristic
356C4×Dic3C22×C411yescharacteristic
357C4×Dic3C22×C411yescharacteristic
358C4×Dic3C22×C411yescharacteristic
359C4×Dic3C22×C411yescharacteristic
360C4×Dic3C22×C414yes—
361C4×Dic3C22×C414yes—
362C4×Dic3C2411yescharacteristic
363C4×Dic3C2414yes—
364C4×Dic3C2411yescharacteristic
365#208—44no—
366C2×C3⋊C8—44no—
367C2×C3⋊C8C2412yes—
368C2×C3⋊C8C2412yes—
369C2×C3⋊C8C2414yes—
370ΓL(1,𝔽25)—44no—
371D3×C8—42no—
372D3×C8—42no—
373C2×#41—32no—
374C2×#41—32no—
375C2×#41C22×D312yes—
376C23×C4—31no—
377C23×C4—31no—
378C23×C4—31no—
379C2×M16—34no—
380C2×M16—34no—
381C2×M16C22×D314yes—
382C22×C8—34no—
383C22×C8—32no—
384C22×C8—32no—
385C22×C8C22×D314yes—
386C4⋊Q8—31no—
387C4⋊Q8—31no—
388C4⋊Q8C4×D311yescharacteristic
389#127C4×D311yescharacteristic
390#126—34no—
391#126—34no—
392#125—32no—
393#125—32no—
394#125—32no—
395#124—32no—
396#124—32no—
397#124C4×D312yes—
398#123—34no—
399#123—34no—
400#123—34no—
401C22⋊Q8—32no—
402C22⋊Q8—32no—
403C22⋊Q8—32no—
404C22⋊Q8—32no—
405C22⋊Q8—32no—
406C22⋊Q8—32no—
407#121—32no—
408#121—32no—
409#121—32no—
410#121—32no—
411#121C4×D312yes—
412#121C4×D312yes—
413#120—34no—
414C4×Q8—32no—
415C4×Q8—32no—
416C4×Q8—32no—
417C4×Q8—32no—
418C4×Q8—32no—
419C4×Q8—32no—
420C4×D4—34no—
421C4×D4—34no—
422C4×D4—32no—
423C4×D4—32no—
424C4×D4—32no—
425C4×D4—32no—
426C4×D4—34no—
427C4×D4—34no—
428C4×D4—34no—
429C4×D4—34no—
430C4×D4C22×D312yes—
431C4×D4C22×D312yes—
432#117—32no—
433#117—34no—
434#117—32no—
435#117—32no—
436#117—34no—
437#117—34no—
438C2×C42—31no—
439C2×C42—31no—
440C2×C42—34no—
441C2×C42—31no—
442C2×C42—31no—
443C2×C42—31no—
444C2×C42—31no—
445C2×C42—31no—
446C2×C42—31no—
447C2×C42—31no—
448C2×C42—31no—
449C2×C42—31no—
450C2×C42C22×D311yescharacteristic
451C4⋊C8—32no—
452C4⋊C8—32no—
453C4⋊C8—34no—
454C4⋊C8—34no—
455C4⋊C8—34no—
456C4⋊C8—34no—
457C4⋊C8—34no—
458C4⋊C8—32no—
459C4⋊C8—32no—
460C4⋊C8C22×D312yes—
461C4⋊C8C22×D312yes—
462C22⋊C8—32no—
463C22⋊C8—32no—
464C22⋊C8—34no—
465C22⋊C8—34no—
466C22⋊C8—32no—
467C22⋊C8—32no—
468C22⋊C8—34no—
469C22⋊C8C22×D312yes—
470C22⋊C8C22×D312yes—
471C22⋊C8C22×D314yes—
472C22⋊C8C22×D314yes—
473#97—34no—
474#97—34no—
475#97—32no—
476#97C22×D312yes—
477C4×C8—32no—
478C4×C8—34no—
479C4×C8—32no—
480C4×C8—34no—
481C4×C8—34no—
482C4×C8—31no—
483C4×C8—31no—
484C4×C8C22×D311yescharacteristic
485C4×C8C22×D311yescharacteristic
486C23×C3C23×C414yes—
487C23×C3C23×C411yescharacteristic
488C22×D3—22no—
489C22×D3—41no—
490C22×D3—41no—
491C22×D3C23×C411yescharacteristic
492C22×D3C23×C411yescharacteristic
493C3×Q8—42no—
494C3×D4—24no—
495C3×D4—42no—
496C3×D4—42no—
497C3×D4—44no—
498C2×C3×C4—22no—
499C2×C3×C4—24no—
500C2×C3×C4—24no—
501C2×C3×C4—22no—
502C2×C3×C4—41no—
503C2×C3×C4C23×C411yescharacteristic
504C2×C3×C4C23×C411yescharacteristic
505C2×C3×C4C23×C414yes—
506C2×C3×C4C23×C411yescharacteristic
507C2×C3×C4C23×C411yescharacteristic
508C2×C3×C4C23×C411yescharacteristic
509C2×C3×C4C2511yescharacteristic
510#67—28no—
511#67—44no—
512C2×Dic3—22no—
513C2×Dic3—28no—
514C2×Dic3—22no—
515C2×Dic3—28no—
516C2×Dic3—41no—
517C2×Dic3C23×C411yescharacteristic
518C2×Dic3C23×C411yescharacteristic
519C2×Dic3C23×C411yescharacteristic
520C2×Dic3C23×C411yescharacteristic
521C2×Dic3C23×C414yes—
522C2×Dic3C23×C414yes—
523C2×Dic3C23×C411yescharacteristic
524C2×Dic3C23×C411yescharacteristic
525C4×D3—22no—
526C4×D3—22no—
527C4×D3—22no—
528C4×D3—22no—
529C4×D3—22no—
530C4×D3—22no—
531C4×D3—22no—
532C4×D3—41no—
533C4×D3—41no—
534C4×D3—41no—
535C4×D3—41no—
536C4×D3#13114yes—
537Dic6—24no—
538Dic6—42no—
539C3×C8—22no—
540C3×C8—22no—
541C3×C8—24no—
542C3⋊C8—22no—
543C3⋊C8—22no—
544C3⋊C8—24no—
545C24—31no—
546#41—44no—
547#41—68no—
548#41—124no—
549C2×Q8—32no—
550C2×Q8—32no—
551C2×Q8C2×C4×D312yes—
552C2×D4—34no—
553C2×D4—34no—
554C2×D4C2×C4×D312yes—
555C2×D4C2×C4×D314yes—
556C2×D4C2×C4×D312yes—
557C2×D4C2×C4×D312yes—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—34no—
562C22×C4—34no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—64no—
576C22×C4—122no—
577C22×C4—122no—
578C22×C4C2×C4×D311yescharacteristic
579C22×C4C2×C4×D311yescharacteristic
580C22×C4C23×D311yescharacteristic
581C22×C4C23×D314yes—
582M16—44no—
583M16—124no—
584M16—124no—
585C2×C8—32no—
586C2×C8—34no—
587C2×C8—32no—
588C2×C8—44no—
589C2×C8—122no—
590C2×C8—122no—
591C2×C8—124no—
592C2×C8C23×D312yes—
593C2×C8C23×D314yes—
594C2×C8C23×D312yes—
595C4⋊C4—32no—
596C4⋊C4—32no—
597C4⋊C4—32no—
598C4⋊C4—32no—
599C4⋊C4—34no—
600C4⋊C4—34no—
601C4⋊C4—34no—
602C4⋊C4—34no—
603C4⋊C4—34no—
604C4⋊C4—34no—
605C4⋊C4C2×C4×D312yes—
606C4⋊C4C2×C4×D312yes—
607C22⋊C4—34no—
608C22⋊C4—34no—
609C22⋊C4—34no—
610C22⋊C4—34no—
611C22⋊C4—34no—
612C22⋊C4—34no—
613C22⋊C4—34no—
614C22⋊C4C2×C4×D314yes—
615C22⋊C4C2×C4×D314yes—
616C42—31no—
617C42—31no—
618C42—31no—
619C42—31no—
620C42—31no—
621C42—31no—
622C42—31no—
623C42—31no—
624C42—31no—
625C42—31no—
626C42—34no—
627C42—34no—
628C42—31no—
629C42—34no—
630C42—31no—
631C42C2×C4×D311yescharacteristic
632C42C2×C4×D311yescharacteristic
633C42C23×D311yescharacteristic
634C42C23×D311yescharacteristic
635C22×C3—21no—
636C22×C3—24no—
637C22×C3—24no—
638C22×C3—21no—
639C22×C3—24no—
640C22×C3—21no—
641C22×C3C24×C411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—44no—
648C2×D3C2×#13112yes—
649C3×C4—21no—
650C3×C4—24no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4C2×#13112yes—
655C3×C4#58512yes—
656Dic3—21no—
657Dic3—21no—
658Dic3—24no—
659Dic3—21no—
660Dic3—24no—
661Dic3—21no—
662Dic3C2×#13112yes—
663Dic3#56812yes—
664C23—31no—
665C23—31no—
666C23—62no—
667C23—121no—
668C23—121no—
669C23C22×C4×D314yes—
670C23C22×C4×D311yescharacteristic
671Q8—42no—
672Q8—64no—
673Q8—122no—
674D4—24no—
675D4—42no—
676D4—44no—
677D4—42no—
678D4—68no—
679D4—124no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—34no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—34no—
692C2×C4—34no—
693C2×C4—41no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—68no—
701C2×C4—68no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4C22×C4×D311yescharacteristic
711C2×C4C22×C4×D311yescharacteristic
712C2×C4C22×C4×D311yescharacteristic
713C2×C4C22×C4×D311yescharacteristic
714C2×C4C22×C4×D314yes—
715C2×C4C22×C4×D311yescharacteristic
716C2×C4C24×D311yescharacteristic
717C8—22no—
718C8—24no—
719C8—22no—
720C8—62no—
721C8—62no—
722C8—64no—
723C2×C3—41no—
724C2×C3—44no—
725C2×C3#342811yescharacteristic
726C2×C3C22×#13111yescharacteristic
727C2×C3C2×#56811yescharacteristic
728D3—22no—
729D3—41no—
730C22—21no—
731C22—24no—
732C22—21no—
733C22—24no—
734C22—21no—
735C22—24no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22—124no—
743C22C23×C4×D311yescharacteristic
744C4—21no—
745C4—24no—
746C4—21no—
747C4—21no—
748C4—21no—
749C4—32no—
750C4—32no—
751C4—61no—
752C4—61no—
753C4—61no—
754C4—64no—
755C4—61no—
756C4—64no—
757C4D3×#13112yes—
758C4#596612yes—
759C3#6027911yescharacteristic, complemented, Sylow
760C2—41no—
761C2—44no—
762C2—62no—
763C2—121no—
764C2#8585611yescharacteristic
765C2C2×D3×#13111yescharacteristic
766C2D3×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2981C2
prime radical#86219C2
cosocleC2×C3×C4C25
hypercenter#2981D3
hypocenterC3#60279
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2981

Complements

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

NH ≅ G/Ntype
2. C3×#2981C2semidirect
3. #83280C2semidirect
4. #79526C2semidirect
5. #79517C2semidirect
6. #79464C2semidirect
7. #79453C2semidirect
8. #79408C2semidirect
9. C8×#237C2semidirect
10. #79331C2semidirect
11. #79316C2semidirect
12. D3×#431C2semidirect
13. #79266C2semidirect
14. #78664C2semidirect
15. #78648C2semidirect
36. C3×#436C22semidirect
37. C3×#435C22semidirect
38. C3×C8×D4C22semidirect
45. #5119C22semidirect
46. Dic3×M16C22semidirect
49. #5102C22semidirect
50. C2×C8×Dic3C22semidirect
51. #5012C22semidirect
52. #5011C22semidirect
53. D4×C3⋊C8C22semidirect
60. #4831C22semidirect
61. #4830C22semidirect
62. #4828C22semidirect
71. #4720C22semidirect
72. #4720C22semidirect
75. #4718C22semidirect
76. #4718C22semidirect
79. #4701C22semidirect
84. #4679C22semidirect
85. C8×Dic6C22semidirect
93. #2981D3semidirect
242. #436C2×D3semidirect
248. #435C2×D3semidirect
252. C8×D4C2×D3semidirect
759. C3#60279semidirect

Maximal subgroups

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

subgroupindex
#862192
C3×#29812
#832802
#795262
#795172
#794642
#794532
#794082
C8×#2372
#793312
#793162
D3×#4312
#792662
#786642
#786482
#602793