Finite Group Databasebeta

← #10763231

Subgroups — #10763231

Order 768.

974 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86119C211yesmaximal, characteristic
2#78517C211yesmaximal, characteristic, complemented
3C2×#4705C211yesmaximal, characteristic, complemented
4C3×#1524C211yesmaximal, characteristic, complemented
5#71746C211yesmaximal, characteristic, complemented
6#69858C211yesmaximal, characteristic, complemented
7#69797C211yesmaximal, characteristic, complemented
8#68369C212yesmaximal, complemented
9#68368C212yesmaximal, complemented
10#68349C212yesmaximal, complemented
11#68348C212yesmaximal, complemented
12#17662—31nomaximal, Sylow
13C3×#529C2211yescharacteristic
14#5706—21no—
15#5706—21no—
16#5691C2211yescharacteristic
17#5688C2211yescharacteristic
18#5680C2211yescharacteristic
19#5668C2211yescharacteristic
20#5656—21no—
21#5649—21no—
22#5627C411yescharacteristic
23#5622C411yescharacteristic
24#5606C411yescharacteristic
25#5596C411yescharacteristic
26#5578C411yescharacteristic
27C4×#239C411yescharacteristic
28#5548C411yescharacteristic
29#5547—21no—
30C4×#237—21no—
31C4×#237C411yescharacteristic
32#5528—21no—
33#5522—21no—
34#5479C2211yescharacteristic
35C2×C42×D3C2211yescharacteristic
36C3×C4×M16C2211yescharacteristic
37C2×C3×#97C2211yescharacteristic
38#5126—21no—
39#5118—21no—
40C2×(C2×D3)⋊C8—21no—
41C2×Dic3⋊C8—21no—
42C4×#208C2211yescharacteristic
43C2×#803C2211yescharacteristic
44#4705—21no—
45#4705—21no—
46#4705C2212yes—
47#4705C2212yes—
48#4705C2212yes—
49#4705C2212yes—
50#4685—21no—
51#4685—21no—
52C3×#330C2212yescomplemented
53C3×#329C2212yescomplemented
54#4543C2212yescomplemented
55#4540C2212yescomplemented
56#4465C2212yescomplemented
57#4465C2212yescomplemented
58#4464C2212yescomplemented
59#4464C2212yescomplemented
60#3444—31no—
61#2920—31no—
62C2×#432—31no—
63#1537—32no—
64#1536—32no—
65#1535—32no—
66#1535—32no—
67#1524—31no—
68#1524—31no—
69#1524—31no—
70#1524D311yescharacteristic, complemented
71C2×#239C2×C411yescharacteristic
72C2×#237—21no—
73C2×#237C2×C411yescharacteristic
74C2×#235—21no—
75C22×C4×D3C2×C411yescharacteristic
76C22×C4×D3D411yescharacteristic
77C22×C4×D3D411yescharacteristic
78C2×C3×M16—21no—
79C22×C3×C8—21no—
80C3×#126—21no—
81C3×#125C2311yescharacteristic
82C3×#124C2311yescharacteristic
83C3×#123—21no—
84C3×C22⋊Q8C2×C411yescharacteristic
85C3×#121C2×C411yescharacteristic
86C3×C4×Q8C2×C411yescharacteristic
87C3×C4×D4—21no—
88C3×C4×D4C2×C411yescharacteristic
89C3×#117—21no—
90C2×C3×C42C2311yescharacteristic
91#946C2×C411yescharacteristic
92Q8×Dic3C2×C411yescharacteristic
93#944C2×C411yescharacteristic
94#940C2×C411yescharacteristic
95#939—21no—
96#938C2×C411yescharacteristic
97#937—21no—
98D4×Dic3—21no—
99D4×Dic3C2×C411yescharacteristic
100#930C2×C411yescharacteristic
101#929—21no—
102C4×#67—21no—
103C4×#67—21no—
104C4×#67—21no—
105#924C2×C411yescharacteristic
106C2×C4×Dic3—21no—
107C2×C4×Dic3C2×C411yescharacteristic
108C2×C4×Dic3D411yescharacteristic
109C2×C4×Dic3D411yescharacteristic
110C2×#208—21no—
111C22×C3⋊C8—21no—
112#898—21no—
113#897C2×C411yescharacteristic
114#896—21no—
115#896—21no—
116#896—21no—
117#895C2×C411yescharacteristic
118#894—21no—
119#894—21no—
120#893—21no—
121#893—21no—
122#893—21no—
123#893C2×C411yescharacteristic
124#892—21no—
125#892—21no—
126#892C2×C411yescharacteristic
127#892C2×C411yescharacteristic
128#889—21no—
129#889—21no—
130#888C2×C411yescharacteristic
131#888C2×C411yescharacteristic
132#887—21no—
133#887—21no—
134#887—21no—
135#887C2×C411yescharacteristic
136#885—21no—
137#885—21no—
138#884—21no—
139#884—21no—
140#884—21no—
141#883—21no—
142#883—21no—
143#882—21no—
144#67⋊C4—21no—
145#67⋊C4—21no—
146#67⋊C4—21no—
147#67⋊C4—21no—
148#67⋊C4—21no—
149#67⋊C4—21no—
150#67⋊C4—21no—
151#879—21no—
152#878—21no—
153#877—21no—
154#877—21no—
155#877—21no—
156#876—21no—
157#875C2311yescharacteristic
158C4×D12—21no—
159C4×D12C2×C411yescharacteristic
160#872—21no—
161#872—21no—
162C42×D3—21no—
163C42×D3C2×C411yescharacteristic
164C42×D3C2×C411yescharacteristic
165C42×D3D411yescharacteristic
166C42×D3D411yescharacteristic
167C42×D3D411yescharacteristic
168C42×D3D411yescharacteristic
169C42×D3C2311yescharacteristic
170C42×D3C2311yescharacteristic
171#870C2311yescharacteristic
172C4×Dic6—21no—
173C4×Dic6C2×C411yescharacteristic
174C3×#97—21no—
175C3×#97C2312yes—
176C3×#97C2312yes—
177C3×C4×C8—21no—
178(C2×D3)⋊C8—22no—
179(C2×D3)⋊C8—22no—
180(C2×D3)⋊C8—22no—
181(C2×D3)⋊C8—22no—
182Dic3⋊C8—22no—
183Dic3⋊C8—22no—
184Dic3⋊C8—22no—
185Dic3⋊C8—22no—
186#803—21no—
187#803C2312yes—
188#803C2312yes—
189C4×C3⋊C8—21no—
190#533—31no—
191#533—31no—
192#533—31no—
193#532—31no—
194#532—31no—
195#532—31no—
196#529—31no—
197#529—31no—
198#529—31no—
199#529—61no—
200#529—61no—
201#529—61no—
202#529—61no—
203#529C2×D311yescharacteristic
204#525—31no—
205#525—31no—
206#525—61no—
207#525—61no—
208C4×#41—31no—
209C4×#41—31no—
210C4×#41—61no—
211C4×#41—61no—
212C22×C42—31no—
213#432—32no—
214#432—32no—
215#432—32no—
216#432—32no—
217#432—61no—
218#432—61no—
219#431—61no—
220#431—61no—
221#423—61no—
222C2×C4⋊C8—61no—
223#407—61no—
224C2×C22⋊C8—61no—
225C4×M16—31no—
226C4×M16C2×D311yescharacteristic
227C2×#97—31no—
228C2×#97C2×D311yescharacteristic
229#330—32no—
230#330—32no—
231#330—32no—
232#330C2×D312yescomplemented
233#329—32no—
234#329—32no—
235#329—32no—
236#329C2×D312yescomplemented
237C23×D3C22⋊C411yescharacteristic
238C2×C3×Q8C22×C411yescharacteristic
239C2×C3×D4—21no—
240C2×C3×D4C22×C411yescharacteristic
241C22×C3×C4—21no—
242C22×C3×C4C22×C411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C2×#67—21no—
246C2×#67—21no—
247C2×#67—21no—
248C2×#67—21no—
249C2×#67—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3C22⋊C411yescharacteristic
253C22×Dic3C22⋊C411yescharacteristic
254C22×Dic3C22⋊C411yescharacteristic
255#239—42no—
256#237—42no—
257#237—44no—
258#235—44no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12C22×C411yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—42no—
266C2×C4×D3—42no—
267C2×C4×D3—42no—
268C2×C4×D3C22⋊C411yescharacteristic
269C2×C4×D3C22⋊C411yescharacteristic
270C2×C4×D3C22⋊C411yescharacteristic
271C2×C4×D3C22⋊C411yescharacteristic
272C2×C4×D3C22⋊C411yescharacteristic
273C2×C4×D3C22⋊C411yescharacteristic
274C2×C4×D3C22×C411yescharacteristic
275C2×C4×D3C22×C411yescharacteristic
276C2×C4×D3C2×D411yescharacteristic
277C2×C4×D3C2×D411yescharacteristic
278C2×C4×D3C2×D411yescharacteristic
279C2×C4×D3C2×D411yescharacteristic
280C2×Dic6—21no—
281C2×Dic6—21no—
282C2×Dic6C22×C411yescharacteristic
283C3×M16—42no—
284C2×C3×C8—22no—
285C2×C3×C8—22no—
286C2×C3×C8—42no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4C22×C411yescharacteristic
292C3×C4⋊C4C22×C411yescharacteristic
293C3×C22⋊C4—21no—
294C3×C22⋊C4—21no—
295C3×C22⋊C4—21no—
296C3×C22⋊C4—21no—
297C3×C22⋊C4—21no—
298C3×C42—21no—
299C3×C42C22×C411yescharacteristic
300C3×C42C2×D411yescharacteristic
301C3×C42C2×D411yescharacteristic
302C3×C42C2411yescharacteristic
303#217—21no—
304#217—21no—
305#217—21no—
306(C2×D3)⋊C4—21no—
307(C2×D3)⋊C4—21no—
308(C2×D3)⋊C4—21no—
309(C2×D3)⋊C4—21no—
310(C2×D3)⋊C4—21no—
311(C2×D3)⋊C4—21no—
312(C2×D3)⋊C4—21no—
313(C2×D3)⋊C4—21no—
314(C2×D3)⋊C4—21no—
315(C2×D3)⋊C4—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3C22×C411yescharacteristic
319C4⋊Dic3C22×C411yescharacteristic
320Dic3⋊C4—21no—
321Dic3⋊C4—21no—
322Dic3⋊C4—21no—
323Dic3⋊C4—21no—
324Dic3⋊C4—21no—
325Dic3⋊C4—21no—
326Dic3⋊C4—21no—
327Dic3⋊C4—21no—
328Dic3⋊C4—21no—
329Dic3⋊C4—21no—
330C4×Dic3—21no—
331C4×Dic3—21no—
332C4×Dic3—21no—
333C4×Dic3—21no—
334C4×Dic3—21no—
335C4×Dic3C22⋊C411yescharacteristic
336C4×Dic3C22⋊C411yescharacteristic
337C4×Dic3C22⋊C411yescharacteristic
338C4×Dic3C22⋊C411yescharacteristic
339C4×Dic3C22⋊C411yescharacteristic
340C4×Dic3C22⋊C411yescharacteristic
341C4×Dic3C22×C411yescharacteristic
342C4×Dic3C22×C411yescharacteristic
343C4×Dic3C2×D411yescharacteristic
344C4×Dic3C2×D411yescharacteristic
345C4×Dic3C2×D411yescharacteristic
346C4×Dic3C2×D411yescharacteristic
347#208—42no—
348C2×C3⋊C8—22no—
349C2×C3⋊C8—22no—
350C2×C3⋊C8—42no—
351C2×#41—31no—
352C2×#41—31no—
353C2×#41—61no—
354C2×#41—61no—
355C23×C4—31no—
356C23×C4—31no—
357C23×C4—31no—
358C2×M16—21no—
359C2×M16—61no—
360C22×C8—21no—
361C22×C8—61no—
362C4⋊Q8—31no—
363C4⋊Q8—31no—
364C4⋊Q8—31no—
365#127—31no—
366#126—21no—
367#126—61no—
368#126—61no—
369#126—61no—
370#125—31no—
371#125—61no—
372#125—61no—
373#125C22×D311yescharacteristic
374#124—31no—
375#124—61no—
376#124—61no—
377#124C22×D311yescharacteristic
378#123—21no—
379#123—61no—
380#123—61no—
381#123—61no—
382#123—61no—
383#123—61no—
384C22⋊Q8—31no—
385C22⋊Q8—31no—
386C22⋊Q8—31no—
387C22⋊Q8—61no—
388C22⋊Q8—61no—
389C22⋊Q8—61no—
390C22⋊Q8—61no—
391C22⋊Q8C4×D311yescharacteristic
392#121—31no—
393#121—31no—
394#121—31no—
395#121—61no—
396#121—61no—
397#121—61no—
398#121—61no—
399#121C4×D311yescharacteristic
400#120—61no—
401#120—61no—
402C4×Q8—31no—
403C4×Q8—31no—
404C4×Q8—31no—
405C4×Q8—61no—
406C4×Q8—61no—
407C4×Q8—61no—
408C4×Q8—61no—
409C4×Q8C4×D311yescharacteristic
410C4×D4—21no—
411C4×D4—31no—
412C4×D4—31no—
413C4×D4—31no—
414C4×D4—61no—
415C4×D4—61no—
416C4×D4—61no—
417C4×D4—61no—
418C4×D4—61no—
419C4×D4—61no—
420C4×D4—61no—
421C4×D4—61no—
422C4×D4—61no—
423C4×D4—61no—
424C4×D4—61no—
425C4×D4—61no—
426C4×D4—61no—
427C4×D4—61no—
428C4×D4—61no—
429C4×D4C4×D311yescharacteristic
430#117—21no—
431#117—31no—
432#117—31no—
433#117—61no—
434#117—61no—
435#117—61no—
436#117—61no—
437#117—61no—
438#117—61no—
439#117—61no—
440C2×C42—31no—
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×C42—31no—
451C2×C42—61no—
452C2×C42—61no—
453C2×C42C22×D311yescharacteristic
454C4⋊C8—62no—
455C4⋊C8—62no—
456C4⋊C8—62no—
457C4⋊C8—62no—
458C22⋊C8—62no—
459C22⋊C8—62no—
460C22⋊C8—62no—
461C22⋊C8—62no—
462#97—21no—
463#97—32no—
464#97—32no—
465#97—61no—
466#97C22×D312yes—
467#97C22×D312yes—
468C4×C8—21no—
469C4×C8—61no—
470C23×C3—21no—
471C23×C3C2×C22⋊C411yescharacteristic
472C22×D3—22no—
473C22×D3—21no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3C2×C22⋊C411yescharacteristic
477C22×D3C2×C22⋊C411yescharacteristic
478C3×Q8—41no—
479C3×D4—41no—
480C3×D4—42no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—41no—
487C2×C3×C4—42no—
488C2×C3×C4C2×C22⋊C411yescharacteristic
489C2×C3×C4C2×C22⋊C411yescharacteristic
490C2×C3×C4C2×C22⋊C411yescharacteristic
491C2×C3×C4C23×C411yescharacteristic
492C2×C3×C4C22×D411yescharacteristic
493C2×C3×C4C22×D411yescharacteristic
494#67—42no—
495#67—42no—
496#67—42no—
497#67—42no—
498#67—42no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—41no—
505C2×Dic3—42no—
506C2×Dic3—42no—
507C2×Dic3C2×C22⋊C411yescharacteristic
508C2×Dic3C2×C22⋊C411yescharacteristic
509C2×Dic3C2×C22⋊C411yescharacteristic
510C2×Dic3C2×C22⋊C411yescharacteristic
511C2×Dic3C2×C22⋊C411yescharacteristic
512C2×Dic3C2×C22⋊C411yescharacteristic
513D12—41no—
514D12—42no—
515D12—42no—
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—22no—
519C4×D3—22no—
520C4×D3—41no—
521C4×D3—41no—
522C4×D3—41no—
523C4×D3—41no—
524C4×D3—41no—
525C4×D3—41no—
526C4×D3—41no—
527C4×D3—41no—
528C4×D3—42no—
529C4×D3—42no—
530C4×D3—42no—
531Dic6—42no—
532Dic6—42no—
533Dic6—41no—
534C3×C8—42no—
535C3×C8—42no—
536C3⋊C8—42no—
537C3⋊C8—42no—
538C24—31no—
539#41—124no—
540#41—124no—
541#41—122no—
542#41—122no—
543C2×Q8—31no—
544C2×Q8—61no—
545C2×Q8—61no—
546C2×Q8C2×C4×D311yescharacteristic
547C2×D4—21no—
548C2×D4—31no—
549C2×D4—61no—
550C2×D4—61no—
551C2×D4—61no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4—61no—
555C2×D4—61no—
556C2×D4C2×C4×D311yescharacteristic
557C22×C4—21no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
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—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—122no—
579C22×C4—122no—
580C22×C4—122no—
581C22×C4C2×C4×D311yescharacteristic
582C22×C4D3×D411yescharacteristic
583C22×C4D3×D411yescharacteristic
584M16—42no—
585M16—122no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—42no—
589C2×C8—62no—
590C2×C8—62no—
591C2×C8—122no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4C2×C4×D311yescharacteristic
611C4⋊C4C2×C4×D311yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C42—21no—
631C42—31no—
632C42—31no—
633C42—31no—
634C42—31no—
635C42—31no—
636C42—31no—
637C42—31no—
638C42—31no—
639C42—31no—
640C42—31no—
641C42—31no—
642C42—31no—
643C42—61no—
644C42—61no—
645C42—61no—
646C42—61no—
647C42—61no—
648C42C2×C4×D311yescharacteristic
649C42D3×D411yescharacteristic
650C42D3×D411yescharacteristic
651C42C23×D311yescharacteristic
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3#42112yes—
658C22×C3C22×C22⋊C411yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—44no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4#42112yes—
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—21no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3#41312yes—
687C23—21no—
688C23—31no—
689C23—31no—
690C23—62no—
691C23—61no—
692C23—121no—
693C23—121no—
694C23D3×C22⋊C411yescharacteristic
695Q8—41no—
696Q8—121no—
697Q8—122no—
698Q8—122no—
699D4—41no—
700D4—42no—
701D4—121no—
702D4—122no—
703D4—122no—
704D4—122no—
705D4—122no—
706D4—122no—
707D4—122no—
708D4—122no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—121no—
743C2×C4—122no—
744C2×C4—122no—
745C2×C4D3×C22⋊C411yescharacteristic
746C2×C4D3×C22⋊C411yescharacteristic
747C2×C4D3×C22⋊C411yescharacteristic
748C2×C4C22×C4×D311yescharacteristic
749C2×C4C2×D3×D411yescharacteristic
750C2×C4C2×D3×D411yescharacteristic
751C8—42no—
752C8—42no—
753C8—122no—
754C8—122no—
755C2×C3—22no—
756C2×C3—81no—
757C2×C3C2×#41311yescharacteristic
758C2×C3C2×#42111yescharacteristic
759C2×C3C2×#42111yescharacteristic
760D3—41no—
761D3—41no—
762D3—81no—
763C22—21no—
764C22—21no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—124no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22#482112yes—
779C22C2×D3×C22⋊C411yescharacteristic
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—32no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—61no—
793C4—61no—
794C4—121no—
795C4—121no—
796C4—121no—
797C4#482112yes—
798C3#1766211yescharacteristic, complemented, Sylow
799C2—22no—
800C2—81no—
801C2—121no—
802C2—121no—
803C2—241no—
804C2D3×#41311yescharacteristic
805C2C2×#482111yescharacteristic
806C2C2×#482111yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#1524C2
socleC22×C3C22×C22⋊C4
prime radical#86119C2
cosocleC3×C42C24
hypercenter#1524D3
hypocenterC3#17662
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1524

Complements

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

NH ≅ G/Ntype
2. #78517C2semidirect
3. C2×#4705C2semidirect
4. C3×#1524C2semidirect
5. #71746C2semidirect
6. #69858C2semidirect
7. #69797C2semidirect
8. #68369C2semidirect
9. #68368C2semidirect
10. #68349C2semidirect
11. #68348C2semidirect
52. C3×#330C22semidirect
53. C3×#329C22semidirect
54. #4543C22semidirect
55. #4540C22semidirect
56. #4465C22semidirect
57. #4465C22semidirect
58. #4464C22semidirect
59. #4464C22semidirect
70. #1524D3semidirect
232. #330C2×D3semidirect
236. #329C2×D3semidirect
798. C3#17662semidirect

Maximal subgroups

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

subgroupindex
#861192
#785172
C2×#47052
C3×#15242
#717462
#698582
#697972
#683692
#683682
#683492
#683482
#176623