Finite Group Databasebeta

← #10763262

Subgroups — #10763262

Order 768.

984 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
1D3×#529C211yesmaximal, characteristic
2#79331C211yesmaximal, characteristic, complemented
3C2×#4705C211yesmaximal, characteristic, complemented
4C3×#1532C211yesmaximal, characteristic, complemented
5#71748C211yesmaximal, characteristic, complemented
6#70807C211yesmaximal, characteristic, complemented
7#69799C211yesmaximal, characteristic, complemented
8#68368C212yesmaximal, complemented
9#68363C212yesmaximal, complemented
10#68348C212yesmaximal, complemented
11#68343C212yesmaximal, complemented
12#17668—31nomaximal, Sylow
13C3×#529C2211yescharacteristic
14#5706—21no—
15D3×#126—21no—
16#5691C2211yescharacteristic
17D3×#125C2211yescharacteristic
18#5680C2211yescharacteristic
19D3×#124C2211yescharacteristic
20D3×#123—21no—
21#5649—21no—
22D3×C22⋊Q8C411yescharacteristic
23#5624C411yescharacteristic
24D3×#121C411yescharacteristic
25#5600C411yescharacteristic
26#5580C411yescharacteristic
27C4×D3×Q8C411yescharacteristic
28#5557C411yescharacteristic
29C4×D3×D4—21no—
30C4×D3×D4C411yescharacteristic
31#5538—21no—
32#5528—21no—
33D3×#117—21no—
34#5479C2211yescharacteristic
35C2×C42×D3C2211yescharacteristic
36C3×#432C2211yescharacteristic, complemented
37C2×C3×#97C2211yescharacteristic, complemented
38C2×(C2×D3)⋊C8—21no—
39C2×Dic3⋊C8—21no—
40#4926C2211yescharacteristic, complemented
41C2×#803C2211yescharacteristic, complemented
42#4837—21no—
43#4833—21no—
44#4726—21no—
45#4718—21no—
46#4707C2212yes—
47#4705—21no—
48#4705—21no—
49#4705C2212yes—
50#4705C2212yescomplemented
51#4705C2212yescomplemented
52C3×#330C2212yescomplemented
53C3×#329C2212yescomplemented
54#4543C2212yescomplemented
55#4540C2212yescomplemented
56#4465C2212yescomplemented
57#4465C2212yescomplemented
58#4464C2212yescomplemented
59#4464C2212yescomplemented
60C2×#529—31no—
61#2920—31no—
62C2×#432—31no—
63#1535—32no—
64#1535—32no—
65#1532—31no—
66#1532—31no—
67#1532—31no—
68#1532D311yescharacteristic, complemented
69#1528—32no—
70#1527—32no—
71C2×D3×Q8C2×C411yescharacteristic
72C2×D3×D4—21no—
73C2×D3×D4C2×C411yescharacteristic
74C22×C4×D3—21no—
75C22×C4×D3C2×C411yescharacteristic
76C22×C4×D3D411yescharacteristic
77C22×C4×D3D411yescharacteristic
78C22×C3×C8—21no—
79C3×#126—21no—
80C3×#125C2311yescharacteristic
81C3×#124C2311yescharacteristic
82C3×#123—21no—
83C3×C22⋊Q8C2×C411yescharacteristic
84C3×#121C2×C411yescharacteristic
85C3×C4×Q8C2×C411yescharacteristic
86C3×C4×D4—21no—
87C3×C4×D4C2×C411yescharacteristic
88C3×#117—21no—
89C2×C3×C42C2311yescharacteristic
90#947C2×C411yescharacteristic
91#946C2×C411yescharacteristic
92Q8×Dic3C2×C411yescharacteristic
93#939—21no—
94#938C2×C411yescharacteristic
95#936C2×C411yescharacteristic
96#935—21no—
97D4×Dic3—21no—
98D4×Dic3C2×C411yescharacteristic
99#930C2×C411yescharacteristic
100#929—21no—
101C4×#67—21no—
102C4×#67—21no—
103C4×#67—21no—
104#926—21no—
105#924C2×C411yescharacteristic
106C2×C4×Dic3C2×C411yescharacteristic
107C2×C4×Dic3D411yescharacteristic
108C2×C4×Dic3D411yescharacteristic
109C22×C3⋊C8—21no—
110C2×ΓL(1,𝔽25)—22no—
111#898—21no—
112#898—21no—
113#898—21no—
114#897C2×C411yescharacteristic
115#896—21no—
116#895C2×C411yescharacteristic
117#894—21no—
118#894—21no—
119#893—21no—
120#893C2×C411yescharacteristic
121#892—21no—
122#892—21no—
123D3×C4⋊C4—21no—
124D3×C4⋊C4—21no—
125D3×C4⋊C4—21no—
126D3×C4⋊C4—21no—
127D3×C4⋊C4C2×C411yescharacteristic
128D3×C4⋊C4C2×C411yescharacteristic
129#890C2×C411yescharacteristic
130#890C2×C411yescharacteristic
131#889—21no—
132#889—21no—
133#887—21no—
134#887C2×C411yescharacteristic
135#886—21no—
136#885—21no—
137#885—21no—
138#884—21no—
139#883—21no—
140#883—21no—
141#67⋊C4—21no—
142#67⋊C4—21no—
143#67⋊C4—21no—
144D3×C22⋊C4—21no—
145D3×C22⋊C4—21no—
146D3×C22⋊C4—21no—
147D3×C22⋊C4—21no—
148D3×C22⋊C4—21no—
149#879—21no—
150#879—21no—
151#879—21no—
152#878—21no—
153#877—21no—
154#877—21no—
155#876—21no—
156#875C2311yescharacteristic
157C4×D12—21no—
158C4×D12C2×C411yescharacteristic
159#872—21no—
160#872—21no—
161C42×D3—21no—
162C42×D3C2×C411yescharacteristic
163C42×D3C2×C411yescharacteristic
164C42×D3D411yescharacteristic
165C42×D3D411yescharacteristic
166C42×D3D411yescharacteristic
167C42×D3D411yescharacteristic
168C42×D3C2311yescharacteristic
169C42×D3C2311yescharacteristic
170#870C2311yescharacteristic
171C4×Dic6—21no—
172C4×Dic6C2×C411yescharacteristic
173C3×C4⋊C8—21no—
174C3×C22⋊C8—21no—
175C3×#97—21no—
176C3×#97C2312yes—
177C3×#97C2312yes—
178#830—21no—
179(C2×D3)⋊C8—22no—
180(C2×D3)⋊C8—22no—
181(C2×D3)⋊C8—22no—
182Dic3⋊C8—22no—
183Dic3⋊C8—22no—
184Dic3⋊C8—22no—
185C8×Dic3—22no—
186C4⋊(C3⋊C8)—21no—
187#803—21no—
188#803C2312yes—
189#803C2312yes—
190#529—31no—
191#529—31no—
192#529—31no—
193#529—31no—
194#529—31no—
195#529—31no—
196#529—31no—
197#529—61no—
198#529—61no—
199#529—61no—
200#529—61no—
201#529C2×D311yescharacteristic
202C2×#126—61no—
203C2×#125—31no—
204C2×#124—31no—
205C2×#123—61no—
206C2×C22⋊Q8—31no—
207C2×#121—31no—
208C2×C4×Q8—31no—
209C2×C4×D4—31no—
210C2×C4×D4—61no—
211C2×#117—61no—
212C22×C42—31no—
213#432—31no—
214#432—32no—
215#432—32no—
216#432—32no—
217#432—61no—
218#432—61no—
219#432C2×D311yescharacteristic, complemented
220#431—61no—
221#431—61no—
222#423—61no—
223C2×C4⋊C8—61no—
224#407—61no—
225C2×C22⋊C8—61no—
226C4×M16—32no—
227C2×#97—31no—
228C2×#97C2×D311yescharacteristic, complemented
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×D3—21no—
238C23×D3C22⋊C411yescharacteristic
239C2×C3×Q8C22×C411yescharacteristic
240C2×C3×D4—21no—
241C2×C3×D4C22×C411yescharacteristic
242C22×C3×C4—21no—
243C22×C3×C4C22×C411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C2×#67—21no—
247C2×#67—21no—
248C2×#67—21no—
249C22×Dic3—21no—
250C22×Dic3C22⋊C411yescharacteristic
251C22×Dic3C22⋊C411yescharacteristic
252C22×Dic3C22⋊C411yescharacteristic
253D3×Q8—42no—
254D3×D4—42no—
255D3×D4—44no—
256C2×D12—21no—
257C2×D12C22×C411yescharacteristic
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—42no—
264C2×C4×D3—42no—
265C2×C4×D3—44no—
266C2×C4×D3—42no—
267C2×C4×D3C22⋊C411yescharacteristic
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×D3C2×D411yescharacteristic
276C2×C4×D3C2×D411yescharacteristic
277C2×C4×D3C2×D411yescharacteristic
278C2×C4×D3C2×D411yescharacteristic
279C2×Dic6—21no—
280C2×Dic6C22×C411yescharacteristic
281C2×C3×C8—22no—
282C2×C3×C8—22no—
283C2×C3×C8—42no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4C22×C411yescharacteristic
289C3×C4⋊C4C22×C411yescharacteristic
290C3×C22⋊C4—21no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—21no—
294C3×C22⋊C4—21no—
295C3×C42—21no—
296C3×C42C22×C411yescharacteristic
297C3×C42C2×D411yescharacteristic
298C3×C42C2×D411yescharacteristic
299C3×C42C2411yescharacteristic
300#217—21no—
301#217—21no—
302#217—21no—
303#217—21no—
304#217—21no—
305(C2×D3)⋊C4—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—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3—21no—
318C4⋊Dic3—21no—
319C4⋊Dic3C22×C411yescharacteristic
320C4⋊Dic3C22×C411yescharacteristic
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—
330Dic3⋊C4—21no—
331C4×Dic3—21no—
332C4×Dic3—21no—
333C4×Dic3—21no—
334C4×Dic3C22⋊C411yescharacteristic
335C4×Dic3C22⋊C411yescharacteristic
336C4×Dic3C22⋊C411yescharacteristic
337C4×Dic3C22⋊C411yescharacteristic
338C4×Dic3C22⋊C411yescharacteristic
339C4×Dic3C22⋊C411yescharacteristic
340C4×Dic3C22×C411yescharacteristic
341C4×Dic3C22×C411yescharacteristic
342C4×Dic3C2×D411yescharacteristic
343C4×Dic3C2×D411yescharacteristic
344C4×Dic3C2×D411yescharacteristic
345C4×Dic3C2×D411yescharacteristic
346C2×C3⋊C8—22no—
347C2×C3⋊C8—22no—
348C2×C3⋊C8—42no—
349ΓL(1,𝔽25)—44no—
350C22×Q8—31no—
351C22×D4—31no—
352C22×D4—61no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—61no—
357C2×M16—62no—
358C22×C8—21no—
359C22×C8—61no—
360#126—21no—
361#126—61no—
362#126—61no—
363#126—61no—
364#126—61no—
365#126—61no—
366#126—61no—
367#126—61no—
368#125—31no—
369#125—31no—
370#125—31no—
371#125—61no—
372#125—61no—
373#125C22×D311yescharacteristic
374#124—31no—
375#124—31no—
376#124—31no—
377#124—61no—
378#124—61no—
379#124C22×D311yescharacteristic
380#123—21no—
381#123—61no—
382#123—61no—
383#123—61no—
384#123—61no—
385#123—61no—
386#123—61no—
387#123—61no—
388C22⋊Q8—31no—
389C22⋊Q8—31no—
390C22⋊Q8—31no—
391C22⋊Q8—61no—
392C22⋊Q8—61no—
393C22⋊Q8C4×D311yescharacteristic
394#121—31no—
395#121—31no—
396#121—31no—
397#121—61no—
398#121—61no—
399#121C4×D311yescharacteristic
400C4×Q8—31no—
401C4×Q8—31no—
402C4×Q8—31no—
403C4×Q8—61no—
404C4×Q8—61no—
405C4×Q8C4×D311yescharacteristic
406C4×D4—21no—
407C4×D4—31no—
408C4×D4—31no—
409C4×D4—31no—
410C4×D4—61no—
411C4×D4—61no—
412C4×D4—61no—
413C4×D4—61no—
414C4×D4—61no—
415C4×D4—61no—
416C4×D4—61no—
417C4×D4—61no—
418C4×D4—61no—
419C4×D4C4×D311yescharacteristic
420#117—21no—
421#117—61no—
422#117—61no—
423#117—61no—
424#117—61no—
425#117—61no—
426#117—61no—
427#117—61no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—61no—
431C2×C4⋊C4—61no—
432C2×C4⋊C4—61no—
433C2×C4⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C42—31no—
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—61no—
451C2×C42C22×D311yescharacteristic
452C4⋊C8—21no—
453C4⋊C8—62no—
454C4⋊C8—62no—
455C4⋊C8—62no—
456C4⋊C8—61no—
457C22⋊C8—21no—
458C22⋊C8—62no—
459C22⋊C8—62no—
460C22⋊C8—62no—
461C22⋊C8—61no—
462#97—21no—
463#97—32no—
464#97—32no—
465#97—61no—
466#97C22×D312yes—
467#97C22×D312yes—
468C4×C8—62no—
469C23×C3—21no—
470C23×C3C2×C22⋊C411yescharacteristic
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—21no—
474C22×D3—41no—
475C22×D3—42no—
476C22×D3—42no—
477C22×D3—42no—
478C22×D3C2×C22⋊C411yescharacteristic
479C22×D3C2×C22⋊C411yescharacteristic
480C3×Q8—41no—
481C3×D4—41no—
482C3×D4—42no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—42no—
490C2×C3×C4C2×C22⋊C411yescharacteristic
491C2×C3×C4C2×C22⋊C411yescharacteristic
492C2×C3×C4C2×C22⋊C411yescharacteristic
493C2×C3×C4C23×C411yescharacteristic
494C2×C3×C4C22×D411yescharacteristic
495C2×C3×C4C22×D411yescharacteristic
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×Dic3C2×C22⋊C411yescharacteristic
507C2×Dic3C2×C22⋊C411yescharacteristic
508C2×Dic3C2×C22⋊C411yescharacteristic
509C2×Dic3C2×C22⋊C411yescharacteristic
510C2×Dic3C2×C22⋊C411yescharacteristic
511C2×Dic3C2×C22⋊C411yescharacteristic
512D12—41no—
513D12—42no—
514C4×D3—22no—
515C4×D3—22no—
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—41no—
519C4×D3—41no—
520C4×D3—41no—
521C4×D3—41no—
522C4×D3—41no—
523C4×D3—41no—
524C4×D3—41no—
525C4×D3—41no—
526C4×D3—42no—
527C4×D3—42no—
528C4×D3—42no—
529C4×D3—42no—
530C4×D3—42no—
531Dic6—42no—
532Dic6—41no—
533C3×C8—42no—
534C3×C8—42no—
535C3⋊C8—42no—
536C3⋊C8—42no—
537C24—31no—
538C24—61no—
539C2×Q8—31no—
540C2×Q8—61no—
541C2×Q8—122no—
542C2×Q8C2×C4×D311yescharacteristic
543C2×D4—21no—
544C2×D4—31no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—61no—
548C2×D4—61no—
549C2×D4—122no—
550C2×D4—124no—
551C2×D4C2×C4×D311yescharacteristic
552C22×C4—21no—
553C22×C4—31no—
554C22×C4—31no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
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—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—122no—
575C22×C4—122no—
576C22×C4—122no—
577C22×C4—124no—
578C22×C4C2×C4×D311yescharacteristic
579C22×C4D3×D411yescharacteristic
580C22×C4D3×D411yescharacteristic
581M16—124no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—42no—
585C2×C8—62no—
586C2×C8—62no—
587C2×C8—122no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
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⋊C4C2×C4×D311yescharacteristic
609C4⋊C4C2×C4×D311yescharacteristic
610C22⋊C4—21no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—21no—
615C22⋊C4—61no—
616C22⋊C4—61no—
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—
646C42C2×C4×D311yescharacteristic
647C42D3×D411yescharacteristic
648C42D3×D411yescharacteristic
649C42C23×D311yescharacteristic
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3#42112yes—
656C22×C3C22×C22⋊C411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—44no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—84no—
667C2×D3#42112yes—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677Dic3—21no—
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3#41312yes—
686C23—21no—
687C23—31no—
688C23—31no—
689C23—62no—
690C23—62no—
691C23—61no—
692C23—121no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23D3×C22⋊C411yescharacteristic
697Q8—41no—
698Q8—121no—
699Q8—122no—
700D4—41no—
701D4—42no—
702D4—121no—
703D4—122no—
704D4—122no—
705D4—122no—
706D4—122no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—62no—
721C2×C4—62no—
722C2×C4—62no—
723C2×C4—62no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4—122no—
742C2×C4—121no—
743C2×C4—122no—
744C2×C4D3×C22⋊C411yescharacteristic
745C2×C4D3×C22⋊C411yescharacteristic
746C2×C4D3×C22⋊C411yescharacteristic
747C2×C4C22×C4×D311yescharacteristic
748C2×C4C2×D3×D411yescharacteristic
749C2×C4C2×D3×D411yescharacteristic
750C8—42no—
751C8—42no—
752C8—122no—
753C8—122no—
754C2×C3—22no—
755C2×C3—81no—
756C2×C3C2×#41311yescharacteristic
757C2×C3C2×#42111yescharacteristic
758C2×C3C2×#42111yescharacteristic
759D3—22no—
760D3—41no—
761D3—81no—
762C22—21no—
763C22—21no—
764C22—32no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—61no—
773C22—124no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—244no—
778C22#482112yes—
779C22C2×D3×C22⋊C411yescharacteristic
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—32no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—61no—
791C4—61no—
792C4—61no—
793C4—61no—
794C4—61no—
795C4—121no—
796C4—121no—
797C4—121no—
798C3#1766811yescharacteristic, complemented, Sylow
799C2—22no—
800C2—62no—
801C2—81no—
802C2—121no—
803C2—241no—
804C2D3×#41311yescharacteristic
805C2C2×#482111yescharacteristic
806C2D3×#42111yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#1532C2
socleC22×C3C22×C22⋊C4
prime radicalD3×#121C4
cosocleC3×C42C24
hypercenter#1532D3
hypocenterC3#17668
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1532

Complements

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

NH ≅ G/Ntype
2. #79331C2semidirect
3. C2×#4705C2semidirect
4. C3×#1532C2semidirect
5. #71748C2semidirect
6. #70807C2semidirect
7. #69799C2semidirect
8. #68368C2semidirect
9. #68363C2semidirect
10. #68348C2semidirect
11. #68343C2semidirect
36. C3×#432C22semidirect
37. C2×C3×#97C22semidirect
40. #4926C22semidirect
41. C2×#803C22semidirect
50. #4705C22semidirect
51. #4705C22semidirect
52. C3×#330C22semidirect
53. C3×#329C22semidirect
54. #4543C22semidirect
55. #4540C22semidirect
56. #4465C22semidirect
57. #4465C22semidirect
58. #4464C22semidirect
59. #4464C22semidirect
68. #1532D3semidirect
219. #432C2×D3semidirect
228. C2×#97C2×D3semidirect
232. #330C2×D3semidirect
236. #329C2×D3semidirect
798. C3#17668semidirect

Maximal subgroups

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

subgroupindex
D3×#5292
#793312
C2×#47052
C3×#15322
#717482
#708072
#697992
#683682
#683632
#683482
#683432
#176683