Finite Group Databasebeta

← #10764040

Subgroups — #10764040

Order 768.

990 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#85848C211yesmaximal, characteristic
2C3×#2990C211yesmaximal, characteristic, complemented
3#82522C211yesmaximal, characteristic, complemented
4#70820C211yesmaximal, characteristic, complemented
5#70819C211yesmaximal, characteristic, complemented
6#70818C211yesmaximal, characteristic, complemented
7#70817C211yesmaximal, characteristic, complemented
8#70775C211yesmaximal, characteristic, complemented
9#70772C211yesmaximal, characteristic, complemented
10#70504C211yesmaximal, characteristic, complemented
11#70503C211yesmaximal, characteristic, complemented
12#70439C211yesmaximal, characteristic, complemented
13#70432C211yesmaximal, characteristic, complemented
14#70431C211yesmaximal, characteristic, complemented
15C2×#4485C211yesmaximal, characteristic, complemented
16#17771—31nomaximal, Sylow
17C3×C4×#41C2211yescharacteristic
18#5830C412yes—
19#5585—21no—
20#5585—21no—
21#5553—21no—
22#5553—21no—
23#5550—21no—
24#5550—21no—
25#5550—21no—
26#5550—21no—
27#5535C412yes—
28#5535C412yes—
29#5521C412yes—
30#5477C2211yescharacteristic
31#5477C2211yescharacteristic
32#5477C2211yescharacteristic
33#5477C2211yescharacteristic
34C2×#874C2211yescharacteristic
35#5470C2211yescharacteristic
36C3×#446—21no—
37C3×#435—21no—
38C3×#435—21no—
39C3×C8×D4—21no—
40C3×#432C2211yescharacteristic
41C3×#432C2211yescharacteristic, complemented
42C3×#431C2211yescharacteristic, complemented
43C3×#423C2211yescharacteristic, complemented
44C2×C3×C4⋊C8C2211yescharacteristic
45C2×C3×C4⋊C8C2211yescharacteristic, complemented
46#5024—21no—
47#5011—21no—
48#5011—21no—
49D4×C3⋊C8—21no—
50#4926C2211yescharacteristic
51#4926C2211yescharacteristic, complemented
52#4925C2211yescharacteristic, complemented
53#4924C2211yescharacteristic, complemented
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56#4486C2211yescharacteristic, complemented
57#4486C2211yescharacteristic, complemented
58#4486C2211yescharacteristic, complemented
59#4486C2211yescharacteristic, complemented
60#4485C2211yescharacteristic
61#4485C2211yescharacteristic
62#4485C2211yescharacteristic
63#4485C2211yescharacteristic
64#4485C2211yescharacteristic
65#4485C2211yescharacteristic
66#4485C2211yescharacteristic
67#4485C2211yescharacteristic
68#4482C2211yescharacteristic, complemented
69#4482C2211yescharacteristic, complemented
70#4482C2211yescharacteristic, complemented
71#4482C2211yescharacteristic, complemented
72#3508—31no—
73#2990—31no—
74#2990D311yescharacteristic, complemented
75#1557—31no—
76#1557—31no—
77#1555—31no—
78#1553—31no—
79#1553—31no—
80#1552—31no—
81#1552—31no—
82#1547—31no—
83#1547—31no—
84#1540—31no—
85#1540—31no—
86C2×#331—31no—
87C2×C3×#41C2×C411yescharacteristic
88C2×#235—21no—
89C2×#235—21no—
90C2×#235—21no—
91C2×#235—21no—
92C22×D12—21no—
93C22×D12—21no—
94C22×D12C2×C412yes—
95C2×C3×M16—21no—
96C22×C3×C8—21no—
97C22×C3×C8—21no—
98C3×C4×Q8D411yescharacteristic
99C3×C4×Q8D411yescharacteristic
100C3×C4×D4D411yescharacteristic
101C3×C4×D4D411yescharacteristic
102C3×C4×D4D411yescharacteristic
103C3×C4×D4D411yescharacteristic
104C3×C4×D4D411yescharacteristic
105C3×C4×D4D411yescharacteristic
106C3×#117C2×C411yescharacteristic
107C3×#117C2×C411yescharacteristic
108C3×#117C2×C411yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×C3×C42C2311yescharacteristic
111C2×C3×C42C2311yescharacteristic
112#947—22no—
113#940—22no—
114#937—22no—
115#937—22no—
116#930—21no—
117#930—21no—
118#930—21no—
119#930—21no—
120#930C2×C412yes—
121#930C2×C412yes—
122#930C2×C412yes—
123#930C2×C412yes—
124#926C2×C412yes—
125#924—21no—
126#924—21no—
127C2×#208—21no—
128C22×C3⋊C8—21no—
129C22×C3⋊C8—21no—
130#894—22no—
131#894—22no—
132#894—22no—
133#894—22no—
134#893—22no—
135#893—22no—
136#884—22no—
137#884—22no—
138#884—22no—
139#884—22no—
140D3×C22⋊C4—22no—
141D3×C22⋊C4—22no—
142#875—21no—
143#875—21no—
144#875—21no—
145#875—21no—
146#874—21no—
147#874—21no—
148#874C2×C412yes—
149#874C2311yescharacteristic
150#874C2311yescharacteristic
151C4×D12—21no—
152C4×D12—21no—
153C4×D12—21no—
154C4×D12—21no—
155C4×D12C2×C412yes—
156C4×D12C2×C412yes—
157C4×D12C2×C412yes—
158C4×D12C2×C412yes—
159#870C2×C412yes—
160#869C2311yescharacteristic
161#869C2311yescharacteristic
162C4×Dic6—21no—
163C4×Dic6—21no—
164C3×C4⋊C8—21no—
165C3×C4⋊C8—21no—
166C3×C4⋊C8—21no—
167C3×C4⋊C8C2311yescharacteristic
168C3×C4⋊C8C2311yescharacteristic
169C3×C4⋊C8C2311yescharacteristic
170C3×C4⋊C8C2311yescharacteristic
171C3×C22⋊C8—21no—
172C3×C22⋊C8—21no—
173C3×C22⋊C8—21no—
174C3×#97—21no—
175C3×#97—21no—
176C3×C4×C8—21no—
177#830—21no—
178#830—21no—
179#830—21no—
180C4⋊(C3⋊C8)—21no—
181C4⋊(C3⋊C8)—21no—
182C4⋊(C3⋊C8)—21no—
183C4⋊(C3⋊C8)C2311yescharacteristic
184C4⋊(C3⋊C8)C2311yescharacteristic
185C4⋊(C3⋊C8)C2311yescharacteristic
186C4⋊(C3⋊C8)C2311yescharacteristic
187#803—21no—
188#803—21no—
189C4×C3⋊C8—21no—
190#559—61no—
191#559—61no—
192#550—61no—
193#550—61no—
194#546—61no—
195#546—61no—
196#546—61no—
197#546—61no—
198#540—32no—
199#540—32no—
200#535—32no—
201#533—31no—
202#532—31no—
203#532—31no—
204#532—31no—
205#532—31no—
206C2×#127—31no—
207#518—32no—
208C4×#41C2×D311yescharacteristic
209#446—21no—
210#446—61no—
211#435—21no—
212#435—21no—
213#435—61no—
214#435—61no—
215C8×D4—21no—
216C8×D4—61no—
217#432—31no—
218#432—31no—
219#432C2×D311yescharacteristic
220#432C2×D311yescharacteristic, complemented
221#431—31no—
222#431C2×D311yescharacteristic, complemented
223#423—31no—
224#423C2×D311yescharacteristic, complemented
225C2×C4⋊C8—31no—
226C2×C4⋊C8—31no—
227C2×C4⋊C8C2×D311yescharacteristic
228C2×C4⋊C8C2×D311yescharacteristic, complemented
229#332—31no—
230#332—31no—
231#332—31no—
232#332—31no—
233#332—31no—
234#332—31no—
235#332—31no—
236#332—31no—
237#331—31no—
238#331—31no—
239#331—31no—
240#331—31no—
241#331—31no—
242#331—31no—
243#331—31no—
244#331—31no—
245C23×D3—22no—
246C3×#41—42no—
247C2×C3×Q8C22⋊C411yescharacteristic
248C2×C3×D4C22⋊C411yescharacteristic
249C2×C3×D4C22⋊C411yescharacteristic
250C2×C3×D4C22⋊C411yescharacteristic
251C22×C3×C4C22×C411yescharacteristic
252C22×C3×C4C22×C411yescharacteristic
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—22no—
263C2×#67—22no—
264#235—81no—
265#235—81no—
266#235—81no—
267#235—81no—
268#235—81no—
269#235—81no—
270#235—81no—
271#235—81no—
272C2×D12—22no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—22no—
278C2×D12—22no—
279C2×D12—44no—
280C2×D12—81no—
281C2×D12—81no—
282C2×D12—81no—
283C2×D12—81no—
284C2×D12C22×C412yes—
285C2×D12C22×C412yes—
286C2×C4×D3—22no—
287C2×C4×D3—22no—
288C2×C4×D3—22no—
289C2×C4×D3—22no—
290C2×Dic6—21no—
291C2×Dic6—21no—
292C3×M16—81no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—81no—
298C2×C3×C8—81no—
299C3×C4⋊C4C22⋊C411yescharacteristic
300C3×C4⋊C4C22⋊C411yescharacteristic
301C3×C4⋊C4C22⋊C411yescharacteristic
302C3×C4⋊C4C22⋊C411yescharacteristic
303C3×C4⋊C4C22⋊C411yescharacteristic
304C3×C4⋊C4C22⋊C411yescharacteristic
305C3×C22⋊C4C22⋊C411yescharacteristic
306C3×C22⋊C4C22⋊C411yescharacteristic
307C3×C22⋊C4C22⋊C411yescharacteristic
308C3×C22⋊C4C22⋊C411yescharacteristic
309C3×C22⋊C4C22⋊C411yescharacteristic
310C3×C22⋊C4C22⋊C411yescharacteristic
311C3×C42C22×C411yescharacteristic
312C3×C42C22×C411yescharacteristic
313C3×C42C22×C411yescharacteristic
314C3×C42C2×D411yescharacteristic
315C3×C42C2×D411yescharacteristic
316C3×C42C2×D411yescharacteristic
317C3×C42C2×D411yescharacteristic
318C3×C42C2×D411yescharacteristic
319C3×C42C2×D411yescharacteristic
320C3×C42C2411yescharacteristic
321#217—22no—
322(C2×D3)⋊C4—22no—
323(C2×D3)⋊C4—22no—
324(C2×D3)⋊C4—22no—
325(C2×D3)⋊C4—22no—
326(C2×D3)⋊C4—22no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—22no—
329(C2×D3)⋊C4—22no—
330C4⋊Dic3—21no—
331C4⋊Dic3—21no—
332C4⋊Dic3C22×C412yes—
333C4⋊Dic3C22×C412yes—
334Dic3⋊C4—22no—
335Dic3⋊C4—22no—
336C4×Dic3—22no—
337#208—81no—
338C2×C3⋊C8—21no—
339C2×C3⋊C8—21no—
340C2×C3⋊C8—21no—
341C2×C3⋊C8—21no—
342C2×C3⋊C8—81no—
343C2×C3⋊C8—81no—
344C2×#41—61no—
345C2×#41—61no—
346C2×#41—61no—
347C2×#41—61no—
348C2×#41C4×D311yescharacteristic
349C22×D4—32no—
350C22×D4—61no—
351C22×D4—61no—
352C2×M16—21no—
353C2×M16—61no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—61no—
357C22×C8—61no—
358C4⋊Q8—31no—
359C4⋊Q8—31no—
360#127—32no—
361#127—31no—
362#127—31no—
363#127—62no—
364#127—61no—
365#127—61no—
366#125—32no—
367#124—62no—
368#124—61no—
369#124—61no—
370#124—61no—
371#124—61no—
372#123—62no—
373#123—62no—
374#123—62no—
375#123—62no—
376C22⋊Q8—61no—
377C22⋊Q8—61no—
378#121—32no—
379#121—32no—
380#121—32no—
381#121—32no—
382#121—61no—
383#121—61no—
384#121—61no—
385#121—61no—
386#121—62no—
387#121—62no—
388#121—62no—
389#121—62no—
390#120—62no—
391#120—62no—
392C4×Q8—61no—
393C4×Q8—61no—
394C4×Q8D1211yescharacteristic
395C4×Q8#6711yescharacteristic
396C4×D4—32no—
397C4×D4—32no—
398C4×D4—32no—
399C4×D4—32no—
400C4×D4—62no—
401C4×D4—62no—
402C4×D4—61no—
403C4×D4—61no—
404C4×D4—61no—
405C4×D4—61no—
406C4×D4D1211yescharacteristic
407C4×D4D1211yescharacteristic
408C4×D4D1211yescharacteristic
409C4×D4#6711yescharacteristic
410C4×D4#6711yescharacteristic
411C4×D4#6711yescharacteristic
412#117—32no—
413#117C4×D311yescharacteristic
414#117C4×D311yescharacteristic
415#117C4×D311yescharacteristic
416C2×C22⋊C4—62no—
417C2×C22⋊C4—62no—
418C2×C42C22×D311yescharacteristic
419C2×C42C22×D311yescharacteristic
420C2×C42C22×D311yescharacteristic
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—31no—
425C4⋊C8—31no—
426C4⋊C8—31no—
427C4⋊C8—31no—
428C4⋊C8—61no—
429C4⋊C8—61no—
430C4⋊C8—61no—
431C4⋊C8C22×D311yescharacteristic
432C4⋊C8C22×D311yescharacteristic
433C4⋊C8C22×D311yescharacteristic
434C4⋊C8C22×D311yescharacteristic
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—61no—
439C22⋊C8—61no—
440C22⋊C8—61no—
441#97—21no—
442#97—21no—
443#97—61no—
444#97—61no—
445C4×C8—21no—
446C4×C8—61no—
447C23×C3C2×C22⋊C411yescharacteristic
448C23×C3C2×C22⋊C411yescharacteristic
449C23×C3C2×C22⋊C411yescharacteristic
450C22×D3—22no—
451C22×D3—22no—
452C22×D3—44no—
453C22×D3—82no—
454C22×D3—82no—
455C3×Q8—41no—
456C3×D4—22no—
457C3×D4—22no—
458C3×D4—41no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4C2×C22⋊C411yescharacteristic
475C2×C3×C4C2×C22⋊C411yescharacteristic
476C2×C3×C4C2×C22⋊C411yescharacteristic
477C2×C3×C4C2×C22⋊C411yescharacteristic
478C2×C3×C4C2×C22⋊C411yescharacteristic
479C2×C3×C4C2×C22⋊C411yescharacteristic
480C2×C3×C4C2×C22⋊C411yescharacteristic
481C2×C3×C4C2×C22⋊C411yescharacteristic
482C2×C3×C4C2×C22⋊C411yescharacteristic
483C2×C3×C4C23×C411yescharacteristic
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C22×D411yescharacteristic
486#67—82no—
487#67—82no—
488#67—82no—
489#67—82no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492D12—42no—
493D12—42no—
494D12—44no—
495D12—41no—
496D12—41no—
497D12—41no—
498D12—41no—
499D12—41no—
500D12—41no—
501D12—41no—
502D12—41no—
503D12—82no—
504D12—82no—
505C4×D3—82no—
506C4×D3—82no—
507C4×D3—82no—
508C4×D3—82no—
509Dic6—41no—
510Dic6—41no—
511Dic6—41no—
512Dic6—41no—
513C3×C8—41no—
514C3×C8—41no—
515C3×C8—41no—
516C3×C8—41no—
517C3⋊C8—41no—
518C3⋊C8—41no—
519C3⋊C8—41no—
520C3⋊C8—41no—
521C24—62no—
522#41—42no—
523#41—241no—
524#41—241no—
525#41—241no—
526#41—241no—
527#41—241no—
528#41—241no—
529#41—241no—
530#41—241no—
531C2×Q8—61no—
532C2×Q8—61no—
533C2×Q8(C2×D3)⋊C411yescharacteristic
534C2×D4—32no—
535C2×D4—32no—
536C2×D4—62no—
537C2×D4—62no—
538C2×D4—62no—
539C2×D4—62no—
540C2×D4—62no—
541C2×D4—62no—
542C2×D4—62no—
543C2×D4—61no—
544C2×D4—61no—
545C2×D4—61no—
546C2×D4—61no—
547C2×D4—124no—
548C2×D4—241no—
549C2×D4—241no—
550C2×D4—241no—
551C2×D4—241no—
552C2×D4(C2×D3)⋊C411yescharacteristic
553C2×D4(C2×D3)⋊C411yescharacteristic
554C2×D4(C2×D3)⋊C411yescharacteristic
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4C2×C4×D311yescharacteristic
560C22×C4C2×C4×D311yescharacteristic
561C22×C4C2×C4×D311yescharacteristic
562C22×C4C2×D1211yescharacteristic
563C22×C4C2×D1211yescharacteristic
564C22×C4C2×D1211yescharacteristic
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C22×C4C2×#6711yescharacteristic
568M16—81no—
569M16—241no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—81no—
579C2×C8—81no—
580C2×C8—241no—
581C2×C8—241no—
582C4⋊C4—32no—
583C4⋊C4—32no—
584C4⋊C4—62no—
585C4⋊C4—62no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4(C2×D3)⋊C411yescharacteristic
589C4⋊C4(C2×D3)⋊C411yescharacteristic
590C4⋊C4(C2×D3)⋊C411yescharacteristic
591C4⋊C4(C2×D3)⋊C411yescharacteristic
592C4⋊C4(C2×D3)⋊C411yescharacteristic
593C4⋊C4(C2×D3)⋊C411yescharacteristic
594C22⋊C4—62no—
595C22⋊C4—62no—
596C22⋊C4—62no—
597C22⋊C4—62no—
598C22⋊C4—62no—
599C22⋊C4—62no—
600C22⋊C4—62no—
601C22⋊C4—62no—
602C22⋊C4—62no—
603C22⋊C4(C2×D3)⋊C411yescharacteristic
604C22⋊C4(C2×D3)⋊C411yescharacteristic
605C22⋊C4(C2×D3)⋊C411yescharacteristic
606C22⋊C4(C2×D3)⋊C411yescharacteristic
607C22⋊C4(C2×D3)⋊C411yescharacteristic
608C22⋊C4(C2×D3)⋊C411yescharacteristic
609C42—62no—
610C42C2×C4×D311yescharacteristic
611C42C2×C4×D311yescharacteristic
612C42C2×C4×D311yescharacteristic
613C42C2×D1211yescharacteristic
614C42C2×D1211yescharacteristic
615C42C2×D1211yescharacteristic
616C42C2×#6711yescharacteristic
617C42C2×#6711yescharacteristic
618C42C2×#6711yescharacteristic
619C42C23×D311yescharacteristic
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3#41312yes—
629C22×C3C22×C22⋊C411yescharacteristic
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—164no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4#57611yescharacteristic
648C3×C4#57611yescharacteristic
649C3×C4#57711yescharacteristic
650C3×C4#57711yescharacteristic
651Dic3—42no—
652Dic3—42no—
653C23—62no—
654C23—62no—
655C23—124no—
656C23—242no—
657C23—242no—
658C23C2×(C2×D3)⋊C411yescharacteristic
659C23C2×(C2×D3)⋊C411yescharacteristic
660C23C2×(C2×D3)⋊C411yescharacteristic
661Q8—41no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665Q8—121no—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—122no—
670D4—122no—
671D4—124no—
672D4—121no—
673D4—121no—
674D4—121no—
675D4—121no—
676D4—121no—
677D4—121no—
678D4—121no—
679D4—121no—
680D4—242no—
681D4—242no—
682D4—242no—
683D4—242no—
684D4—242no—
685D4—242no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—242no—
704C2×C4—242no—
705C2×C4—242no—
706C2×C4—242no—
707C2×C4C2×(C2×D3)⋊C411yescharacteristic
708C2×C4C2×(C2×D3)⋊C411yescharacteristic
709C2×C4C2×(C2×D3)⋊C411yescharacteristic
710C2×C4C2×(C2×D3)⋊C411yescharacteristic
711C2×C4C2×(C2×D3)⋊C411yescharacteristic
712C2×C4C2×(C2×D3)⋊C411yescharacteristic
713C2×C4C2×(C2×D3)⋊C411yescharacteristic
714C2×C4C2×(C2×D3)⋊C411yescharacteristic
715C2×C4C2×(C2×D3)⋊C411yescharacteristic
716C2×C4C22×C4×D311yescharacteristic
717C2×C4C22×D1211yescharacteristic
718C2×C4C22×#6711yescharacteristic
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—121no—
724C8—121no—
725C8—121no—
726C8—121no—
727C2×C3—22no—
728C2×C3—41no—
729C2×C3—41no—
730C2×C3C2×#41311yescharacteristic
731C2×C3#289711yescharacteristic
732C2×C3#289711yescharacteristic
733D3—82no—
734D3—82no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—122no—
744C22—122no—
745C22—122no—
746C22—122no—
747C22—122no—
748C22—122no—
749C22—484no—
750C22#513212yes—
751C22C22×(C2×D3)⋊C411yescharacteristic
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—122no—
763C4—122no—
764C4#575111yescharacteristic
765C4#575211yescharacteristic
766C4#583511yescharacteristic
767C4#583711yescharacteristic
768C3#1777111yescharacteristic, complemented, Sylow
769C2—22no—
770C2—41no—
771C2—41no—
772C2—242no—
773C2—242no—
774C2#8256311yescharacteristic
775C2C2×#513211yescharacteristic
776C2#8379711yescharacteristic
subgroupG/H
centerC22C22×(C2×D3)⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#2990C2
socleC22×C3C22×C22⋊C4
prime radical#85848C2
cosocleC3×C42C24
hypercenter#2990D3
hypocenterC3#17771
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. C3×#2990C2semidirect
3. #82522C2semidirect
4. #70820C2semidirect
5. #70819C2semidirect
6. #70818C2semidirect
7. #70817C2semidirect
8. #70775C2semidirect
9. #70772C2semidirect
10. #70504C2semidirect
11. #70503C2semidirect
12. #70439C2semidirect
13. #70432C2semidirect
14. #70431C2semidirect
15. C2×#4485C2semidirect
41. C3×#432C22semidirect
42. C3×#431C22semidirect
43. C3×#423C22semidirect
45. C2×C3×C4⋊C8C22semidirect
51. #4926C22semidirect
52. #4925C22semidirect
53. #4924C22semidirect
55. C2×C4⋊(C3⋊C8)C22semidirect
56. #4486C22semidirect
57. #4486C22semidirect
58. #4486C22semidirect
59. #4486C22semidirect
68. #4482C22semidirect
69. #4482C22semidirect
70. #4482C22semidirect
71. #4482C22semidirect
74. #2990D3semidirect
220. #432C2×D3semidirect
222. #431C2×D3semidirect
224. #423C2×D3semidirect
228. C2×C4⋊C8C2×D3semidirect
768. C3#17771semidirect

Maximal subgroups

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

subgroupindex
#858482
C3×#29902
#825222
#708202
#708192
#708182
#708172
#707752
#707722
#705042
#705032
#704392
#704322
#704312
C2×#44852
#177713