Finite Group Databasebeta

← #10764085

Subgroups — #10764085

Order 768.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85850C211yesmaximal, characteristic
2C3×#2990C211yesmaximal, characteristic, complemented
3#82522C211yesmaximal, characteristic, complemented
4#70823C211yesmaximal, characteristic, complemented
5#70821C211yesmaximal, characteristic, complemented
6#70819C211yesmaximal, characteristic, complemented
7#70816C211yesmaximal, characteristic, complemented
8#70776C211yesmaximal, characteristic, complemented
9#70775C211yesmaximal, characteristic, complemented
10#70510C211yesmaximal, characteristic, complemented
11#70503C211yesmaximal, characteristic, complemented
12#70438C211yesmaximal, characteristic, complemented
13C2×#4482C211yesmaximal, characteristic, complemented
14#70433C211yesmaximal, characteristic, complemented
15#70431C211yesmaximal, characteristic, complemented
16#17775—31nomaximal, Sylow
17C3×C4×#41C2211yescharacteristic
18#5833C412yes—
19#5584—21no—
20#5579—21no—
21#5565—21no—
22#5565—21no—
23#5563—21no—
24#5552—21no—
25#5552—21no—
26#5551—21no—
27#5534C412yes—
28#5534C412yes—
29#5523C412yes—
30#5477C2211yescharacteristic
31#5477C2211yescharacteristic
32#5477C2211yescharacteristic
33#5470C2211yescharacteristic
34#5470C2211yescharacteristic
35C2×#869C2211yescharacteristic
36C3×#446—21no—
37C3×#435—21no—
38C3×#435—21no—
39C3×C8×D4—21no—
40C3×#432C2211yescharacteristic
41C3×#432C2211yescharacteristic
42C3×#431C2211yescharacteristic
43C3×#423C2211yescharacteristic
44C2×C3×C4⋊C8C2211yescharacteristic
45C2×C3×C4⋊C8C2211yescharacteristic
46#5024—21no—
47#5011—21no—
48#5011—21no—
49D4×C3⋊C8—21no—
50#4926C2211yescharacteristic
51#4926C2211yescharacteristic
52#4925C2211yescharacteristic
53#4924C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55C2×C4⋊(C3⋊C8)C2211yescharacteristic
56#4485C2211yescharacteristic
57#4485C2211yescharacteristic
58#4485C2211yescharacteristic
59#4485C2211yescharacteristic
60#4482C2211yescharacteristic
61#4482C2211yescharacteristic
62#4482C2211yescharacteristic
63#4482C2211yescharacteristic
64#4482C2211yescharacteristic
65#4482C2211yescharacteristic
66#4482C2211yescharacteristic
67#4482C2211yescharacteristic
68#4481C2211yescharacteristic
69#4481C2211yescharacteristic
70#4481C2211yescharacteristic
71#4481C2211yescharacteristic
72#3511—31no—
73#2990—31no—
74#2990D311yescharacteristic, complemented
75#1559—31no—
76#1557—31no—
77#1556—31no—
78#1554—31no—
79#1553—31no—
80#1551—31no—
81#1551—31no—
82#1550—31no—
83#1547—31no—
84#1542—31no—
85#1540—31no—
86C2×#332—31no—
87C2×C3×#41C2×C411yescharacteristic
88C2×#235—21no—
89C2×#235—21no—
90C2×#235C2×C412yes—
91C22×Dic6—21no—
92C2×C3×M16—21no—
93C22×C3×C8—21no—
94C22×C3×C8—21no—
95C3×C4×Q8D411yescharacteristic
96C3×C4×Q8D411yescharacteristic
97C3×C4×D4D411yescharacteristic
98C3×C4×D4D411yescharacteristic
99C3×C4×D4D411yescharacteristic
100C3×C4×D4D411yescharacteristic
101C3×C4×D4D411yescharacteristic
102C3×C4×D4D411yescharacteristic
103C3×#117C2×C411yescharacteristic
104C3×#117C2×C411yescharacteristic
105C3×#117C2×C411yescharacteristic
106C2×C3×C42C2311yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C2×C3×C42C2311yescharacteristic
109#946—22no—
110#939—22no—
111#939—22no—
112#938—22no—
113#930—21no—
114#930—21no—
115#930—21no—
116#930—21no—
117#930C2×C412yes—
118#930C2×C412yes—
119#926—21no—
120#926—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3C2×C412yes—
123#924—21no—
124#924—21no—
125#924C2×C412yes—
126#924C2×C412yes—
127C2×#208—21no—
128C22×C3⋊C8—21no—
129C22×C3⋊C8—21no—
130#898—22no—
131#898—22no—
132#896—22no—
133#896—22no—
134#892—22no—
135D3×C4⋊C4—22no—
136#885—22no—
137#885—22no—
138#883—22no—
139#883—22no—
140#67⋊C4—22no—
141#67⋊C4—22no—
142#875—21no—
143#875—21no—
144#875C2×C412yes—
145#874C2311yescharacteristic
146C4×D12—21no—
147C4×D12—21no—
148C4×D12—21no—
149C4×D12—21no—
150C4×D12C2×C412yes—
151C4×D12C2×C412yes—
152#870—21no—
153#870—21no—
154#869—21no—
155#869—21no—
156#869C2×C412yes—
157#869C2311yescharacteristic
158#869C2311yescharacteristic
159#869C2311yescharacteristic
160C4×Dic6—21no—
161C4×Dic6—21no—
162C4×Dic6C2×C412yes—
163C4×Dic6C2×C412yes—
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#556—61no—
191#555—61no—
192#554—61no—
193#553—61no—
194#553—61no—
195#548—61no—
196#548—61no—
197#547—61no—
198#542—32no—
199#542—32no—
200#537—32no—
201#533—31no—
202#533—31no—
203#532—31no—
204#532—31no—
205#532—31no—
206C2×C4⋊Q8—31no—
207#520—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
221#431—31no—
222#431C2×D311yescharacteristic
223#423—31no—
224#423C2×D311yescharacteristic
225C2×C4⋊C8—31no—
226C2×C4⋊C8—31no—
227C2×C4⋊C8C2×D311yescharacteristic
228C2×C4⋊C8C2×D311yescharacteristic
229#333—31no—
230#333—31no—
231#333—31no—
232#333—31no—
233#332—31no—
234#332—31no—
235#332—31no—
236#332—31no—
237#332—31no—
238#332—31no—
239#332—31no—
240#332—31no—
241#331—31no—
242#331—31no—
243#331—31no—
244#331—31no—
245C3×#41—42no—
246C2×C3×Q8C22⋊C411yescharacteristic
247C2×C3×D4C22⋊C411yescharacteristic
248C2×C3×D4C22⋊C411yescharacteristic
249C2×C3×D4C22⋊C411yescharacteristic
250C22×C3×C4C22×C411yescharacteristic
251C22×C3×C4C22×C411yescharacteristic
252C22×C3×C4C22×C411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C2×#67—22no—
260C2×#67—22no—
261C2×#67—22no—
262C22×Dic3—22no—
263#235—44no—
264#235—81no—
265#235—81no—
266#235—81no—
267#235—81no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12C22×C412yes—
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×C4×D3—22no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—22no—
277C2×Dic6—81no—
278C2×Dic6—81no—
279C2×Dic6C22×C412yes—
280C3×M16—81no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—81no—
286C2×C3×C8—81no—
287C3×C4⋊C4C22⋊C411yescharacteristic
288C3×C4⋊C4C22⋊C411yescharacteristic
289C3×C4⋊C4C22⋊C411yescharacteristic
290C3×C4⋊C4C22⋊C411yescharacteristic
291C3×C4⋊C4C22⋊C411yescharacteristic
292C3×C4⋊C4C22⋊C411yescharacteristic
293C3×C22⋊C4C22⋊C411yescharacteristic
294C3×C22⋊C4C22⋊C411yescharacteristic
295C3×C22⋊C4C22⋊C411yescharacteristic
296C3×C22⋊C4C22⋊C411yescharacteristic
297C3×C22⋊C4C22⋊C411yescharacteristic
298C3×C22⋊C4C22⋊C411yescharacteristic
299C3×C42C22×C411yescharacteristic
300C3×C42C22×C411yescharacteristic
301C3×C42C22×C411yescharacteristic
302C3×C42C2×D411yescharacteristic
303C3×C42C2×D411yescharacteristic
304C3×C42C2×D411yescharacteristic
305C3×C42C2×D411yescharacteristic
306C3×C42C2×D411yescharacteristic
307C3×C42C2×D411yescharacteristic
308C3×C42C2411yescharacteristic
309#217—22no—
310#217—22no—
311(C2×D3)⋊C4—22no—
312(C2×D3)⋊C4—22no—
313(C2×D3)⋊C4—22no—
314(C2×D3)⋊C4—22no—
315(C2×D3)⋊C4—22no—
316(C2×D3)⋊C4—22no—
317C4⋊Dic3—22no—
318C4⋊Dic3—22no—
319C4⋊Dic3—21no—
320C4⋊Dic3—21no—
321C4⋊Dic3—21no—
322C4⋊Dic3—21no—
323C4⋊Dic3C22×C412yes—
324C4⋊Dic3C22×C412yes—
325Dic3⋊C4—22no—
326Dic3⋊C4—22no—
327Dic3⋊C4—22no—
328Dic3⋊C4—22no—
329C4×Dic3—22no—
330C4×Dic3—22no—
331#208—81no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—81no—
337C2×C3⋊C8—81no—
338C2×#41—32no—
339C2×#41—61no—
340C2×#41—61no—
341C2×#41C4×D311yescharacteristic
342C22×Q8—61no—
343C2×M16—21no—
344C2×M16—61no—
345C22×C8—21no—
346C22×C8—21no—
347C22×C8—61no—
348C22×C8—61no—
349C4⋊Q8—32no—
350C4⋊Q8—31no—
351C4⋊Q8—31no—
352C4⋊Q8—31no—
353C4⋊Q8—61no—
354C4⋊Q8—61no—
355#127—31no—
356#126—62no—
357#126—62no—
358#125—61no—
359#125—61no—
360#124—32no—
361#124—62no—
362#124—62no—
363#124—61no—
364#124—61no—
365#123—62no—
366#123—62no—
367C22⋊Q8—32no—
368C22⋊Q8—32no—
369C22⋊Q8—62no—
370C22⋊Q8—61no—
371C22⋊Q8—61no—
372C22⋊Q8—62no—
373C22⋊Q8—62no—
374#121—32no—
375#121—32no—
376#121—62no—
377#121—62no—
378#121—62no—
379#121—61no—
380#121—61no—
381#121—61no—
382#121—61no—
383C4×Q8—32no—
384C4×Q8—32no—
385C4×Q8—61no—
386C4×Q8—61no—
387C4×Q8D1211yescharacteristic
388C4×Q8#6711yescharacteristic
389C4×D4—32no—
390C4×D4—32no—
391C4×D4—62no—
392C4×D4—62no—
393C4×D4—61no—
394C4×D4—61no—
395C4×D4—61no—
396C4×D4—61no—
397C4×D4D1211yescharacteristic
398C4×D4D1211yescharacteristic
399C4×D4D1211yescharacteristic
400C4×D4#6711yescharacteristic
401C4×D4#6711yescharacteristic
402C4×D4#6711yescharacteristic
403#117—61no—
404#117—61no—
405#117—62no—
406#117C4×D311yescharacteristic
407#117C4×D311yescharacteristic
408#117C4×D311yescharacteristic
409C2×C4⋊C4—32no—
410C2×C4⋊C4—61no—
411C2×C4⋊C4—62no—
412C2×C42C22×D311yescharacteristic
413C2×C42C22×D311yescharacteristic
414C2×C42C22×D311yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8—31no—
419C4⋊C8—31no—
420C4⋊C8—31no—
421C4⋊C8—31no—
422C4⋊C8—61no—
423C4⋊C8—61no—
424C4⋊C8—61no—
425C4⋊C8C22×D311yescharacteristic
426C4⋊C8C22×D311yescharacteristic
427C4⋊C8C22×D311yescharacteristic
428C4⋊C8C22×D311yescharacteristic
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—21no—
432C22⋊C8—61no—
433C22⋊C8—61no—
434C22⋊C8—61no—
435#97—21no—
436#97—21no—
437#97—61no—
438#97—61no—
439C4×C8—21no—
440C4×C8—61no—
441C23×C3C2×C22⋊C411yescharacteristic
442C23×C3C2×C22⋊C411yescharacteristic
443C23×C3C2×C22⋊C411yescharacteristic
444C22×D3—22no—
445C3×Q8—41no—
446C3×D4—22no—
447C3×D4—22no—
448C3×D4—41no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4C2×C22⋊C411yescharacteristic
465C2×C3×C4C2×C22⋊C411yescharacteristic
466C2×C3×C4C2×C22⋊C411yescharacteristic
467C2×C3×C4C2×C22⋊C411yescharacteristic
468C2×C3×C4C2×C22⋊C411yescharacteristic
469C2×C3×C4C2×C22⋊C411yescharacteristic
470C2×C3×C4C2×C22⋊C411yescharacteristic
471C2×C3×C4C2×C22⋊C411yescharacteristic
472C2×C3×C4C2×C22⋊C411yescharacteristic
473C2×C3×C4C23×C411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C22×D411yescharacteristic
476#67—44no—
477#67—82no—
478#67—82no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—82no—
483D12—42no—
484D12—41no—
485D12—41no—
486D12—41no—
487D12—41no—
488C4×D3—44no—
489C4×D3—82no—
490C4×D3—82no—
491Dic6—41no—
492Dic6—41no—
493Dic6—41no—
494Dic6—41no—
495Dic6—42no—
496Dic6—82no—
497C3×C8—41no—
498C3×C8—41no—
499C3×C8—41no—
500C3×C8—41no—
501C3⋊C8—41no—
502C3⋊C8—41no—
503C3⋊C8—41no—
504C3⋊C8—41no—
505#41—42no—
506#41—124no—
507#41—241no—
508#41—241no—
509#41—241no—
510#41—241no—
511C2×Q8—32no—
512C2×Q8—62no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—241no—
516C2×Q8—241no—
517C2×Q8(C2×D3)⋊C411yescharacteristic
518C2×D4—32no—
519C2×D4—62no—
520C2×D4—62no—
521C2×D4—62no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4(C2×D3)⋊C411yescharacteristic
525C2×D4(C2×D3)⋊C411yescharacteristic
526C2×D4(C2×D3)⋊C411yescharacteristic
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4C2×C4×D311yescharacteristic
532C22×C4C2×C4×D311yescharacteristic
533C22×C4C2×C4×D311yescharacteristic
534C22×C4C2×D1211yescharacteristic
535C22×C4C2×D1211yescharacteristic
536C22×C4C2×D1211yescharacteristic
537C22×C4C2×#6711yescharacteristic
538C22×C4C2×#6711yescharacteristic
539C22×C4C2×#6711yescharacteristic
540M16—81no—
541M16—241no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—81no—
551C2×C8—81no—
552C2×C8—241no—
553C2×C8—241no—
554C4⋊C4—32no—
555C4⋊C4—32no—
556C4⋊C4—62no—
557C4⋊C4—62no—
558C4⋊C4—62no—
559C4⋊C4—62no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4(C2×D3)⋊C411yescharacteristic
567C4⋊C4(C2×D3)⋊C411yescharacteristic
568C4⋊C4(C2×D3)⋊C411yescharacteristic
569C4⋊C4(C2×D3)⋊C411yescharacteristic
570C4⋊C4(C2×D3)⋊C411yescharacteristic
571C4⋊C4(C2×D3)⋊C411yescharacteristic
572C22⋊C4—62no—
573C22⋊C4—62no—
574C22⋊C4—62no—
575C22⋊C4—62no—
576C22⋊C4—62no—
577C22⋊C4—62no—
578C22⋊C4—62no—
579C22⋊C4—62no—
580C22⋊C4(C2×D3)⋊C411yescharacteristic
581C22⋊C4(C2×D3)⋊C411yescharacteristic
582C22⋊C4(C2×D3)⋊C411yescharacteristic
583C22⋊C4(C2×D3)⋊C411yescharacteristic
584C22⋊C4(C2×D3)⋊C411yescharacteristic
585C22⋊C4(C2×D3)⋊C411yescharacteristic
586C42—62no—
587C42—62no—
588C42C2×C4×D311yescharacteristic
589C42C2×C4×D311yescharacteristic
590C42C2×C4×D311yescharacteristic
591C42C2×D1211yescharacteristic
592C42C2×D1211yescharacteristic
593C42C2×D1211yescharacteristic
594C42C2×#6711yescharacteristic
595C42C2×#6711yescharacteristic
596C42C2×#6711yescharacteristic
597C42C23×D311yescharacteristic
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3#41312yes—
607C22×C3C22×C22⋊C411yescharacteristic
608C2×D3—42no—
609C2×D3—42no—
610C2×D3—42no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4#57611yescharacteristic
622C3×C4#57711yescharacteristic
623C3×C4#57711yescharacteristic
624C3×C4#57811yescharacteristic
625Dic3—42no—
626Dic3—42no—
627Dic3—42no—
628C23—62no—
629C23C2×(C2×D3)⋊C411yescharacteristic
630C23C2×(C2×D3)⋊C411yescharacteristic
631C23C2×(C2×D3)⋊C411yescharacteristic
632Q8—41no—
633Q8—122no—
634Q8—121no—
635Q8—121no—
636Q8—121no—
637Q8—121no—
638Q8—242no—
639D4—22no—
640D4—22no—
641D4—41no—
642D4—122no—
643D4—124no—
644D4—121no—
645D4—121no—
646D4—121no—
647D4—121no—
648D4—242no—
649D4—242no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—62no—
668C2×C4—124no—
669C2×C4—242no—
670C2×C4—242no—
671C2×C4—242no—
672C2×C4C2×(C2×D3)⋊C411yescharacteristic
673C2×C4C2×(C2×D3)⋊C411yescharacteristic
674C2×C4C2×(C2×D3)⋊C411yescharacteristic
675C2×C4C2×(C2×D3)⋊C411yescharacteristic
676C2×C4C2×(C2×D3)⋊C411yescharacteristic
677C2×C4C2×(C2×D3)⋊C411yescharacteristic
678C2×C4C2×(C2×D3)⋊C411yescharacteristic
679C2×C4C2×(C2×D3)⋊C411yescharacteristic
680C2×C4C2×(C2×D3)⋊C411yescharacteristic
681C2×C4C22×C4×D311yescharacteristic
682C2×C4C22×D1211yescharacteristic
683C2×C4C22×#6711yescharacteristic
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C8—121no—
689C8—121no—
690C8—121no—
691C8—121no—
692C2×C3—22no—
693C2×C3—41no—
694C2×C3—41no—
695C2×C3C2×#41311yescharacteristic
696C2×C3#289711yescharacteristic
697C2×C3#289811yescharacteristic
698D3—82no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—122no—
708C22—122no—
709C22—122no—
710C22#513212yes—
711C22C22×(C2×D3)⋊C411yescharacteristic
712C4—21no—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—21no—
720C4—21no—
721C4—21no—
722C4—122no—
723C4—122no—
724C4—122no—
725C4#575111yescharacteristic
726C4#575311yescharacteristic
727C4#583511yescharacteristic
728C4#583711yescharacteristic
729C3#1777511yescharacteristic, complemented, Sylow
730C2—22no—
731C2—41no—
732C2—41no—
733C2—242no—
734C2#8256311yescharacteristic
735C2C2×#513211yescharacteristic
736C2#8380611yescharacteristic
subgroupG/H
centerC22C22×(C2×D3)⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#2990C2
socleC22×C3C22×C22⋊C4
prime radical#85850C2
cosocleC3×C42C24
hypercenter#2990D3
hypocenterC3#17775
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. #70823C2semidirect
5. #70821C2semidirect
6. #70819C2semidirect
7. #70816C2semidirect
8. #70776C2semidirect
9. #70775C2semidirect
10. #70510C2semidirect
11. #70503C2semidirect
12. #70438C2semidirect
13. C2×#4482C2semidirect
14. #70433C2semidirect
15. #70431C2semidirect
74. #2990D3semidirect
729. C3#17775semidirect

Maximal subgroups

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

subgroupindex
#858502
C3×#29902
#825222
#708232
#708212
#708192
#708162
#707762
#707752
#705102
#705032
#704382
C2×#44822
#704332
#704312
#177753