Finite Group Databasebeta

← #11069514

Subgroups — #11069514

Order 768.

2624 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5644C212yesmaximal, complemented
2C3×#2857C211yesmaximal, characteristic, complemented
3#83257C212yesmaximal, complemented
4#82822C212yesmaximal, complemented
5C4×#930C211yesmaximal, characteristic, complemented
6C2×#4939C211yesmaximal, characteristic, complemented
7#76651C214yesmaximal, complemented
8#76260C212yesmaximal, complemented
9#76211C212yesmaximal, complemented
10#76132C212yesmaximal, complemented
11#76047C212yesmaximal, complemented
12#74328C212yesmaximal, complemented
13#74021C214yesmaximal, complemented
14#74016C212yesmaximal, complemented
15#74010C212yesmaximal, complemented
16#39375—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic, complemented
19C2×C3×C22⋊Q8C2212yes—
20C22×C3×C42C2211yescharacteristic
21C2×#947C2214yescomplemented
22C2×#930C2211yescharacteristic
23C2×C4×#67C2212yes—
24C22×(C2×D3)⋊C4C2212yes—
25C22×(C2×D3)⋊C4C2212yes—
26C22×C4⋊Dic3C2211yescharacteristic
27#5644—216no—
28C2×#898C2214yescomplemented
29C2×#895C2212yes—
30C2×#895C2212yes—
31C2×#895C2214yescomplemented
32C2×#894C2214yescomplemented
33C2×#894C2214yescomplemented
34C2×D3×C4⋊C4C2212yescomplemented
35C2×#882C2214yes—
36C2×#67⋊C4C2214yes—
37C2×C4×D12C2211yescharacteristic, complemented
38C3×#391C2212yescomplemented
39C3×#389C2212yescomplemented
40C3×#389C2212yescomplemented
41C3×#384C2211yescharacteristic, complemented
42C3×#380C2212yes—
43C3×#380C2212yes—
44#5231C2214yescomplemented
45#5213C2212yes—
46#5212C2211yescharacteristic
47#4994C2214yescomplemented
48#4994C2214yescomplemented
49#4993C2214yescomplemented
50#4993C2214yescomplemented
51#4991C2214yescomplemented
52#4990C2214yescomplemented
53#4988C2212yes—
54#4988C2212yes—
55#4987C2212yescomplemented
56#4975C2212yescomplemented
57Dic3×C4⋊C4C2212yescomplemented
58#4955C2214yes—
59#4946C2214yes—
60#4940C2212yescomplemented
61#4939C2212yes—
62#4939C2212yes—
63#4939C2212yes—
64#4939C2212yes—
65#4939C2211yescharacteristic, complemented
66C4×(C2×D3)⋊C4C2212yescomplemented
67C4×C4⋊Dic3C2211yescharacteristic, complemented
68#4928C2211yescharacteristic, complemented
69#4675C2214yescomplemented
70#4672C2214yes—
71#4672C2214yescomplemented
72#4671C2214yes—
73#4669C2214yescomplemented
74#4668C2214yescomplemented
75#4665C2214yescomplemented
76#4647C2214yescomplemented
77C2×#538—32no—
78#2857D311yescharacteristic, complemented
79#2727—32no—
80#2710—34no—
81#2682—32no—
82#2626—32no—
83#2512—32no—
84#2501—32no—
85#2491—32no—
86#2418—34no—
87#2416—32no—
88#2408—32no—
89D4×C4⋊C4—32no—
90C4×#121—31no—
91C2×#390—31no—
92C24×D3C2312yes—
93C22×C3×Q8C2312yes—
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67C2312yes—
98C23×Dic3C2312yes—
99C22×D12—24no—
100C22×D12—42no—
101C22×D12—42no—
102C22×D12C2312yes—
103C22×D12C2314yes—
104C22×D12C2312yes—
105C22×D12C2314yes—
106C22×D12C2311yescharacteristic
107C22×C4×D3C2312yes—
108C22×C4×D3C2314yes—
109C3×C4⋊Q8—42no—
110C3×C22⋊Q8—28no—
111C2×C3×C4⋊C4C2312yes—
112C2×C3×C4⋊C4C2312yes—
113C2×C3×C4⋊C4C2312yes—
114C2×C3×C4⋊C4C2312yes—
115C2×C3×C4⋊C4C2314yes—
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C22⋊C4C2314yes—
118C2×C3×C42—42no—
119C2×C3×C42C2311yescharacteristic
120C2×C3×C42C2311yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217C2312yes—
124#947—216no—
125#930D418yescomplemented
126C4×#67—28no—
127C2×(C2×D3)⋊C4—28no—
128C2×(C2×D3)⋊C4—44no—
129C2×(C2×D3)⋊C4C2312yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×(C2×D3)⋊C4C2312yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2312yes—
144C2×C4⋊Dic3—42no—
145C2×C4⋊Dic3C2312yes—
146C2×C4⋊Dic3C2312yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×Dic3⋊C4C2312yes—
151C2×Dic3⋊C4C2314yes—
152C2×Dic3⋊C4C2314yes—
153C2×Dic3⋊C4C2314yes—
154C2×C4×Dic3C2314yes—
155C2×C4×Dic3C2312yes—
156#898—216no—
157#895—216no—
158#895—44no—
159#895—44no—
160#894—216no—
161#894—48no—
162D3×C4⋊C4—44no—
163#882—216no—
164#67⋊C4—216no—
165C4×D12—42no—
166C3×#95C2314yes—
167C3×#95C2314yes—
168C3⋊#95C2314yes—
169C3⋊#95C2314yes—
170C3⋊#95C2312yes—
171C3⋊#95C2312yes—
172C3⋊#95C2312yes—
173C23×D4—31no—
174#538—616no—
175C2×C4⋊Q8C2×D311yescharacteristic, complemented
176C2×#126—34no—
177C2×#124—34no—
178C2×#123—34no—
179C2×#123—34no—
180C2×C22⋊Q8C2×D312yes—
181C2×#121—31no—
182C2×#121—34no—
183C2×#121—32no—
184C2×#121—32no—
185C2×#120—34no—
186C2×C4×D4—32no—
187C2×C4×D4—34no—
188C2×C4×D4—31no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—32no—
191C22×C22⋊C4—32no—
192C22×C22⋊C4—32no—
193C22×C42C2×D311yescharacteristic
194#399—34no—
195#399—34no—
196#397—34no—
197#396—34no—
198#396—34no—
199#394—34no—
200#394—34no—
201#394—34no—
202#393—34no—
203#392—34no—
204#391C2×D312yescomplemented
205#390—32no—
206#390—32no—
207#390—32no—
208#390—32no—
209#390—32no—
210#390—32no—
211#390—31no—
212#389—31no—
213#389—34no—
214#389C2×D312yescomplemented
215#389C2×D312yescomplemented
216#388—34no—
217#388—32no—
218#388—34no—
219#386—32no—
220#386—34no—
221#385—34no—
222#385—34no—
223#384—32no—
224#384C2×D311yescharacteristic, complemented
225#380—31no—
226#380—32no—
227#380C2×D312yes—
228#380C2×D312yes—
229#379—34no—
230C4×C4⋊C4—32no—
231C4×C4⋊C4—31no—
232C4×C22⋊C4—32no—
233C24×C3C2411yescharacteristic
234C23×D3—24no—
235C23×D3—24no—
236C23×D3—24no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3—42no—
241C23×D3C2414yes—
242C23×D3C2412yes—
243C2×C3×Q8—24no—
244C2×C3×Q8—42no—
245C2×C3×Q8—42no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—41no—
251C22×C3×C4—41no—
252C22×C3×C4—41no—
253C22×C3×C4C2×D414yes—
254C22×C3×C4#4114yes—
255C22×C3×C4C2411yescharacteristic
256C22×C3×C4C2414yes—
257C22×C3×C4C2414yes—
258C22×C3×C4C2411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C22×C3×C4C2411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C22×C3×C4C2411yescharacteristic
263C2×#67—24no—
264C2×#67—24no—
265C2×#67C2×D418yes—
266C22×Dic3—24no—
267C22×Dic3—42no—
268C22×Dic3—42no—
269C22×Dic3C2412yes—
270C22×Dic3C2412yes—
271C22×Dic3C2414yes—
272C22×Dic3C2412yes—
273C2×D12—24no—
274C2×D12—24no—
275C2×D12—24no—
276C2×D12—24no—
277C2×D12—28no—
278C2×D12—28no—
279C2×D12—41no—
280C2×D12—42no—
281C2×D12—42no—
282C2×D12—41no—
283C2×D12—416no—
284C2×D12—44no—
285C2×D12—44no—
286C2×D12—44no—
287C2×D12—44no—
288C2×D12C2×D414yescomplemented
289C2×C4×D3—24no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—28no—
293C2×C4×D3—44no—
294C2×C4×D3—44no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—28no—
297C3×C4⋊C4—24no—
298C3×C4⋊C4—24no—
299C3×C4⋊C4—24no—
300C3×C4⋊C4—42no—
301C3×C22⋊C4—28no—
302C3×C42—22no—
303C3×C42—22no—
304C3×C42—41no—
305C3×C42—41no—
306#217—24no—
307(C2×D3)⋊C4—28no—
308(C2×D3)⋊C4—28no—
309(C2×D3)⋊C4—28no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—24no—
312(C2×D3)⋊C4—28no—
313(C2×D3)⋊C4—28no—
314(C2×D3)⋊C4—28no—
315(C2×D3)⋊C4—42no—
316(C2×D3)⋊C4—44no—
317(C2×D3)⋊C4—44no—
318(C2×D3)⋊C4—44no—
319(C2×D3)⋊C4—44no—
320(C2×D3)⋊C4—44no—
321(C2×D3)⋊C4C2×D418yescomplemented
322C4⋊Dic3—24no—
323C4⋊Dic3—41no—
324C4⋊Dic3—42no—
325C4⋊Dic3—41no—
326C4⋊Dic3C2×D414yescomplemented
327Dic3⋊C4—24no—
328Dic3⋊C4—28no—
329Dic3⋊C4—44no—
330Dic3⋊C4—44no—
331C4×Dic3—24no—
332C4×Dic3—28no—
333C25—32no—
334C22×Q8C22×D312yes—
335C22×D4—32no—
336C22×D4—31no—
337C22×D4—32no—
338C22×D4—34no—
339C22×D4—34no—
340C22×D4—32no—
341C22×D4—64no—
342C22×D4—122no—
343C22×D4—122no—
344C23×C4—32no—
345C23×C4—32no—
346C23×C4—34no—
347C23×C4C22×D311yescharacteristic
348C23×C4C22×D311yescharacteristic
349C23×C4C22×D311yescharacteristic
350C4⋊Q8—42no—
351#126—616no—
352#124—616no—
353#123—616no—
354#123—128no—
355C22⋊Q8—28no—
356#121—38no—
357#121—616no—
358#121—124no—
359#121—124no—
360#120—616no—
361C4×D4—616no—
362C4×D4—68no—
363C4×D4—122no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—32no—
366C2×C4⋊C4—34no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—32no—
369C2×C4⋊C4—34no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—34no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—124no—
374C2×C4⋊C4—122no—
375C2×C4⋊C4C22×D312yes—
376C2×C4⋊C4C22×D314yes—
377C2×C4⋊C4C22×D312yes—
378C2×C4⋊C4C22×D312yes—
379C2×C4⋊C4C22×D312yes—
380C2×C4⋊C4C22×D312yes—
381C2×C22⋊C4—32no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—34no—
384C2×C22⋊C4—34no—
385C2×C22⋊C4—34no—
386C2×C22⋊C4—34no—
387C2×C22⋊C4—32no—
388C2×C22⋊C4—34no—
389C2×C22⋊C4—34no—
390C2×C22⋊C4—32no—
391C2×C22⋊C4—34no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—34no—
394C2×C22⋊C4—34no—
395C2×C22⋊C4—34no—
396C2×C22⋊C4—34no—
397C2×C22⋊C4—68no—
398C2×C22⋊C4—124no—
399C2×C22⋊C4C22×D314yes—
400C2×C42—34no—
401C2×C42—32no—
402C2×C42—42no—
403C2×C42C22×D311yescharacteristic
404C2×C42C22×D311yescharacteristic
405C2×C42C22×D311yescharacteristic
406C2×C42C22×D311yescharacteristic
407#95—32no—
408#95—32no—
409#95—34no—
410#95—32no—
411#95—34no—
412#95C22×D314yes—
413#95C22×D314yes—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3C22×D412yes—
419C23×C3C2×#4112yes—
420C23×C32−1+412yes—
421C23×C3C2511yescharacteristic
422C22×D3—22no—
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—22no—
426C22×D3—22no—
427C22×D3—22no—
428C22×D3—24no—
429C22×D3—24no—
430C22×D3—24no—
431C22×D3—24no—
432C22×D3—24no—
433C22×D3—24no—
434C22×D3—24no—
435C22×D3—48no—
436C22×D3—48no—
437C22×D3—48no—
438C22×D3—84no—
439C22×D3—84no—
440C22×D3—84no—
441C22×D3—84no—
442C22×D3C22×D414yes—
443C3×Q8—84no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—28no—
453C2×C3×C4—24no—
454C2×C3×C4—24no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—24no—
460C2×C3×C4—21no—
461C2×C3×C4—24no—
462C2×C3×C4—44no—
463C2×C3×C4—44no—
464C2×C3×C4C22×D412yes—
465C2×C3×C4C22×D412yes—
466C2×C3×C4C2×#4112yes—
467C2×C3×C4C2×#4112yes—
468C2×C3×C4H(5,𝔽2)12yes—
469C2×C3×C4H(5,𝔽2)12yes—
470C2×C3×C4H(5,𝔽2)12yes—
471#67—216no—
472C2×Dic3—22no—
473C2×Dic3—22no—
474C2×Dic3—24no—
475C2×Dic3—22no—
476C2×Dic3—22no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—24no—
480C2×Dic3—24no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—84no—
484C2×Dic3C22×D414yes—
485D12—44no—
486D12—48no—
487D12—48no—
488D12—88no—
489D12—88no—
490C4×D3—48no—
491C4×D3—88no—
492C24—32no—
493C24—34no—
494C24—64no—
495C24—64no—
496C24—64no—
497C24—122no—
498C24—122no—
499C24—122no—
500C24—122no—
501C24C23×D311yescharacteristic
502C2×Q8—24no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×D4—38no—
506C2×D4—34no—
507C2×D4—68no—
508C2×D4—68no—
509C2×D4—64no—
510C2×D4—64no—
511C2×D4—64no—
512C2×D4—64no—
513C2×D4—64no—
514C2×D4—64no—
515C2×D4—121no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—121no—
519C2×D4—1216no—
520C2×D4—124no—
521C2×D4—124no—
522C2×D4—124no—
523C2×D4—124no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—32no—
529C22×C4—32no—
530C22×C4—32no—
531C22×C4—34no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—68no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—64no—
539C22×C4—64no—
540C22×C4—124no—
541C22×C4—124no—
542C22×C4—122no—
543C22×C4—122no—
544C22×C4D3×D414yes—
545C22×C4#23914yes—
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D314yes—
548C22×C4C23×D314yes—
549C22×C4C23×D311yescharacteristic
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D311yescharacteristic
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D311yescharacteristic
554C4⋊C4—28no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—24no—
559C4⋊C4—34no—
560C4⋊C4—42no—
561C4⋊C4—68no—
562C4⋊C4—64no—
563C4⋊C4—64no—
564C4⋊C4—124no—
565C4⋊C4—122no—
566C4⋊C4—121no—
567C4⋊C4—124no—
568C4⋊C4—121no—
569C22⋊C4—28no—
570C22⋊C4—38no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—68no—
574C22⋊C4—64no—
575C22⋊C4—68no—
576C22⋊C4—68no—
577C22⋊C4—64no—
578C22⋊C4—68no—
579C22⋊C4—64no—
580C22⋊C4—124no—
581C22⋊C4—122no—
582C22⋊C4—124no—
583C22⋊C4—124no—
584C22⋊C4—124no—
585C22⋊C4—124no—
586C42—22no—
587C42—22no—
588C42—41no—
589C42—41no—
590C42—68no—
591C42—64no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3#54714yes—
599C22×C3C23×D411yescharacteristic
600C22×C3C22×#4111yescharacteristic
601C22×C3C2×H(5,𝔽2)11yescharacteristic
602C22×C3C2×H(5,𝔽2)11yescharacteristic
603C22×C3C2×H(5,𝔽2)11yescharacteristic
604C22×C3C2×2−1+411yescharacteristic
605C22×C3#58511yescharacteristic
606C2×D3—24no—
607C2×D3—24no—
608C2×D3—24no—
609C2×D3—42no—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—44no—
614C2×D3—44no—
615C2×D3—44no—
616C2×D3—44no—
617C2×D3—44no—
618C2×D3—44no—
619C2×D3—44no—
620C2×D3—816no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—44no—
626C3×C4—44no—
627C3×C4—41no—
628C3×C4#53814yescomplemented
629Dic3—24no—
630Dic3—42no—
631Dic3—44no—
632Dic3—42no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—34no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—64no—
645C23—64no—
646C23—64no—
647C23—64no—
648C23—64no—
649C23—64no—
650C23—64no—
651C23—128no—
652C23—128no—
653C23—128no—
654C23—244no—
655C23—244no—
656C23—244no—
657C23—244no—
658C23C2×D3×D412yes—
659C23C2×#23912yes—
660C23#100712yes—
661C23C24×D311yescharacteristic
662Q8—84no—
663D4—616no—
664D4—124no—
665D4—128no—
666D4—128no—
667D4—248no—
668D4—248no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—28no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—21no—
681C2×C4—24no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—34no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—62no—
699C2×C4—64no—
700C2×C4—62no—
701C2×C4—128no—
702C2×C4—248no—
703C2×C4—244no—
704C2×C4C2×D3×D412yes—
705C2×C4C2×D3×D412yes—
706C2×C4#100412yes—
707C2×C4C2×#23912yes—
708C2×C4C2×#23912yes—
709C2×C4#100912yes—
710C2×C4#100912yes—
711C2×C3—24no—
712C2×C3C2×#53811yescharacteristic
713C2×C3C2×#54711yescharacteristic
714C2×C3#349611yescharacteristic
715C2×C3#349811yescharacteristic
716C2×C3#350611yescharacteristic
717C2×C3#353611yescharacteristic
718C2×C3#356111yescharacteristic
719D3—44no—
720D3—84no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—64no—
728C22—64no—
729C22—64no—
730C22—122no—
731C22—122no—
732C22—122no—
733C22—122no—
734C22—124no—
735C22—124no—
736C22—124no—
737C22—124no—
738C22—124no—
739C22—124no—
740C22—124no—
741C22—2416no—
742C22#572614yes—
743C22C22×D3×D411yescharacteristic
744C22C2×#100411yescharacteristic
745C22C22×#23911yescharacteristic
746C22C2×#100711yescharacteristic
747C22C2×#100911yescharacteristic
748C22C2×#100911yescharacteristic
749C22#596411yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—44no—
755C4—44no—
756C4—41no—
757C4—64no—
758C4—122no—
759C4—124no—
760C4—122no—
761C4#564414yescomplemented
762C3#3937511yescharacteristic, complemented, Sylow
763C2—24no—
764C2—124no—
765C2—244no—
766C2#8595011yescharacteristic
767C2C2×#564411yescharacteristic
768C2#8599011yescharacteristic
769C2C2×#572611yescharacteristic
770C2#8624211yescharacteristic
771C2#8625911yescharacteristic
772C2#8629111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2857C2
hypercenter#2857D3
hypocenterC3#39375
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×#5644C2semidirect
2. C3×#2857C2semidirect
3. #83257C2semidirect
4. #82822C2semidirect
5. C4×#930C2semidirect
6. C2×#4939C2semidirect
7. #76651C2semidirect
8. #76260C2semidirect
9. #76211C2semidirect
10. #76132C2semidirect
11. #76047C2semidirect
12. #74328C2semidirect
13. #74021C2semidirect
14. #74016C2semidirect
15. #74010C2semidirect
18. C2×C3×C4⋊Q8C22semidirect
21. C2×#947C22semidirect
28. C2×#898C22semidirect
31. C2×#895C22semidirect
32. C2×#894C22semidirect
33. C2×#894C22semidirect
34. C2×D3×C4⋊C4C22semidirect
37. C2×C4×D12C22semidirect
38. C3×#391C22semidirect
39. C3×#389C22semidirect
40. C3×#389C22semidirect
41. C3×#384C22semidirect
44. #5231C22semidirect
47. #4994C22semidirect
48. #4994C22semidirect
49. #4993C22semidirect
50. #4993C22semidirect
51. #4991C22semidirect
52. #4990C22semidirect
55. #4987C22semidirect
56. #4975C22semidirect
57. Dic3×C4⋊C4C22semidirect
60. #4940C22semidirect
65. #4939C22semidirect
66. C4×(C2×D3)⋊C4C22semidirect
67. C4×C4⋊Dic3C22semidirect
68. #4928C22semidirect
69. #4675C22semidirect
71. #4672C22semidirect
73. #4669C22semidirect
74. #4668C22semidirect
75. #4665C22semidirect
76. #4647C22semidirect
78. #2857D3semidirect
125. #930D4semidirect
175. C2×C4⋊Q8C2×D3semidirect
204. #391C2×D3semidirect
214. #389C2×D3semidirect
215. #389C2×D3semidirect
224. #384C2×D3semidirect
288. C2×D12C2×D4semidirect
321. (C2×D3)⋊C4C2×D4semidirect
326. C4⋊Dic3C2×D4semidirect
628. C3×C4#538semidirect
761. C4#5644semidirect
762. C3#39375semidirect

Maximal subgroups

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

subgroupindex
C2×#56442
C3×#28572
#832572
#828222
C4×#9302
C2×#49392
#766512
#762602
#762112
#761322
#760472
#743282
#740212
#740162
#740102
#393753