Finite Group Databasebeta

← #10967037

Subgroups — #10967037

Order 768.

2580 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5624C212yesmaximal, complemented
2C3×#2538C211yesmaximal, characteristic, complemented
3#82755C212yesmaximal, complemented
4#82476C211yesmaximal, characteristic, complemented
5C4×Q8×Dic3C211yesmaximal, characteristic, complemented
6#82378C211yesmaximal, characteristic
7C4×D4×Dic3C211yesmaximal, characteristic, complemented
8#77316C214yesmaximal, complemented
9#77281C214yesmaximal, complemented
10#76317C212yesmaximal, complemented
11#76293C212yesmaximal, complemented
12#76047C212yesmaximal, complemented
13#75961C212yesmaximal, complemented
14#74336C211yesmaximal, characteristic, complemented
15#74319C211yesmaximal, characteristic, complemented
16#73914C212yesmaximal, complemented
17#73865C212yesmaximal, complemented
18#34934—31nomaximal, Sylow
19C2×C3×C22⋊Q8C2212yes—
20C2×C3×C4×Q8C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×#947C2212yes—
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×#940C2212yes—
26C2×D4×Dic3C2211yescharacteristic
27C2×D4×Dic3C2211yescharacteristic
28C2×#930C2212yes—
29C2×#930C2212yes—
30C22×C4×Dic3C2212yes—
31#5624—216no—
32C2×#898C2214yes—
33C2×#893C2212yes—
34C2×#893C2212yes—
35C2×#893C2212yes—
36C2×#892C2214yes—
37C2×#890C2212yes—
38C2×#886C2214yes—
39C2×#67⋊C4C2214yes—
40C2×#67⋊C4C2214yes—
41C2×#874C2211yescharacteristic
42C3×#396C2214yes—
43C3×#390C2212yes—
44C3×#389C2212yes—
45C3×#384C2211yescharacteristic
46C3×#380C2212yes—
47C4×#217C2212yes—
48#4994C2214yes—
49#4991C2214yes—
50#4990C2214yes—
51#4988C2212yes—
52#4988C2212yes—
53#4988C2212yes—
54#4988C2212yes—
55#4988C2212yes—
56#4984C2212yes—
57#4982C2214yes—
58#4975C2212yes—
59Dic3×C4⋊C4C2212yes—
60Dic3×C4⋊C4C2211yescharacteristic
61Dic3×C4⋊C4C2211yescharacteristic
62Dic3×C4⋊C4C2211yescharacteristic
63Dic3×C4⋊C4C2212yes—
64Dic3×C4⋊C4C2211yescharacteristic
65#4972C2212yes—
66#4961C2214yes—
67#4961C2214yes—
68#4960C2214yes—
69#4958C2214yes—
70#4957C2214yes—
71#4957C2214yes—
72Dic3×C22⋊C4C2212yes—
73Dic3×C22⋊C4C2212yes—
74#4939C2212yes—
75#4939C2212yes—
76C4×C4⋊Dic3C2212yes—
77C4×C4⋊Dic3C2211yescharacteristic
78C4×C4⋊Dic3C2211yescharacteristic
79C42×Dic3C2212yes—
80C42×Dic3C2211yescharacteristic
81#4675C2214yes—
82#4670C2214yes—
83#4669C2214yes—
84#4666C2214yes—
85C2×#529—32no—
86#2554—34no—
87#2552—31no—
88#2548—31no—
89#2541—31no—
90#2538D311yescharacteristic, complemented
91#2512—32no—
92#2490—32no—
93#2445—32no—
94#2426—32no—
95#2392—34no—
96C4×#127—32no—
97C4×#127—31no—
98C4×#121—32no—
99#2293—32no—
100C42×Q8—31no—
101C42×D4—31no—
102C22×C3×Q8C2311yescharacteristic
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4C2312yes—
105C22×#67C2314yes—
106C22×#67C2314yes—
107C23×Dic3C2312yes—
108C23×Dic3C2312yes—
109C22×D12C2312yes—
110C22×D12C2312yes—
111C22×D12C2312yes—
112C22×C4×D3C2314yes—
113C3×C22⋊Q8—28no—
114C3×C4×Q8—24no—
115C3×C4×D4—24no—
116C2×C3×C4⋊C4C2312yes—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2312yes—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C4⋊C4C2314yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C22⋊C4C2312yes—
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C42C2312yes—
127C2×C3×C42C2311yescharacteristic
128C2×#217C2312yes—
129C2×#217C2312yes—
130#947—28no—
131Q8×Dic3—24no—
132Q8×Dic3D418yescomplemented
133#940—28no—
134D4×Dic3—24no—
135D4×Dic3—24no—
136#930—28no—
137#930—28no—
138C2×(C2×D3)⋊C4C2314yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×C4⋊Dic3C2314yes—
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2311yescharacteristic
154C2×Dic3⋊C4C2314yes—
155C2×Dic3⋊C4C2314yes—
156C2×C4×Dic3—28no—
157C2×C4×Dic3C2312yes—
158C2×C4×Dic3C2312yes—
159C2×C4×Dic3C2312yes—
160C2×C4×Dic3C2311yescharacteristic
161C2×C4×Dic3C2312yes—
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2311yescharacteristic
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2311yescharacteristic
168C2×C4×Dic3C2312yes—
169C2×C4×Dic3C2311yescharacteristic
170C2×C4×Dic3C2311yescharacteristic
171#898—216no—
172#893—28no—
173#893—28no—
174#893—44no—
175#892—216no—
176#890—28no—
177#886—216no—
178#67⋊C4—216no—
179#67⋊C4—48no—
180#874—24no—
181C3×#95C2314yes—
182C3⋊#95C2314yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2312yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189C2×#127—32no—
190C2×#127—31no—
191#529—616no—
192C2×#126—34no—
193C2×#125—32no—
194C2×#124—32no—
195C2×#123—34no—
196C2×C22⋊Q8C2×D312yes—
197C2×#121—32no—
198C2×#121—32no—
199C2×C4×Q8—31no—
200C2×C4×Q8—31no—
201C2×C4×Q8C2×D311yescharacteristic
202C2×C4×D4—31no—
203C2×C4×D4—31no—
204C2×C4×D4—32no—
205C2×C4×D4—32no—
206C2×C4×D4—32no—
207C2×C4×D4—34no—
208C2×C4×D4—34no—
209C2×C4×D4C2×D311yescharacteristic
210C2×#117—34no—
211C22×C42—32no—
212#398—34no—
213#397—34no—
214#396—34no—
215#396C2×D314yes—
216#394—34no—
217#394—34no—
218#394—34no—
219#392—34no—
220#390—32no—
221#390—32no—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—34no—
226#390—34no—
227#390—32no—
228#390—32no—
229#390C2×D312yes—
230#389—32no—
231#389—32no—
232#389C2×D312yes—
233#388—34no—
234#388—34no—
235#388—34no—
236#386—34no—
237#384—32no—
238#384C2×D311yescharacteristic
239#380C2×D312yes—
240C4×C4⋊C4—32no—
241C4×C4⋊C4—31no—
242C4×C4⋊C4—31no—
243C4×C4⋊C4—31no—
244C4×C4⋊C4—32no—
245C4×C4⋊C4—31no—
246C4×C4⋊C4—32no—
247C4×C4⋊C4—31no—
248C4×C4⋊C4—31no—
249C4×C22⋊C4—32no—
250C4×C22⋊C4—32no—
251C4×C22⋊C4—32no—
252C4×C22⋊C4—34no—
253C43—31no—
254C43—32no—
255C24×C3C2412yes—
256C23×D3C2414yes—
257C2×C3×Q8—22no—
258C2×C3×Q8—22no—
259C2×C3×Q8C2×D414yes—
260C2×C3×D4—22no—
261C2×C3×D4—22no—
262C2×C3×D4#4114yes—
263C22×C3×C4—24no—
264C22×C3×C4—24no—
265C22×C3×C4—24no—
266C22×C3×C4C2412yes—
267C22×C3×C4C2412yes—
268C22×C3×C4C2414yes—
269C22×C3×C4C2412yes—
270C22×C3×C4C2411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C2×#67—28no—
274C2×#67—28no—
275C2×#67—28no—
276C2×#67—28no—
277C2×#67—44no—
278C2×#67—44no—
279C22×Dic3—24no—
280C22×Dic3—24no—
281C22×Dic3—24no—
282C22×Dic3—24no—
283C22×Dic3—24no—
284C22×Dic3—42no—
285C22×Dic3C2411yescharacteristic
286C22×Dic3C2412yes—
287C22×Dic3C2412yes—
288C22×Dic3C2411yescharacteristic
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2411yescharacteristic
292C22×Dic3C2411yescharacteristic
293C2×D12—24no—
294C2×D12—24no—
295C2×D12—24no—
296C2×D12—24no—
297C2×D12—24no—
298C2×D12—24no—
299C2×D12—24no—
300C2×D12—42no—
301C2×D12—42no—
302C2×C4×D3—28no—
303C2×C4×D3—28no—
304C2×C4×D3—28no—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—28no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—22no—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—42no—
312C3×C22⋊C4—28no—
313C3×C22⋊C4—24no—
314C3×C22⋊C4—44no—
315C3×C42—24no—
316C3×C42#4114yes—
317#217—24no—
318#217—24no—
319(C2×D3)⋊C4—28no—
320(C2×D3)⋊C4—28no—
321(C2×D3)⋊C4—28no—
322(C2×D3)⋊C4—28no—
323(C2×D3)⋊C4—28no—
324(C2×D3)⋊C4—28no—
325(C2×D3)⋊C4—44no—
326(C2×D3)⋊C4—44no—
327(C2×D3)⋊C4—44no—
328C4⋊Dic3—22no—
329C4⋊Dic3—22no—
330C4⋊Dic3—28no—
331C4⋊Dic3—24no—
332C4⋊Dic3C2×D418yes—
333C4⋊Dic3C2×D414yes—
334C4⋊Dic3#4114yes—
335Dic3⋊C4—28no—
336Dic3⋊C4—44no—
337C4×Dic3—24no—
338C4×Dic3—22no—
339C4×Dic3—24no—
340C4×Dic3—22no—
341C4×Dic3—24no—
342C4×Dic3—24no—
343C4×Dic3—24no—
344C4×Dic3—24no—
345C4×Dic3—22no—
346C4×Dic3—41no—
347C4×Dic3—42no—
348C4×Dic3C2×D418yes—
349C4×Dic3C2×D414yes—
350C4×Dic3#4114yes—
351C22×Q8C22×D311yescharacteristic
352C22×D4—34no—
353C22×D4—34no—
354C22×D4—32no—
355C22×D4—32no—
356C22×D4—32no—
357C22×D4C22×D311yescharacteristic
358C23×C4—32no—
359C23×C4—32no—
360C23×C4—34no—
361C23×C4C22×D312yes—
362#127—68no—
363#127—64no—
364#126—616no—
365#125—68no—
366#124—68no—
367#123—616no—
368C22⋊Q8—28no—
369#121—68no—
370#121—68no—
371C4×Q8—24no—
372C4×Q8—38no—
373C4×Q8—64no—
374C4×D4—24no—
375C4×D4—616no—
376C4×D4—68no—
377C4×D4—68no—
378C4×D4—64no—
379C4×D4—64no—
380C4×D4—128no—
381C4×D4—124no—
382#117—616no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4C22×D314yes—
393C2×C4⋊C4C22×D312yes—
394C2×C4⋊C4C22×D312yes—
395C2×C4⋊C4C22×D311yescharacteristic
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D312yes—
398C2×C4⋊C4C22×D312yes—
399C2×C22⋊C4—32no—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—34no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—34no—
405C2×C22⋊C4—34no—
406C2×C22⋊C4—34no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4C22×D314yes—
411C2×C22⋊C4C22×D312yes—
412C2×C22⋊C4C22×D314yes—
413C2×C42—32no—
414C2×C42—31no—
415C2×C42—31no—
416C2×C42—32no—
417C2×C42—32no—
418C2×C42—31no—
419C2×C42—31no—
420C2×C42—31no—
421C2×C42—32no—
422C2×C42—32no—
423C2×C42—32no—
424C2×C42—32no—
425C2×C42—31no—
426C2×C42—32no—
427C2×C42—68no—
428C2×C42C22×D312yes—
429C2×C42C22×D311yescharacteristic
430#95—32no—
431#95—32no—
432#95—32no—
433#95—34no—
434#95—32no—
435#95—32no—
436#95—32no—
437#95C22×D314yes—
438C23×C3—22no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3C2×#4114yes—
445C23×C3C2511yescharacteristic
446C22×D3—24no—
447C22×D3—24no—
448C22×D3—24no—
449C22×D3—24no—
450C22×D3—24no—
451C22×D3—24no—
452C22×D3—24no—
453C3×Q8—28no—
454C3×D4—28no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—22no—
460C2×C3×C4—24no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—24no—
467C2×C3×C4—22no—
468C2×C3×C4—48no—
469C2×C3×C4C22×D414yes—
470C2×C3×C4C22×D412yes—
471C2×C3×C4C2×#4112yes—
472C2×C3×C4C2×#4112yes—
473C2×C3×C4C2×#4112yes—
474C2×C3×C4C2×#4112yes—
475C2×C3×C4C2×#4112yes—
476C2×C3×C4C2×#4112yes—
477#67—416no—
478#67—416no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—22no—
482C2×Dic3—22no—
483C2×Dic3—22no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—48no—
497C2×Dic3—48no—
498C2×Dic3C22×D412yes—
499C2×Dic3C22×D414yes—
500C2×Dic3C22×D412yes—
501C2×Dic3C2×#4114yes—
502C2×Dic3C2×#4112yes—
503C2×Dic3C2×#4112yes—
504C2×Dic3H(5,𝔽2)12yes—
505D12—48no—
506D12—48no—
507D12—48no—
508C4×D3—416no—
509C24—34no—
510C24C23×D312yes—
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8D3×D414yes—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—68no—
517C2×D4—68no—
518C2×D4—68no—
519C2×D4—68no—
520C2×D4—64no—
521C2×D4—64no—
522C2×D4—64no—
523C2×D4—64no—
524C2×D4—64no—
525C2×D4—64no—
526C2×D4—64no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—124no—
530C2×D4—124no—
531C2×D4#23914yes—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—31no—
536C22×C4—32no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—32no—
540C22×C4—31no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—68no—
544C22×C4—68no—
545C22×C4—68no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—64no—
549C22×C4—64no—
550C22×C4—64no—
551C22×C4—122no—
552C22×C4C23×D312yes—
553C22×C4C23×D312yes—
554C22×C4C23×D314yes—
555C22×C4C23×D312yes—
556C22×C4C23×D311yescharacteristic
557C22×C4C23×D311yescharacteristic
558C22×C4C23×D311yescharacteristic
559C4⋊C4—28no—
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—24no—
565C4⋊C4—34no—
566C4⋊C4—38no—
567C4⋊C4—34no—
568C4⋊C4—42no—
569C4⋊C4—68no—
570C4⋊C4—68no—
571C4⋊C4—64no—
572C4⋊C4—62no—
573C4⋊C4—62no—
574C4⋊C4—124no—
575C22⋊C4—28no—
576C22⋊C4—24no—
577C22⋊C4—44no—
578C22⋊C4—68no—
579C22⋊C4—68no—
580C22⋊C4—68no—
581C22⋊C4—68no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—68no—
585C22⋊C4—68no—
586C22⋊C4—124no—
587C22⋊C4—124no—
588C22⋊C4—124no—
589C42—24no—
590C42—34no—
591C42—38no—
592C42—34no—
593C42—64no—
594C42—64no—
595C42—62no—
596C42—64no—
597C42—64no—
598C42—64no—
599C42—62no—
600C42—64no—
601C42—62no—
602C42—121no—
603C42—122no—
604C42#23714yes—
605C22×C3—24no—
606C22×C3—24no—
607C22×C3—24no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3C23×D411yescharacteristic
613C22×C3C22×#4111yescharacteristic
614C22×C3C22×#4111yescharacteristic
615C22×C3C22×#4111yescharacteristic
616C22×C3C22×#4111yescharacteristic
617C22×C3C2×H(5,𝔽2)11yescharacteristic
618C22×C3#58511yescharacteristic
619C2×D3—44no—
620C2×D3—44no—
621C2×D3—44no—
622C2×D3—44no—
623C2×D3—44no—
624C2×D3—44no—
625C2×D3—44no—
626C3×C4—24no—
627C3×C4—22no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4—44no—
631C3×C4#52914yescomplemented
632C3×C4#53214yes—
633Dic3—22no—
634Dic3—24no—
635Dic3—22no—
636Dic3—24no—
637Dic3—42no—
638Dic3—42no—
639Dic3—41no—
640Dic3#55014yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—64no—
648C23—64no—
649C23—64no—
650C23—64no—
651C23—64no—
652C23—64no—
653C23—64no—
654C23C2×#23914yes—
655C23C24×D311yescharacteristic
656Q8—28no—
657D4—28no—
658D4—128no—
659D4—1216no—
660D4—1216no—
661D4—128no—
662D4—128no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—32no—
680C2×C4—34no—
681C2×C4—32no—
682C2×C4—34no—
683C2×C4—48no—
684C2×C4—61no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—61no—
697C2×C4—62no—
698C2×C4—61no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—1216no—
702C2×C4—128no—
703C2×C4—128no—
704C2×C4C2×D3×D414yes—
705C2×C4C2×D3×D412yes—
706C2×C4C2×#23712yes—
707C2×C4C2×#23712yes—
708C2×C4C2×#23712yes—
709C2×C4C2×#23912yes—
710C2×C4D3×#4112yes—
711C2×C4D3×#4112yes—
712C2×C3—44no—
713C2×C3C2×#52911yescharacteristic
714C2×C3C2×#53211yescharacteristic
715C2×C3#346011yescharacteristic
716C2×C3C2×#55011yescharacteristic
717C2×C3D4×#4111yescharacteristic
718C2×C3#348011yescharacteristic
719C2×C3#348111yescharacteristic
720D3—84no—
721C22—24no—
722C22—24no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—124no—
729C22—124no—
730C22—124no—
731C22—124no—
732C22—124no—
733C22—124no—
734C22—124no—
735C22C22×D3×D411yescharacteristic
736C22C22×#23711yescharacteristic
737C22C22×#23911yescharacteristic
738C22C2×D3×#4111yescharacteristic
739C22C2×D3×#4111yescharacteristic
740C22D3×H(5,𝔽2)11yescharacteristic
741C22#596811yescharacteristic
742C4—22no—
743C4—24no—
744C4—34no—
745C4—42no—
746C4—42no—
747C4—44no—
748C4—64no—
749C4—62no—
750C4—62no—
751C4—64no—
752C4—121no—
753C4—122no—
754C4—122no—
755C4#559614yes—
756C4#562414yescomplemented
757C3#3493411yescharacteristic, complemented, Sylow
758C2—44no—
759C2—244no—
760C2C2×#559611yescharacteristic
761C2C2×#562411yescharacteristic
762C2#8636411yescharacteristic
763C2D4×#23911yescharacteristic
764C2D3×#55011yescharacteristic
765C2#8692411yescharacteristic
766C2#8698011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2538C2
prime radical#82378C2
hypercenter#2538D3
hypocenterC3#34934
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#5624C2semidirect
2. C3×#2538C2semidirect
3. #82755C2semidirect
4. #82476C2semidirect
5. C4×Q8×Dic3C2semidirect
7. C4×D4×Dic3C2semidirect
8. #77316C2semidirect
9. #77281C2semidirect
10. #76317C2semidirect
11. #76293C2semidirect
12. #76047C2semidirect
13. #75961C2semidirect
14. #74336C2semidirect
15. #74319C2semidirect
16. #73914C2semidirect
17. #73865C2semidirect
90. #2538D3semidirect
132. Q8×Dic3D4semidirect
631. C3×C4#529semidirect
756. C4#5624semidirect
757. C3#34934semidirect

Maximal subgroups

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

subgroupindex
C2×#56242
C3×#25382
#827552
#824762
C4×Q8×Dic32
#823782
C4×D4×Dic32
#773162
#772812
#763172
#762932
#760472
#759612
#743362
#743192
#739142
#738652
#349343