Finite Group Databasebeta

← #10973018

Subgroups — #10973018

Order 768.

2394 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×#5500C211yesmaximal, characteristic, complemented
2C2×C4×#235C211yesmaximal, characteristic
3C2×C3×#389C211yesmaximal, characteristic, complemented
4#82186C211yesmaximal, characteristic
5#82186C211yesmaximal, characteristic
6#82173C214yesmaximal, complemented
7#82157C211yesmaximal, characteristic, complemented
8#82069C211yesmaximal, characteristic, complemented
9#76288C212yesmaximal, complemented
10#76285C212yesmaximal, complemented
11#76251C212yesmaximal, complemented
12#76250C212yesmaximal, complemented
13#76015C212yesmaximal, complemented
14#76012C212yesmaximal, complemented
15#76010C212yesmaximal, complemented
16#76008C212yesmaximal, complemented
17#73351C214yesmaximal, complemented
18#35257—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C4⋊C4C2212yes—
23C22×C3×C42C2211yescharacteristic
24C2×C4×#67C2212yes—
25C2×C4×#67C2212yes—
26C2×#926C2211yescharacteristic
27C2×#926C2211yescharacteristic
28C2×#926C2211yescharacteristic
29C2×#924C2214yes—
30C2×#896C2214yes—
31#5500—28no—
32C2×#890C2212yes—
33C2×#890C2212yes—
34C2×#888C2212yes—
35C2×#888C2212yes—
36C4×#235—28no—
37C2×C4×D12C2211yescharacteristic
38C2×C4×D12C2211yescharacteristic
39C2×#872C2212yes—
40C2×C42×D3C2212yes—
41C2×C4×Dic6C2211yescharacteristic
42C2×C4×Dic6C2211yescharacteristic
43C3×#389C2212yes—
44C3×#389C2212yes—
45C3×#389C2212yes—
46C3×#389C2212yes—
47C2×C3×#95C2212yes—
48#5213C2214yes—
49#5213C2214yes—
50#5210C2212yes—
51#5210C2214yes—
52#5210C2212yes—
53#4994C2214yes—
54#4993C2214yes—
55#4989C2214yes—
56#4988C2212yes—
57#4988C2212yes—
58#4987C2212yes—
59#4987C2212yes—
60#4987C2212yes—
61#4987C2212yes—
62#4983C2214yes—
63#4980C2214yes—
64#4979C2214yes—
65#4977C2212yes—
66#4976C2214yes—
67#4975C2212yes—
68#4973C2212yes—
69#4973C2212yes—
70#4972C2212yes—
71#4972C2212yes—
72C4×Dic3⋊C4C2212yes—
73C4×Dic3⋊C4C2212yes—
74#4928C2211yescharacteristic
75#4928C2211yescharacteristic
76#4928C2211yescharacteristic
77#4928C2211yescharacteristic
78#4676C2214yes—
79#4673C2214yes—
80#4668C2214yes—
81#4667C2214yes—
82#4658C2214yes—
83#4657C2214yes—
84#4652C2214yes—
85#4646C2214yes—
86C2×#544—31no—
87C2×C4×#41—31no—
88#2857—32no—
89#2851—32no—
90#2629—32no—
91#2628—32no—
92#2454—32no—
93#2453—32no—
94#2452—32no—
95#2451—32no—
96#2450—34no—
97#2449—34no—
98#2317—31no—
99#2311—31no—
100#2311—31no—
101#2296—31no—
102C2×#389D311yescharacteristic, complemented
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2312yes—
106C23×C3×C4C2312yes—
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C2×#235—24no—
110C2×#235—24no—
111C2×#235Q818yescomplemented
112C22×D12C2311yescharacteristic
113C22×C4×D3C2312yes—
114C22×C4×D3C2312yes—
115C22×C4×D3C2312yes—
116C22×Dic6C2311yescharacteristic
117C22×Dic6C2314yes—
118C2×C3×C4⋊C4—24no—
119C2×C3×C4⋊C4—24no—
120C2×C3×C4⋊C4—44no—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2312yes—
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C4⋊C4C2314yes—
125C2×C3×C4⋊C4C2312yes—
126C2×C3×C4⋊C4C2314yes—
127C2×C3×C42—24no—
128C2×C3×C42C2311yescharacteristic
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C2×C3×C42C2311yescharacteristic
132C2×#217C2312yes—
133C2×#217C2312yes—
134C2×#217C2312yes—
135C4×#67—28no—
136C4×#67—28no—
137C2×(C2×D3)⋊C4C2312yes—
138C2×(C2×D3)⋊C4C2312yes—
139C2×(C2×D3)⋊C4C2314yes—
140C2×(C2×D3)⋊C4C2314yes—
141C2×(C2×D3)⋊C4C2314yes—
142C2×(C2×D3)⋊C4C2314yes—
143#926—24no—
144#926—24no—
145#926D418yes—
146C2×C4⋊Dic3C2314yes—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×C4⋊Dic3C2311yescharacteristic
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2311yescharacteristic
153#924—216no—
154C2×Dic3⋊C4C2312yes—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2312yes—
157C2×Dic3⋊C4C2314yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2312yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2312yes—
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2312yes—
169#896—48no—
170#890—28no—
171#890—28no—
172#888—28no—
173#888—28no—
174C4×D12—24no—
175C4×D12—24no—
176#872—28no—
177C42×D3—28no—
178C4×Dic6—24no—
179C4×Dic6—24no—
180C3×#95C2314yes—
181C3×#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2314yes—
190C3⋊#95C2312yes—
191C3⋊#95C2312yes—
192C22×#41—31no—
193#544—68no—
194C2×C4⋊Q8—32no—
195C2×C4⋊Q8—32no—
196C2×#125—32no—
197C2×#125—32no—
198C2×C22⋊Q8—34no—
199C2×C22⋊Q8—34no—
200C4×#41—68no—
201C2×C4×Q8—31no—
202C2×C4×Q8—31no—
203C2×C4×D4—32no—
204C2×C4×D4—32no—
205C2×C4×D4—31no—
206C2×C4×D4—31no—
207C2×#117—31no—
208C2×#117—31no—
209C2×#117—31no—
210C2×#117—32no—
211C22×C4⋊C4C2×D311yescharacteristic
212C22×C4⋊C4C2×D311yescharacteristic
213C22×C4⋊C4C2×D312yes—
214C22×C42—32no—
215C22×C42C2×D311yescharacteristic
216#400—34no—
217#399—34no—
218#398—34no—
219#398—34no—
220#396—34no—
221#396—34no—
222#395—34no—
223#393—34no—
224#391—32no—
225#391—32no—
226#391—34no—
227#390—32no—
228#390—32no—
229#389—32no—
230#389—32no—
231#389—34no—
232#389—31no—
233#389—31no—
234#389—31no—
235#389—31no—
236#389C2×D312yes—
237#389C2×D312yes—
238#389C2×D312yes—
239#389C2×D312yes—
240#387—34no—
241#387—34no—
242#386—34no—
243#386—34no—
244#385—34no—
245#385—32no—
246#385—32no—
247#385—34no—
248#385—34no—
249#384—32no—
250#382—32no—
251#380—32no—
252#380—32no—
253#380—32no—
254#380—32no—
255#380—34no—
256C4×C4⋊C4—32no—
257C4×C4⋊C4—32no—
258C2×#95C2×D312yes—
259C24×C3C2411yescharacteristic
260C23×D3C2412yes—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—24no—
264C22×C3×C4—24no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—42no—
268C22×C3×C4—41no—
269C22×C3×C4—41no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4C2×D414yes—
274C22×C3×C4C2×Q814yes—
275C22×C3×C4#4114yes—
276C22×C3×C4C2414yes—
277C22×C3×C4C2411yescharacteristic
278C22×C3×C4C2414yes—
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C2×#67—24no—
285C2×#67—24no—
286C2×#67C2×Q818yes—
287C22×Dic3C2412yes—
288C22×Dic3C2412yes—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C22×Dic3C2412yes—
293C22×Dic3C2412yes—
294#235—232no—
295C2×D12—22no—
296C2×D12—22no—
297C2×D12C2×Q814yes—
298C2×C4×D3—24no—
299C2×C4×D3—24no—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3—42no—
305C2×C4×D3—42no—
306C2×C4×D3C2×Q818yes—
307C2×Dic6—22no—
308C2×Dic6—22no—
309C2×Dic6—28no—
310C2×Dic6—44no—
311C2×Dic6—44no—
312C2×Dic6C2×Q814yes—
313C3×C4⋊C4—24no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—24no—
317C3×C4⋊C4—28no—
318C3×C4⋊C4—44no—
319C3×C42—22no—
320C3×C42—22no—
321C3×C42—22no—
322C3×C42—22no—
323#217—24no—
324#217—24no—
325#217C2×D418yes—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—44no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332C4⋊Dic3—22no—
333C4⋊Dic3—22no—
334C4⋊Dic3—22no—
335C4⋊Dic3—22no—
336C4⋊Dic3—28no—
337C4⋊Dic3C2×D414yes—
338C4⋊Dic3C2×D414yes—
339Dic3⋊C4—24no—
340Dic3⋊C4—24no—
341Dic3⋊C4—24no—
342Dic3⋊C4—24no—
343Dic3⋊C4—28no—
344Dic3⋊C4—28no—
345Dic3⋊C4—44no—
346Dic3⋊C4—44no—
347Dic3⋊C4—42no—
348Dic3⋊C4—42no—
349C4×Dic3—24no—
350C4×Dic3—24no—
351C4×Dic3—24no—
352C4×Dic3—24no—
353C4×Dic3C2×D418yes—
354C2×#41—38no—
355C2×#41—64no—
356C2×#41—64no—
357C22×Q8—31no—
358C22×Q8—34no—
359C22×D4—32no—
360C22×D4—31no—
361C23×C4—32no—
362C23×C4—32no—
363C23×C4—32no—
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D311yescharacteristic
366C23×C4C22×D312yes—
367C23×C4C22×D312yes—
368C23×C4C22×D311yescharacteristic
369C4⋊Q8—68no—
370C4⋊Q8—68no—
371#125—68no—
372#125—68no—
373C22⋊Q8—616no—
374C22⋊Q8—128no—
375C4×Q8—64no—
376C4×Q8—64no—
377C4×D4—64no—
378C4×D4—64no—
379C4×D4—68no—
380C4×D4—68no—
381#117—38no—
382#117—68no—
383#117—64no—
384#117—64no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4C22×D314yes—
406C2×C4⋊C4C22×D312yes—
407C2×C4⋊C4C22×D312yes—
408C2×C4⋊C4C22×D312yes—
409C2×C4⋊C4C22×D312yes—
410C2×C4⋊C4C22×D314yes—
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C42—24no—
421C2×C42—32no—
422C2×C42—32no—
423C2×C42—32no—
424C2×C42—32no—
425C2×C42—32no—
426C2×C42—68no—
427C2×C42C22×D311yescharacteristic
428C2×C42C22×D311yescharacteristic
429C2×C42C22×D311yescharacteristic
430C2×C42C22×D311yescharacteristic
431#95—32no—
432#95—32no—
433#95—32no—
434#95—32no—
435#95—34no—
436#95—34no—
437#95—34no—
438#95—34no—
439#95—34no—
440#95—34no—
441#95C22×D314yes—
442#95C22×D314yes—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3C22×D412yes—
448C23×C3C22×Q812yes—
449C23×C3C2×#4112yes—
450C23×C3C2511yescharacteristic
451C22×D3—22no—
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—22no—
457C22×D3C22×Q814yes—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—24no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—24no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—44no—
475C2×C3×C4—44no—
476C2×C3×C4—48no—
477C2×C3×C4—84no—
478C2×C3×C4C22⋊Q8116yescomplemented
479C2×C3×C4C22×D412yes—
480C2×C3×C4C22×D412yes—
481C2×C3×C4C22×Q812yes—
482C2×C3×C4C22×Q812yes—
483C2×C3×C4C2×#4112yes—
484C2×C3×C4C2×#4112yes—
485C2×C3×C4H(5,𝔽2)12yes—
486C2×C3×C42−1+412yes—
487#67—216no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—22no—
495C2×Dic3—22no—
496C2×Dic3—22no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3C22×D414yes—
507C2×Dic3C22×D414yes—
508C2×Dic3C22×Q814yes—
509D12—28no—
510C4×D3—216no—
511C4×D3—48no—
512C4×D3—48no—
513Dic6—28no—
514Dic6—88no—
515C24—32no—
516C24C23×D311yescharacteristic
517#41—632no—
518C2×Q8—34no—
519C2×Q8—68no—
520C2×Q8—62no—
521C2×Q8—62no—
522C2×Q8—124no—
523C2×Q8—124no—
524C2×D4—38no—
525C2×D4—34no—
526C2×D4—64no—
527C2×D4—64no—
528C2×D4—62no—
529C2×D4—62no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—38no—
540C22×C4—32no—
541C22×C4—32no—
542C22×C4—32no—
543C22×C4—32no—
544C22×C4—42no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—64no—
551C22×C4—64no—
552C22×C4—64no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—64no—
556C22×C4—122no—
557C22×C4—122no—
558C22×C4#23514yes—
559C22×C4D3×D414yes—
560C22×C4D3×Q814yes—
561C22×C4C23×D314yes—
562C22×C4C23×D311yescharacteristic
563C22×C4C23×D314yes—
564C22×C4C23×D311yescharacteristic
565C22×C4C23×D311yescharacteristic
566C22×C4C23×D311yescharacteristic
567C22×C4C23×D311yescharacteristic
568C22×C4C23×D311yescharacteristic
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—28no—
574C4⋊C4—34no—
575C4⋊C4—34no—
576C4⋊C4—44no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C4⋊C4—68no—
580C4⋊C4—68no—
581C4⋊C4—68no—
582C4⋊C4—62no—
583C4⋊C4—62no—
584C4⋊C4—62no—
585C4⋊C4—62no—
586C4⋊C4—64no—
587C4⋊C4—64no—
588C4⋊C4—124no—
589C4⋊C4—124no—
590C4⋊C4—122no—
591C4⋊C4—122no—
592C22⋊C4—38no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—124no—
598C22⋊C4—124no—
599C22⋊C4—124no—
600C22⋊C4—124no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—38no—
606C42—64no—
607C42—64no—
608C42—64no—
609C42—64no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3C2×C22⋊Q814yes—
617C22×C3C23×D411yescharacteristic
618C22×C3C23×Q811yescharacteristic
619C22×C3C22×#4111yescharacteristic
620C22×C3C2×H(5,𝔽2)11yescharacteristic
621C22×C3C2×2−1+411yescharacteristic
622C22×C3#58511yescharacteristic
623C22×C3#58511yescharacteristic
624C2×D3—24no—
625C2×D3—24no—
626C2×D3—24no—
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—44no—
634C3×C4—44no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4C2×C22⋊Q814yes—
638C3×C4C2×C22⋊Q814yes—
639Dic3—24no—
640Dic3—24no—
641Dic3—24no—
642Dic3—42no—
643Dic3—42no—
644Dic3—42no—
645Dic3—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—34no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23C2×#23512yes—
658C23C2×D3×D412yes—
659C23C2×D3×Q812yes—
660C23C24×D311yescharacteristic
661Q8—68no—
662Q8—248no—
663D4—616no—
664D4—68no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—24no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—34no—
682C2×C4—34no—
683C2×C4—34no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—48no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—616no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—84no—
707C2×C4—128no—
708C2×C4—128no—
709C2×C4#896116yescomplemented
710C2×C4C2×#23512yes—
711C2×C4C2×#23512yes—
712C2×C4C2×D3×D412yes—
713C2×C4C2×D3×D412yes—
714C2×C4#100412yes—
715C2×C4C2×D3×Q812yes—
716C2×C4C2×D3×Q812yes—
717C2×C4#100712yes—
718C2×C3—24no—
719C2×C3C22×C22⋊Q811yescharacteristic
720C2×C3#346011yescharacteristic
721C2×C3#346111yescharacteristic
722C2×C3#348811yescharacteristic
723C2×C3#348911yescharacteristic
724C2×C3#350311yescharacteristic
725C2×C3#350411yescharacteristic
726D3—44no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—64no—
734C22—64no—
735C22—64no—
736C22—122no—
737C22—122no—
738C22—122no—
739C22—122no—
740C22C2×#89614yes—
741C22C22×#23511yescharacteristic
742C22C22×D3×D411yescharacteristic
743C22C2×#100411yescharacteristic
744C22C22×D3×Q811yescharacteristic
745C22C2×#100711yescharacteristic
746C22#596411yescharacteristic
747C22#596411yescharacteristic
748C4—22no—
749C4—22no—
750C4—44no—
751C4—41no—
752C4—44no—
753C4—41no—
754C4—64no—
755C4—64no—
756C4—64no—
757C4—122no—
758C4—122no—
759C4—122no—
760C4—122no—
761C4C2×#89614yes—
762C4C2×#89614yes—
763C3#3525711yescharacteristic, complemented, Sylow
764C2—24no—
765C2—124no—
766C2C22×#89611yescharacteristic
767C2#8577711yescharacteristic
768C2#8581111yescharacteristic
769C2#8594911yescharacteristic
770C2#8598511yescharacteristic
771C2#8609811yescharacteristic
772C2#8621511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#389C2
prime radicalC22×#235C22
hypercenterC2×#389D3
hypocenterC3#35257
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#5500C2semidirect
3. C2×C3×#389C2semidirect
6. #82173C2semidirect
7. #82157C2semidirect
8. #82069C2semidirect
9. #76288C2semidirect
10. #76285C2semidirect
11. #76251C2semidirect
12. #76250C2semidirect
13. #76015C2semidirect
14. #76012C2semidirect
15. #76010C2semidirect
16. #76008C2semidirect
17. #73351C2semidirect
102. C2×#389D3semidirect
111. C2×#235Q8semidirect
478. C2×C3×C4C22⋊Q8semidirect
709. C2×C4#896semidirect
763. C3#35257semidirect

Maximal subgroups

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

subgroupindex
C2×#55002
C2×C4×#2352
C2×C3×#3892
#821862
#821732
#821572
#820692
#762882
#762852
#762512
#762502
#760152
#760122
#760102
#760082
#733512
#352573