Finite Group Databasebeta

← #10973014

Subgroups — #10973014

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×C3×#544C211yesmaximal, characteristic, complemented
2C2×#5522C211yesmaximal, characteristic
3#83269C212yesmaximal, complemented
4#83262C212yesmaximal, complemented
5#83236C212yesmaximal, complemented
6#83235C212yesmaximal, complemented
7#83072C212yesmaximal, complemented
8#83065C212yesmaximal, complemented
9#83030C212yesmaximal, complemented
10#83029C212yesmaximal, complemented
11#82765C214yesmaximal, complemented
12#82764C214yesmaximal, complemented
13#82270C211yesmaximal, characteristic
14#82233C211yesmaximal, characteristic, complemented
15#82226C211yesmaximal, characteristic, complemented
16#82186C211yesmaximal, characteristic
17C2×#4972C211yesmaximal, characteristic, complemented
18#35257—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C3×#544—28no—
21C2×C3×C4⋊Q8C2212yes—
22C2×C3×C4⋊Q8C2212yes—
23C2×C3×#125C2212yes—
24C2×C3×#125C2212yes—
25C2×C3×C22⋊Q8C2214yes—
26C2×C3×#117C2211yescharacteristic
27C2×C3×#117C2211yescharacteristic
28C22×C3×C4⋊C4C2211yescharacteristic
29C2×#946C2214yes—
30C2×#926C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2212yes—
33C22×C4×Dic3C2211yescharacteristic
34#5522—28no—
35C2×#893C2211yescharacteristic
36C2×#893C2211yescharacteristic
37C2×#887C2211yescharacteristic
38C2×#887C2211yescharacteristic
39C2×#67⋊C4C2212yes—
40C2×#67⋊C4C2212yes—
41C2×#872C2212yes—
42C2×C42×D3C2212yes—
43#5231C2214yes—
44#5230C2214yes—
45#5229C2214yes—
46#5213C2214yes—
47C2×C3⋊#95C2212yes—
48#4994C2214yes—
49#4994C2214yes—
50#4993C2214yes—
51#4989C2214yes—
52#4989C2214yes—
53#4988C2212yes—
54#4987C2212yes—
55#4987C2212yes—
56#4987C2212yes—
57#4987C2214yes—
58#4987C2212yes—
59#4985C2214yes—
60#4984C2212yes—
61#4984C2212yes—
62#4982C2214yes—
63#4982C2214yes—
64#4978C2214yes—
65#4978C2214yes—
66#4973C2212yes—
67#4972C2212yes—
68#4972C2212yes—
69#4972C2211yescharacteristic
70#4972C2211yescharacteristic
71#4972C2211yescharacteristic
72#4972C2211yescharacteristic
73#4972C2212yes—
74#4972C2214yes—
75#4972C2212yes—
76#4958C2214yes—
77#4950C2214yes—
78#4946C2212yes—
79#4946C2212yes—
80#4939C2212yes—
81#4936C2212yes—
82#4935C2212yes—
83C4×Dic3⋊C4C2212yes—
84C4×Dic3⋊C4C2212yes—
85#4929C2212yes—
86C2×#544D311yescharacteristic, complemented
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×#389—31no—
103C22×C3×Q8C2314yes—
104C23×C3×C4C2312yes—
105C23×C3×C4C2311yescharacteristic
106C22×#67C2312yes—
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2312yes—
110C2×#235—24no—
111C2×#235—24no—
112C2×#235Q818yescomplemented
113C22×D12C2311yescharacteristic
114C22×C4×D3C2312yes—
115C22×C4×D3C2312yes—
116C22×C4×D3C2312yes—
117C22×Dic6C2311yescharacteristic
118C3×C4⋊Q8—28no—
119C3×C4⋊Q8—28no—
120C3×#125—28no—
121C3×#125—28no—
122C3×C22⋊Q8—216no—
123C3×#117—24no—
124C3×#117D418yes—
125C2×C3×C4⋊C4—24no—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2314yes—
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C22⋊C4C2312yes—
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C42C2312yes—
138C2×C3×C42C2312yes—
139C2×#217C2312yes—
140#946—48no—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147#926—24no—
148C2×C4⋊Dic3—24no—
149C2×C4⋊Dic3C2312yes—
150C2×C4⋊Dic3C2311yescharacteristic
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2311yescharacteristic
153C2×C4⋊Dic3C2314yes—
154C2×C4⋊Dic3C2314yes—
155C2×Dic3⋊C4—44no—
156C2×Dic3⋊C4C2312yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2312yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2312yes—
163C2×Dic3⋊C4C2314yes—
164C2×C4×Dic3—24no—
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2312yes—
168C2×C4×Dic3C2311yescharacteristic
169C2×C4×Dic3C2312yes—
170C2×C4×Dic3C2312yes—
171C2×C4×Dic3C2311yescharacteristic
172#893—24no—
173#893—24no—
174#887—24no—
175#887—24no—
176#67⋊C4—28no—
177#67⋊C4—28no—
178#872—28no—
179C42×D3—28no—
180C3⋊#95C2314yes—
181C3⋊#95C2314yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C22×#41—31no—
193#544—28no—
194C2×C4⋊Q8C2×D312yes—
195C2×C4⋊Q8C2×D312yes—
196C2×#125C2×D312yes—
197C2×#125C2×D312yes—
198C2×C22⋊Q8—34no—
199C2×C22⋊Q8C2×D314yes—
200C4×#41—68no—
201C2×C4×Q8—31no—
202C2×C4×Q8—31no—
203C2×C4×D4—31no—
204C2×C4×D4—31no—
205C2×C4×D4—32no—
206C2×C4×D4—32no—
207C2×#117—31no—
208C2×#117—32no—
209C2×#117C2×D311yescharacteristic
210C2×#117C2×D311yescharacteristic
211C22×C4⋊C4—31no—
212C22×C4⋊C4—32no—
213C22×C4⋊C4C2×D311yescharacteristic
214C22×C42—31no—
215C22×C42—32no—
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—34no—
225#391—32no—
226#391—32no—
227#390—32no—
228#390—32no—
229#389—32no—
230#389—32no—
231#389—31no—
232#389—32no—
233#389—31no—
234#389—34no—
235#389—31no—
236#389—32no—
237#389—31no—
238#389—32no—
239#389—32no—
240#387—34no—
241#387—34no—
242#386—34no—
243#386—34no—
244#385—34no—
245#385—34no—
246#385—34no—
247#385—32no—
248#385—32no—
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×#95—32no—
259C24×C3C2411yescharacteristic
260C23×D3C2412yes—
261C2×C3×Q8—28no—
262C2×C3×Q8—44no—
263C2×C3×Q8—44no—
264C22×C3×C4—24no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4C2×D414yes—
268C22×C3×C4C2×Q814yes—
269C22×C3×C4#4114yes—
270C22×C3×C4C2412yes—
271C22×C3×C4C2412yes—
272C22×C3×C4C2414yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2412yes—
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C2×#67—24no—
278C2×#67—24no—
279C2×#67C2×Q818yes—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—24no—
283C22×Dic3—22no—
284C22×Dic3—22no—
285C22×Dic3—42no—
286C22×Dic3—41no—
287C22×Dic3—41no—
288C22×Dic3—42no—
289C22×Dic3C2412yes—
290C22×Dic3C2411yescharacteristic
291C22×Dic3C2414yes—
292C22×Dic3C2412yes—
293C22×Dic3C2411yescharacteristic
294C22×Dic3C2412yes—
295C22×Dic3C2411yescharacteristic
296C22×Dic3C2411yescharacteristic
297#235—232no—
298C2×D12—22no—
299C2×D12—22no—
300C2×D12C2×Q814yes—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—42no—
308C2×C4×D3—42no—
309C2×C4×D3C2×Q818yes—
310C2×Dic6—22no—
311C2×Dic6—22no—
312C2×Dic6C2×Q814yes—
313C3×C4⋊C4—24no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—28no—
318C3×C4⋊C4—28no—
319C3×C4⋊C4—28no—
320C3×C4⋊C4C2×D414yes—
321C3×C4⋊C4C2×D414yes—
322C3×C22⋊C4—24no—
323C3×C22⋊C4C2×D418yes—
324C3×C42—24no—
325C3×C42C2×D418yes—
326#217—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—24no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332(C2×D3)⋊C4—44no—
333C4⋊Dic3—24no—
334C4⋊Dic3—24no—
335C4⋊Dic3—22no—
336C4⋊Dic3—22no—
337C4⋊Dic3—44no—
338C4⋊Dic3—44no—
339Dic3⋊C4—24no—
340Dic3⋊C4—24no—
341Dic3⋊C4—28no—
342Dic3⋊C4—24no—
343Dic3⋊C4—24no—
344Dic3⋊C4—44no—
345Dic3⋊C4—42no—
346Dic3⋊C4—42no—
347C4×Dic3—22no—
348C4×Dic3—24no—
349C4×Dic3—24no—
350C4×Dic3—22no—
351C4×Dic3—22no—
352C4×Dic3—22no—
353C4×Dic3—24no—
354C2×#41—38no—
355C2×#41—64no—
356C2×#41—64no—
357C22×Q8—31no—
358C22×Q8C22×D314yes—
359C22×D4—32no—
360C22×D4—31no—
361C23×C4—32no—
362C23×C4—31no—
363C23×C4—31no—
364C23×C4—32no—
365C23×C4—32no—
366C23×C4—32no—
367C23×C4C22×D312yes—
368C23×C4C22×D311yescharacteristic
369C4⋊Q8—28no—
370C4⋊Q8—28no—
371#125—28no—
372#125—28no—
373C22⋊Q8—216no—
374C22⋊Q8—128no—
375C4×Q8—64no—
376C4×Q8—64no—
377C4×D4—64no—
378C4×D4—64no—
379C4×D4—68no—
380C4×D4—68no—
381#117—24no—
382#117—64no—
383#117—68no—
384#117#6718yes—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—34no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—32no—
389C2×C4⋊C4—32no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—34no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—34no—
400C2×C4⋊C4—64no—
401C2×C4⋊C4—124no—
402C2×C4⋊C4C22×D312yes—
403C2×C4⋊C4C22×D312yes—
404C2×C4⋊C4C22×D311yescharacteristic
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D314yes—
407C2×C4⋊C4C22×D314yes—
408C2×C4⋊C4C22×D314yes—
409C2×C4⋊C4C22×D311yescharacteristic
410C2×C4⋊C4C22×D311yescharacteristic
411C2×C22⋊C4—32no—
412C2×C22⋊C4—32no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4C22×D312yes—
419C2×C22⋊C4C22×D312yes—
420C2×C42—31no—
421C2×C42—32no—
422C2×C42—31no—
423C2×C42—31no—
424C2×C42—32no—
425C2×C42—32no—
426C2×C42—31no—
427C2×C42—64no—
428C2×C42—68no—
429C2×C42C22×D312yes—
430C2×C42C22×D312yes—
431#95—34no—
432#95—34no—
433#95—32no—
434#95—32no—
435#95—32no—
436#95—32no—
437#95—34no—
438#95—34no—
439#95—34no—
440#95—34no—
441#95—34no—
442#95—34no—
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—
458C3×Q8—88no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—24no—
466C2×C3×C4—24no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—24no—
472C2×C3×C4—84no—
473C2×C3×C4C22⋊Q8116yescomplemented
474C2×C3×C4C22×D414yes—
475C2×C3×C4C22×D414yes—
476C2×C3×C4C22×D412yes—
477C2×C3×C4C22×D412yes—
478C2×C3×C4C22×Q812yes—
479C2×C3×C4C22×Q812yes—
480C2×C3×C4C2×#4112yes—
481C2×C3×C4C2×#4112yes—
482#67—216no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—24no—
494C2×Dic3—24no—
495C2×Dic3—22no—
496C2×Dic3—21no—
497C2×Dic3—22no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—24no—
504C2×Dic3—44no—
505C2×Dic3—44no—
506C2×Dic3—48no—
507C2×Dic3C22×Q814yes—
508C2×Dic3H(5,𝔽2)12yes—
509C2×Dic32−1+412yes—
510D12—28no—
511C4×D3—216no—
512C4×D3—48no—
513C4×D3—48no—
514Dic6—28no—
515C24—32no—
516C24C23×D311yescharacteristic
517#41—632no—
518C2×Q8—28no—
519C2×Q8—34no—
520C2×Q8—44no—
521C2×Q8—44no—
522C2×Q8—62no—
523C2×Q8—62no—
524C2×D4—38no—
525C2×D4—34no—
526C2×D4—64no—
527C2×D4—64no—
528C2×D4—62no—
529C2×D4—62no—
530C22×C4—24no—
531C22×C4—32no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—38no—
535C22×C4—32no—
536C22×C4—31no—
537C22×C4—34no—
538C22×C4—32no—
539C22×C4—31no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—64no—
543C22×C4—64no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—64no—
547C22×C4—64no—
548C22×C4—64no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—64no—
552C22×C4—64no—
553C22×C4—122no—
554C22×C4—122no—
555C22×C4—122no—
556C22×C4—121no—
557C22×C4—121no—
558C22×C4—122no—
559C22×C4D3×Q814yes—
560C22×C4#23914yes—
561C22×C4C2×#6714yes—
562C22×C4C23×D312yes—
563C22×C4C23×D312yes—
564C22×C4C23×D314yes—
565C22×C4C23×D312yes—
566C22×C4C23×D312yes—
567C22×C4C23×D311yescharacteristic
568C22×C4C23×D311yescharacteristic
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—28no—
574C4⋊C4—28no—
575C4⋊C4—28no—
576C4⋊C4—68no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C4⋊C4—64no—
580C4⋊C4—64no—
581C4⋊C4—62no—
582C4⋊C4—62no—
583C4⋊C4—64no—
584C4⋊C4—64no—
585C4⋊C4—124no—
586C4⋊C4—124no—
587C4⋊C4—122no—
588C4⋊C4—122no—
589C4⋊C4—124no—
590C4⋊C4C2×#6714yes—
591C4⋊C4C2×#6714yes—
592C22⋊C4—24no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—124no—
597C22⋊C4—124no—
598C22⋊C4—124no—
599C22⋊C4—124no—
600C22⋊C4C2×#6718yes—
601C42—24no—
602C42—64no—
603C42—62no—
604C42—62no—
605C42—64no—
606C42—64no—
607C42—62no—
608C42—62no—
609C42C2×#6718yes—
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—24no—
632C3×C4—24no—
633C3×C4—44no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4C2×C22⋊Q814yes—
637C3×C4C2×C22⋊Q814yes—
638Dic3—24no—
639Dic3—22no—
640Dic3—22no—
641Dic3—42no—
642Dic3—44no—
643Dic3—42no—
644Dic3—41no—
645Dic3—41no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—34no—
651C23—62no—
652C23—62no—
653C23—62no—
654C23—62no—
655C23—62no—
656C23—62no—
657C23C2×D3×Q812yes—
658C23C2×#23912yes—
659C23C22×#6712yes—
660C23C24×D311yescharacteristic
661Q8—68no—
662Q8—88no—
663D4—616no—
664D4—68no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—34no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—62no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—62no—
687C2×C4—616no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—64no—
691C2×C4—62no—
692C2×C4—64no—
693C2×C4—61no—
694C2×C4—62no—
695C2×C4—61no—
696C2×C4—62no—
697C2×C4—61no—
698C2×C4—64no—
699C2×C4—62no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—84no—
704C2×C4—128no—
705C2×C4—128no—
706C2×C4—124no—
707C2×C4—124no—
708C2×C4—128no—
709C2×C4#946116yescomplemented
710C2×C4C2×D3×Q812yes—
711C2×C4C2×D3×Q812yes—
712C2×C4C2×#23912yes—
713C2×C4C2×#23912yes—
714C2×C4C22×#6714yes—
715C2×C4C22×#6714yes—
716C2×C4C22×#6712yes—
717C2×C4C22×#6712yes—
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×#94614yes—
741C22C22×D3×Q811yescharacteristic
742C22C22×#23911yescharacteristic
743C22D3×H(5,𝔽2)11yescharacteristic
744C22#596611yescharacteristic
745C22D3×2−1+411yescharacteristic
746C22#596811yescharacteristic
747C22C23×#6711yescharacteristic
748C4—24no—
749C4—24no—
750C4—44no—
751C4—42no—
752C4—42no—
753C4—64no—
754C4—62no—
755C4—62no—
756C4—124no—
757C4—122no—
758C4—122no—
759C4—121no—
760C4—121no—
761C4C2×#94614yes—
762C4C2×#94614yes—
763C3#3525711yescharacteristic, complemented, Sylow
764C2—24no—
765C2—124no—
766C2#8658211yescharacteristic
767C2#8658311yescharacteristic
768C2#8658611yescharacteristic
769C2#8658711yescharacteristic
770C2C22×#94611yescharacteristic
771C2#8728511yescharacteristic
772C2#8729511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#544C2
prime radicalC22×#235C22
hypercenterC2×#544D3
hypocenterC3#35257
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. C2×C3×#544C2semidirect
3. #83269C2semidirect
4. #83262C2semidirect
5. #83236C2semidirect
6. #83235C2semidirect
7. #83072C2semidirect
8. #83065C2semidirect
9. #83030C2semidirect
10. #83029C2semidirect
11. #82765C2semidirect
12. #82764C2semidirect
14. #82233C2semidirect
15. #82226C2semidirect
17. C2×#4972C2semidirect
86. C2×#544D3semidirect
112. C2×#235Q8semidirect
473. C2×C3×C4C22⋊Q8semidirect
709. C2×C4#946semidirect
763. C3#35257semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5442
C2×#55222
#832692
#832622
#832362
#832352
#830722
#830652
#830302
#830292
#827652
#827642
#822702
#822332
#822262
#821862
C2×#49722
#352573