Finite Group Databasebeta

← #10966694

Subgroups — #10966694

Order 768.

2570 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×C3×C4×#41C211yesmaximal, characteristic, complemented
2C2×#5479C211yesmaximal, characteristic, complemented
3#84095C212yesmaximal, complemented
4#82485C212yesmaximal, complemented
5#82484C211yesmaximal, characteristic, complemented
6#82483C211yesmaximal, characteristic, complemented
7#82390C212yesmaximal, complemented
8#82389C214yesmaximal, complemented
9#82383C211yesmaximal, characteristic, complemented
10#82377C211yesmaximal, characteristic, complemented
11#82351C212yesmaximal, complemented
12#82350C212yesmaximal, complemented
13#82274C212yesmaximal, complemented
14#82225C214yesmaximal, complemented
15C4×#924C212yesmaximal, complemented
16C4×#930C212yesmaximal, complemented
17C4×#926C211yesmaximal, characteristic, complemented
18#34911—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C3×C4×#41—28no—
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×D4C2212yes—
24C2×C3×C4×D4C2211yescharacteristic
25C2×C3×C4×D4C2212yes—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×#117C2212yes—
28C2×C3×#117C2211yescharacteristic
29C22×C3×C42C2212yes—
30C22×C3×C42C2211yescharacteristic
31C2×#930C2212yes—
32C2×#930C2211yescharacteristic
33C2×#929C2212yes—
34C2×C4×#67C2214yes—
35C2×C4×#67C2212yes—
36C2×#926C2212yes—
37C2×#924C2212yes—
38C2×#924C2211yescharacteristic
39#5479—28no—
40C2×#876C2212yes—
41C2×#875C2211yescharacteristic
42C2×C4×D12C2211yescharacteristic
43C2×#872C2212yes—
44C2×#870C2211yescharacteristic
45C2×C4×Dic6C2211yescharacteristic
46#5231C2212yes—
47#5230C2212yes—
48#5223C2214yes—
49#5223C2212yes—
50#5222C2214yes—
51#5222C2212yes—
52#5213C2214yes—
53#5212C2212yes—
54#5212C2212yes—
55#5210C2214yes—
56C4×#217C2214yes—
57C4×#217C2212yes—
58C4×#217C2212yes—
59#4993C2212yes—
60#4992C2212yes—
61#4990C2214yes—
62#4990C2214yes—
63#4985C2212yes—
64#4983C2212yes—
65#4976C2214yes—
66#4976C2214yes—
67#4959C2214yes—
68#4957C2214yes—
69#4957C2214yes—
70#4952C2214yes—
71#4945C2214yes—
72#4945C2214yes—
73#4940C2214yes—
74#4939C2212yes—
75C4×(C2×D3)⋊C4C2214yes—
76C4×C4⋊Dic3C2211yescharacteristic
77C4×C4⋊Dic3C2211yescharacteristic
78C4×C4⋊Dic3C2212yes—
79#4933C2214yes—
80#4932C2212yes—
81C4×Dic3⋊C4C2214yes—
82C42×Dic3C2212yes—
83#4929C2212yes—
84#4928C2212yes—
85#4928C2212yes—
86C2×#529—31no—
87C2×C4×#41D311yescharacteristic, complemented
88#2604—32no—
89#2603—32no—
90#2602—34no—
91#2592—31no—
92#2584—31no—
93#2562—31no—
94#2540—31no—
95#2415—32no—
96#2414—32no—
97#2395—32no—
98#2388—32no—
99C4×C22⋊Q8—32no—
100C4×#121—32no—
101#2293—34no—
102C4×#117—31no—
103C2×C3×#41—24no—
104C2×C3×#41—28no—
105C22×C3×Q8C2311yescharacteristic
106C22×C3×D4C2311yescharacteristic
107C22×C3×D4C2312yes—
108C23×C3×C4C2312yes—
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2312yes—
112C23×C3×C4C2312yes—
113C23×C3×C4C2311yescharacteristic
114C22×#67C2314yes—
115C22×#67C2312yes—
116C22×D12C2311yescharacteristic
117C22×C4×D3C2312yes—
118C22×Dic6C2311yescharacteristic
119C3×C4×Q8—24no—
120C3×C4×Q8—24no—
121C3×C4×D4—28no—
122C3×C4×D4—28no—
123C3×C4×D4—24no—
124C3×C4×D4—24no—
125C3×#117—24no—
126C3×#117—28no—
127C2×C3×C4⋊C4C2312yes—
128C2×C3×C4⋊C4C2312yes—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C22⋊C4C2312yes—
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C42—28no—
135C2×C3×C42D418yescomplemented
136C2×C3×C42C2312yes—
137C2×C3×C42C2312yes—
138C2×C3×C42C2312yes—
139C2×C3×C42C2311yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C2×#217C2314yes—
144C2×#217C2314yes—
145C2×#217C2312yes—
146C2×#217C2314yes—
147C2×#217C2314yes—
148#930—24no—
149#930—28no—
150#929—28no—
151C4×#67—28no—
152C4×#67—216no—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2312yes—
156C2×(C2×D3)⋊C4C2312yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2314yes—
160#926—28no—
161C2×C4⋊Dic3C2311yescharacteristic
162C2×C4⋊Dic3C2311yescharacteristic
163C2×C4⋊Dic3C2312yes—
164C2×C4⋊Dic3C2312yes—
165#924—24no—
166#924—28no—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2312yes—
170C2×Dic3⋊C4C2312yes—
171C2×Dic3⋊C4C2312yes—
172C2×Dic3⋊C4C2312yes—
173C2×Dic3⋊C4C2314yes—
174C2×C4×Dic3C2314yes—
175C2×C4×Dic3C2314yes—
176C2×C4×Dic3C2312yes—
177C2×C4×Dic3C2312yes—
178C2×C4×Dic3C2312yes—
179#876—28no—
180#875—24no—
181C4×D12—24no—
182#872—28no—
183#870—24no—
184C4×Dic6—24no—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2312yes—
193C3⋊#95C2314yes—
194C22×#41C2×D311yescharacteristic
195#529—68no—
196C2×#126—32no—
197C2×#125—31no—
198C2×#124—31no—
199C2×#123—32no—
200C2×C22⋊Q8—31no—
201C2×C22⋊Q8—32no—
202C2×#121—31no—
203C2×#121—32no—
204C4×#41—28no—
205C2×C4×Q8—31no—
206C2×C4×Q8C2×D311yescharacteristic
207C2×C4×Q8C2×D311yescharacteristic
208C2×C4×D4—32no—
209C2×C4×D4—34no—
210C2×C4×D4—31no—
211C2×C4×D4C2×D311yescharacteristic
212C2×C4×D4C2×D312yes—
213C2×C4×D4C2×D311yescharacteristic
214C2×C4×D4C2×D312yes—
215C2×#117—32no—
216C2×#117—32no—
217C2×#117C2×D311yescharacteristic
218C2×#117C2×D312yes—
219C22×C42C2×D312yes—
220C22×C42C2×D311yescharacteristic
221#400—32no—
222#399—32no—
223#398—32no—
224#397—32no—
225#397—34no—
226#395—32no—
227#394—32no—
228#394—34no—
229#394—34no—
230#393—32no—
231#392—34no—
232#392—32no—
233#391—32no—
234#390—34no—
235#390—34no—
236#390—32no—
237#389—34no—
238#389—34no—
239#389—32no—
240#389—32no—
241#388—34no—
242#388—34no—
243#388—34no—
244#388—34no—
245#388—34no—
246#387—34no—
247#386—34no—
248#385—34no—
249#380—32no—
250#380—32no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—31no—
253C4×C4⋊C4—34no—
254C4×C4⋊C4—32no—
255C4×C22⋊C4—32no—
256C4×C22⋊C4—32no—
257C4×C22⋊C4—34no—
258C4×C22⋊C4—34no—
259#376—32no—
260C43—32no—
261C24×C3C2411yescharacteristic
262C24×C3C2412yes—
263C23×D3C2412yes—
264C3×#41—232no—
265C2×C3×Q8—22no—
266C2×C3×Q8—24no—
267C2×C3×D4—24no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—22no—
271C2×C3×D4—24no—
272C22×C3×C4—24no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—24no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—24no—
279C22×C3×C4—24no—
280C22×C3×C4—41no—
281C22×C3×C4—41no—
282C22×C3×C4—42no—
283C22×C3×C4—42no—
284C22×C3×C4C2×D414yes—
285C22×C3×C4C2×D414yes—
286C22×C3×C4C2×D414yes—
287C22×C3×C4#4118yes—
288C22×C3×C4C2412yes—
289C22×C3×C4C2412yes—
290C22×C3×C4C2411yescharacteristic
291C22×C3×C4C2411yescharacteristic
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2411yescharacteristic
294C22×C3×C4C2412yes—
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2411yescharacteristic
297C2×#67—24no—
298C2×#67—28no—
299C2×#67—28no—
300C2×#67—44no—
301C2×#67—42no—
302C2×#67—42no—
303C22×Dic3C2414yes—
304C22×Dic3C2412yes—
305C22×Dic3C2412yes—
306C22×Dic3C2412yes—
307C22×Dic3C2414yes—
308C2×D12—22no—
309C2×D12—24no—
310C2×C4×D3—24no—
311C2×C4×D3—28no—
312C2×Dic6—22no—
313C2×Dic6—24no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—22no—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—24no—
321C3×C42—24no—
322C3×C42—24no—
323C3×C42—24no—
324C3×C42C2×D414yes—
325C3×C42C2×D414yes—
326C3×C42C2×D414yes—
327C3×C42C2×D414yes—
328#217—24no—
329#217—28no—
330#217—28no—
331#217—28no—
332#217—44no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—28no—
338(C2×D3)⋊C4—28no—
339(C2×D3)⋊C4—44no—
340C4⋊Dic3—22no—
341C4⋊Dic3—22no—
342C4⋊Dic3—24no—
343C4⋊Dic3#4118yescomplemented
344Dic3⋊C4—24no—
345Dic3⋊C4—24no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—28no—
349Dic3⋊C4—28no—
350Dic3⋊C4—44no—
351C4×Dic3—24no—
352C4×Dic3—28no—
353C4×Dic3—28no—
354C4×Dic3—42no—
355C4×Dic3—42no—
356C2×#41—28no—
357C2×#41—24no—
358C22×Q8—31no—
359C22×Q8C22×D311yescharacteristic
360C22×D4—34no—
361C22×D4—32no—
362C22×D4—31no—
363C22×D4C22×D312yes—
364C22×D4C22×D311yescharacteristic
365C23×C4—32no—
366C23×C4C22×D312yes—
367C23×C4C22×D312yes—
368C23×C4C22×D311yescharacteristic
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D312yes—
371C23×C4C22×D311yescharacteristic
372#126—68no—
373#125—64no—
374#124—64no—
375#123—68no—
376C22⋊Q8—68no—
377C22⋊Q8—64no—
378#121—68no—
379#121—64no—
380C4×Q8—24no—
381C4×Q8—24no—
382C4×Q8—64no—
383C4×D4—28no—
384C4×D4—28no—
385C4×D4—24no—
386C4×D4—24no—
387C4×D4—616no—
388C4×D4—68no—
389C4×D4—64no—
390#117—24no—
391#117—28no—
392#117—68no—
393#117—68no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4C22×D312yes—
406C2×C4⋊C4C22×D312yes—
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C22⋊C4—34no—
410C2×C22⋊C4—32no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4C22×D312yes—
422C2×C22⋊C4C22×D312yes—
423C2×C22⋊C4C22×D312yes—
424C2×C42—28no—
425C2×C42—34no—
426C2×C42—32no—
427C2×C42—34no—
428C2×C42—32no—
429C2×C42—32no—
430C2×C42#6718yescomplemented
431C2×C42C22×D312yes—
432C2×C42C22×D312yes—
433C2×C42C22×D312yes—
434C2×C42C22×D311yescharacteristic
435C2×C42C22×D311yescharacteristic
436C2×C42C22×D311yescharacteristic
437C2×C42C22×D311yescharacteristic
438#95—34no—
439#95—32no—
440#95—32no—
441#95—34no—
442#95—34no—
443#95—34no—
444#95—34no—
445#95—34no—
446#95—34no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—22no—
457C23×C3C22×D412yes—
458C23×C3C2×#4114yes—
459C23×C3C2511yescharacteristic
460C22×D3—22no—
461C22×D3—24no—
462C22×D3—24no—
463C22×D3—22no—
464C22×D3—22no—
465C3×Q8—28no—
466C3×D4—28no—
467C3×D4—216no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—28no—
477C2×C3×C4—216no—
478C2×C3×C4—28no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—44no—
486C2×C3×C4—48no—
487C2×C3×C4—48no—
488C2×C3×C4C22×D412yes—
489C2×C3×C4C22×D412yes—
490C2×C3×C4C22×D412yes—
491C2×C3×C4C22×D412yes—
492C2×C3×C4C22×D412yes—
493C2×C3×C4C22×D412yes—
494C2×C3×C4C2×#4114yes—
495C2×C3×C4C2×#4114yes—
496C2×C3×C4C2×#4114yes—
497#67—416no—
498#67—48no—
499C2×Dic3—24no—
500C2×Dic3—24no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—24no—
505C2×Dic3—24no—
506C2×Dic3—24no—
507C2×Dic3—24no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—22no—
511C2×Dic3C2×#4118yes—
512D12—44no—
513C4×D3—48no—
514Dic6—44no—
515C24—32no—
516C24C23×D312yes—
517C24C23×D311yescharacteristic
518#41—232no—
519C2×Q8—24no—
520C2×Q8—22no—
521C2×Q8—64no—
522C2×Q8—62no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—22no—
528C2×D4—68no—
529C2×D4—68no—
530C2×D4—64no—
531C2×D4—64no—
532C2×D4—62no—
533C2×D4—124no—
534C2×D4—122no—
535C2×D4—122no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—34no—
545C22×C4—34no—
546C22×C4—32no—
547C22×C4—32no—
548C22×C4—32no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—68no—
554C22×C4—64no—
555C22×C4#23518yes—
556C22×C4C2×#6714yes—
557C22×C4C2×#6714yes—
558C22×C4C2×#6714yes—
559C22×C4C23×D312yes—
560C22×C4C23×D312yes—
561C22×C4C23×D312yes—
562C22×C4C23×D311yescharacteristic
563C22×C4C23×D311yescharacteristic
564C22×C4C23×D311yescharacteristic
565C22×C4C23×D311yescharacteristic
566C22×C4C23×D311yescharacteristic
567C22×C4C23×D311yescharacteristic
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—38no—
573C4⋊C4—68no—
574C4⋊C4—68no—
575C4⋊C4—64no—
576C4⋊C4—64no—
577C4⋊C4—64no—
578C4⋊C4—62no—
579C4⋊C4—64no—
580C4⋊C4—62no—
581C4⋊C4—64no—
582C4⋊C4—124no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—68no—
587C22⋊C4—68no—
588C22⋊C4—68no—
589C22⋊C4—68no—
590C22⋊C4—64no—
591C22⋊C4—68no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—124no—
597C22⋊C4—124no—
598C42—24no—
599C42—24no—
600C42—24no—
601C42—68no—
602C42—68no—
603C42—64no—
604C42—122no—
605C42—122no—
606C42C2×#6714yes—
607C42C2×#6714yes—
608C42C2×#6714yes—
609C42C2×#6714yes—
610C22×C3—22no—
611C22×C3—24no—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—24no—
615C22×C3—24no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3C23×D411yescharacteristic
623C22×C3C22×#4112yes—
624C22×C3C22×#4112yes—
625C22×C3#58511yescharacteristic
626C22×C3#58511yescharacteristic
627C2×D3—42no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—44no—
631C2×D3—44no—
632C3×C4—22no—
633C3×C4—24no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4#52514yes—
640C3×C4#53214yes—
641Dic3—28no—
642Dic3—42no—
643Dic3—42no—
644Dic3—42no—
645Dic3—44no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—21no—
654C23—21no—
655C23—22no—
656C23—64no—
657C23—64no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23C2×#23514yes—
662C23C22×#6712yes—
663C23C24×D311yescharacteristic
664Q8—28no—
665Q8—124no—
666D4—216no—
667D4—28no—
668D4—1216no—
669D4—128no—
670D4—124no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—216no—
680C2×C4—28no—
681C2×C4—28no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—38no—
689C2×C4—44no—
690C2×C4—48no—
691C2×C4—48no—
692C2×C4—64no—
693C2×C4—64no—
694C2×C4—64no—
695C2×C4—64no—
696C2×C4—64no—
697C2×C4—64no—
698C2×C4—64no—
699C2×C4—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—128no—
705C2×C4C2×#23514yes—
706C2×C4C2×#23514yes—
707C2×C4D3×#4114yes—
708C2×C4C22×#6712yes—
709C2×C4C22×#6712yes—
710C2×C4C22×#6712yes—
711C2×C4C22×#6712yes—
712C2×C4C22×#6712yes—
713C2×C4C22×#6712yes—
714C2×C3—42no—
715C2×C3—44no—
716C2×C3C2×#52511yescharacteristic
717C2×C3C2×#53211yescharacteristic
718C2×C3#344911yescharacteristic
719C2×C3#347512yes—
720C2×C3#348012yes—
721D3—82no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—124no—
735C22—124no—
736C22—122no—
737C22—122no—
738C22—122no—
739C22C22×#23512yes—
740C22C2×D3×#4112yes—
741C22#596411yescharacteristic
742C22#596411yescharacteristic
743C22C23×#6711yescharacteristic
744C4—24no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—42no—
751C4—68no—
752C4—124no—
753C4—122no—
754C4—122no—
755C4—122no—
756C4#579114yes—
757C4#583214yes—
758C3#3491111yescharacteristic, complemented, Sylow
759C2—44no—
760C2—42no—
761C2—242no—
762C2#8582512yes—
763C2#8584012yes—
764C2C2×#579111yescharacteristic
765C2C2×#583211yescharacteristic
766C2#8726811yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutator, socle, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×C4×#41C2
hypercenterC2×C4×#41D3
hypocenterC3#34911
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#41C2semidirect
2. C2×#5479C2semidirect
3. #84095C2semidirect
4. #82485C2semidirect
5. #82484C2semidirect
6. #82483C2semidirect
7. #82390C2semidirect
8. #82389C2semidirect
9. #82383C2semidirect
10. #82377C2semidirect
11. #82351C2semidirect
12. #82350C2semidirect
13. #82274C2semidirect
14. #82225C2semidirect
15. C4×#924C2semidirect
16. C4×#930C2semidirect
17. C4×#926C2semidirect
87. C2×C4×#41D3semidirect
135. C2×C3×C42D4semidirect
343. C4⋊Dic3#41semidirect
430. C2×C42#67semidirect
758. C3#34911semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#412
C2×#54792
#840952
#824852
#824842
#824832
#823902
#823892
#823832
#823772
#823512
#823502
#822742
#822252
C4×#9242
C4×#9302
C4×#9262
#349113