Finite Group Databasebeta

← #10966702

Subgroups — #10966702

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×#529C211yesmaximal, characteristic, complemented
2C2×C4×#235C211yesmaximal, characteristic, complemented
3#83088C212yesmaximal, complemented
4#83087C212yesmaximal, complemented
5#83063C211yesmaximal, characteristic, complemented
6#83041C211yesmaximal, characteristic, complemented
7#82998C211yesmaximal, characteristic, complemented
8#82976C211yesmaximal, characteristic, complemented
9#82902C214yesmaximal, complemented
10#82814C212yesmaximal, complemented
11#82704C212yesmaximal, complemented
12C4×#946C212yesmaximal, complemented
13#82400C212yesmaximal, complemented
14C4×#938C212yesmaximal, complemented
15#82346C212yesmaximal, complemented
16#82225C214yesmaximal, complemented
17C4×#926C211yesmaximal, characteristic, complemented
18#34911—31nomaximal, Sylow
19C22×#235C2211yescharacteristic
20C3×#529—28no—
21C2×C3×#126C2212yes—
22C2×C3×#125C2211yescharacteristic
23C2×C3×#124C2211yescharacteristic
24C2×C3×#123C2212yes—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2212yes—
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×#117C2212yes—
31C22×C3×C42C2211yescharacteristic
32C2×#946C2212yes—
33C2×#938C2212yes—
34C2×C4×#67C2212yes—
35C2×C4×#67C2214yes—
36C2×C4×#67C2212yes—
37C2×#926C2212yes—
38C2×#926C2211yescharacteristic
39C4×#235—28no—
40C2×C4×D12C2211yescharacteristic
41C2×C4×D12C2211yescharacteristic
42C2×#872C2212yes—
43C2×C42×D3C2212yes—
44C2×C4×Dic6C2211yescharacteristic
45C2×C4×Dic6C2211yescharacteristic
46#5229C2212yes—
47#5223C2214yes—
48#5222C2214yes—
49#5221C2212yes—
50C4×#217C2214yes—
51C4×#217C2212yes—
52C4×#217C2212yes—
53#4991C2212yes—
54#4990C2214yes—
55#4990C2214yes—
56#4989C2214yes—
57#4987C2212yes—
58#4987C2212yes—
59#4986C2212yes—
60#4981C2212yes—
61#4979C2212yes—
62#4978C2214yes—
63#4976C2214yes—
64#4976C2214yes—
65#4972C2212yes—
66#4972C2212yes—
67#4960C2212yes—
68#4959C2214yes—
69#4957C2214yes—
70#4957C2214yes—
71#4956C2214yes—
72#4953C2212yes—
73#4952C2214yes—
74#4949C2212yes—
75#4947C2212yes—
76#4945C2214yes—
77#4945C2214yes—
78#4944C2214yes—
79C4×(C2×D3)⋊C4C2214yes—
80C4×C4⋊Dic3C2211yescharacteristic
81C4×C4⋊Dic3C2211yescharacteristic
82C4×C4⋊Dic3C2212yes—
83#4932C2212yes—
84C4×Dic3⋊C4C2214yes—
85C42×Dic3C2212yes—
86C2×#529D311yescharacteristic, complemented
87C2×C4×#41—31no—
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—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2312yes—
106C23×C3×C4C2312yes—
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C22×#67C2312yes—
111C22×#67C2314yes—
112C2×#235—24no—
113C2×#235—28no—
114C22×D12C2311yescharacteristic
115C22×C4×D3C2312yes—
116C22×C4×D3C2312yes—
117C22×C4×D3C2312yes—
118C22×Dic6C2311yescharacteristic
119C3×#126—28no—
120C3×#125—24no—
121C3×#124—24no—
122C3×#123—28no—
123C3×C22⋊Q8—24no—
124C3×#121—24no—
125C3×C4×Q8—24no—
126C3×C4×D4—28no—
127C3×C4×D4—24no—
128C3×#117—28no—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2312yes—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C22⋊C4C2312yes—
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C22⋊C4C2312yes—
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C42D418yescomplemented
141C2×C3×C42C2312yes—
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2311yescharacteristic
144C2×C3×C42C2311yescharacteristic
145C2×C3×C42C2311yescharacteristic
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2312yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151#946—28no—
152#938—28no—
153C4×#67—28no—
154C4×#67—28no—
155C4×#67—216no—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2314yes—
161#926—24no—
162#926—28no—
163C2×C4⋊Dic3C2312yes—
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2311yescharacteristic
166C2×C4⋊Dic3C2312yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2312yes—
170C2×Dic3⋊C4C2312yes—
171C2×Dic3⋊C4C2314yes—
172C2×C4×Dic3C2314yes—
173C2×C4×Dic3C2314yes—
174C2×C4×Dic3C2312yes—
175C2×C4×Dic3C2312yes—
176C2×C4×Dic3C2312yes—
177C2×C4×Dic3C2312yes—
178C2×C4×Dic3C2312yes—
179C4×D12—24no—
180C4×D12—24no—
181#872—28no—
182C42×D3—28no—
183C4×Dic6—24no—
184C4×Dic6—24no—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2314yes—
194C22×#41—31no—
195#529—28no—
196C2×#126C2×D312yes—
197C2×#125C2×D311yescharacteristic
198C2×#124C2×D311yescharacteristic
199C2×#123C2×D312yes—
200C2×C22⋊Q8—32no—
201C2×C22⋊Q8C2×D311yescharacteristic
202C2×#121—32no—
203C2×#121C2×D311yescharacteristic
204C4×#41—68no—
205C2×C4×Q8—31no—
206C2×C4×Q8—31no—
207C2×C4×Q8C2×D311yescharacteristic
208C2×C4×D4—32no—
209C2×C4×D4—34no—
210C2×C4×D4—32no—
211C2×C4×D4—31no—
212C2×C4×D4—31no—
213C2×C4×D4C2×D312yes—
214C2×C4×D4C2×D311yescharacteristic
215C2×#117—31no—
216C2×#117—32no—
217C2×#117—32no—
218C2×#117C2×D312yes—
219C22×C42—32no—
220C22×C42C2×D311yescharacteristic
221#400—32no—
222#399—32no—
223#398—32no—
224#397—32no—
225#397—34no—
226#395—32no—
227#394—34no—
228#394—32no—
229#394—34no—
230#393—32no—
231#392—34no—
232#392—32no—
233#391—32no—
234#390—32no—
235#390—34no—
236#390—34no—
237#389—34no—
238#389—32no—
239#389—32no—
240#389—34no—
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×C3C2412yes—
262C24×C3C2411yescharacteristic
263C23×D3C2412yes—
264C2×C3×Q8—22no—
265C2×C3×Q8—24no—
266C2×C3×D4—24no—
267C2×C3×D4—22no—
268C2×C3×D4—24no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C22×C3×C4—24no—
272C22×C3×C4—24no—
273C22×C3×C4—24no—
274C22×C3×C4—28no—
275C22×C3×C4—41no—
276C22×C3×C4—41no—
277C22×C3×C4C2×D414yes—
278C22×C3×C4C2×D414yes—
279C22×C3×C4C2×D414yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2412yes—
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2411yescharacteristic
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C2×#67—24no—
290C2×#67—24no—
291C2×#67—28no—
292C2×#67—24no—
293C2×#67—28no—
294C2×#67—44no—
295C22×Dic3C2414yes—
296C22×Dic3C2412yes—
297C22×Dic3C2412yes—
298C22×Dic3C2414yes—
299C22×Dic3C2412yes—
300#235—232no—
301C2×D12—24no—
302C2×D12—22no—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—24no—
308C2×C4×D3—24no—
309C2×C4×D3—42no—
310C2×C4×D3—42no—
311C2×C4×D3#4118yes—
312C2×Dic6—22no—
313C2×Dic6—24no—
314C3×C4⋊C4—24no—
315C3×C4⋊C4—24no—
316C3×C4⋊C4—22no—
317C3×C4⋊C4—24no—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—24no—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—24no—
322C3×C22⋊C4—24no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—24no—
325C3×C42—24no—
326C3×C42C2×D414yes—
327C3×C42C2×D414yes—
328C3×C42C2×D414yes—
329C3×C42C2×D414yes—
330#217—24no—
331#217—28no—
332#217—28no—
333#217—28no—
334#217—44no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—24no—
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—28no—
347Dic3⋊C4—28no—
348Dic3⋊C4—44no—
349C4×Dic3—24no—
350C4×Dic3—24no—
351C4×Dic3—24no—
352C4×Dic3—28no—
353C4×Dic3—28no—
354C4×Dic3—42no—
355C4×Dic3—42no—
356C2×#41—68no—
357C2×#41—64no—
358C22×Q8—31no—
359C22×Q8C22×D311yescharacteristic
360C22×D4—32no—
361C22×D4—34no—
362C22×D4—31no—
363C22×D4C22×D311yescharacteristic
364C22×D4C22×D312yes—
365C23×C4—32no—
366C23×C4—32no—
367C23×C4—32no—
368C23×C4C22×D312yes—
369C23×C4C22×D311yescharacteristic
370C23×C4C22×D311yescharacteristic
371C23×C4C22×D311yescharacteristic
372#126—28no—
373#125—24no—
374#124—24no—
375#123—28no—
376C22⋊Q8—24no—
377C22⋊Q8—68no—
378#121—24no—
379#121—68no—
380C4×Q8—24no—
381C4×Q8—64no—
382C4×Q8—64no—
383C4×D4—28no—
384C4×D4—24no—
385C4×D4—616no—
386C4×D4—68no—
387C4×D4—68no—
388C4×D4—64no—
389C4×D4—64no—
390#117—28no—
391#117—68no—
392#117—64no—
393#117—68no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—32no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4C22×D312yes—
404C2×C4⋊C4C22×D312yes—
405C2×C4⋊C4C22×D311yescharacteristic
406C2×C4⋊C4C22×D312yes—
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D312yes—
409C2×C22⋊C4—32no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—32no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4C22×D312yes—
420C2×C22⋊C4C22×D312yes—
421C2×C22⋊C4C22×D312yes—
422C2×C22⋊C4C22×D312yes—
423C2×C22⋊C4C22×D312yes—
424C2×C42—34no—
425C2×C42—32no—
426C2×C42—32no—
427C2×C42—32no—
428C2×C42—34no—
429C2×C42—32no—
430C2×C42—32no—
431C2×C42—68no—
432C2×C42#6718yescomplemented
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—21no—
450C23×C3—21no—
451C23×C3—22no—
452C23×C3—24no—
453C23×C3—24no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3C22×D412yes—
457C23×C3C2511yescharacteristic
458C22×D3—22no—
459C22×D3—22no—
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3—22no—
464C22×D3C2×#4114yes—
465C3×Q8—44no—
466C3×D4—48no—
467C3×D4—44no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—28no—
475C2×C3×C4—28no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—24no—
480C2×C3×C4—24no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—44no—
484C2×C3×C4—48no—
485C2×C3×C4C22×D412yes—
486C2×C3×C4C22×D412yes—
487C2×C3×C4C22×D412yes—
488C2×C3×C4C22×D412yes—
489C2×C3×C4C22×D412yes—
490C2×C3×C4C22×D412yes—
491C2×C3×C4C2×#4114yes—
492C2×C3×C4C2×#4114yes—
493#67—216no—
494#67—416no—
495C2×Dic3—22no—
496C2×Dic3—24no—
497C2×Dic3—22no—
498C2×Dic3—24no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—24no—
502C2×Dic3—24no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—24no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3C2×#4118yes—
509C2×Dic3C2×#4114yes—
510D12—28no—
511C4×D3—216no—
512C4×D3—48no—
513C4×D3—48no—
514Dic6—28no—
515C24—32no—
516C24C23×D312yes—
517C24C23×D311yescharacteristic
518#41—632no—
519C2×Q8—24no—
520C2×Q8—22no—
521C2×Q8—64no—
522C2×Q8—62no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—22no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—64no—
529C2×D4—64no—
530C2×D4—68no—
531C2×D4—64no—
532C2×D4—64no—
533C2×D4—68no—
534C2×D4—62no—
535C2×D4—124no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—28no—
539C22×C4—24no—
540C22×C4—34no—
541C22×C4—32no—
542C22×C4—38no—
543C22×C4—34no—
544C22×C4—32no—
545C22×C4—32no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—64no—
549C22×C4—64no—
550C22×C4—64no—
551C22×C4—64no—
552C22×C4—64no—
553C22×C4—64no—
554C22×C4—122no—
555C22×C4—122no—
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—24no—
572C4⋊C4—22no—
573C4⋊C4—24no—
574C4⋊C4—38no—
575C4⋊C4—68no—
576C4⋊C4—68no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C4⋊C4—64no—
580C4⋊C4—62no—
581C4⋊C4—62no—
582C4⋊C4—124no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—24no—
587C22⋊C4—24no—
588C22⋊C4—68no—
589C22⋊C4—68no—
590C22⋊C4—68no—
591C22⋊C4—68no—
592C22⋊C4—68no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—124no—
597C22⋊C4—124no—
598C42—24no—
599C42—68no—
600C42—68no—
601C42—64no—
602C42—64no—
603C42—64no—
604C42—122no—
605C42—122no—
606C42C2×#6714yes—
607C42C2×#6714yes—
608C42C2×#6714yes—
609C42C2×#6714yes—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—22no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3C23×D411yescharacteristic
621C22×C3C22×#4112yes—
622C22×C3C22×#4112yes—
623C22×C3#58511yescharacteristic
624C22×C3#58511yescharacteristic
625C2×D3—24no—
626C2×D3—24no—
627C2×D3—24no—
628C2×D3—42no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—42no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4#52514yes—
640C3×C4#53214yes—
641Dic3—24no—
642Dic3—28no—
643Dic3—42no—
644Dic3—42no—
645Dic3—44no—
646C23—22no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—34no—
656C23—62no—
657C23—62no—
658C23—62no—
659C23—62no—
660C23—62no—
661C23—62no—
662C23C22×#6712yes—
663C23C24×D311yescharacteristic
664Q8—44no—
665Q8—68no—
666D4—48no—
667D4—44no—
668D4—68no—
669D4—616no—
670D4—1216no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—38no—
687C2×C4—34no—
688C2×C4—44no—
689C2×C4—48no—
690C2×C4—64no—
691C2×C4—62no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—616no—
695C2×C4—64no—
696C2×C4—64no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—64no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—128no—
705C2×C4—128no—
706C2×C4D3×#4114yes—
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—82no—
716C2×C3C2×#52511yescharacteristic
717C2×C3C2×#53211yescharacteristic
718C2×C3#344911yescharacteristic
719C2×C3#347512yes—
720C2×C3#348012yes—
721D3—44no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—42no—
726C22—42no—
727C22—44no—
728C22—44no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—64no—
733C22—64no—
734C22—64no—
735C22—122no—
736C22—122no—
737C22—122no—
738C22—122no—
739C22C2×D3×#4112yes—
740C22C2×D3×#4112yes—
741C22#596411yescharacteristic
742C22#596411yescharacteristic
743C22C23×#6711yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—68no—
752C4—64no—
753C4—124no—
754C4—122no—
755C4—122no—
756C4#582814yes—
757C4#583214yes—
758C3#3491111yescharacteristic, complemented, Sylow
759C2—42no—
760C2—82no—
761C2—124no—
762C2#8615112yes—
763C2#8615212yes—
764C2C2×#583211yescharacteristic
765C2C2×#582811yescharacteristic
766C2#8726811yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutator, socle, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#529C2
hypercenterC2×#529D3
hypocenterC3#34911
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. C2×C4×#235C2semidirect
3. #83088C2semidirect
4. #83087C2semidirect
5. #83063C2semidirect
6. #83041C2semidirect
7. #82998C2semidirect
8. #82976C2semidirect
9. #82902C2semidirect
10. #82814C2semidirect
11. #82704C2semidirect
12. C4×#946C2semidirect
13. #82400C2semidirect
14. C4×#938C2semidirect
15. #82346C2semidirect
16. #82225C2semidirect
17. C4×#926C2semidirect
86. C2×#529D3semidirect
140. C2×C3×C42D4semidirect
343. C4⋊Dic3#41semidirect
432. 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×#5292
C2×C4×#2352
#830882
#830872
#830632
#830412
#829982
#829762
#829022
#828142
#827042
C4×#9462
#824002
C4×#9382
#823462
#822252
C4×#9262
#349113