Finite Group Databasebeta

← #10966658

Subgroups — #10966658

Order 768.

2726 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#41C211yesmaximal, characteristic, complemented
2C2×C4×#235C211yesmaximal, characteristic, complemented
3#84095C212yesmaximal, complemented
4#82502C212yesmaximal, complemented
5#82501C211yesmaximal, characteristic, complemented
6#82480C211yesmaximal, characteristic, complemented
7#82419C214yesmaximal, complemented
8#82418C212yesmaximal, complemented
9#82415C211yesmaximal, characteristic, complemented
10#82402C212yesmaximal, complemented
11#82375C211yesmaximal, characteristic, complemented
12#82372C212yesmaximal, complemented
13#82274C212yesmaximal, complemented
14#82268C214yesmaximal, complemented
15C4×#924C212yesmaximal, complemented
16C4×#930C212yesmaximal, complemented
17#82060C211yesmaximal, characteristic, complemented
18#34909—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C3×C4×#41—28no—
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×D4C2212yes—
25C2×C3×C4×D4C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2212yes—
28C2×C3×#117C2212yes—
29C2×C3×#117C2211yescharacteristic
30C22×C3×C42C2212yes—
31C22×C3×C42C2211yescharacteristic
32C2×#930C2212yes—
33C2×C4×#67C2214yes—
34C2×C4×#67C2212yes—
35C2×C4×#67C2212yes—
36C2×#926C2211yescharacteristic
37C2×#924C2212yes—
38C4×#235—28no—
39C2×C4×D12C2211yescharacteristic
40C2×C4×D12C2211yescharacteristic
41C2×#872C2212yes—
42C2×C42×D3C2212yes—
43C2×C4×Dic6C2211yescharacteristic
44C2×C4×Dic6C2211yescharacteristic
45#5231C2212yes—
46#5230C2212yes—
47#5223C2214yes—
48#5223C2212yes—
49#5222C2214yes—
50#5222C2212yes—
51#5213C2214yes—
52#5212C2212yes—
53#5212C2212yes—
54#5212C2212yes—
55#5211C2212yes—
56#5210C2214yes—
57C4×#217C2214yes—
58C4×#217C2212yes—
59#4993C2212yes—
60#4992C2212yes—
61#4989C2214yes—
62#4989C2214yes—
63#4985C2212yes—
64#4983C2212yes—
65#4978C2214yes—
66#4978C2214yes—
67#4959C2214yes—
68#4956C2214yes—
69#4956C2214yes—
70#4952C2214yes—
71#4944C2214yes—
72#4944C2214yes—
73#4940C2214yes—
74#4939C2212yes—
75C4×(C2×D3)⋊C4C2214yes—
76#4937C2212yes—
77#4936C2211yescharacteristic
78#4936C2211yescharacteristic
79C4×C4⋊Dic3C2212yes—
80#4933C2214yes—
81#4932C2212yes—
82C4×Dic3⋊C4C2214yes—
83#4929C2212yes—
84#4928C2212yes—
85#4928C2212yes—
86C2×C4×#41—31no—
87C2×C4×#41D311yescharacteristic, complemented
88#2600—34no—
89#2599—32no—
90#2598—32no—
91#2581—31no—
92#2580—31no—
93#2536—31no—
94#2535—31no—
95#2485—32no—
96#2407—32no—
97#2395—32no—
98#2388—32no—
99C4×C22⋊Q8—32no—
100C4×#121—32no—
101#2290—34no—
102#2283—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×#67C2312yes—
115C22×#67C2314yes—
116C2×#235—24no—
117C2×#235—24no—
118C2×#235—24no—
119C22×D12C2311yescharacteristic
120C22×C4×D3C2312yes—
121C22×C4×D3C2312yes—
122C22×C4×D3C2312yes—
123C22×Dic6C2311yescharacteristic
124C3×C4×Q8—24no—
125C3×C4×Q8—24no—
126C3×C4×D4—28no—
127C3×C4×D4—28no—
128C3×C4×D4—24no—
129C3×C4×D4—24no—
130C3×#117—24no—
131C3×#117—28no—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2312yes—
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C22⋊C4C2312yes—
139C2×C3×C42—28no—
140C2×C3×C42D418yescomplemented
141C2×C3×C42C2312yes—
142C2×C3×C42C2312yes—
143C2×C3×C42C2312yes—
144C2×C3×C42C2311yescharacteristic
145C2×C3×C42C2311yescharacteristic
146C2×C3×C42C2311yescharacteristic
147C2×C3×C42C2311yescharacteristic
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2312yes—
151C2×#217C2314yes—
152C2×#217C2314yes—
153#930—28no—
154C4×#67—28no—
155C4×#67—28no—
156C4×#67—216no—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2312yes—
161C2×(C2×D3)⋊C4C2314yes—
162#926—24no—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2312yes—
166C2×C4⋊Dic3C2312yes—
167#924—28no—
168C2×Dic3⋊C4C2314yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2312yes—
171C2×Dic3⋊C4C2312yes—
172C2×Dic3⋊C4C2314yes—
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2314yes—
175C2×C4×Dic3C2312yes—
176C2×C4×Dic3C2312yes—
177C4×D12—24no—
178C4×D12—24no—
179#872—28no—
180C42×D3—28no—
181C4×Dic6—24no—
182C4×Dic6—24no—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2312yes—
189C3⋊#95C2312yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2312yes—
193C3⋊#95C2312yes—
194C3⋊#95C2314yes—
195C22×#41—31no—
196C22×#41C2×D311yescharacteristic
197C2×C22⋊Q8—32no—
198C2×#121—32no—
199C4×#41—28no—
200C4×#41—68no—
201C2×C4×Q8—31no—
202C2×C4×Q8—31no—
203C2×C4×Q8C2×D311yescharacteristic
204C2×C4×Q8C2×D311yescharacteristic
205C2×C4×D4—32no—
206C2×C4×D4—32no—
207C2×C4×D4—34no—
208C2×C4×D4—31no—
209C2×C4×D4—31no—
210C2×C4×D4C2×D311yescharacteristic
211C2×C4×D4C2×D312yes—
212C2×C4×D4C2×D312yes—
213C2×C4×D4C2×D311yescharacteristic
214C2×#117—31no—
215C2×#117—32no—
216C2×#117C2×D311yescharacteristic
217C2×#117C2×D312yes—
218C22×C42—32no—
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—32no—
232#392—34no—
233#391—32no—
234#390—32no—
235#389—32no—
236#389—32no—
237#388—34no—
238#388—34no—
239#388—34no—
240#387—34no—
241#387—34no—
242#387—34no—
243#386—34no—
244#386—34no—
245#386—34no—
246#385—34no—
247#385—34no—
248#385—34no—
249#383—32no—
250#382—31no—
251#382—31no—
252#381—32no—
253#380—32no—
254#380—32no—
255#380—32no—
256C4×C4⋊C4—34no—
257C4×C4⋊C4—32no—
258C4×C22⋊C4—32no—
259C4×C22⋊C4—34no—
260C4×C22⋊C4—34no—
261#376—32no—
262C24×C3C2411yescharacteristic
263C24×C3C2412yes—
264C23×D3C2412yes—
265C3×#41—232no—
266C2×C3×Q8—22no—
267C2×C3×Q8—24no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—24no—
271C2×C3×D4—22no—
272C2×C3×D4—24no—
273C22×C3×C4—24no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—24no—
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4—24no—
282C22×C3×C4—42no—
283C22×C3×C4—42no—
284C22×C3×C4—42no—
285C22×C3×C4C2×D414yes—
286C22×C3×C4C2×D414yes—
287C22×C3×C4C2×D414yes—
288C22×C3×C4#4118yescomplemented
289C22×C3×C4C2412yes—
290C22×C3×C4C2412yes—
291C22×C3×C4C2411yescharacteristic
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2411yescharacteristic
294C22×C3×C4C2411yescharacteristic
295C22×C3×C4C2412yes—
296C22×C3×C4C2411yescharacteristic
297C22×C3×C4C2411yescharacteristic
298C2×#67—24no—
299C2×#67—24no—
300C2×#67—28no—
301C2×#67—28no—
302C2×#67—24no—
303C2×#67—44no—
304C22×Dic3C2414yes—
305C22×Dic3C2414yes—
306C22×Dic3C2412yes—
307C22×Dic3C2412yes—
308C22×Dic3C2412yes—
309#235—232no—
310C2×D12—22no—
311C2×D12—22no—
312C2×D12#4114yescomplemented
313C2×C4×D3—24no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—24no—
317C2×C4×D3—24no—
318C2×C4×D3—28no—
319C2×C4×D3—44no—
320C2×Dic6—22no—
321C2×Dic6—22no—
322C2×Dic6#4114yescomplemented
323C3×C4⋊C4—24no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—22no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—24no—
330C3×C42—24no—
331C3×C42—24no—
332C3×C42—24no—
333C3×C42C2×D414yes—
334C3×C42C2×D414yes—
335C3×C42C2×D414yes—
336C3×C42C2×D414yes—
337#217—24no—
338#217—28no—
339#217—28no—
340#217—44no—
341#217—44no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—44no—
347C4⋊Dic3—22no—
348C4⋊Dic3—22no—
349C4⋊Dic3—24no—
350C4⋊Dic3—24no—
351Dic3⋊C4—24no—
352Dic3⋊C4—24no—
353Dic3⋊C4—28no—
354Dic3⋊C4—28no—
355Dic3⋊C4—44no—
356C4×Dic3—24no—
357C4×Dic3—24no—
358C4×Dic3—24no—
359C4×Dic3—28no—
360C2×#41—28no—
361C2×#41—24no—
362C2×#41—64no—
363C2×#41—64no—
364C2×#41—64no—
365C22×Q8—31no—
366C22×Q8C22×D311yescharacteristic
367C22×D4—32no—
368C22×D4—34no—
369C22×D4—31no—
370C22×D4C22×D312yes—
371C22×D4C22×D311yescharacteristic
372C23×C4—32no—
373C23×C4—32no—
374C23×C4—32no—
375C23×C4C22×D312yes—
376C23×C4C22×D312yes—
377C23×C4C22×D311yescharacteristic
378C23×C4C22×D311yescharacteristic
379C23×C4C22×D312yes—
380C23×C4C22×D311yescharacteristic
381C22⋊Q8—68no—
382#121—68no—
383C4×Q8—24no—
384C4×Q8—24no—
385C4×Q8—64no—
386C4×Q8—64no—
387C4×D4—28no—
388C4×D4—28no—
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—616no—
392C4×D4—68no—
393C4×D4—68no—
394C4×D4—64no—
395C4×D4—64no—
396#117—24no—
397#117—28no—
398#117—64no—
399#117—68no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—32no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4C22×D312yes—
410C2×C4⋊C4C22×D312yes—
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D311yescharacteristic
413C2×C22⋊C4—32no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4C22×D312yes—
424C2×C22⋊C4C22×D312yes—
425C2×C22⋊C4C22×D312yes—
426C2×C42—28no—
427C2×C42—32no—
428C2×C42—32no—
429C2×C42—32no—
430C2×C42—34no—
431C2×C42—68no—
432C2×C42#6718yescomplemented
433C2×C42C22×D312yes—
434C2×C42C22×D312yes—
435C2×C42C22×D312yes—
436C2×C42C22×D311yescharacteristic
437C2×C42C22×D311yescharacteristic
438C2×C42C22×D311yescharacteristic
439C2×C42C22×D311yescharacteristic
440#95—34no—
441#95—32no—
442#95—32no—
443#95—34no—
444#95—32no—
445#95—32no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3C22×D412yes—
463C23×C3C2×#4114yes—
464C23×C3C2511yescharacteristic
465C22×D3—22no—
466C22×D3—24no—
467C22×D3—22no—
468C22×D3—24no—
469C22×D3C2×#4114yes—
470C3×Q8—28no—
471C3×D4—28no—
472C3×D4—216no—
473C2×C3×C4—22no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—28no—
481C2×C3×C4—28no—
482C2×C3×C4—216no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—44no—
490C2×C3×C4—48no—
491C2×C3×C4—48no—
492C2×C3×C4C22×D412yes—
493C2×C3×C4C22×D412yes—
494C2×C3×C4C22×D412yes—
495C2×C3×C4C22×D412yes—
496C2×C3×C4C22×D412yes—
497C2×C3×C4C22×D412yes—
498C2×C3×C4C2×#4114yes—
499C2×C3×C4C2×#4114yes—
500C2×C3×C4C2×#4112yes—
501C2×C3×C4C2×#4112yes—
502#67—216no—
503#67—416no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—24no—
509C2×Dic3—24no—
510C2×Dic3—24no—
511C2×Dic3—24no—
512C2×Dic3—24no—
513C2×Dic3—24no—
514C2×Dic3—24no—
515C2×Dic3—24no—
516C2×Dic3C2×#4114yes—
517D12—28no—
518C4×D3—216no—
519C4×D3—48no—
520C4×D3—48no—
521Dic6—28no—
522C24—32no—
523C24C23×D312yes—
524C24C23×D311yescharacteristic
525#41—232no—
526#41—632no—
527C2×Q8—24no—
528C2×Q8—22no—
529C2×Q8—34no—
530C2×Q8—62no—
531C2×Q8—62no—
532C2×D4—24no—
533C2×D4—24no—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—22no—
537C2×D4—34no—
538C2×D4—64no—
539C2×D4—64no—
540C2×D4—64no—
541C2×D4—68no—
542C2×D4—68no—
543C2×D4—62no—
544C2×D4—62no—
545C2×D4—124no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—32no—
556C22×C4—34no—
557C22×C4—34no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—64no—
564C22×C4—64no—
565C22×C4—64no—
566C22×C4—68no—
567C22×C4—64no—
568C22×C4—64no—
569C22×C4—124no—
570C22×C4#23518yescomplemented
571C22×C4C2×#6714yes—
572C22×C4C2×#6714yes—
573C22×C4C2×#6714yes—
574C22×C4C23×D312yes—
575C22×C4C23×D312yes—
576C22×C4C23×D312yes—
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C22×C4C23×D311yescharacteristic
580C22×C4C23×D311yescharacteristic
581C22×C4C23×D311yescharacteristic
582C22×C4C23×D311yescharacteristic
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—68no—
588C4⋊C4—68no—
589C4⋊C4—64no—
590C4⋊C4—64no—
591C4⋊C4—64no—
592C4⋊C4—64no—
593C4⋊C4—62no—
594C4⋊C4—62no—
595C4⋊C4—124no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—68no—
600C22⋊C4—68no—
601C22⋊C4—68no—
602C22⋊C4—64no—
603C22⋊C4—68no—
604C22⋊C4—64no—
605C22⋊C4—64no—
606C22⋊C4—124no—
607C22⋊C4—124no—
608C22⋊C4—124no—
609C42—24no—
610C42—24no—
611C42—24no—
612C42—68no—
613C42—64no—
614C42—64no—
615C42—64no—
616C42C2×#6714yes—
617C42C2×#6714yes—
618C42C2×#6714yes—
619C42C2×#6714yes—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—24no—
623C22×C3—22no—
624C22×C3—24no—
625C22×C3—24no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3C23×D411yescharacteristic
633C22×C3C22×#4112yes—
634C22×C3C22×#4111yescharacteristic
635C22×C3C22×#4111yescharacteristic
636C22×C3#58512yes—
637C2×D3—24no—
638C2×D3—28no—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—44no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—24no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4#52514yes—
650C3×C4#52514yes—
651Dic3—24no—
652Dic3—42no—
653Dic3—42no—
654Dic3—44no—
655Dic3—44no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—34no—
667C23—64no—
668C23—62no—
669C23—64no—
670C23—62no—
671C23C2×#23514yes—
672C23C22×#6712yes—
673C23C24×D311yescharacteristic
674Q8—28no—
675Q8—68no—
676D4—216no—
677D4—28no—
678D4—616no—
679D4—68no—
680D4—1216no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—216no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—34no—
698C2×C4—44no—
699C2×C4—48no—
700C2×C4—48no—
701C2×C4—616no—
702C2×C4—62no—
703C2×C4—62no—
704C2×C4—64no—
705C2×C4—64no—
706C2×C4—64no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—64no—
711C2×C4—64no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—128no—
715C2×C4—128no—
716C2×C4C2×#23514yes—
717C2×C4C2×#23514yes—
718C2×C4D3×#4112yes—
719C2×C4D3×#4112yes—
720C2×C4C22×#6712yes—
721C2×C4C22×#6712yes—
722C2×C4C22×#6712yes—
723C2×C4C22×#6712yes—
724C2×C4C22×#6712yes—
725C2×C4C22×#6712yes—
726C2×C3—42no—
727C2×C3—44no—
728C2×C3C2×#52511yescharacteristic
729C2×C3C2×#52511yescharacteristic
730C2×C3#344911yescharacteristic
731C2×C3#347512yes—
732C2×C3#348012yes—
733D3—44no—
734C22—24no—
735C22—24no—
736C22—24no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—68no—
747C22—64no—
748C22—124no—
749C22—122no—
750C22—122no—
751C22C22×#23512yes—
752C22C2×D3×#4111yescharacteristic
753C22C2×D3×#4111yescharacteristic
754C22#596412yes—
755C22C23×#6711yescharacteristic
756C4—24no—
757C4—22no—
758C4—22no—
759C4—22no—
760C4—22no—
761C4—42no—
762C4—42no—
763C4—64no—
764C4—124no—
765C4—124no—
766C4—122no—
767C4—122no—
768C4#579114yes—
769C4#582814yes—
770C3#3490911yescharacteristic, complemented, Sylow
771C2—44no—
772C2—42no—
773C2—124no—
774C2#8582512yes—
775C2#8584012yes—
776C2C2×#579111yescharacteristic
777C2C2×#582811yescharacteristic
778C2#8726811yescharacteristic
subgroupG/H
centerC22×C4C23×D3
commutator, socle, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×C4×#41C2
hypercenterC2×C4×#41D3
hypocenterC3#34909
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×C4×#235C2semidirect
3. #84095C2semidirect
4. #82502C2semidirect
5. #82501C2semidirect
6. #82480C2semidirect
7. #82419C2semidirect
8. #82418C2semidirect
9. #82415C2semidirect
10. #82402C2semidirect
11. #82375C2semidirect
12. #82372C2semidirect
13. #82274C2semidirect
14. #82268C2semidirect
15. C4×#924C2semidirect
16. C4×#930C2semidirect
17. #82060C2semidirect
87. C2×C4×#41D3semidirect
140. C2×C3×C42D4semidirect
288. C22×C3×C4#41semidirect
312. C2×D12#41semidirect
322. C2×Dic6#41semidirect
432. C2×C42#67semidirect
570. C22×C4#235semidirect
770. C3#34909semidirect

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×C4×#2352
#840952
#825022
#825012
#824802
#824192
#824182
#824152
#824022
#823752
#823722
#822742
#822682
C4×#9242
C4×#9302
#820602
#349093