Finite Group Databasebeta

← #11857969

Subgroups — #11857969

Order 1152.

1623 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic, complemented
3C22×#3711C211yesmaximal, characteristic, complemented
4#10592932C211yesmaximal, characteristic, complemented
5C3×#5233C211yesmaximal, characteristic, complemented
6#10591557C212yesmaximal, complemented
7#10591550C212yesmaximal, complemented
8#10591421C212yesmaximal, complemented
9#10591414C212yesmaximal, complemented
10#10591084C211yesmaximal, characteristic, complemented
11#10591083C211yesmaximal, characteristic, complemented
12#84072—31nomaximal
13#78830—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C3×D3×#41—24no—
16C3×D3×#41C418yescomplemented
17C2×C3×#239C2211yescharacteristic
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#237—21no—
20C2×C3×#237C2211yescharacteristic
21C2×C3×D3×D4—21no—
22C2×C3×D3×D4C2211yescharacteristic
23C2×C3×#235—21no—
24C2×C3×#235C2211yescharacteristic
25C22×C3×C4×D3—21no—
26C22×C3×C4×D3C2211yescharacteristic
27#64135C2211yescharacteristic, complemented
28C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
29C3×#926C2211yescharacteristic, complemented
30C22×C3×C3⋊C8C2211yescharacteristic, complemented
31D3×#217—21no—
32#63955—21no—
33D3×C4⋊Dic3C2212yescomplemented
34C4×D3×Dic3—21no—
35#63855—21no—
36#63841C2212yes—
37C2×#3711—24no—
38C2×#3711C2212yes—
39C2×#3711C2212yescomplemented
40#63662C2212yescomplemented
41#63659C2212yescomplemented
42C3×#835C2212yescomplemented
43C3×#832C2212yescomplemented
44#63566C2212yescomplemented
45#63565C2212yescomplemented
46#63563C2212yescomplemented
47#63562C2212yescomplemented
48C22×C3×#41—31no—
49C2×D3×#41D311yescharacteristic
50C2×#926—31no—
51C22×#208—31no—
52C22×ΓL(1,𝔽25)—31no—
53D3×#117—31no—
54C3×#416—31no—
55#5233—31no—
56#5233—31no—
57#5233—31no—
58#5233—31no—
59#5233—61no—
60#5233D311yescharacteristic, complemented
61#5232—32no—
62#5232—32no—
63#5225—32no—
64#5215—32no—
65#5113—31no—
66#5002—31no—
67#4803—32no—
68#4802—32no—
69#4771—32no—
70#4770—32no—
71C23×C3×D3—21no—
72C23×C3×D3D411yescharacteristic
73C32×#41—22no—
74C32×#41C2×C414yescomplemented
75C2×C32×Q8C2311yescharacteristic
76C2×C32×D4—21no—
77C2×C32×D4C2311yescharacteristic
78C22×C32×C4—21no—
79C22×C32×C4C2311yescharacteristic
80C2×C3×#67—21no—
81C2×C3×#67—21no—
82C2×C3×#67—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3D411yescharacteristic
85C3×#239—22no—
86C3×#239C2×C414yes—
87C3×D3×Q8—22no—
88C3×D3×Q8C2×C414yescomplemented
89C3×#237—28no—
90C3×#237—22no—
91C3×#237C2×C414yes—
92C3×D3×D4—28no—
93C3×D3×D4—22no—
94C3×D3×D4C2×C414yescomplemented
95C3×#235—22no—
96C3×#235—28no—
97C3×#235C2×C414yescomplemented
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—28no—
104C2×C3×C4×D3C2×C414yes—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D414yes—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×D3×Dic3—22no—
113#3757—21no—
114C4⋊(C3⋊Dic3)C2312yes—
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)—22no—
117C2×C3⋊(C3⋊C8)C2312yes—
118C3×#217—21no—
119C3×C4⋊Dic3C2312yes—
120C3×C4×Dic3—21no—
121C2×C3×C3⋊C8—22no—
122C2×C3×C3⋊C8C2312yes—
123Dic3⋊Dic3—22no—
124(C2×D3)⋊Dic3—22no—
125Dic32—22no—
126#3711—24no—
127#3711—24no—
128#2896—91noSylow
129C2×C3×#41—21no—
130C2×C3×#41—38no—
131C2×C3×#41—31no—
132C2×C3×#41—31no—
133C2×C3×#41—31no—
134C2×C3×#41—61no—
135C2×C3×#41—61no—
136C2×C3×#41—64no—
137C2×C3×#41C2×D311yescharacteristic
138C2×C3×#41C2×D311yescharacteristic
139C22×C3×Q8—31no—
140C22×C3×D4—31no—
141C22×C3×D4—61no—
142C23×C3×C4—31no—
143C23×C3×C4—61no—
144D3×#41—24no—
145D3×#41Dic318yescomplemented
146C2×#239C2×D311yescharacteristic
147C2×D3×Q8C2×D311yescharacteristic
148C2×#237—21no—
149C2×#237C2×D311yescharacteristic
150C2×D3×D4—21no—
151C2×D3×D4C2×D311yescharacteristic
152C2×#235—21no—
153C2×#235C2×D311yescharacteristic
154C22×C4×D3—21no—
155C22×C4×D3C2×D311yescharacteristic
156C22×C3×C8—31no—
157C3×#117—31no—
158C2×#217—61no—
159#926—31no—
160#926—31no—
161#926—32no—
162#926—61no—
163#926—61no—
164#926—61no—
165#926C2×D311yescharacteristic, complemented
166C2×C4⋊Dic3—32no—
167C2×C4×Dic3—61no—
168C2×#208—32no—
169C2×#208—32no—
170C2×#208—64no—
171C22×C3⋊C8—31no—
172C22×C3⋊C8—31no—
173C22×C3⋊C8—61no—
174C22×C3⋊C8C2×D311yescharacteristic, complemented
175C2×ΓL(1,𝔽25)—32no—
176C2×ΓL(1,𝔽25)—32no—
177C2×ΓL(1,𝔽25)—64no—
178#892—32no—
179D3×C4⋊C4—32no—
180D3×C22⋊C4—61no—
181#877—61no—
182#872—61no—
183C42×D3—61no—
184C3×#103—32no—
185C3×#102—32no—
186#835—32no—
187#835—32no—
188#835—32no—
189#835—32no—
190#835—62no—
191#835C2×D312yescomplemented
192#832—32no—
193#832—32no—
194#832—32no—
195#832—32no—
196#832—62no—
197#832C2×D312yescomplemented
198#821—32no—
199#816—32no—
200#810—32no—
201#809—32no—
202C23×C32—21no—
203C23×C32C2×D411yescharacteristic
204C22×C3×D3—21no—
205C22×C3×D3—24no—
206C22×C3×D3—42no—
207C22×C3×D3—44no—
208C22×C3×D3C22⋊C414yes—
209C22×C3×D3C2×D411yescharacteristic
210C22×C3×D3C2×D411yescharacteristic
211C32×Q8—21no—
212C32×Q8C22×C412yes—
213C32×D4—24no—
214C32×D4—21no—
215C32×D4C22×C412yes—
216C2×C32×C4—21no—
217C2×C32×C4—24no—
218C2×C32×C4C22×C412yes—
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2×D412yes—
221C2×C32×C4C2411yescharacteristic
222C2×C3⋊Dic3—22no—
223C3×#67—24no—
224C3×#67—24no—
225C3×#67—24no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—24no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3C22⋊C414yes—
230C2×C3×Dic3C2×D411yescharacteristic
231C2×C3×Dic3C2×D411yescharacteristic
232C3×D12—24no—
233C3×D12—21no—
234C3×D12C22×C412yes—
235C3×C4×D3—24no—
236C3×C4×D3—24no—
237C3×C4×D3—24no—
238C3×C4×D3C22⋊C414yes—
239C3×C4×D3C22⋊C414yes—
240C3×C4×D3C22×C412yes—
241C3×C4×D3C22×C412yes—
242C3×C4×D3C2×D412yes—
243C3×C4×D3C2×D412yes—
244C3×Dic6—21no—
245C3×Dic6—24no—
246C3×Dic6C22×C412yes—
247D3×Dic3—44no—
248C3⋊(C3⋊C8)—22no—
249C3×C3⋊C8—22no—
250C22×#41—31no—
251C22×M16—91no—
252C2×#117—91no—
253#419—92no—
254#418—92no—
255#417—92no—
256#417—92no—
257#416—31no—
258#416—91no—
259#416—91no—
260#416—91no—
261C24×C3—31no—
262C24×C3—61no—
263C23×D3—21no—
264C23×D3#6711yescharacteristic
265C3×#41—22no—
266C3×#41—22no—
267C3×#41—24no—
268C3×#41—34no—
269C3×#41—34no—
270C3×#41—34no—
271C3×#41—42no—
272C3×#41—68no—
273C3×#41—68no—
274C3×#41—62no—
275C3×#41—62no—
276C3×#41—62no—
277C3×#41C4×D314yescomplemented
278C3×#41C2×Dic314yescomplemented
279C2×C3×Q8—21no—
280C2×C3×Q8—34no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×Q8—62no—
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×D4—21no—
287C2×C3×D4—21no—
288C2×C3×D4—21no—
289C2×C3×D4—34no—
290C2×C3×D4—31no—
291C2×C3×D4—41no—
292C2×C3×D4—61no—
293C2×C3×D4—62no—
294C2×C3×D4—61no—
295C2×C3×D4—68no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—34no—
305C22×C3×C4—34no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—41no—
311C22×C3×C4—61no—
312C22×C3×C4—68no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—21no—
321C22×Dic3—21no—
322C22×Dic3—62no—
323C22×Dic3#6711yescharacteristic
324#239—22no—
325#239C2×Dic314yes—
326D3×Q8—22no—
327D3×Q8C2×Dic314yescomplemented
328#237—28no—
329#237—22no—
330#237C2×Dic314yes—
331D3×D4—28no—
332D3×D4—22no—
333D3×D4C2×Dic314yescomplemented
334#235—22no—
335#235—28no—
336#235C2×Dic314yescomplemented
337C2×D12—21no—
338C2×D12C22×D311yescharacteristic
339C2×C4×D3—21no—
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3—28no—
343C2×C4×D3—62no—
344C2×C4×D3C2×Dic314yes—
345C2×C4×D3#6711yescharacteristic
346C2×C4×D3#6711yescharacteristic
347C2×C4×D3#6714yes—
348C2×C4×D3C22×D311yescharacteristic
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—21no—
351C2×Dic6C22×D311yescharacteristic
352C2×C3×C8—32no—
353C2×C3×C8—62no—
354C3×C4⋊C4—32no—
355C3×C22⋊C4—61no—
356C3×C42—61no—
357#217—21no—
358#217—62no—
359#217—61no—
360#217—61no—
361#217—121no—
362(C2×D3)⋊C4—62no—
363C4⋊Dic3—32no—
364C4⋊Dic3—32no—
365C4⋊Dic3—62no—
366C4⋊Dic3—62no—
367C4⋊Dic3C22×D312yes—
368Dic3⋊C4—62no—
369C4×Dic3—21no—
370C4×Dic3—62no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—62no—
374C4×Dic3—121no—
375#208—64no—
376#208—64no—
377C2×C3⋊C8—22no—
378C2×C3⋊C8—32no—
379C2×C3⋊C8—32no—
380C2×C3⋊C8—62no—
381C2×C3⋊C8—62no—
382C2×C3⋊C8—62no—
383C2×C3⋊C8—122no—
384C2×C3⋊C8C22×D312yes—
385ΓL(1,𝔽25)—64no—
386ΓL(1,𝔽25)—64no—
387C22×C32—22no—
388C22×C32—22no—
389C22×C32—42no—
390C22×C32C2×C22⋊C412yes—
391C22×C32C22×D411yescharacteristic
392C2×C3×D3—22no—
393C2×C3×D3—22no—
394C2×C3×D3—22no—
395C2×C3×D3—44no—
396C2×C3×D3—48no—
397C2×C3×D3—42no—
398C2×C3×D3C2×C22⋊C412yes—
399C2×C3×D3C2×C22⋊C412yes—
400C32×C4—22no—
401C32×C4C2×C22⋊C412yes—
402C32×C4C23×C411yescharacteristic
403C32×C4C22×D411yescharacteristic
404C3⋊Dic3—42no—
405C3×Dic3—22no—
406C3×Dic3—42no—
407C3×Dic3C2×C22⋊C412yes—
408C3×Dic3C2×C22⋊C412yes—
409C2×#41—38no—
410C2×#41—31no—
411C2×#41—31no—
412C2×#41—31no—
413C2×#41—61no—
414C2×#41—61no—
415C2×#41—64no—
416C2×#41D3211yescharacteristic
417C22×Q8—31no—
418C22×D4—31no—
419C22×D4—61no—
420C23×C4—31no—
421C23×C4—61no—
422C2×M16—92no—
423C2×M16—92no—
424C2×M16—184no—
425C22×C8—31no—
426C22×C8—91no—
427#117—31no—
428#117—92no—
429#117—91no—
430#117—181no—
431#117—181no—
432C2×C4⋊C4—92no—
433C2×C22⋊C4—181no—
434C2×C42—181no—
435#103—32no—
436#103—92no—
437#103—92no—
438#103—92no—
439#102—32no—
440#102—92no—
441#102—92no—
442#102—92no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—31no—
447C23×C3—31no—
448C23×C3—34no—
449C23×C3—41no—
450C23×C3—64no—
451C23×C3—61no—
452C23×C3—122no—
453C23×C3—124no—
454C23×C3D3×D411yescharacteristic
455C23×C3C2×#6711yescharacteristic
456C22×D3—21no—
457C22×D3—24no—
458C22×D3—42no—
459C22×D3—44no—
460C22×D3#21714yes—
461C22×D3C2×#6711yescharacteristic
462C22×D3C2×#6711yescharacteristic
463C3×Q8—21no—
464C3×Q8—21no—
465C3×Q8—22no—
466C3×Q8—32no—
467C3×Q8—41no—
468C3×Q8—64no—
469C3×Q8—61no—
470C3×Q8C2×C4×D312yes—
471C3×Q8C22×Dic312yes—
472C3×D4—24no—
473C3×D4—24no—
474C3×D4—21no—
475C3×D4—21no—
476C3×D4—22no—
477C3×D4—32no—
478C3×D4—41no—
479C3×D4—44no—
480C3×D4—64no—
481C3×D4—64no—
482C3×D4—64no—
483C3×D4—64no—
484C3×D4—61no—
485C3×D4C2×C4×D312yes—
486C3×D4C22×Dic312yes—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—24no—
490C2×C3×C4—24no—
491C2×C3×C4—21no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—34no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—34no—
499C2×C3×C4—34no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—32no—
504C2×C3×C4—44no—
505C2×C3×C4—41no—
506C2×C3×C4—64no—
507C2×C3×C4—64no—
508C2×C3×C4—64no—
509C2×C3×C4—61no—
510C2×C3×C4—64no—
511C2×C3×C4—62no—
512C2×C3×C4C2×C4×D312yes—
513C2×C3×C4D3×D412yes—
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C22×Dic312yes—
516C2×C3×C4C2×#6712yes—
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—24no—
521#67—24no—
522#67—24no—
523C2×Dic3—21no—
524C2×Dic3—24no—
525C2×Dic3—22no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—122no—
529C2×Dic3—124no—
530C2×Dic3#21714yes—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533D12—24no—
534D12—21no—
535D12C22×Dic312yes—
536C4×D3—24no—
537C4×D3—24no—
538C4×D3—24no—
539C4×D3—124no—
540C4×D3#21714yes—
541C4×D3#21714yes—
542C4×D3C22×Dic312yes—
543C4×D3C22×Dic312yes—
544C4×D3C2×#6712yes—
545C4×D3C2×#6712yes—
546Dic6—21no—
547Dic6—24no—
548Dic6C22×Dic312yes—
549C3×C8—62no—
550C3⋊C8—22no—
551C3⋊C8—62no—
552C3⋊C8—62no—
553C3⋊C8—122no—
554C2×C32—22no—
555C2×C32—42no—
556C2×C32C22×C22⋊C411yescharacteristic
557C2×C32#57512yes—
558C3×D3—22no—
559C3×D3—22no—
560C3×D3—42no—
561C24—31no—
562C24—61no—
563#41—22no—
564#41—34no—
565#41—34no—
566#41—34no—
567#41—68no—
568#41—68no—
569#41—62no—
570#41—62no—
571#41—62no—
572#41D3×Dic314yescomplemented
573C2×Q8—34no—
574C2×Q8—31no—
575C2×Q8—61no—
576C2×Q8—62no—
577C2×Q8C2×D3211yescharacteristic
578C2×D4—21no—
579C2×D4—34no—
580C2×D4—31no—
581C2×D4—61no—
582C2×D4—62no—
583C2×D4—61no—
584C2×D4—68no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4C2×D3211yescharacteristic
588C22×C4—21no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—34no—
593C22×C4—34no—
594C22×C4—31no—
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—68no—
598C22×C4—61no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—182no—
602C22×C4C2×D3211yescharacteristic
603M16—184no—
604M16—184no—
605C2×C8—32no—
606C2×C8—62no—
607C2×C8—92no—
608C2×C8—182no—
609C4⋊C4—32no—
610C4⋊C4—92no—
611C4⋊C4—182no—
612C22⋊C4—61no—
613C22⋊C4—182no—
614C22⋊C4—181no—
615C42—61no—
616C42—182no—
617C42—181no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—22no—
624C22×C3—32no—
625C22×C3—32no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—62no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—82no—
634C22×C3—124no—
635C22×C3—128no—
636C22×C3—122no—
637C22×C3D3×C22⋊C412yes—
638C22×C3C2×#21712yes—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×#6711yescharacteristic
641C2×D3—22no—
642C2×D3—22no—
643C2×D3—22no—
644C2×D3—44no—
645C2×D3—48no—
646C2×D3—42no—
647C2×D3C2×#21712yes—
648C2×D3C2×#21712yes—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—22no—
654C3×C4—32no—
655C3×C4—32no—
656C3×C4—42no—
657C3×C4—62no—
658C3×C4—122no—
659C3×C4D3×C22⋊C412yes—
660C3×C4C2×#21712yes—
661C3×C4C22×C4×D311yescharacteristic
662C3×C4C2×D3×D411yescharacteristic
663C3×C4C23×Dic311yescharacteristic
664C3×C4C22×#6711yescharacteristic
665Dic3—22no—
666Dic3—42no—
667Dic3—122no—
668Dic3—122no—
669Dic3—242no—
670Dic3C2×#21712yes—
671Dic3C2×#21712yes—
672C32#289611yescharacteristic, complemented, Sylow
673C23—21no—
674C23—31no—
675C23—31no—
676C23—34no—
677C23—64no—
678C23—61no—
679C23—122no—
680C23—124no—
681C23D3×#6711yescharacteristic
682Q8—21no—
683Q8—32no—
684Q8—64no—
685Q8—61no—
686Q8C2×D3×Dic312yes—
687D4—24no—
688D4—21no—
689D4—32no—
690D4—64no—
691D4—64no—
692D4—64no—
693D4—64no—
694D4—61no—
695D4C2×D3×Dic312yes—
696C2×C4—21no—
697C2×C4—24no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—34no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—34no—
706C2×C4—34no—
707C2×C4—64no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—61no—
711C2×C4—64no—
712C2×C4—62no—
713C2×C4—182no—
714C2×C4—364no—
715C2×C4C2×D3×Dic312yes—
716C2×C4D3×#6712yes—
717C2×C4D3×#6711yescharacteristic
718C2×C4C22×D3211yescharacteristic
719C8—62no—
720C8—182no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—42no—
726C2×C3—42no—
727C2×C3—42no—
728C2×C3—62no—
729C2×C3—62no—
730C2×C3—82no—
731C2×C3—122no—
732C2×C3C2×D3×C22⋊C411yescharacteristic
733C2×C3#576812yes—
734C2×C3#582212yes—
735C2×C3C22×#21711yescharacteristic
736D3—22no—
737D3—22no—
738D3—42no—
739C22—22no—
740C22—22no—
741C22—32no—
742C22—32no—
743C22—42no—
744C22—62no—
745C22—62no—
746C22—62no—
747C22—124no—
748C22—128no—
749C22—122no—
750C22D3×#21712yes—
751C22C2×D3×#6711yescharacteristic
752C4—22no—
753C4—32no—
754C4—32no—
755C4—62no—
756C4—122no—
757C4—362no—
758C4D3×#21712yes—
759C4C22×D3×Dic311yescharacteristic
760C4C2×D3×#6711yescharacteristic
761C3—21no—
762C3#7883011yescharacteristic, complemented
763C3#8407211yescharacteristic, complemented
764C2—22no—
765C2—42no—
766C2—62no—
767C2—62no—
768C2—122no—
769C2#1059545312yes—
770C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×#41C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. D3×#926C2semidirect
3. C22×#3711C2semidirect
4. #10592932C2semidirect
5. C3×#5233C2semidirect
6. #10591557C2semidirect
7. #10591550C2semidirect
8. #10591421C2semidirect
9. #10591414C2semidirect
10. #10591084C2semidirect
11. #10591083C2semidirect
16. C3×D3×#41C4semidirect
27. #64135C22semidirect
28. C22×C3⋊(C3⋊C8)C22semidirect
29. C3×#926C22semidirect
30. C22×C3×C3⋊C8C22semidirect
33. D3×C4⋊Dic3C22semidirect
39. C2×#3711C22semidirect
40. #63662C22semidirect
41. #63659C22semidirect
42. C3×#835C22semidirect
43. C3×#832C22semidirect
44. #63566C22semidirect
45. #63565C22semidirect
46. #63563C22semidirect
47. #63562C22semidirect
60. #5233D3semidirect
74. C32×#41C2×C4semidirect
88. C3×D3×Q8C2×C4semidirect
94. C3×D3×D4C2×C4semidirect
97. C3×#235C2×C4semidirect
145. D3×#41Dic3semidirect
165. #926C2×D3semidirect
174. C22×C3⋊C8C2×D3semidirect
191. #835C2×D3semidirect
197. #832C2×D3semidirect
277. C3×#41C4×D3semidirect
278. C3×#41C2×Dic3semidirect
327. D3×Q8C2×Dic3semidirect
333. D3×D4C2×Dic3semidirect
336. #235C2×Dic3semidirect
572. #41D3×Dic3semidirect
672. C32#2896semidirect
762. C3#78830semidirect
763. C3#84072semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
D3×#9262
C22×#37112
#105929322
C3×#52332
#105915572
#105915502
#105914212
#105914142
#105910842
#105910832
#840723
#788303