Finite Group Databasebeta

← C2×#75631 #10965760

Subgroups — C2×#75631 #10965760

Order 768.

2442 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×#388C211yesmaximal, characteristic, complemented
2C2×#4990C211yesmaximal, characteristic, complemented
3C2×#4980C211yesmaximal, characteristic, complemented
4C2×#4959C211yesmaximal, characteristic
5C2×#4956C211yesmaximal, characteristic
6C2×#4953C211yesmaximal, characteristic, complemented
7C2×#4957C211yesmaximal, characteristic
8C2×#4945C211yesmaximal, characteristic, complemented
9C2×#4951C211yesmaximal, characteristic, complemented
10C2×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#75631C2116yesmaximal, direct product factor
13C2×#4668C211yesmaximal, characteristic, complemented
14C2×#4658C211yesmaximal, characteristic, complemented
15C2×#4674C211yesmaximal, characteristic, complemented
16C2×#4655C211yesmaximal, characteristic, complemented
17C2×#2595—31nomaximal, Sylow
18C23×#67C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×C4⋊Dic3C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×Dic3⋊C4C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C22×C4×Dic3C2211yescharacteristic
41C3×#388C2218yescomplemented
42C2×C3×#95C2211yescharacteristic
43C2×C3×#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54#4990C2218yescomplemented
55#4980C2218yescomplemented
56#4959C2218yes—
57#4957C2218yes—
58#4956C2218yes—
59#4953C2218yescomplemented
60#4951C2218yescomplemented
61#4945C2218yescomplemented
62C4×(C2×D3)⋊C4C2218yescomplemented
63C4×Dic3⋊C4C2218yescomplemented
64#4674C2218yescomplemented
65#4668C2218yescomplemented
66#4658C2218yescomplemented
67#4655C2218yescomplemented
68#2595—316no—
69C2×#400—31no—
70C2×#397—31no—
71C2×#397—31no—
72C2×#394—31no—
73C2×#390—31no—
74C2×#388—31no—
75C2×#388—31no—
76C2×#388—31no—
77C2×#388D311yescharacteristic, complemented
78C2×#387—31no—
79C2×#387—31no—
80C2×#386—31no—
81C2×#385—31no—
82C2×C4×C4⋊C4—31no—
83C2×C4×C22⋊C4—31no—
84C25×C3C2311yescharacteristic
85C24×D3C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C22×#67—24no—
93C22×#67—24no—
94C22×#67—42no—
95C22×#67C2314yes—
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2311yescharacteristic
102C23×Dic3C2311yescharacteristic
103C22×C4×D3—24no—
104C22×C4×D3—42no—
105C22×C4×D3—42no—
106C22×C4×D3C2314yes—
107C2×C3×C4⋊C4—24no—
108C2×C3×C4⋊C4C2314yes—
109C2×C3×C22⋊C4—24no—
110C2×C3×C22⋊C4—24no—
111C2×C3×C22⋊C4—42no—
112C2×C3×C22⋊C4C2314yes—
113C2×C3×C22⋊C4C2314yes—
114C2×C3×C22⋊C4C2314yes—
115C2×C3×C42—42no—
116C2×C3×C42C2314yes—
117C2×#217—24no—
118C2×#217—42no—
119C2×#217—42no—
120C2×#217C2314yes—
121C2×#217C2314yes—
122C2×#217C2314yes—
123C2×(C2×D3)⋊C4—24no—
124C2×(C2×D3)⋊C4—24no—
125C2×(C2×D3)⋊C4—24no—
126C2×(C2×D3)⋊C4—24no—
127C2×(C2×D3)⋊C4—42no—
128C2×(C2×D3)⋊C4C2314yes—
129C2×(C2×D3)⋊C4C2314yes—
130C2×(C2×D3)⋊C4C2314yes—
131C2×(C2×D3)⋊C4C2314yes—
132C2×(C2×D3)⋊C4C2314yes—
133C2×C4⋊Dic3—42no—
134C2×C4⋊Dic3—42no—
135C2×C4⋊Dic3C2314yes—
136C2×C4⋊Dic3C2314yes—
137C2×Dic3⋊C4—24no—
138C2×Dic3⋊C4—24no—
139C2×Dic3⋊C4—24no—
140C2×Dic3⋊C4C2314yes—
141C2×Dic3⋊C4C2314yes—
142C2×Dic3⋊C4C2314yes—
143C2×C4×Dic3—24no—
144C2×C4×Dic3—42no—
145C2×C4×Dic3—42no—
146C2×C4×Dic3C2314yes—
147C2×C4×Dic3C2314yes—
148C2×C4×Dic3C2314yes—
149C3×#95C2314yes—
150C3×#95C2314yes—
151C3⋊#95C2314yes—
152C3⋊#95C2314yes—
153C3⋊#95C2314yes—
154C3⋊#95C2314yes—
155C3⋊#95C2314yes—
156C3⋊#95C2314yes—
157C3⋊#95C2314yes—
158C3⋊#95C2314yes—
159C3⋊#95C2314yes—
160C3⋊#95C2314yes—
161C23×D4—31no—
162C24×C4—31no—
163C22×C4⋊C4—31no—
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4C2×D311yescharacteristic
169C22×C22⋊C4—31no—
170C22×C22⋊C4—31no—
171C22×C22⋊C4—31no—
172C22×C22⋊C4—31no—
173C22×C22⋊C4—31no—
174C22×C22⋊C4—31no—
175C22×C22⋊C4—31no—
176C22×C22⋊C4—31no—
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C22⋊C4C2×D311yescharacteristic
180C22×C42—31no—
181C22×C42—31no—
182C22×C42—31no—
183C22×C42C2×D311yescharacteristic
184#400—38no—
185#397—38no—
186#397—38no—
187#394—38no—
188#390—38no—
189#388—38no—
190#388—38no—
191#388—38no—
192#388C2×D318yescomplemented
193#387—38no—
194#387—38no—
195#386—38no—
196#385—38no—
197C4×C4⋊C4—38no—
198C4×C22⋊C4—38no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C24×C3—22no—
212C24×C3—22no—
213C24×C3—22no—
214C24×C3—22no—
215C24×C3—22no—
216C24×C3—22no—
217C24×C3—22no—
218C24×C3C2412yes—
219C24×C3C2411yescharacteristic
220C23×D3—22no—
221C23×D3—22no—
222C23×D3—22no—
223C23×D3—22no—
224C23×D3—22no—
225C23×D3—22no—
226C23×D3#4114yes—
227C23×D3C2412yes—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—22no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4#4114yes—
245C22×C3×C4#4114yes—
246C22×C3×C4C2412yes—
247C22×C3×C4C2412yes—
248C22×C3×C4C2412yes—
249C22×C3×C4C2412yes—
250C22×C3×C4C2412yes—
251C22×C3×C4C2412yes—
252C2×#67—28no—
253C2×#67—28no—
254C2×#67—44no—
255C2×#67—416no—
256C22×Dic3—22no—
257C22×Dic3—22no—
258C22×Dic3—22no—
259C22×Dic3—22no—
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—22no—
266C22×Dic3—22no—
267C22×Dic3—22no—
268C22×Dic3—22no—
269C22×Dic3—22no—
270C22×Dic3—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3#4114yes—
276C22×Dic3#4114yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C22×Dic3C2412yes—
281C22×Dic3C2412yes—
282C22×Dic3C2412yes—
283C22×Dic3C2412yes—
284C2×C4×D3—28no—
285C2×C4×D3—44no—
286C2×C4×D3—44no—
287C2×C4×D3—416no—
288C3×C4⋊C4—28no—
289C3×C22⋊C4—28no—
290C3×C22⋊C4—28no—
291C3×C22⋊C4—44no—
292C3×C42—44no—
293#217—28no—
294#217—44no—
295#217—44no—
296(C2×D3)⋊C4—28no—
297(C2×D3)⋊C4—28no—
298(C2×D3)⋊C4—28no—
299(C2×D3)⋊C4—28no—
300(C2×D3)⋊C4—44no—
301C4⋊Dic3—44no—
302C4⋊Dic3—44no—
303Dic3⋊C4—28no—
304Dic3⋊C4—28no—
305Dic3⋊C4—28no—
306C4×Dic3—28no—
307C4×Dic3—44no—
308C4×Dic3—44no—
309C25—31no—
310C25C22×D311yescharacteristic
311C22×D4—34no—
312C22×D4—64no—
313C22×D4—64no—
314C22×D4—122no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—34no—
323C23×C4—64no—
324C23×C4—122no—
325C23×C4—122no—
326C23×C4C22×D311yescharacteristic
327C23×C4C22×D311yescharacteristic
328C23×C4C22×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C2×C4⋊C4—24no—
333C2×C4⋊C4—34no—
334C2×C4⋊C4—34no—
335C2×C4⋊C4—34no—
336C2×C4⋊C4—34no—
337C2×C4⋊C4—34no—
338C2×C4⋊C4—64no—
339C2×C4⋊C4—64no—
340C2×C4⋊C4—64no—
341C2×C4⋊C4—122no—
342C2×C4⋊C4—122no—
343C2×C4⋊C4C22×D314yes—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—34no—
347C2×C22⋊C4—34no—
348C2×C22⋊C4—34no—
349C2×C22⋊C4—34no—
350C2×C22⋊C4—34no—
351C2×C22⋊C4—34no—
352C2×C22⋊C4—34no—
353C2×C22⋊C4—34no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—64no—
356C2×C22⋊C4—64no—
357C2×C22⋊C4—64no—
358C2×C22⋊C4—64no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—122no—
361C2×C22⋊C4—122no—
362C2×C22⋊C4—122no—
363C2×C22⋊C4C22×D314yes—
364C2×C22⋊C4C22×D314yes—
365C2×C22⋊C4C22×D314yes—
366C2×C42—34no—
367C2×C42—34no—
368C2×C42—34no—
369C2×C42—42no—
370C2×C42—64no—
371C2×C42—122no—
372C2×C42—122no—
373C2×C42C22×D314yes—
374#95—34no—
375#95—34no—
376#95—34no—
377#95—34no—
378#95—34no—
379#95—34no—
380#95—34no—
381#95—34no—
382#95—34no—
383#95—34no—
384#95C22×D314yes—
385#95C22×D314yes—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3—44no—
399C23×C3—44no—
400C23×C3C2×#4112yes—
401C23×C3C2×#4112yes—
402C23×C3C2×#4112yes—
403C23×C3C2×#4112yes—
404C23×C3C2×#4112yes—
405C23×C3H(5,𝔽2)12yes—
406C23×C3H(5,𝔽2)12yes—
407C23×C3C2511yescharacteristic
408C22×D3—28no—
409C22×D3—28no—
410C22×D3—28no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—44no—
418C22×D3—44no—
419C22×D3—44no—
420C22×D3—44no—
421C22×D3C2×#4114yes—
422C2×C3×C4—28no—
423C2×C3×C4—28no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—44no—
441C2×C3×C4—44no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4C2×#4114yes—
445C2×C3×C4C2×#4114yes—
446#67—416no—
447C2×Dic3—28no—
448C2×Dic3—28no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—44no—
469C2×Dic3—44no—
470C2×Dic3—44no—
471C2×Dic3—44no—
472C2×Dic3—44no—
473C2×Dic3C2×#4114yes—
474C2×Dic3C2×#4114yes—
475C4×D3—416no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—34no—
484C24—32no—
485C24—62no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24C23×D312yes—
492C24C23×D311yescharacteristic
493C2×D4—68no—
494C2×D4—68no—
495C2×D4—124no—
496C2×D4—1216no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—34no—
514C22×C4—34no—
515C22×C4—32no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—32no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—62no—
527C22×C4—62no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—62no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—68no—
542C22×C4—124no—
543C22×C4—124no—
544C22×C4—1216no—
545C22×C4#23514yes—
546C22×C4#23714yes—
547C22×C4C23×D312yes—
548C22×C4C23×D312yes—
549C22×C4C23×D312yes—
550C22×C4C23×D312yes—
551C22×C4C23×D312yes—
552C22×C4C23×D312yes—
553C4⋊C4—28no—
554C4⋊C4—68no—
555C4⋊C4—68no—
556C4⋊C4—68no—
557C4⋊C4—124no—
558C4⋊C4—124no—
559C22⋊C4—28no—
560C22⋊C4—28no—
561C22⋊C4—44no—
562C22⋊C4—68no—
563C22⋊C4—68no—
564C22⋊C4—68no—
565C22⋊C4—68no—
566C22⋊C4—68no—
567C22⋊C4—124no—
568C22⋊C4—124no—
569C22⋊C4—124no—
570C42—44no—
571C42—68no—
572C42—124no—
573C42—124no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—88no—
582C22×C3#52914yes—
583C22×C3#52914yes—
584C22×C3#53814yes—
585C22×C3#55114yes—
586C22×C3#55314yes—
587C22×C3#55314yes—
588C22×C3#55914yes—
589C22×C3C22×#4111yescharacteristic
590C22×C3C22×#4111yescharacteristic
591C22×C3C22×#4111yescharacteristic
592C22×C3C22×#4111yescharacteristic
593C22×C3C22×#4111yescharacteristic
594C22×C3C2×H(5,𝔽2)11yescharacteristic
595C22×C3C2×H(5,𝔽2)11yescharacteristic
596C2×D3—24no—
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—416no—
600C2×D3—42no—
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—42no—
604C3×C4—24no—
605C3×C4—24no—
606C3×C4—42no—
607C3×C4—42no—
608C3×C4—42no—
609C3×C4—42no—
610Dic3—24no—
611Dic3—24no—
612Dic3—42no—
613Dic3—42no—
614Dic3—42no—
615Dic3—42no—
616Dic3—42no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—34no—
625C23—44no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—68no—
633C23—62no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—68no—
640C23—68no—
641C23—124no—
642C23—124no—
643C23—124no—
644C23—124no—
645C23C2×#23512yes—
646C23C2×#23712yes—
647C23#100412yes—
648C23D3×#4112yes—
649C23D3×#4112yes—
650C23D3×#4112yes—
651C23#100912yes—
652C23C24×D311yescharacteristic
653D4—1216no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—28no—
659C2×C4—28no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—34no—
673C2×C4—34no—
674C2×C4—44no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—68no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—68no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—62no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—62no—
698C2×C4—62no—
699C2×C4—1216no—
700C2×C4—124no—
701C2×C4—124no—
702C2×C4—124no—
703C2×C4—124no—
704C2×C4—124no—
705C2×C4C2×#23514yes—
706C2×C4C2×#23714yes—
707C2×C3—82no—
708C2×C3#259518yescomplemented
709C2×C3C2×#52911yescharacteristic
710C2×C3C2×#52911yescharacteristic
711C2×C3C2×#53811yescharacteristic
712C2×C3C2×#55111yescharacteristic
713C2×C3C2×#55311yescharacteristic
714C2×C3C2×#55311yescharacteristic
715C2×C3C2×#55911yescharacteristic
716D3—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—64no—
725C22—64no—
726C22—64no—
727C22—88no—
728C22—122no—
729C22—122no—
730C22—1216no—
731C22—122no—
732C22—122no—
733C22#552814yes—
734C22#555714yes—
735C22#556014yes—
736C22#560114yes—
737C22#565914yes—
738C22#568114yes—
739C22#570914yes—
740C22C22×#23511yescharacteristic
741C22C22×#23711yescharacteristic
742C22C2×#100411yescharacteristic
743C22C2×D3×#4111yescharacteristic
744C22C2×D3×#4111yescharacteristic
745C22C2×D3×#4111yescharacteristic
746C22C2×#100911yescharacteristic
747C4—24no—
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—64no—
754C4—64no—
755C4—122no—
756C4—122no—
757C4—122no—
758C4—122no—
759C4—122no—
760C3C2×#259511yescharacteristic, complemented, Sylow
761C2—82no—
762C2—124no—
763C2#7563118yesdirect product factor
764C2C2×#552811yescharacteristic
765C2C2×#555711yescharacteristic
766C2C2×#556011yescharacteristic
767C2C2×#560111yescharacteristic
768C2C2×#565911yescharacteristic
769C2C2×#568111yescharacteristic
770C2C2×#570911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#388C2
socleC24×C3C24
prime radicalC23×#67C22
hypercenterC2×#388D3
hypocenterC3C2×#2595
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#388C2semidirect
2. C2×#4990C2semidirect
3. C2×#4980C2semidirect
6. C2×#4953C2semidirect
8. C2×#4945C2semidirect
9. C2×#4951C2semidirect
10. C2×C4×Dic3⋊C4C2semidirect
11. C2×C4×(C2×D3)⋊C4C2semidirect
12. #75631C2direct (N × H)
13. C2×#4668C2semidirect
14. C2×#4658C2semidirect
15. C2×#4674C2semidirect
16. C2×#4655C2semidirect
41. C3×#388C22semidirect
54. #4990C22semidirect
55. #4980C22semidirect
59. #4953C22semidirect
60. #4951C22semidirect
61. #4945C22semidirect
62. C4×(C2×D3)⋊C4C22semidirect
63. C4×Dic3⋊C4C22semidirect
64. #4674C22semidirect
65. #4668C22semidirect
66. #4658C22semidirect
67. #4655C22semidirect
77. C2×#388D3semidirect
192. #388C2×D3semidirect
708. C2×C3#2595semidirect
760. C3C2×#2595semidirect
763. C2#75631direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3882
C2×#49902
C2×#49802
C2×#49592
C2×#49562
C2×#49532
C2×#49572
C2×#49452
C2×#49512
C2×C4×Dic3⋊C42
C2×C4×(C2×D3)⋊C42
#756312
C2×#46682
C2×#46582
C2×#46742
C2×#46552
C2×#25953