Finite Group Databasebeta

← C2×#74766 #10965641

Subgroups — C2×#74766 #10965641

Order 768.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#386C211yesmaximal, characteristic
2C2×#5222C211yesmaximal, characteristic
3C2×#5220C211yesmaximal, characteristic
4C2×#5210C211yesmaximal, characteristic, complemented
5C2×C4×#217C211yesmaximal, characteristic, complemented
6C2×#4952C211yesmaximal, characteristic, complemented
7C2×#4948C211yesmaximal, characteristic, complemented
8C2×#4945C211yesmaximal, characteristic, complemented
9C2×#4951C211yesmaximal, characteristic, complemented
10C2×#4943C211yesmaximal, characteristic, complemented
11C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
12#74766C2116yesmaximal, direct product factor
13C2×C3⋊#401C211yesmaximal, characteristic, complemented
14C2×#4654C211yesmaximal, characteristic, complemented
15C2×#4652C211yesmaximal, characteristic, complemented
16C2×#4650C211yesmaximal, characteristic, complemented
17C2×#2576—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C24×Dic3C2211yescharacteristic
21C22×C3×C22⋊C4C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2211yescharacteristic
26C22×#217C2211yescharacteristic
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×C4⋊Dic3C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×Dic3⋊C4C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×C4×Dic3C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C3×#386C2218yes—
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
42#5222C2218yes—
43#5220C2218yes—
44#5210C2218yescomplemented
45C4×#217C2218yescomplemented
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57C2×C3⋊#95C2211yescharacteristic
58#4952C2218yescomplemented
59#4951C2218yescomplemented
60#4948C2218yescomplemented
61#4945C2218yescomplemented
62#4943C2218yescomplemented
63Dic3×C22⋊C4C2218yescomplemented
64C3⋊#401C2218yescomplemented
65#4654C2218yescomplemented
66#4652C2218yescomplemented
67#4650C2218yescomplemented
68#2576—316no—
69C2×#401—31no—
70C2×#397—31no—
71C2×#396—31no—
72C2×#394—31no—
73C2×#388—31no—
74C2×#388—31no—
75C2×#387—31no—
76C2×#387—31no—
77C2×#386—31no—
78C2×#386D311yescharacteristic
79C2×#385—31no—
80C2×#382—31no—
81C2×#381—31no—
82C2×C4×C22⋊C4—31no—
83C2×C4×C22⋊C4—31no—
84C25×C3C2311yescharacteristic
85C25×C3C2311yescharacteristic
86C22×C3×D4—24no—
87C22×C3×D4—24no—
88C22×C3×D4—42no—
89C22×C3×D4C2314yes—
90C23×C3×C4—24no—
91C23×C3×C4—42no—
92C23×C3×C4—42no—
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C2311yescharacteristic
98C23×C3×C4C2314yes—
99C23×Dic3—24no—
100C23×Dic3—24no—
101C23×Dic3—42no—
102C23×Dic3C2311yescharacteristic
103C23×Dic3C2311yescharacteristic
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2314yes—
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C2×C3×C22⋊C4—24no—
112C2×C3×C22⋊C4—24no—
113C2×C3×C22⋊C4—42no—
114C2×C3×C22⋊C4C2314yes—
115C2×C3×C22⋊C4C2314yes—
116C2×C3×C22⋊C4C2314yes—
117C2×#217—24no—
118C2×#217—24no—
119C2×#217—24no—
120C2×#217—24no—
121C2×#217—24no—
122C2×#217—42no—
123C2×#217—42no—
124C2×#217C2314yes—
125C2×#217C2314yes—
126C2×#217C2314yes—
127C2×#217C2314yes—
128C2×#217C2314yes—
129C2×#217C2314yes—
130C2×#217C2314yes—
131C2×C4⋊Dic3—24no—
132C2×C4⋊Dic3C2314yes—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—42no—
135C2×Dic3⋊C4—42no—
136C2×Dic3⋊C4—42no—
137C2×Dic3⋊C4C2314yes—
138C2×Dic3⋊C4C2314yes—
139C2×Dic3⋊C4C2314yes—
140C2×Dic3⋊C4C2314yes—
141C2×C4×Dic3—24no—
142C2×C4×Dic3—42no—
143C2×C4×Dic3—42no—
144C2×C4×Dic3C2314yes—
145C2×C4×Dic3C2314yes—
146C2×C4×Dic3C2314yes—
147C3×#95C2314yes—
148C3×#95C2314yes—
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×D4C2×D311yescharacteristic
162C24×C4—31no—
163C24×C4C2×D311yescharacteristic
164C22×C4⋊C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
177C22×C22⋊C4C2×D311yescharacteristic
178C22×C22⋊C4C2×D311yescharacteristic
179C22×C42—31no—
180C22×C42—31no—
181C22×C42—31no—
182#401—38no—
183#397—38no—
184#396—38no—
185#394—38no—
186#388—38no—
187#388—38no—
188#387—38no—
189#387—38no—
190#386—38no—
191#386C2×D318yes—
192#385—38no—
193#382—38no—
194#381—38no—
195C4×C22⋊C4—38no—
196C4×C22⋊C4—38no—
197C2×#95—31no—
198C2×#95—31no—
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×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—22no—
222C24×C3—22no—
223C24×C3#4114yes—
224C24×C3#4114yes—
225C24×C3C2412yes—
226C24×C3C2412yes—
227C24×C3C2411yescharacteristic
228C2×C3×D4—28no—
229C2×C3×D4—28no—
230C2×C3×D4—44no—
231C2×C3×D4—416no—
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—22no—
245C22×C3×C4—22no—
246C22×C3×C4—28no—
247C22×C3×C4—44no—
248C22×C3×C4—44no—
249C22×C3×C4—416no—
250C22×C3×C4#4114yes—
251C22×C3×C4C2412yes—
252C22×C3×C4C2412yes—
253C22×C3×C4C2412yes—
254C22×C3×C4C2412yes—
255C22×C3×C4C2412yes—
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—28no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—22no—
275C22×Dic3—22no—
276C22×Dic3—22no—
277C22×Dic3—22no—
278C22×Dic3—22no—
279C22×Dic3—28no—
280C22×Dic3—44no—
281C22×Dic3—416no—
282C22×Dic3#4114yes—
283C22×Dic3#4114yes—
284C22×Dic3C2412yes—
285C22×Dic3C2412yes—
286C22×Dic3C2412yes—
287C22×Dic3C2412yes—
288C22×Dic3C2412yes—
289C22×Dic3C2412yes—
290C22×Dic3C2412yes—
291C22×Dic3C2412yes—
292C3×C22⋊C4—28no—
293C3×C22⋊C4—28no—
294C3×C22⋊C4—44no—
295#217—28no—
296#217—28no—
297#217—28no—
298#217—28no—
299#217—28no—
300#217—44no—
301#217—44no—
302C4⋊Dic3—28no—
303Dic3⋊C4—28no—
304Dic3⋊C4—44no—
305Dic3⋊C4—44no—
306Dic3⋊C4—44no—
307C4×Dic3—28no—
308C4×Dic3—44no—
309C4×Dic3—44no—
310C25C22×D311yescharacteristic
311C25C22×D311yescharacteristic
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—42no—
315C22×D4C22×D314yes—
316C23×C4—24no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—34no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—64no—
329C23×C4—64no—
330C23×C4—122no—
331C23×C4C22×D311yescharacteristic
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D314yes—
337C2×C4⋊C4—34no—
338C2×C4⋊C4—34no—
339C2×C4⋊C4—34no—
340C2×C4⋊C4—34no—
341C2×C4⋊C4—34no—
342C2×C4⋊C4—64no—
343C2×C4⋊C4—64no—
344C2×C4⋊C4—122no—
345C2×C4⋊C4—122no—
346C2×C4⋊C4—122no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—34no—
350C2×C22⋊C4—34no—
351C2×C22⋊C4—34no—
352C2×C22⋊C4—34no—
353C2×C22⋊C4—34no—
354C2×C22⋊C4—34no—
355C2×C22⋊C4—34no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—64no—
358C2×C22⋊C4—64no—
359C2×C22⋊C4—64no—
360C2×C22⋊C4—64no—
361C2×C22⋊C4—64no—
362C2×C22⋊C4—122no—
363C2×C22⋊C4—122no—
364C2×C22⋊C4C22×D314yes—
365C2×C22⋊C4C22×D314yes—
366C2×C22⋊C4C22×D314yes—
367C2×C42—34no—
368C2×C42—34no—
369C2×C42—34no—
370C2×C42—64no—
371C2×C42—122no—
372C2×C42—122no—
373#95—34no—
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#95—34no—
385#95C22×D314yes—
386#95C22×D314yes—
387C23×C3—28no—
388C23×C3—28no—
389C23×C3—28no—
390C23×C3—28no—
391C23×C3—28no—
392C23×C3—28no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—44no—
406C23×C3—44no—
407C23×C3—44no—
408C23×C3—44no—
409C23×C3—44no—
410C23×C3—44no—
411C23×C3—44no—
412C23×C3—44no—
413C23×C3C2×#4114yes—
414C23×C3C2×#4112yes—
415C23×C3C2×#4114yes—
416C23×C3C2×#4112yes—
417C23×C3C2×#4112yes—
418C23×C3C2×#4112yes—
419C23×C3C2×#4112yes—
420C23×C3H(5,𝔽2)12yes—
421C23×C3H(5,𝔽2)12yes—
422C23×C3C2511yescharacteristic
423C3×D4—416no—
424C2×C3×C4—28no—
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—416no—
440C2×C3×C4—44no—
441C2×C3×C4—44no—
442C2×C3×C4—44no—
443C2×C3×C4—44no—
444C2×C3×C4C2×#4114yes—
445C2×Dic3—28no—
446C2×Dic3—28no—
447C2×Dic3—22no—
448C2×Dic3—22no—
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—22no—
469C2×Dic3—416no—
470C2×Dic3—44no—
471C2×Dic3—44no—
472C2×Dic3—44no—
473C2×Dic3—44no—
474C2×Dic3—44no—
475C2×Dic3—44no—
476C2×Dic3C2×#4114yes—
477C2×Dic3C2×#4114yes—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24#23514yes—
491C24#23714yes—
492C24C23×D312yes—
493C24C23×D312yes—
494C24C23×D311yescharacteristic
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—44no—
498C2×D4—416no—
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—28no—
514C22×C4—34no—
515C22×C4—34no—
516C22×C4—32no—
517C22×C4—32no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—32no—
522C22×C4—32no—
523C22×C4—32no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—416no—
527C22×C4—68no—
528C22×C4—62no—
529C22×C4—62no—
530C22×C4—62no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—62no—
534C22×C4—68no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—62no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—124no—
552C22×C4—1216no—
553C22×C4#23714yes—
554C22×C4C23×D312yes—
555C22×C4C23×D312yes—
556C22×C4C23×D312yes—
557C22×C4C23×D312yes—
558C22×C4C23×D312yes—
559C4⋊C4—68no—
560C4⋊C4—68no—
561C4⋊C4—124no—
562C4⋊C4—124no—
563C4⋊C4—124no—
564C22⋊C4—28no—
565C22⋊C4—28no—
566C22⋊C4—44no—
567C22⋊C4—68no—
568C22⋊C4—68no—
569C22⋊C4—68no—
570C22⋊C4—68no—
571C22⋊C4—68no—
572C22⋊C4—124no—
573C22⋊C4—124no—
574C42—68no—
575C42—124no—
576C42—124no—
577C22×C3—24no—
578C22×C3—24no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—416no—
584C22×C3—416no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—42no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3#52914yes—
594C22×C3#52914yes—
595C22×C3#53814yes—
596C22×C3#55114yes—
597C22×C3#55114yes—
598C22×C3#55314yes—
599C22×C3#55314yes—
600C22×C3C22×#4111yescharacteristic
601C22×C3C22×#4111yescharacteristic
602C22×C3C22×#4111yescharacteristic
603C22×C3C22×#4111yescharacteristic
604C22×C3C22×#4111yescharacteristic
605C22×C3C2×H(5,𝔽2)11yescharacteristic
606C22×C3C2×H(5,𝔽2)11yescharacteristic
607C3×C4—24no—
608C3×C4—42no—
609C3×C4—42no—
610C3×C4—42no—
611C3×C4—42no—
612Dic3—24no—
613Dic3—24no—
614Dic3—42no—
615Dic3—42no—
616Dic3—42no—
617Dic3—42no—
618Dic3—42no—
619Dic3—42no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—28no—
633C23—28no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—28no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23C2×#23514yes—
647C23C2×#23512yes—
648C23C2×#23714yes—
649C23C2×#23712yes—
650C23C2×#23712yes—
651C23#100412yes—
652C23#100412yes—
653C23D3×#4112yes—
654C23D3×#4112yes—
655C23C24×D311yescharacteristic
656D4—416no—
657C2×C4—22no—
658C2×C4—22no—
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—416no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—68no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—68no—
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—62no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—62no—
703C2×C4—1216no—
704C2×C4—124no—
705C2×C4—124no—
706C2×C4—124no—
707C2×C4—124no—
708C2×C4—124no—
709C2×C4—124no—
710C2×C4C2×#23714yes—
711C2×C3—44no—
712C2×C3—44no—
713C2×C3#257618yescomplemented
714C2×C3C2×#52911yescharacteristic
715C2×C3C2×#52911yescharacteristic
716C2×C3C2×#53811yescharacteristic
717C2×C3C2×#55111yescharacteristic
718C2×C3C2×#55111yescharacteristic
719C2×C3C2×#55311yescharacteristic
720C2×C3C2×#55311yescharacteristic
721C22—24no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—416no—
728C22—416no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22#549514yes—
738C22#553814yes—
739C22#555614yes—
740C22#559314yes—
741C22#560014yes—
742C22#560114yes—
743C22#566114yes—
744C22C22×#23511yescharacteristic
745C22C22×#23711yescharacteristic
746C22C22×#23711yescharacteristic
747C22C2×#100411yescharacteristic
748C22C2×#100411yescharacteristic
749C22C2×D3×#4111yescharacteristic
750C22C2×D3×#4111yescharacteristic
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—64no—
757C4—64no—
758C4—122no—
759C4—122no—
760C4—122no—
761C4—122no—
762C4—122no—
763C4—122no—
764C3C2×#257611yescharacteristic, complemented, Sylow
765C2—44no—
766C2—44no—
767C2#7476618yesdirect product factor
768C2C2×#549511yescharacteristic
769C2C2×#553811yescharacteristic
770C2C2×#555611yescharacteristic
771C2C2×#559311yescharacteristic
772C2C2×#560011yescharacteristic
773C2C2×#560111yescharacteristic
774C2C2×#566111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#386C2
socleC24×C3C24
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3C2×#2576
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
4. C2×#5210C2semidirect
5. C2×C4×#217C2semidirect
6. C2×#4952C2semidirect
7. C2×#4948C2semidirect
8. C2×#4945C2semidirect
9. C2×#4951C2semidirect
10. C2×#4943C2semidirect
11. C2×Dic3×C22⋊C4C2semidirect
12. #74766C2direct (N × H)
13. C2×C3⋊#401C2semidirect
14. C2×#4654C2semidirect
15. C2×#4652C2semidirect
16. C2×#4650C2semidirect
44. #5210C22semidirect
45. C4×#217C22semidirect
58. #4952C22semidirect
59. #4951C22semidirect
60. #4948C22semidirect
61. #4945C22semidirect
62. #4943C22semidirect
63. Dic3×C22⋊C4C22semidirect
64. C3⋊#401C22semidirect
65. #4654C22semidirect
66. #4652C22semidirect
67. #4650C22semidirect
713. C2×C3#2576semidirect
764. C3C2×#2576semidirect
767. C2#74766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#3862
C2×#52222
C2×#52202
C2×#52102
C2×C4×#2172
C2×#49522
C2×#49482
C2×#49452
C2×#49512
C2×#49432
C2×Dic3×C22⋊C42
#747662
C2×C3⋊#4012
C2×#46542
C2×#46522
C2×#46502
C2×#25763