Finite Group Databasebeta

← C2×#78362 #10961639

Subgroups — C2×#78362 #10961639

Order 768.

2546 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×#400C211yesmaximal, characteristic, complemented
2C2×#4992C211yesmaximal, characteristic, complemented
3C2×#4994C211yesmaximal, characteristic, complemented
4C2×#4989C211yesmaximal, characteristic, complemented
5C2×#4989C211yesmaximal, characteristic, complemented
6#78362C2116yesmaximal, direct product factor
7C2×#4675C211yesmaximal, characteristic, complemented
8C2×#4675C211yesmaximal, characteristic, complemented
9C2×#4665C211yesmaximal, characteristic
10C2×#4665C211yesmaximal, characteristic
11C2×#4665C211yesmaximal, characteristic
12C2×#4668C211yesmaximal, characteristic, complemented
13C2×D3×#95C211yesmaximal, characteristic, complemented
14C2×C3⋊#401C211yesmaximal, characteristic, complemented
15C2×#4659C211yesmaximal, characteristic, complemented
16C2×#4658C211yesmaximal, characteristic, complemented
17C2×#2643—31nomaximal, Sylow
18C23×D12C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C23×C4×D3C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×C4⋊Dic3C2211yescharacteristic
34C22×Dic3⋊C4C2211yescharacteristic
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C3×#400C2218yescomplemented
38C2×C3×#95C2211yescharacteristic
39C2×C3×#95C2211yescharacteristic
40C2×C3×#95C2211yescharacteristic
41C2×C3×#95C2211yescharacteristic
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#4994C2218yescomplemented
55#4992C2218yescomplemented
56#4989C2218yescomplemented
57#4989C2218yescomplemented
58#4675C2218yescomplemented
59#4675C2218yescomplemented
60#4668C2218yescomplemented
61#4665C2218yes—
62#4665C2218yes—
63#4665C2218yes—
64D3×#95C2218yescomplemented
65C3⋊#401C2218yescomplemented
66#4659C2218yescomplemented
67#4658C2218yescomplemented
68#2643—316no—
69C2×#401—31no—
70C2×#400—31no—
71C2×#400—31no—
72C2×#400D311yescharacteristic, complemented
73C2×#397—31no—
74C2×#397—31no—
75C2×#397—31no—
76C2×#396—31no—
77C2×#386—31no—
78C2×#386—31no—
79C2×#386—31no—
80C2×#385—31no—
81C2×#385—31no—
82C2×#385—31no—
83C22×#95—31no—
84C24×D3C2311yescharacteristic
85C24×D3C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C23×C3×C4C2311yescharacteristic
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×Dic3C2311yescharacteristic
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2311yescharacteristic
96C23×Dic3C2311yescharacteristic
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C22×D12—24no—
100C22×D12—24no—
101C22×D12—24no—
102C22×D12C2314yes—
103C22×C4×D3—24no—
104C22×C4×D3—24no—
105C22×C4×D3—24no—
106C22×C4×D3—42no—
107C22×C4×D3—42no—
108C22×C4×D3—42no—
109C22×C4×D3—42no—
110C22×C4×D3—42no—
111C22×C4×D3—42no—
112C22×C4×D3C2314yes—
113C22×C4×D3C2314yes—
114C22×C4×D3C2314yes—
115C2×C3×C4⋊C4—42no—
116C2×C3×C4⋊C4—42no—
117C2×C3×C4⋊C4C2314yes—
118C2×C3×C4⋊C4C2314yes—
119C2×(C2×D3)⋊C4—24no—
120C2×(C2×D3)⋊C4—24no—
121C2×(C2×D3)⋊C4—24no—
122C2×(C2×D3)⋊C4—42no—
123C2×(C2×D3)⋊C4—42no—
124C2×(C2×D3)⋊C4—42no—
125C2×(C2×D3)⋊C4—42no—
126C2×(C2×D3)⋊C4—42no—
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×(C2×D3)⋊C4C2314yes—
134C2×(C2×D3)⋊C4C2314yes—
135C2×(C2×D3)⋊C4C2314yes—
136C2×(C2×D3)⋊C4C2314yes—
137C2×C4⋊Dic3—42no—
138C2×C4⋊Dic3C2314yes—
139C2×Dic3⋊C4—42no—
140C2×Dic3⋊C4—42no—
141C2×Dic3⋊C4—42no—
142C2×Dic3⋊C4C2314yes—
143C2×Dic3⋊C4C2314yes—
144C2×Dic3⋊C4C2314yes—
145C3×#95C2314yes—
146C3×#95C2314yes—
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×D4—31no—
162C24×C4—31no—
163C24×C4—31no—
164C24×C4—31no—
165C22×C4⋊C4—31no—
166C22×C4⋊C4—31no—
167C22×C4⋊C4—31no—
168C22×C4⋊C4—31no—
169C22×C4⋊C4C2×D311yescharacteristic
170C22×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
178C22×C22⋊C4—31no—
179C22×C22⋊C4—31no—
180#401—38no—
181#400—38no—
182#400—38no—
183#400C2×D318yescomplemented
184#397—38no—
185#397—38no—
186#397—38no—
187#396—38no—
188#386—38no—
189#386—38no—
190#386—38no—
191#385—38no—
192#385—38no—
193#385—38no—
194C2×#95—31no—
195C2×#95—31no—
196C2×#95—31no—
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—38no—
206C2×#95C2×D311yescharacteristic
207C2×#95C2×D311yescharacteristic
208C2×#95C2×D311yescharacteristic
209C2×#95C2×D311yescharacteristic
210C2×#95C2×D311yescharacteristic
211C24×C3C2411yescharacteristic
212C23×D3—22no—
213C23×D3—22no—
214C23×D3—22no—
215C23×D3—22no—
216C23×D3—22no—
217C23×D3—22no—
218C23×D3—22no—
219C23×D3—22no—
220C23×D3—22no—
221C23×D3—22no—
222C23×D3—22no—
223C23×D3#4114yes—
224C23×D3#4114yes—
225C23×D3#4114yes—
226C23×D3C2412yes—
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—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—22no—
248C22×C3×C4—22no—
249C22×C3×C4C2412yes—
250C22×C3×C4C2412yes—
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—22no—
271C22×Dic3—22no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3C2412yes—
275C22×Dic3C2412yes—
276C22×Dic3C2412yes—
277C22×Dic3C2412yes—
278C22×Dic3C2412yes—
279C22×Dic3C2412yes—
280C2×D12—28no—
281C2×D12—28no—
282C2×D12—28no—
283C2×D12—416no—
284C2×C4×D3—28no—
285C2×C4×D3—28no—
286C2×C4×D3—28no—
287C2×C4×D3—44no—
288C2×C4×D3—44no—
289C2×C4×D3—44no—
290C2×C4×D3—44no—
291C2×C4×D3—44no—
292C2×C4×D3—44no—
293C2×C4×D3—416no—
294C2×C4×D3—416no—
295C2×C4×D3—416no—
296C3×C4⋊C4—44no—
297C3×C4⋊C4—44no—
298(C2×D3)⋊C4—28no—
299(C2×D3)⋊C4—28no—
300(C2×D3)⋊C4—28no—
301(C2×D3)⋊C4—44no—
302(C2×D3)⋊C4—44no—
303(C2×D3)⋊C4—44no—
304(C2×D3)⋊C4—44no—
305(C2×D3)⋊C4—44no—
306(C2×D3)⋊C4—44no—
307C4⋊Dic3—44no—
308Dic3⋊C4—44no—
309Dic3⋊C4—44no—
310Dic3⋊C4—44no—
311C25—31no—
312C25—31no—
313C22×D4—34no—
314C22×D4—64no—
315C22×D4—64no—
316C22×D4—64no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—31no—
323C23×C4—34no—
324C23×C4—34no—
325C23×C4—34no—
326C23×C4—64no—
327C23×C4—64no—
328C23×C4—64no—
329C23×C4—122no—
330C23×C4—122no—
331C23×C4—122no—
332C23×C4—122no—
333C23×C4—122no—
334C23×C4—122no—
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337C23×C4C22×D311yescharacteristic
338C23×C4C22×D311yescharacteristic
339C23×C4C22×D311yescharacteristic
340C23×C4C22×D311yescharacteristic
341C23×C4C22×D311yescharacteristic
342C2×C4⋊C4—34no—
343C2×C4⋊C4—34no—
344C2×C4⋊C4—34no—
345C2×C4⋊C4—34no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—122no—
349C2×C4⋊C4—122no—
350C2×C4⋊C4—122no—
351C2×C4⋊C4—122no—
352C2×C4⋊C4C22×D314yes—
353C2×C4⋊C4C22×D314yes—
354C2×C22⋊C4—34no—
355C2×C22⋊C4—34no—
356C2×C22⋊C4—34no—
357C2×C22⋊C4—34no—
358C2×C22⋊C4—34no—
359C2×C22⋊C4—34no—
360C2×C22⋊C4—34no—
361C2×C22⋊C4—34no—
362C2×C22⋊C4—34no—
363C2×C22⋊C4—64no—
364C2×C22⋊C4—64no—
365C2×C22⋊C4—64no—
366C2×C22⋊C4—122no—
367C2×C22⋊C4—122no—
368C2×C22⋊C4—122no—
369C2×C22⋊C4—122no—
370C2×C22⋊C4—122no—
371C2×C22⋊C4—122no—
372#95—34no—
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#95C22×D314yes—
384#95C22×D314yes—
385#95C22×D314yes—
386#95C22×D314yes—
387#95C22×D314yes—
388C23×C3C2×#4112yes—
389C23×C3C2×#4112yes—
390C23×C3C2×#4112yes—
391C23×C3H(5,𝔽2)12yes—
392C23×C3H(5,𝔽2)12yes—
393C23×C3H(5,𝔽2)12yes—
394C23×C32−1+412yes—
395C23×C3C2511yescharacteristic
396C22×D3—28no—
397C22×D3—28no—
398C22×D3—28no—
399C22×D3—28no—
400C22×D3—28no—
401C22×D3—28no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—22no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—44no—
414C22×D3—44no—
415C22×D3—44no—
416C22×D3—44no—
417C22×D3—44no—
418C22×D3—44no—
419C22×D3—44no—
420C22×D3#126116yes—
421C22×D3C2×#4114yes—
422C22×D3C2×#4114yes—
423C22×D3C2×#4114yes—
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—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—44no—
446C2×C3×C4—44no—
447C2×C3×C4—44no—
448C2×C3×C4—44no—
449C2×C3×C4—44no—
450C2×C3×C4—44no—
451C2×C3×C4—44no—
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—22no—
470C2×Dic3—44no—
471C2×Dic3—44no—
472C2×Dic3—44no—
473C2×Dic3—44no—
474C2×Dic3—44no—
475C2×Dic3—44no—
476D12—416no—
477C4×D3—416no—
478C4×D3—416no—
479C4×D3—416no—
480C24—34no—
481C24—34no—
482C24—34no—
483C24—32no—
484C24—32no—
485C24—62no—
486C24—62no—
487C24—62no—
488C24—62no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24—62no—
496C24C23×D311yescharacteristic
497C2×D4—68no—
498C2×D4—68no—
499C2×D4—68no—
500C2×D4—1216no—
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—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—32no—
523C22×C4—32no—
524C22×C4—32no—
525C22×C4—32no—
526C22×C4—32no—
527C22×C4—32no—
528C22×C4—68no—
529C22×C4—68no—
530C22×C4—68no—
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—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—124no—
550C22×C4—124no—
551C22×C4—124no—
552C22×C4—124no—
553C22×C4—124no—
554C22×C4—124no—
555C22×C4—1216no—
556C22×C4—1216no—
557C22×C4—1216no—
558C22×C4C23×D312yes—
559C22×C4C23×D312yes—
560C22×C4C23×D312yes—
561C22×C4C23×D312yes—
562C22×C4C23×D312yes—
563C22×C4C23×D312yes—
564C22×C4C23×D312yes—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—124no—
568C4⋊C4—124no—
569C4⋊C4—124no—
570C4⋊C4—124no—
571C22⋊C4—68no—
572C22⋊C4—68no—
573C22⋊C4—68no—
574C22⋊C4—124no—
575C22⋊C4—124no—
576C22⋊C4—124no—
577C22⋊C4—124no—
578C22⋊C4—124no—
579C22⋊C4—124no—
580C22×C3C2×#12614yes—
581C22×C3#53814yes—
582C22×C3#53814yes—
583C22×C3#53814yes—
584C22×C3#53914yes—
585C22×C3#53914yes—
586C22×C3#53914yes—
587C22×C3C22×#4111yescharacteristic
588C22×C3C22×#4111yescharacteristic
589C22×C3C22×#4111yescharacteristic
590C22×C3C2×H(5,𝔽2)11yescharacteristic
591C22×C3C2×H(5,𝔽2)11yescharacteristic
592C22×C3C2×H(5,𝔽2)11yescharacteristic
593C22×C3C2×2−1+411yescharacteristic
594C2×D3—232no—
595C2×D3—24no—
596C2×D3—24no—
597C2×D3—24no—
598C2×D3—24no—
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—88no—
609C2×D3C2×#12618yes—
610C3×C4—42no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4—42no—
617Dic3—42no—
618Dic3—42no—
619Dic3—42no—
620Dic3—42no—
621Dic3—42no—
622Dic3—42no—
623C23—316no—
624C23—34no—
625C23—34no—
626C23—34no—
627C23—68no—
628C23—68no—
629C23—68no—
630C23—68no—
631C23—68no—
632C23—62no—
633C23—68no—
634C23—62no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—124no—
645C23—124no—
646C23—124no—
647C23—124no—
648C23—124no—
649C23—124no—
650C23—124no—
651C23#100412yes—
652C23#100712yes—
653C23D3×#4112yes—
654C23D3×#4112yes—
655C23D3×#4112yes—
656C23#100912yes—
657C23#100912yes—
658C23C24×D311yescharacteristic
659D4—1216no—
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—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
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—62no—
704C2×C4—62no—
705C2×C4—62no—
706C2×C4—1216no—
707C2×C4—1216no—
708C2×C4—1216no—
709C2×C4—124no—
710C2×C4—124no—
711C2×C4—124no—
712C2×C4—124no—
713C2×C4—124no—
714C2×C4—124no—
715C2×C3#264318yescomplemented
716C2×C3C22×#12611yescharacteristic
717C2×C3C2×#53811yescharacteristic
718C2×C3C2×#53811yescharacteristic
719C2×C3C2×#53811yescharacteristic
720C2×C3C2×#53911yescharacteristic
721C2×C3C2×#53911yescharacteristic
722C2×C3C2×#53911yescharacteristic
723D3—28no—
724D3—82no—
725C22—38no—
726C22—632no—
727C22—64no—
728C22—64no—
729C22—64no—
730C22—64no—
731C22—64no—
732C22—64no—
733C22—122no—
734C22—122no—
735C22—122no—
736C22—122no—
737C22—122no—
738C22—122no—
739C22—122no—
740C22—248no—
741C22#563814yes—
742C22#565714yes—
743C22#567814yes—
744C22#569214yes—
745C22#569214yes—
746C22D3×#12614yes—
747C22#570414yes—
748C22C2×#100411yescharacteristic
749C22C2×#100711yescharacteristic
750C22C2×D3×#4111yescharacteristic
751C22C2×D3×#4111yescharacteristic
752C22C2×D3×#4111yescharacteristic
753C22C2×#100911yescharacteristic
754C22C2×#100911yescharacteristic
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—122no—
763C4—122no—
764C4—122no—
765C4—122no—
766C4—122no—
767C4—122no—
768C3C2×#264311yescharacteristic, complemented, Sylow
769C2—68no—
770C2—242no—
771C2#7836218yesdirect product factor
772C2C2×#563811yescharacteristic
773C2C2×#565711yescharacteristic
774C2C2×#567811yescharacteristic
775C2C2×#569211yescharacteristic
776C2C2×#569211yescharacteristic
777C2C2×D3×#12611yescharacteristic
778C2C2×#570411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#400C2
socleC24×C3C24
prime radicalC23×D12C22
hypercenterC2×#400D3
hypocenterC3C2×#2643
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C2×C3×#400C2semidirect
2. C2×#4992C2semidirect
3. C2×#4994C2semidirect
4. C2×#4989C2semidirect
5. C2×#4989C2semidirect
6. #78362C2direct (N × H)
7. C2×#4675C2semidirect
8. C2×#4675C2semidirect
12. C2×#4668C2semidirect
13. C2×D3×#95C2semidirect
14. C2×C3⋊#401C2semidirect
15. C2×#4659C2semidirect
16. C2×#4658C2semidirect
37. C3×#400C22semidirect
54. #4994C22semidirect
55. #4992C22semidirect
56. #4989C22semidirect
57. #4989C22semidirect
58. #4675C22semidirect
59. #4675C22semidirect
60. #4668C22semidirect
64. D3×#95C22semidirect
65. C3⋊#401C22semidirect
66. #4659C22semidirect
67. #4658C22semidirect
72. C2×#400D3semidirect
183. #400C2×D3semidirect
715. C2×C3#2643semidirect
768. C3C2×#2643semidirect
771. C2#78362direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4002
C2×#49922
C2×#49942
C2×#49892
#783622
C2×#46752
C2×#46652
C2×#46682
C2×D3×#952
C2×C3⋊#4012
C2×#46592
C2×#46582
C2×#26433