Finite Group Databasebeta

← #10810821

Subgroups — #10810821

Order 768.

1426 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×#67C211yesmaximal, characteristic
2C2×#5225C211yesmaximal, characteristic, complemented
3C2×#4802C211yesmaximal, characteristic, complemented
4C2×#4729C211yesmaximal, characteristic
5#73885C211yesmaximal, characteristic
6C3×#1787C211yesmaximal, characteristic, complemented
7#70271C211yesmaximal, characteristic, complemented
8#70269C211yesmaximal, characteristic, complemented
9#70266C211yesmaximal, characteristic, complemented
10#70229C211yesmaximal, characteristic, complemented
11#70225C211yesmaximal, characteristic, complemented
12#70221C211yesmaximal, characteristic, complemented
13Dic3×#103C211yesmaximal, characteristic, complemented
14#69931C211yesmaximal, characteristic, complemented
15#69516C211yesmaximal, characteristic, complemented
16#22430—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19Q8×#67—24no—
20Q8×#67C418yescomplemented
21C2×#946—21no—
22C2×#946C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×#944—21no—
25C2×#944C2211yescharacteristic
26C2×C4×#67—21no—
27C2×C4×#67C2211yescharacteristic
28C2×#926C2211yescharacteristic
29C2×#924—21no—
30C2×#924C2211yescharacteristic
31C22×#208C2211yescharacteristic
32C22×ΓL(1,𝔽25)C2211yescharacteristic
33C2×#892C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C3×#380C2211yescharacteristic
40#5225—24no—
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#835C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×Dic3⋊C8C2211yescharacteristic
49C2×C8×Dic3C2211yescharacteristic
50#4987C2211yescharacteristic
51#4975C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#810C2211yescharacteristic
55#4957—21no—
56#4945—21no—
57#4802—24no—
58#4729—24no—
59#4669—21no—
60#4649—21no—
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×D4×Q8—31no—
66C2×#436—31no—
67C2×#419—31no—
68C2×#419—31no—
69#2354—31no—
70#1981—31no—
71#1956—31no—
72#1894—31no—
73#1894—31no—
74#1873—31no—
75#1873—31no—
76#1803—31no—
77#1787—31no—
78#1787D311yescharacteristic, complemented
79C4×#103—31no—
80C22×C3×Q8—21no—
81C22×C3×Q8—22no—
82C22×C3×Q8—22no—
83C22×C3×Q8—22no—
84C22×C3×Q8—41no—
85C22×C3×Q8—41no—
86C22×C3×Q8C2×C414yes—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C23×C3×C4—21no—
90C23×C3×C4C2311yescharacteristic
91C22×#67D411yescharacteristic
92C2×D3×Q8—22no—
93C2×D3×Q8—22no—
94C2×D3×Q8—22no—
95C2×D3×Q8—41no—
96C2×D3×Q8—41no—
97C2×D3×Q8C2×C414yes—
98C22×C4×D3—21no—
99C22×C4×D3C2311yescharacteristic
100C22×Dic6—21no—
101C22×Dic6C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C22⋊C4—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#217D411yescharacteristic
110#946—22no—
111#946—28no—
112#946C2×C414yes—
113Q8×Dic3—22no—
114Q8×Dic3C2×C414yes—
115#944—28no—
116#944—22no—
117#944C2×C414yes—
118C4×#67—28no—
119C4×#67C2×C414yes—
120C4×#67D414yes—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124C2×(C2×D3)⋊C4D411yescharacteristic
125#926—22no—
126#926—41no—
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131#924—22no—
132#924—28no—
133#924C2×C414yes—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3—21no—
143C2×C4×Dic3—21no—
144C2×C4×Dic3—21no—
145C2×C4×Dic3C2311yescharacteristic
146C2×#208—22no—
147C2×#208—22no—
148C2×#208—41no—
149C22×C3⋊C8C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C2×ΓL(1,𝔽25)—22no—
152C2×ΓL(1,𝔽25)—22no—
153C2×ΓL(1,𝔽25)—41no—
154#892—22no—
155#892—41no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#103—41no—
159C3×#103—41no—
160C3×C22⋊C8—22no—
161C3×#95—21no—
162#835—22no—
163#835—22no—
164#835—22no—
165#835D414yescomplemented
166C3⋊#95—21no—
167C3⋊#95—21no—
168(C2×D3)⋊C8—22no—
169#816—22no—
170#816—41no—
171Dic3⋊C8—22no—
172C8×Dic3—22no—
173#810—22no—
174#810—41no—
175C23×Q8—31no—
176C23×Q8C2×D311yescharacteristic
177C22×M16—31no—
178C22×M16—31no—
179D4×Q8—38no—
180D4×Q8—64no—
181C2×C4⋊Q8—31no—
182C2×C4⋊Q8—61no—
183C2×C22⋊Q8—31no—
184C2×C22⋊Q8—31no—
185C2×C22⋊Q8—61no—
186C2×C22⋊Q8—61no—
187C2×C4×Q8—31no—
188C2×C4×D4—31no—
189C2×C4×D4—61no—
190C2×#117—31no—
191C2×#117—31no—
192#436—64no—
193C2×C4⋊C8—31no—
194#419—64no—
195#419—64no—
196C2×#103—31no—
197C2×#103—31no—
198C2×#103—31no—
199C2×#103—31no—
200C2×#103—31no—
201C2×#103—31no—
202C2×#103—31no—
203C2×#103—31no—
204C2×#103C2×D311yescharacteristic
205C2×#103C2×D311yescharacteristic
206C2×#103C2×D311yescharacteristic
207C2×#103C2×D311yescharacteristic
208C2×C22⋊C8—31no—
209C2×C22⋊C8C2×D311yescharacteristic
210C2×C4×C8—31no—
211#390—61no—
212#388—61no—
213#388—61no—
214#384—31no—
215#380—31no—
216#380C2×D311yescharacteristic
217C4×C4⋊C4—31no—
218C4×C4⋊C4—61no—
219#340—31no—
220#340—31no—
221#340—31no—
222#340—31no—
223C24×C3C2×D411yescharacteristic
224C23×D3C2×D411yescharacteristic
225C2×C3×Q8—24no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—28no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—42no—
236C2×C3×Q8—42no—
237C2×C3×Q8—44no—
238C2×C3×Q8—44no—
239C2×C3×Q8—44no—
240C2×C3×Q8C22×C412yes—
241C2×C3×Q8C22×C412yes—
242C2×C3×Q8C2×D412yes—
243C2×C3×Q8#4112yes—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—42no—
254C22×C3×C4—42no—
255C22×C3×C4C22×C412yes—
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2411yescharacteristic
259C2×#67—22no—
260C2×#67—22no—
261C2×#67C22⋊C414yes—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269D3×Q8—28no—
270D3×Q8—44no—
271D3×Q8—44no—
272D3×Q8—44no—
273C2×C4×D3—21no—
274C2×C4×D3—21no—
275C2×C4×D3—21no—
276C2×C4×D3—21no—
277C2×C4×D3—24no—
278C2×C4×D3—42no—
279C2×C4×D3—42no—
280C2×C4×D3C22×C412yes—
281C2×C4×D3C2×D412yes—
282C2×Dic6—21no—
283C2×Dic6—21no—
284C2×Dic6—21no—
285C2×Dic6—21no—
286C2×Dic6—21no—
287C2×Dic6—24no—
288C2×Dic6—42no—
289C2×Dic6—42no—
290C2×Dic6C22×C412yes—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C22⋊C4—81no—
302#217—24no—
303#217—42no—
304#217C22⋊C414yes—
305(C2×D3)⋊C4—24no—
306(C2×D3)⋊C4—42no—
307(C2×D3)⋊C4—81no—
308(C2×D3)⋊C4C22⋊C414yes—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—24no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314C4⋊Dic3C22×C412yes—
315C4⋊Dic3C2×D412yes—
316Dic3⋊C4—24no—
317Dic3⋊C4—24no—
318Dic3⋊C4—24no—
319Dic3⋊C4—24no—
320Dic3⋊C4—42no—
321Dic3⋊C4—81no—
322Dic3⋊C4C22⋊C414yes—
323C4×Dic3—24no—
324C4×Dic3—42no—
325C4×Dic3—42no—
326C4×Dic3—42no—
327C4×Dic3C22×C412yes—
328C4×Dic3C2×D412yes—
329#208—44no—
330C2×C3⋊C8—21no—
331C2×C3⋊C8—21no—
332C2×C3⋊C8—21no—
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8C2×D412yes—
336ΓL(1,𝔽25)—44no—
337C22×Q8—21no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—34no—
342C22×Q8—31no—
343C22×Q8—41no—
344C22×Q8—41no—
345C22×Q8—61no—
346C22×Q8—62no—
347C22×Q8—62no—
348C22×Q8—62no—
349C22×Q8—121no—
350C22×Q8—121no—
351C22×Q8C4×D314yes—
352C22×Q8C22×D311yescharacteristic
353C22×Q8C22×D311yescharacteristic
354C22×D4—31no—
355C23×C4—21no—
356C23×C4—31no—
357C23×C4—61no—
358C23×C4C22×D311yescharacteristic
359C2×M16—62no—
360C2×M16—62no—
361C2×M16—62no—
362C2×M16—62no—
363C2×M16—121no—
364C2×M16—121no—
365C22×C8—31no—
366C22×C8—31no—
367C22×C8C22×D311yescharacteristic
368C22×C8C22×D311yescharacteristic
369C4⋊Q8—34no—
370C4⋊Q8—62no—
371C4⋊Q8—68no—
372C22⋊Q8—34no—
373C22⋊Q8—34no—
374C22⋊Q8—68no—
375C22⋊Q8—68no—
376C22⋊Q8—62no—
377C22⋊Q8—62no—
378C4×Q8—34no—
379C4×Q8—62no—
380C4×D4—34no—
381C4×D4—34no—
382C4×D4—68no—
383#117—62no—
384#117—62no—
385#117—121no—
386#117—121no—
387C2×C4⋊C4—31no—
388C2×C4⋊C4—31no—
389C2×C4⋊C4—31no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—61no—
392C2×C4⋊C4—61no—
393C2×C4⋊C4—61no—
394C2×C4⋊C4—61no—
395C2×C4⋊C4—61no—
396C2×C4⋊C4—61no—
397C2×C4⋊C4—61no—
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C4⋊C4C22×D311yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4—31no—
403C2×C22⋊C4—61no—
404C2×C22⋊C4—61no—
405C2×C22⋊C4—61no—
406C2×C22⋊C4—61no—
407C2×C22⋊C4—61no—
408C2×C42—31no—
409C2×C42—61no—
410C2×C42—61no—
411C2×C42—61no—
412C2×C42—61no—
413C4⋊C8—62no—
414#103—22no—
415#103—22no—
416#103—34no—
417#103—41no—
418#103—41no—
419#103—62no—
420#103—62no—
421#103—62no—
422#103—62no—
423#103—62no—
424#103—121no—
425#103—121no—
426C22⋊C8—22no—
427C22⋊C8—62no—
428C4×C8—62no—
429#95—21no—
430#95—61no—
431#95—61no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3C2×C22⋊C412yes—
439C23×C3C22×D411yescharacteristic
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3—21no—
444C22×D3—21no—
445C22×D3—21no—
446C22×D3C2×C22⋊C412yes—
447C3×Q8—22no—
448C3×Q8—22no—
449C3×Q8—22no—
450C3×Q8—22no—
451C3×Q8—22no—
452C3×Q8—48no—
453C3×Q8—41no—
454C3×Q8—41no—
455C3×Q8C4×D414yes—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—48no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4C2×C22⋊C412yes—
476C2×C3×C4C23×C411yescharacteristic
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4H(5,𝔽2)11yescharacteristic
481C2×C3×C4H(5,𝔽2)11yescharacteristic
482#67—28no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496C2×Dic3—41no—
497C2×Dic3—41no—
498C2×Dic3—41no—
499C2×Dic3C2×C22⋊C412yes—
500C2×Dic3C2×C22⋊C412yes—
501C2×Dic3C2×C22⋊C412yes—
502C2×Dic3#13712yes—
503C2×Dic3#13712yes—
504C4×D3—22no—
505C4×D3—22no—
506C4×D3—22no—
507C4×D3—22no—
508C4×D3—48no—
509Dic6—22no—
510Dic6—22no—
511Dic6—48no—
512Dic6—41no—
513Dic6—41no—
514C3×C8—41no—
515C3×C8—41no—
516C3⋊C8—22no—
517C3⋊C8—41no—
518C24—31no—
519C24D3×D411yescharacteristic
520C2×Q8—24no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—28no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—32no—
531C2×Q8—42no—
532C2×Q8—42no—
533C2×Q8—44no—
534C2×Q8—44no—
535C2×Q8—44no—
536C2×Q8—64no—
537C2×Q8—61no—
538C2×Q8—68no—
539C2×Q8—61no—
540C2×Q8—61no—
541C2×Q8—61no—
542C2×Q8—61no—
543C2×Q8—122no—
544C2×Q8—122no—
545C2×Q8—124no—
546C2×Q8—124no—
547C2×Q8—124no—
548C2×Q8C2×C4×D312yes—
549C2×Q8C2×C4×D312yes—
550C2×Q8D3×D412yes—
551C2×Q8#23712yes—
552C2×D4—34no—
553C2×D4—62no—
554C2×D4—62no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—32no—
568C22×C4—32no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—64no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—122no—
581C22×C4—122no—
582C22×C4C2×C4×D312yes—
583C22×C4D3×D411yescharacteristic
584C22×C4D3×D412yes—
585C22×C4C23×D311yescharacteristic
586M16—124no—
587M16—124no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—32no—
595C2×C8—61no—
596C2×C8—61no—
597C2×C8—61no—
598C2×C8—61no—
599C2×C8—61no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—34no—
605C4⋊C4—32no—
606C4⋊C4—32no—
607C4⋊C4—64no—
608C4⋊C4—64no—
609C4⋊C4—64no—
610C4⋊C4—64no—
611C4⋊C4—64no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—122no—
617C4⋊C4—241no—
618C22⋊C4—34no—
619C22⋊C4—34no—
620C22⋊C4—64no—
621C22⋊C4—64no—
622C22⋊C4—81no—
623C22⋊C4—122no—
624C22⋊C4—122no—
625C22⋊C4—241no—
626C42—32no—
627C42—32no—
628C42—64no—
629C42—122no—
630C42—122no—
631C42—122no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3C22×C22⋊C411yescharacteristic
640C22×C3D4211yescharacteristic
641C22×C3#54611yescharacteristic
642C22×C3C2×#13711yescharacteristic
643C22×C3C2×#13711yescharacteristic
644C22×C3#57711yescharacteristic
645C22×C3#57811yescharacteristic
646C2×D3—22no—
647C2×D3—22no—
648C2×D3—22no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C3×C4—24no—
654C3×C4—22no—
655C3×C4—42no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4C2×C4×D411yescharacteristic
659C3×C4#51811yescharacteristic
660C3×C4D4211yescharacteristic
661C3×C4#54611yescharacteristic
662Dic3—22no—
663Dic3—22no—
664Dic3—42no—
665Dic3—42no—
666Dic3—42no—
667Dic3—81no—
668Dic3#41914yescomplemented
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—32no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23D3×C22⋊C412yes—
683C23C2×D3×D411yescharacteristic
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—22no—
689Q8—48no—
690Q8—41no—
691Q8—41no—
692Q8—62no—
693Q8—62no—
694Q8—128no—
695Q8—121no—
696Q8—121no—
697Q8#67⋊C414yes—
698D4—68no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—32no—
710C2×C4—32no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—32no—
714C2×C4—48no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—128no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4D3×C22⋊C412yes—
745C2×C4C22×C4×D311yescharacteristic
746C2×C4C2×D3×D411yescharacteristic
747C2×C4C2×D3×D411yescharacteristic
748C2×C4C2×#23711yescharacteristic
749C2×C4#100411yescharacteristic
750C2×C4#100411yescharacteristic
751C8—41no—
752C8—41no—
753C8—62no—
754C8—121no—
755C2×C3—42no—
756C2×C3D4×C22⋊C411yescharacteristic
757C2×C3C2×#41911yescharacteristic
758C2×C3#289811yescharacteristic
759C2×C3#327611yescharacteristic
760C2×C3#327811yescharacteristic
761C2×C3#332811yescharacteristic
762C2×C3#332911yescharacteristic
763D3—42no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—62no—
772C22—62no—
773C22—62no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22C2×D3×C22⋊C411yescharacteristic
779C22#559011yescharacteristic
780C22#559111yescharacteristic
781C22#576211yescharacteristic
782C22#576611yescharacteristic
783C22D3×#13711yescharacteristic
784C22D3×#13711yescharacteristic
785C4—22no—
786C4—24no—
787C4—34no—
788C4—42no—
789C4—62no—
790C4—62no—
791C4—81no—
792C4—81no—
793C4—122no—
794C4—122no—
795C4—122no—
796C4—241no—
797C4C2×#67⋊C411yescharacteristic
798C4#548611yescharacteristic
799C4#559011yescharacteristic
800C4#559111yescharacteristic
801C3#2243011yescharacteristic, complemented, Sylow
802C2—42no—
803C2—122no—
804C2#7385011yescharacteristic
805C2#7879011yescharacteristic
806C2D3×#41911yescharacteristic
807C2#8005611yescharacteristic
808C2#8006611yescharacteristic
809C2#8020011yescharacteristic
810C2#8020611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1787C2
socleC23×C3C22×D4
prime radicalC22×#67D4
cosocleC22×C3×C4C24
hypercenter#1787D3
hypocenterC3#22430
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
2. C2×#5225C2semidirect
3. C2×#4802C2semidirect
6. C3×#1787C2semidirect
7. #70271C2semidirect
8. #70269C2semidirect
9. #70266C2semidirect
10. #70229C2semidirect
11. #70225C2semidirect
12. #70221C2semidirect
13. Dic3×#103C2semidirect
14. #69931C2semidirect
15. #69516C2semidirect
20. Q8×#67C4semidirect
78. #1787D3semidirect
165. #835D4semidirect
668. Dic3#419semidirect
801. C3#22430semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#672
C2×#52252
C2×#48022
C2×#47292
#738852
C3×#17872
#702712
#702692
#702662
#702292
#702252
#702212
Dic3×#1032
#699312
#695162
#224303