Finite Group Databasebeta

← #10800531

Subgroups — #10800531

Order 768.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2#84027C211yesmaximal, characteristic, complemented
3C2×C4×#217C211yesmaximal, characteristic, complemented
4#71701C212yesmaximal, complemented
5#71686C212yesmaximal, complemented
6#71670C214yesmaximal, complemented
7C4×#834C214yesmaximal, complemented
8#21420—31nomaximal, Sylow
9C22×C3×#41C411yescharacteristic, complemented
10C24×C3×C4C2211yescharacteristic
11C3×#525—21no—
12C3×#525—21no—
13C3×#525—21no—
14C3×#525—21no—
15C3×#525—21no—
16C3×#525—21no—
17C3×#525—21no—
18C3×#525—21no—
19C2×C3×#123C412yescomplemented
20C2×C3×C22⋊Q8C411yescharacteristic, complemented
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C411yescharacteristic, complemented
23C2×C3×#121C2211yescharacteristic
24C2×C3×#120C2212yes—
25C2×C3×C4×D4C412yescomplemented
26C2×C3×C4×D4C2212yes—
27C2×C3×#117C411yescharacteristic, complemented
28C22×#217C2212yes—
29C2×#926—21no—
30C22×C4×Dic3—21no—
31#5247C2212yes—
32C2×#834C2218yes—
33#5212—21no—
34#5212C2212yes—
35#5211—21no—
36C4×#217—21no—
37C4×#217—21no—
38C4×#217—21no—
39C4×#217C2212yes—
40C4×#217C2212yes—
41C4×#217C2212yes—
42C2×C3⋊#95—21no—
43#4526C2218yes—
44C2×#525D311yescharacteristic
45#2280—31no—
46C2×C4×C22⋊C4—31no—
47#1996—32no—
48#1964—32no—
49#1898—34no—
50C4×#99—34no—
51C25×C3C2311yescharacteristic
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41—44no—
57C22×C3×Q8C2×C411yescharacteristic, complemented
58C22×C3×D4C2×C412yes—
59C22×C3×D4C2×C412yes—
60C22×C3×D4C2×C411yescharacteristic, complemented
61C22×C3×D4C2312yes—
62C23×C3×C4—44no—
63C23×C3×C4C2×C411yescharacteristic
64C23×C3×C4C2×C411yescharacteristic
65C23×C3×C4C2×C411yescharacteristic
66C23×C3×C4C2×C411yescharacteristic
67C23×C3×C4C2×C412yescomplemented
68C23×C3×C4D411yescharacteristic
69C23×C3×C4D411yescharacteristic
70C23×C3×C4D411yescharacteristic
71C23×C3×C4D411yescharacteristic
72C23×C3×C4D411yescharacteristic
73C23×C3×C4D411yescharacteristic
74C23×C3×C4D411yescharacteristic
75C23×C3×C4D411yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×Dic3—22no—
79C3×#123—22no—
80C3×#123—22no—
81C3×#123—22no—
82C3×#123—22no—
83C3×C22⋊Q8—21no—
84C3×C22⋊Q8—21no—
85C3×C22⋊Q8—21no—
86C3×C22⋊Q8—21no—
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C3×C22⋊Q8—21no—
90C3×C22⋊Q8—21no—
91C3×#121—21no—
92C3×#121—21no—
93C3×#121—21no—
94C3×#121—21no—
95C3×#121—21no—
96C3×#121—21no—
97C3×#121—21no—
98C3×#121—21no—
99C3×#120—22no—
100C3×#120—22no—
101C3×#120—22no—
102C3×#120—22no—
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×C4×D4—22no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C3×#117—21no—
112C3×#117—21no—
113C3×#117—21no—
114C3×#117—21no—
115C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
116C2×C3×C4⋊C4C2×C411yescharacteristic, complemented
117C2×C3×C4⋊C4C2×C412yescomplemented
118C2×C3×C4⋊C4C2×C412yescomplemented
119C2×C3×C22⋊C4C2×C412yes—
120C2×C3×C22⋊C4C2×C412yes—
121C2×C3×C22⋊C4C2×C412yescomplemented
122C2×C3×C22⋊C4C2×C412yescomplemented
123C2×C3×C22⋊C4C2312yes—
124C2×C3×C42C2×C412yescomplemented
125C2×#217—22no—
126C2×#217—28no—
127C2×#217—22no—
128C2×#217—22no—
129C2×#217C2314yes—
130C2×#217C2314yes—
131#926—44no—
132C2×C4⋊Dic3—22no—
133C2×C4×Dic3—22no—
134C2×C4×Dic3—22no—
135C2×C4×Dic3—22no—
136C2×C4×Dic3—44no—
137#834—216no—
138C3⋊#95—22no—
139C3⋊#95—22no—
140C3⋊#95—22no—
141C3⋊#95—22no—
142C22×#41Dic311yescharacteristic, complemented
143C24×C4C2×D311yescharacteristic
144#525—21no—
145#525—21no—
146#525—21no—
147#525—21no—
148#525—21no—
149#525—21no—
150#525—21no—
151#525—21no—
152C2×#123Dic312yescomplemented
153C2×C22⋊Q8Dic311yescharacteristic, complemented
154C2×C22⋊Q8C2×D311yescharacteristic
155C2×#121Dic311yescharacteristic, complemented
156C2×#121C2×D311yescharacteristic
157C2×#120C2×D312yes—
158C2×C4×D4Dic312yescomplemented
159C2×C4×D4C2×D312yes—
160C2×#117—61no—
161C2×#117Dic311yescharacteristic, complemented
162C22×C22⋊C4—32no—
163C22×C42—61no—
164C2×#99—38no—
165#381—61no—
166#380—32no—
167#380—61no—
168#379—32no—
169C4×C22⋊C4—32no—
170C4×C22⋊C4—32no—
171C4×C22⋊C4—32no—
172C4×C22⋊C4—61no—
173C4×C22⋊C4—61no—
174C4×C22⋊C4—61no—
175C2×#95—61no—
176#342—38no—
177C24×C3—24no—
178C24×C3—42no—
179C24×C3—42no—
180C24×C3C22×C411yescharacteristic
181C24×C3C22×C411yescharacteristic
182C24×C3C22×C412yes—
183C24×C3C2×D411yescharacteristic
184C24×C3C2×D411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C24×C3C2×D411yescharacteristic
187C24×C3C2411yescharacteristic
188C3×#41—44no—
189C3×#41—44no—
190C3×#41—44no—
191C3×#41—44no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—42no—
195C2×C3×D4—22no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—28no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—42no—
205C2×C3×D4—44no—
206C2×C3×D4—44no—
207C22×C3×C4—24no—
208C22×C3×C4—24no—
209C22×C3×C4—24no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—42no—
213C22×C3×C4—42no—
214C22×C3×C4—42no—
215C22×C3×C4—42no—
216C22×C3×C4—42no—
217C22×C3×C4—42no—
218C22×C3×C4—42no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4—44no—
224C22×C3×C4C22⋊C411yescharacteristic
225C22×C3×C4C22⋊C411yescharacteristic
226C22×C3×C4C22⋊C411yescharacteristic
227C22×C3×C4C22⋊C411yescharacteristic
228C22×C3×C4C22⋊C411yescharacteristic
229C22×C3×C4C22⋊C411yescharacteristic
230C22×C3×C4C22⋊C411yescharacteristic
231C22×C3×C4C22⋊C411yescharacteristic
232C22×C3×C4C22⋊C411yescharacteristic
233C22×C3×C4C22⋊C411yescharacteristic
234C22×C3×C4C22⋊C411yescharacteristic
235C22×C3×C4C22⋊C411yescharacteristic
236C22×C3×C4C22⋊C411yescharacteristic
237C22×C3×C4C22⋊C411yescharacteristic
238C22×C3×C4C22⋊C411yescharacteristic
239C22×C3×C4C22⋊C411yescharacteristic
240C22×C3×C4C22×C412yes—
241C22×C3×C4C22×C411yescharacteristic
242C22×C3×C4C22×C411yescharacteristic
243C22×C3×C4C22×C412yes—
244C22×C3×C4C22×C412yes—
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C22×C411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×Dic3—28no—
256C22×Dic3—24no—
257C22×Dic3—24no—
258C22×Dic3—44no—
259C22×Dic3—44no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—22no—
272C3×C22⋊C4—22no—
273C3×C22⋊C4—22no—
274C3×C22⋊C4—22no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—22no—
278C3×C42—22no—
279C3×C42—22no—
280#217—28no—
281#217—24no—
282#217—28no—
283#217—44no—
284#217—44no—
285#217#4118yescomplemented
286C4⋊Dic3—44no—
287C4×Dic3—44no—
288C4×Dic3—44no—
289C4×Dic3—44no—
290C25C22×D311yescharacteristic
291C2×#41—21no—
292C2×#41—21no—
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—44no—
296C22×Q8C2×Dic311yescharacteristic, complemented
297C22×D4C2×Dic312yes—
298C22×D4C2×Dic312yes—
299C22×D4C2×Dic311yescharacteristic, complemented
300C22×D4C22×D312yes—
301C23×C4—44no—
302C23×C4—62no—
303C23×C4C2×Dic311yescharacteristic
304C23×C4C2×Dic311yescharacteristic
305C23×C4C2×Dic311yescharacteristic
306C23×C4C2×Dic311yescharacteristic
307C23×C4C2×Dic312yescomplemented
308C23×C4#6711yescharacteristic
309C23×C4#6711yescharacteristic
310C23×C4#6711yescharacteristic
311C23×C4#6711yescharacteristic
312C23×C4#6711yescharacteristic
313C23×C4#6711yescharacteristic
314C23×C4#6711yescharacteristic
315C23×C4#6711yescharacteristic
316C23×C4C22×D311yescharacteristic
317C23×C4C22×D311yescharacteristic
318#123—22no—
319#123—22no—
320#123—22no—
321#123—22no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330#121—21no—
331#121—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#120—22no—
339#120—22no—
340#120—22no—
341#120—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350#117—21no—
351#117—21no—
352#117—21no—
353#117—21no—
354#117—124no—
355C2×C4⋊C4—62no—
356C2×C4⋊C4C2×Dic311yescharacteristic, complemented
357C2×C4⋊C4C2×Dic311yescharacteristic, complemented
358C2×C4⋊C4C2×Dic312yescomplemented
359C2×C4⋊C4C2×Dic312yescomplemented
360C2×C22⋊C4—34no—
361C2×C22⋊C4—34no—
362C2×C22⋊C4—68no—
363C2×C22⋊C4—62no—
364C2×C22⋊C4—62no—
365C2×C22⋊C4—62no—
366C2×C22⋊C4C2×Dic312yes—
367C2×C22⋊C4C2×Dic312yes—
368C2×C22⋊C4C2×Dic312yescomplemented
369C2×C22⋊C4C2×Dic312yescomplemented
370C2×C22⋊C4C22×D312yes—
371C2×C42—62no—
372C2×C42—62no—
373C2×C42—62no—
374C2×C42—124no—
375C2×C42C2×Dic312yescomplemented
376#99—616no—
377#95—62no—
378#95—62no—
379#95—62no—
380#95—62no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—24no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—416no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3C2×C22⋊C411yescharacteristic
407C23×C3C2×C22⋊C411yescharacteristic
408C23×C3C2×C22⋊C411yescharacteristic
409C23×C3C2×C22⋊C411yescharacteristic
410C23×C3C23×C411yescharacteristic
411C23×C3C22×D411yescharacteristic
412C23×C3C22×D411yescharacteristic
413C23×C3C2×#4114yes—
414C3×Q8—42no—
415C3×Q8—42no—
416C3×D4—42no—
417C3×D4—44no—
418C3×D4—44no—
419C3×D4—44no—
420C3×D4—44no—
421C3×D4—44no—
422C3×D4—44no—
423C3×D4—42no—
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—24no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—44no—
456C2×C3×C4—44no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4#9914yescomplemented
460C2×C3×C4C2×C22⋊C411yescharacteristic
461C2×C3×C4C2×C22⋊C411yescharacteristic
462C2×C3×C4C2×C22⋊C411yescharacteristic
463C2×C3×C4C2×C22⋊C411yescharacteristic
464C2×C3×C4C2×C22⋊C411yescharacteristic
465C2×C3×C4C2×C22⋊C411yescharacteristic
466C2×C3×C4C2×C22⋊C411yescharacteristic
467C2×C3×C4C2×C22⋊C411yescharacteristic
468C2×Dic3—28no—
469C2×Dic3—44no—
470C2×Dic3—416no—
471C2×Dic3—44no—
472C2×Dic3—44no—
473C2×Dic3—44no—
474C2×Dic3—44no—
475C24—24no—
476C24—42no—
477C24—42no—
478C24C22×Dic311yescharacteristic
479C24C22×Dic311yescharacteristic
480C24C22×Dic312yes—
481C24C2×#6711yescharacteristic
482C24C2×#6711yescharacteristic
483C24C2×#6711yescharacteristic
484C24C2×#6711yescharacteristic
485C24C23×D311yescharacteristic
486#41—44no—
487#41—44no—
488#41—44no—
489#41—44no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—42no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—28no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—42no—
503C2×D4—44no—
504C2×D4—44no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—44no—
522C22×C4—68no—
523C22×C4—64no—
524C22×C4—64no—
525C22×C4—124no—
526C22×C4—124no—
527C22×C4#21711yescharacteristic
528C22×C4#21711yescharacteristic
529C22×C4#21711yescharacteristic
530C22×C4#21711yescharacteristic
531C22×C4#21711yescharacteristic
532C22×C4#21711yescharacteristic
533C22×C4#21711yescharacteristic
534C22×C4#21711yescharacteristic
535C22×C4#21711yescharacteristic
536C22×C4#21711yescharacteristic
537C22×C4#21711yescharacteristic
538C22×C4#21711yescharacteristic
539C22×C4#21711yescharacteristic
540C22×C4#21711yescharacteristic
541C22×C4#21711yescharacteristic
542C22×C4#21711yescharacteristic
543C22×C4C22×Dic312yes—
544C22×C4C22×Dic311yescharacteristic
545C22×C4C22×Dic311yescharacteristic
546C22×C4C22×Dic312yes—
547C22×C4C22×Dic312yes—
548C22×C4C22×Dic311yescharacteristic
549C22×C4C22×Dic311yescharacteristic
550C22×C4C2×#6711yescharacteristic
551C22×C4C2×#6711yescharacteristic
552C22×C4C2×#6711yescharacteristic
553C22×C4C2×#6711yescharacteristic
554C22×C4C2×#6711yescharacteristic
555C22×C4C2×#6711yescharacteristic
556C22×C4C2×#6711yescharacteristic
557C22×C4C2×#6711yescharacteristic
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—124no—
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—38no—
578C22⋊C4—68no—
579C22⋊C4—64no—
580C22⋊C4—68no—
581C22⋊C4—124no—
582C22⋊C4—124no—
583C42—22no—
584C42—22no—
585C42—124no—
586C42—124no—
587C42—124no—
588C22×C3—28no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—84no—
615C22×C3C2×#9912yes—
616C22×C3#41012yes—
617C22×C3C22×C22⋊C411yescharacteristic
618C22×C3C4×#4112yes—
619C22×C3#52512yes—
620C22×C3#53212yes—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4C2×#9912yes—
631C3×C4C2×#9912yes—
632Dic3—48no—
633Dic3—84no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—416no—
657C23—42no—
658C23—42no—
659C23C2×#21711yescharacteristic
660C23C2×#21711yescharacteristic
661C23C2×#21711yescharacteristic
662C23C2×#21711yescharacteristic
663C23D3×#4114yes—
664C23C23×Dic311yescharacteristic
665C23C22×#6711yescharacteristic
666C23C22×#6711yescharacteristic
667Q8—42no—
668Q8—42no—
669D4—42no—
670D4—44no—
671D4—44no—
672D4—44no—
673D4—44no—
674D4—44no—
675D4—44no—
676D4—42no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—68no—
713C2×C4—124no—
714C2×C4—1216no—
715C2×C4—124no—
716C2×C4—124no—
717C2×C4—124no—
718C2×C4—124no—
719C2×C4#83414yescomplemented
720C2×C4C2×#21711yescharacteristic
721C2×C4C2×#21711yescharacteristic
722C2×C4C2×#21711yescharacteristic
723C2×C4C2×#21711yescharacteristic
724C2×C4C2×#21711yescharacteristic
725C2×C4C2×#21711yescharacteristic
726C2×C4C2×#21711yescharacteristic
727C2×C4C2×#21711yescharacteristic
728C2×C3—22no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—22no—
732C2×C3—22no—
733C2×C3—41no—
734C2×C3—41no—
735C2×C3—82no—
736C2×C3#229711yescharacteristic
737C2×C3C22×#9911yescharacteristic
738C2×C3C2×#41011yescharacteristic
739C22—28no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22C2×#83412yes—
767C22#524012yes—
768C22Dic3×#4112yes—
769C22#582812yes—
770C22#583212yes—
771C22C22×#21711yescharacteristic
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—128no—
782C4—244no—
783C4C2×#83412yes—
784C4C2×#83412yes—
785C3#2142011yescharacteristic, complemented, Sylow
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—82no—
794C2C22×#83411yescharacteristic
795C2C2×#524011yescharacteristic
796C2#8408611yescharacteristic
subgroupG/H
centerC2×C4C2×#217
commutatorC23×C3C23×C4
FrattiniC24C23×D3
Fitting, prime radicalC2×C3×#525C2
socleC22×C3C22×C22⋊C4
cosocleC24×C3C24
hypercenterC2×#525D3
hypocenterC3#21420
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
2. #84027C2semidirect
3. C2×C4×#217C2semidirect
4. #71701C2semidirect
5. #71686C2semidirect
6. #71670C2semidirect
7. C4×#834C2semidirect
9. C22×C3×#41C4semidirect
19. C2×C3×#123C4semidirect
20. C2×C3×C22⋊Q8C4semidirect
22. C2×C3×#121C4semidirect
25. C2×C3×C4×D4C4semidirect
27. C2×C3×#117C4semidirect
57. C22×C3×Q8C2×C4semidirect
60. C22×C3×D4C2×C4semidirect
67. C23×C3×C4C2×C4semidirect
115. C2×C3×C4⋊C4C2×C4semidirect
116. C2×C3×C4⋊C4C2×C4semidirect
117. C2×C3×C4⋊C4C2×C4semidirect
118. C2×C3×C4⋊C4C2×C4semidirect
121. C2×C3×C22⋊C4C2×C4semidirect
122. C2×C3×C22⋊C4C2×C4semidirect
124. C2×C3×C42C2×C4semidirect
142. C22×#41Dic3semidirect
152. C2×#123Dic3semidirect
153. C2×C22⋊Q8Dic3semidirect
155. C2×#121Dic3semidirect
158. C2×C4×D4Dic3semidirect
161. C2×#117Dic3semidirect
285. #217#41semidirect
296. C22×Q8C2×Dic3semidirect
299. C22×D4C2×Dic3semidirect
307. C23×C4C2×Dic3semidirect
356. C2×C4⋊C4C2×Dic3semidirect
357. C2×C4⋊C4C2×Dic3semidirect
358. C2×C4⋊C4C2×Dic3semidirect
359. C2×C4⋊C4C2×Dic3semidirect
368. C2×C22⋊C4C2×Dic3semidirect
369. C2×C22⋊C4C2×Dic3semidirect
375. C2×C42C2×Dic3semidirect
459. C2×C3×C4#99semidirect
719. C2×C4#834semidirect
785. C3#21420semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5252
#840272
C2×C4×#2172
#717012
#716862
#716702
C4×#8342
#214203