Finite Group Databasebeta

← #10804993

Subgroups — #10804993

Order 768.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 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×#5212C211yesmaximal, characteristic, complemented
4#71701C212yesmaximal, complemented
5#71686C212yesmaximal, complemented
6#71670C214yesmaximal, complemented
7#71619C214yesmaximal, complemented
8#21874—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#5212—21no—
35#5212—21no—
36#5212C2212yes—
37#5212C2212yes—
38#5212C2212yes—
39#5211—21no—
40C4×#217—21no—
41C4×#217C2212yes—
42C2×C3⋊#95—21no—
43#4526C2218yes—
44C2×#525D311yescharacteristic
45#2280—31no—
46C2×#380—31no—
47#1996—32no—
48#1964—32no—
49#1898—34no—
50#1799—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—22no—
127C2×#217—22no—
128C2×#217—44no—
129C2×#217C2314yes—
130C2×#217C2314yes—
131#926—44no—
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—22no—
135C2×C4⋊Dic3—44no—
136C2×C4×Dic3—22no—
137#834—48no—
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×C4⋊C4—61no—
163C22×C22⋊C4—32no—
164C2×#99—38no—
165#381—61no—
166#380—32no—
167#380—32no—
168#380—32no—
169#380—61no—
170#380—61no—
171#380—61no—
172#379—32no—
173C4×C22⋊C4—32no—
174C4×C22⋊C4—61no—
175C2×#95—61no—
176#342—38no—
177C24×C3—22no—
178C24×C3—22no—
179C24×C3—42no—
180C24×C3—42no—
181C24×C3C22×C411yescharacteristic
182C24×C3C22×C411yescharacteristic
183C24×C3C22×C412yes—
184C24×C3C2×D411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C24×C3C2×D411yescharacteristic
187C24×C3C2×D411yescharacteristic
188C24×C3C2411yescharacteristic
189C3×#41—44no—
190C3×#41—44no—
191C3×#41—44no—
192C3×#41—44no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—42no—
196C2×C3×D4—22no—
197C2×C3×D4—22no—
198C2×C3×D4—22no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—24no—
203C2×C3×D4—24no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—42no—
207C2×C3×D4—44no—
208C2×C3×D4—44no—
209C22×C3×C4—24no—
210C22×C3×C4—24no—
211C22×C3×C4—24no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
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—42no—
224C22×C3×C4—42no—
225C22×C3×C4—44no—
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⋊C411yescharacteristic
241C22×C3×C4C22⋊C411yescharacteristic
242C22×C3×C4C22×C412yes—
243C22×C3×C4C22×C411yescharacteristic
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C22×C412yes—
246C22×C3×C4C22×C412yes—
247C22×C3×C4C22×C411yescharacteristic
248C22×C3×C4C22×C411yescharacteristic
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×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×Dic3—24no—
258C22×Dic3—24no—
259C22×Dic3—44no—
260C22×Dic3—44no—
261C22×Dic3—44no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—22no—
269C3×C4⋊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×C22⋊C4—22no—
279C3×C22⋊C4—22no—
280C3×C42—22no—
281C3×C42—22no—
282#217—24no—
283#217—28no—
284#217—24no—
285#217—44no—
286#217—44no—
287#217—44no—
288C4⋊Dic3—44no—
289C4⋊Dic3—44no—
290C4⋊Dic3—44no—
291C4×Dic3—44no—
292C25C22×D311yescharacteristic
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—21no—
296C2×#41—21no—
297C2×#41—44no—
298C22×Q8C2×Dic311yescharacteristic, complemented
299C22×D4C2×Dic312yes—
300C22×D4C2×Dic312yes—
301C22×D4C2×Dic311yescharacteristic, complemented
302C22×D4C22×D312yes—
303C23×C4—44no—
304C23×C4—62no—
305C23×C4C2×Dic311yescharacteristic
306C23×C4C2×Dic311yescharacteristic
307C23×C4C2×Dic311yescharacteristic
308C23×C4C2×Dic311yescharacteristic
309C23×C4C2×Dic312yescomplemented
310C23×C4#6711yescharacteristic
311C23×C4#6711yescharacteristic
312C23×C4#6711yescharacteristic
313C23×C4#6711yescharacteristic
314C23×C4#6711yescharacteristic
315C23×C4#6711yescharacteristic
316C23×C4#6711yescharacteristic
317C23×C4#6711yescharacteristic
318C23×C4C22×D311yescharacteristic
319C23×C4C22×D311yescharacteristic
320#123—22no—
321#123—22no—
322#123—22no—
323#123—22no—
324C22⋊Q8—21no—
325C22⋊Q8—21no—
326C22⋊Q8—21no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—21no—
331C22⋊Q8—21no—
332#121—21no—
333#121—21no—
334#121—21no—
335#121—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#120—22no—
341#120—22no—
342#120—22no—
343#120—22no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—21no—
353#117—21no—
354#117—21no—
355#117—21no—
356#117—124no—
357C2×C4⋊C4—62no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—124no—
361C2×C4⋊C4C2×Dic311yescharacteristic, complemented
362C2×C4⋊C4C2×Dic311yescharacteristic, complemented
363C2×C4⋊C4C2×Dic312yescomplemented
364C2×C4⋊C4C2×Dic312yescomplemented
365C2×C22⋊C4—34no—
366C2×C22⋊C4—34no—
367C2×C22⋊C4—62no—
368C2×C22⋊C4—62no—
369C2×C22⋊C4—62no—
370C2×C22⋊C4—124no—
371C2×C22⋊C4C2×Dic312yes—
372C2×C22⋊C4C2×Dic312yes—
373C2×C22⋊C4C2×Dic312yescomplemented
374C2×C22⋊C4C2×Dic312yescomplemented
375C2×C22⋊C4C22×D312yes—
376C2×C42—62no—
377C2×C42C2×Dic312yescomplemented
378#99—128no—
379#95—62no—
380#95—62no—
381#95—62no—
382#95—62no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—24no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—48no—
408C23×C3—48no—
409C23×C3—42no—
410C23×C3—42no—
411C23×C3C2×C22⋊C411yescharacteristic
412C23×C3C2×C22⋊C411yescharacteristic
413C23×C3C2×C22⋊C411yescharacteristic
414C23×C3C2×C22⋊C411yescharacteristic
415C23×C3C23×C411yescharacteristic
416C23×C3C22×D411yescharacteristic
417C23×C3C22×D411yescharacteristic
418C23×C3H(5,𝔽2)12yes—
419C23×C32−1+412yes—
420C3×Q8—42no—
421C3×Q8—42no—
422C3×D4—42no—
423C3×D4—44no—
424C3×D4—44no—
425C3×D4—42no—
426C3×D4—42no—
427C3×D4—44no—
428C3×D4—44no—
429C3×D4—44no—
430C3×D4—42no—
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—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—24no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—44no—
463C2×C3×C4—44no—
464C2×C3×C4—42no—
465C2×C3×C4—42no—
466C2×C3×C4#9914yescomplemented
467C2×C3×C4C2×C22⋊C411yescharacteristic
468C2×C3×C4C2×C22⋊C411yescharacteristic
469C2×C3×C4C2×C22⋊C411yescharacteristic
470C2×C3×C4C2×C22⋊C411yescharacteristic
471C2×C3×C4C2×C22⋊C411yescharacteristic
472C2×C3×C4C2×C22⋊C411yescharacteristic
473C2×C3×C4C2×C22⋊C411yescharacteristic
474C2×C3×C4C2×C22⋊C411yescharacteristic
475C2×Dic3—44no—
476C2×Dic3—44no—
477C2×Dic3—44no—
478C2×Dic3—44no—
479C2×Dic3—44no—
480C2×Dic3—44no—
481C2×Dic3—88no—
482C24—22no—
483C24—22no—
484C24—42no—
485C24—42no—
486C24C22×Dic311yescharacteristic
487C24C22×Dic311yescharacteristic
488C24C22×Dic312yes—
489C24C2×#6711yescharacteristic
490C24C2×#6711yescharacteristic
491C24C2×#6711yescharacteristic
492C24C2×#6711yescharacteristic
493C24C23×D311yescharacteristic
494#41—44no—
495#41—44no—
496#41—44no—
497#41—44no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—42no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—24no—
506C2×D4—24no—
507C2×D4—22no—
508C2×D4—22no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—44no—
513C2×D4—44no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—44no—
531C22×C4—64no—
532C22×C4—64no—
533C22×C4—124no—
534C22×C4—124no—
535C22×C4—124no—
536C22×C4#21711yescharacteristic
537C22×C4#21711yescharacteristic
538C22×C4#21711yescharacteristic
539C22×C4#21711yescharacteristic
540C22×C4#21711yescharacteristic
541C22×C4#21711yescharacteristic
542C22×C4#21711yescharacteristic
543C22×C4#21711yescharacteristic
544C22×C4#21711yescharacteristic
545C22×C4#21711yescharacteristic
546C22×C4#21711yescharacteristic
547C22×C4#21711yescharacteristic
548C22×C4#21711yescharacteristic
549C22×C4#21711yescharacteristic
550C22×C4#21711yescharacteristic
551C22×C4#21711yescharacteristic
552C22×C4C22×Dic312yes—
553C22×C4C22×Dic311yescharacteristic
554C22×C4C22×Dic311yescharacteristic
555C22×C4C22×Dic312yes—
556C22×C4C22×Dic312yes—
557C22×C4C22×Dic311yescharacteristic
558C22×C4C22×Dic311yescharacteristic
559C22×C4C2×#6711yescharacteristic
560C22×C4C2×#6711yescharacteristic
561C22×C4C2×#6711yescharacteristic
562C22×C4C2×#6711yescharacteristic
563C22×C4C2×#6711yescharacteristic
564C22×C4C2×#6711yescharacteristic
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—124no—
576C4⋊C4—124no—
577C4⋊C4—124no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—22no—
584C22⋊C4—22no—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—64no—
589C22⋊C4—68no—
590C22⋊C4—64no—
591C22⋊C4—124no—
592C22⋊C4—124no—
593C22⋊C4—124no—
594C42—22no—
595C42—22no—
596C42—124no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—21no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—44no—
618C22×C3—44no—
619C22×C3—44no—
620C22×C3—44no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—42no—
626C22×C3—84no—
627C22×C3C2×#9912yes—
628C22×C3#41012yes—
629C22×C3C22×C22⋊C411yescharacteristic
630C22×C3#52012yes—
631C22×C3#53511yescharacteristic
632C22×C3#53611yescharacteristic
633C22×C3#53712yes—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—42no—
643C3×C4C2×#9912yes—
644C3×C4C2×#9912yes—
645Dic3—84no—
646Dic3—84no—
647C23—22no—
648C23—22no—
649C23—21no—
650C23—21no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—21no—
656C23—22no—
657C23—22no—
658C23—21no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—48no—
672C23—48no—
673C23—42no—
674C23—42no—
675C23C2×#21711yescharacteristic
676C23C2×#21711yescharacteristic
677C23C2×#21711yescharacteristic
678C23C2×#21711yescharacteristic
679C23#100912yes—
680C23#101012yes—
681C23C23×Dic311yescharacteristic
682C23C22×#6711yescharacteristic
683C23C22×#6711yescharacteristic
684Q8—42no—
685Q8—42no—
686D4—42no—
687D4—44no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—42no—
692D4—42no—
693D4—44no—
694D4—42no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—41no—
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—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—124no—
731C2×C4—124no—
732C2×C4—124no—
733C2×C4—124no—
734C2×C4—124no—
735C2×C4—124no—
736C2×C4—248no—
737C2×C4#83414yescomplemented
738C2×C4C2×#21711yescharacteristic
739C2×C4C2×#21711yescharacteristic
740C2×C4C2×#21711yescharacteristic
741C2×C4C2×#21711yescharacteristic
742C2×C4C2×#21711yescharacteristic
743C2×C4C2×#21711yescharacteristic
744C2×C4C2×#21711yescharacteristic
745C2×C4C2×#21711yescharacteristic
746C2×C3—21no—
747C2×C3—22no—
748C2×C3—21no—
749C2×C3—22no—
750C2×C3—22no—
751C2×C3—22no—
752C2×C3—41no—
753C2×C3—41no—
754C2×C3—82no—
755C2×C3#231111yescharacteristic
756C2×C3C22×#9911yescharacteristic
757C2×C3C2×#41011yescharacteristic
758C22—24no—
759C22—24no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—84no—
788C22C2×#83412yes—
789C22#524012yes—
790C22#582511yescharacteristic
791C22#582712yes—
792C22#583011yescharacteristic
793C22#583312yes—
794C22C22×#21711yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—244no—
805C4—244no—
806C4C2×#83412yes—
807C4C2×#83412yes—
808C3#2187411yescharacteristic, complemented, Sylow
809C2—21no—
810C2—22no—
811C2—22no—
812C2—22no—
813C2—21no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2C22×#83411yescharacteristic
819C2C2×#524011yescharacteristic
820C2#8408711yescharacteristic
subgroupG/H
centerC22C22×#217
commutatorC23×C3C23×C4
FrattiniC24C23×D3
Fitting, prime radicalC2×C3×#525C2
socleC22×C3C22×C22⋊C4
cosocleC24×C3C24
hypercenterC2×#525D3
hypocenterC3#21874
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
2. #84027C2semidirect
3. C2×#5212C2semidirect
4. #71701C2semidirect
5. #71686C2semidirect
6. #71670C2semidirect
7. #71619C2semidirect
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
298. C22×Q8C2×Dic3semidirect
301. C22×D4C2×Dic3semidirect
309. C23×C4C2×Dic3semidirect
361. C2×C4⋊C4C2×Dic3semidirect
362. C2×C4⋊C4C2×Dic3semidirect
363. C2×C4⋊C4C2×Dic3semidirect
364. C2×C4⋊C4C2×Dic3semidirect
373. C2×C22⋊C4C2×Dic3semidirect
374. C2×C22⋊C4C2×Dic3semidirect
377. C2×C42C2×Dic3semidirect
466. C2×C3×C4#99semidirect
737. C2×C4#834semidirect
808. C3#21874semidirect

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×#52122
#717012
#716862
#716702
#716192
#218743