Finite Group Databasebeta

← #29685698

Subgroups — #29685698

Order 15616.

1552 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758222C211yesmaximal, characteristic, complemented
2C2×#16839905C211yesmaximal, characteristic
3C2×#16839872C211yesmaximal, characteristic, complemented
4C2×#16839862C211yesmaximal, characteristic, complemented
5#21446177C211yesmaximal, characteristic, complemented
6#21446170C211yesmaximal, characteristic, complemented
7#21446142C211yesmaximal, characteristic, complemented
8#21446086C211yesmaximal, characteristic, complemented
9#21446065C211yesmaximal, characteristic, complemented
10#21446016C211yesmaximal, characteristic, complemented
11#21445757C211yesmaximal, characteristic, complemented
12#21445652C211yesmaximal, characteristic, complemented
13#21445647C211yesmaximal, characteristic, complemented
14#21445581C211yesmaximal, characteristic, complemented
15C4×#121×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C4×#11758222—24no—
20C4×#11758222—24no—
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×C4×C22⋊D61—21no—
26C2×C4×C22⋊D61—21no—
27C2×#14519736C2211yescharacteristic
28C2×#14519734—21no—
29C2×C42×D61—21no—
30#16839905C418yescomplemented
31#16839872—24no—
32#16839862—24no—
33C2×#14519710C2211yescharacteristic
34C2×#14519708C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519697C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×C22⋊#92418C2211yescharacteristic
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519688C2211yescharacteristic
46C2×#14519688C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839517C2211yescharacteristic
52#16839517C2211yescharacteristic
53C2×#121×C61C2211yescharacteristic
54C2×C4×D4×C61—21no—
55C2×C4×D4×C61C2211yescharacteristic
56C22×C42×C61C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#389C2211yescharacteristic
59C61×#388—21no—
60C61×#386—21no—
61C61×#380C2211yescharacteristic
62C4×C4⋊C4×C61C2211yescharacteristic
63C4×C22⋊C4×C61—21no—
64C2×#11758222—22no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222C2×C414yescomplemented
70C22×Dic122C2311yescharacteristic
71C22×D244C2311yescharacteristic
72C22×C22⋊D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C2×#11758200—22no—
77C2×#11758200—22no—
78C2×#11758200C2×C414yescomplemented
79C2×#11758199—22no—
80C2×#11758199—22no—
81C2×#11758199C2×C414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86C4×Dic122—22no—
87C4×Dic122—22no—
88C4×Dic122—22no—
89C4×Dic122D414yescomplemented
90C4×D244—22no—
91C4×D244—22no—
92C4×D244—22no—
93C4×D244D414yescomplemented
94C4×C22⋊D61—28no—
95C4×C22⋊D61—28no—
96#14519736—22no—
97#14519736—22no—
98#14519734—28no—
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×C22⋊Dic61—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C42×D61—28no—
110#14519710—22no—
111#14519708—22no—
112#14519700—22no—
113#14519700—22no—
114#14519700C2×C414yescomplemented
115#14519698—22no—
116#14519698—22no—
117#14519697—22no—
118#14519697—22no—
119#14519697C2×C414yescomplemented
120C22⋊#92418—22no—
121C22⋊#92418C2×C414yescomplemented
122#14519688—22no—
123#14519688—22no—
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C23×C4×C61D411yescharacteristic
128C23×C4×C61D411yescharacteristic
129C23×C4×C61C2311yescharacteristic
130#121×C61—22no—
131#121×C61C2×C414yescomplemented
132C4×D4×C61—22no—
133C4×D4×C61—22no—
134C4×D4×C61—44no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61C2311yescharacteristic
137C2×C4⋊C4×C61C2311yescharacteristic
138C2×C4⋊C4×C61C2311yescharacteristic
139C2×C22⋊C4×C61—21no—
140C2×C22⋊C4×C61—21no—
141C2×C22⋊C4×C61—21no—
142C2×C22⋊C4×C61—21no—
143C2×C22⋊C4×C61—21no—
144C2×C42×C61—22no—
145C2×C42×C61—22no—
146C2×C42×C61—21no—
147C2×C42×C61D411yescharacteristic
148C2×C42×C61D411yescharacteristic
149C2×C42×C61C2311yescharacteristic
150C2×C42×C61C2311yescharacteristic
151#95×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C24×C61—21no—
155C24×C61C2×D411yescharacteristic
156C23×D61—21no—
157C2×D4×C61—24no—
158C2×D4×C61—21no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—42no—
164C2×D4×C61—42no—
165C2×D4×C61C22×C412yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—41no—
177C22×C4×C61—41no—
178C22×C4×C61—41no—
179C22×C4×C61—42no—
180C22×C4×C61—42no—
181C22×C4×C61—42no—
182C22×C4×C61C22×C412yes—
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61#4112yes—
189C22×C4×C61C2411yescharacteristic
190C2×C22⋊D61—24no—
191C2×C22⋊D61—24no—
192C2×C22⋊D61—24no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196#11758222—28no—
197#11758222—28no—
198#11758222—28no—
199#11758222—28no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244C22×C412yes—
204C2×D244C2×D412yes—
205C2×D244#4112yes—
206C2×C4×D61—24no—
207C2×C4×D61—24no—
208C2×C4×D61—24no—
209C2×C4×D61—24no—
210C2×C4×D61—24no—
211C2×C4×D61—42no—
212C2×C4×D61—42no—
213C2×C4×D61—42no—
214C2×C4×D61—42no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122C22×C412yes—
219C2×Dic122C2×D412yes—
220C2×Dic122#4112yes—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—21no—
223C4⋊C4×C61—21no—
224C4⋊C4×C61—21no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—42no—
227C4⋊C4×C61C22×C412yes—
228C22⋊C4×C61—24no—
229C22⋊C4×C61—42no—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—42no—
232C22⋊C4×C61—42no—
233C42×C61—22no—
234C42×C61—22no—
235C42×C61—21no—
236C42×C61—21no—
237C42×C61—42no—
238C42×C61C2×D412yes—
239C42×C61C2×D412yes—
240C22⋊Dic61—24no—
241#11758200—28no—
242#11758199—28no—
243#11758198—24no—
244#11758198—24no—
245C4⋊Dic61—21no—
246C4⋊Dic61—21no—
247C4⋊Dic61C2×D412yes—
248C4⋊Dic61C2×D412yes—
249#11758196—24no—
250#11758196—24no—
251C4×Dic61—24no—
252C4×Dic61—24no—
253C4×Dic61—24no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418—21no—
264C2×#92418C22×C412yes—
265C2×#92418C22×C412yes—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—22no—
273C23×C61—41no—
274C23×C61—41no—
275C23×C61—41no—
276C23×C61—41no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61C4×D412yes—
280C23×C61C22×D411yescharacteristic
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288D4×C61—22no—
289D4×C61—22no—
290D4×C61—48no—
291D4×C61—41no—
292D4×C61—41no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—21no—
299C2×C4×C61—21no—
300C2×C4×C61—21no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—44no—
310C2×C4×C61—44no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61—41no—
317C2×C4×C61—41no—
318C2×C4×C61—41no—
319C2×C4×C61—84no—
320C2×C4×C61C4×D412yes—
321C2×C4×C61#12012yes—
322C2×C4×C61#12012yes—
323C2×C4×C61AGL(1,ℤ/8)12yes—
324C2×C4×C61C23×C411yescharacteristic
325C2×C4×C61C22×D411yescharacteristic
326C2×C4×C61C22×D411yescharacteristic
327C2×C4×C61C2×#4111yescharacteristic
328C2×C4×C61C2×#4111yescharacteristic
329C2×C4×C61C2×#4111yescharacteristic
330C22⋊D61—216no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—41no—
337C2×Dic61—41no—
338C2×Dic61—41no—
339C2×Dic61—41no—
340D244—22no—
341D244—22no—
342D244—22no—
343D244C4×D414yescomplemented
344C4×D61—216no—
345C4×D61—48no—
346C4×D61—48no—
347Dic122—22no—
348Dic122—22no—
349Dic122—22no—
350Dic122C4×D414yescomplemented
351#92418—22no—
352#92418—22no—
353#92418—41no—
354#92418—41no—
355#21456—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—42no—
364C22×C61—42no—
365C22×C61—42no—
366C22×C61—81no—
367C22×C61—81no—
368C22×C61—81no—
369C22×C61—81no—
370C22×C61C2×C4×D411yescharacteristic
371C22×C61C2×#12011yescharacteristic
372C22×C61#52511yescharacteristic
373C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C61#57511yescharacteristic
375C22×C61#57511yescharacteristic
376C22×C61#57511yescharacteristic
377C2×D61—24no—
378C2×D61—42no—
379C2×D61—42no—
380C2×D61—42no—
381C2×D61—42no—
382C2×D61—42no—
383C2×D61—42no—
384C4×C61—22no—
385C4×C61—22no—
386C4×C61—22no—
387C4×C61—22no—
388C4×C61—42no—
389C4×C61—41no—
390C4×C61—81no—
391C4×C61—81no—
392C4×C61C2×C4×D411yescharacteristic
393C4×C61C2×C4×D411yescharacteristic
394C4×C61#52511yescharacteristic
395C4×C61#52511yescharacteristic
396Dic61—24no—
397Dic61—42no—
398Dic61—42no—
399C2×C4×#41—611no—
400C2×#449—611no—
401C2×#442—611no—
402C2×#440—611no—
403C4×#121D6111yescharacteristic, complemented
404#1880—611no—
405#1879—611no—
406#1875—611no—
407#1865—611no—
408#1862—611no—
409#1854—611no—
410#1788—611no—
411#1763—611no—
412#1762—611no—
413#1749—611no—
414C2×C61—42no—
415C2×C61—82no—
416C2×C61C4×#12011yescharacteristic
417C2×C61#294311yescharacteristic
418C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
419C2×C61#300511yescharacteristic
420C2×C61#300611yescharacteristic
421C2×C61#311111yescharacteristic
422C2×C61#311511yescharacteristic
423D61—44no—
424C22×#41—611no—
425C22×SD16—611no—
426C22×D8—611no—
427C2×#121C2×D6111yescharacteristic
428C4×#41—1224no—
429C4×#41—1224no—
430C2×C4×Q8—611no—
431C2×C4×Q8—611no—
432C2×C4×D4—21no—
433C2×C4×D4—611no—
434C2×C4×D4—611no—
435C2×C4×D4—1221no—
436C2×C4×D4—1221no—
437C2×C4×D4C2×D6111yescharacteristic
438C2×#117—611no—
439C2×#117—1221no—
440C22×C42—1221no—
441C22×C42C2×D6111yescharacteristic
442#449—618no—
443#442—1224no—
444#440—1224no—
445C2×#107—611no—
446C2×#106—611no—
447C2×#103—611no—
448C2×#103—611no—
449C2×#103—611no—
450C2×#102—611no—
451C2×#102—611no—
452C2×#102—611no—
453C2×#102—611no—
454C2×#102—611no—
455C2×C22⋊C8—611no—
456C2×C22⋊C8—611no—
457C2×#97—611no—
458C2×#97—611no—
459#390C2×D6111yescharacteristic
460#389C2×D6111yescharacteristic
461#388—21no—
462#386—21no—
463#380C2×D6111yescharacteristic
464C4×C4⋊C4C2×D6111yescharacteristic
465C4×C22⋊C4—21no—
466#340—611no—
467#340—611no—
468#340—611no—
469#340—611no—
470#336—611no—
471#336—611no—
472C61#2145611yescharacteristic, complemented, Sylow
473C2×#41—614no—
474C2×#41—1222no—
475C2×#41—1222no—
476C2×#41—1222no—
477C2×#41—1222no—
478C2×#41—1222no—
479C22×Q8—611no—
480C22×D4—21no—
481C22×D4—611no—
482C22×D4—1221no—
483C22×D4C22×D6111yescharacteristic
484C23×C4—21no—
485C23×C4—1221no—
486C23×C4—1221no—
487C23×C4—1221no—
488C23×C4C22⋊D6111yescharacteristic
489C23×C4C22⋊D6111yescharacteristic
490C23×C4C22×D6111yescharacteristic
491C2×SD16—614no—
492C2×SD16—1222no—
493C2×SD16—1222no—
494C2×D8—614no—
495C2×D8—1222no—
496C2×D8—1222no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501#121—22no—
502#121C4×D6114yescomplemented
503C4×Q8—614no—
504C4×Q8—1222no—
505C4×Q8—1222no—
506C4×Q8—1222no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—44no—
510C4×D4—614no—
511C4×D4—1222no—
512C4×D4—1222no—
513C4×D4—1228no—
514C4×D4—1228no—
515C4×D4—1222no—
516#117—1228no—
517#117—1222no—
518#117—1222no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—611no—
521C2×C4⋊C4—611no—
522C2×C4⋊C4—1221no—
523C2×C4⋊C4—1221no—
524C2×C4⋊C4C22×D6111yescharacteristic
525C2×C4⋊C4C22×D6111yescharacteristic
526C2×C4⋊C4C22×D6111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C22⋊C4—1221no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—21no—
538C2×C42—1228no—
539C2×C42—1221no—
540C2×C42—1221no—
541C2×C42—1221no—
542C2×C42C22⋊D6111yescharacteristic
543C2×C42C22⋊D6111yescharacteristic
544C2×C42C22×D6111yescharacteristic
545C2×C42C22×D6111yescharacteristic
546#107—1222no—
547#106—1222no—
548#103—614no—
549#103—1222no—
550#103—1222no—
551#102—614no—
552#102—1222no—
553#102—1222no—
554#102—1222no—
555#102—1222no—
556C22⋊C8—614no—
557C22⋊C8—1222no—
558#97—1222no—
559#97—1222no—
560#95—21no—
561#95—21no—
562#95—21no—
563C24—21no—
564C24—1221no—
565C24C2×C22⋊D6111yescharacteristic
566#41—1228no—
567#41—1228no—
568#41—1228no—
569#41—1228no—
570C2×Q8—612no—
571C2×Q8—612no—
572C2×Q8—612no—
573C2×Q8—1221no—
574C2×Q8—1221no—
575C2×Q8—1221no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—612no—
585C2×D4—612no—
586C2×D4—612no—
587C2×D4—1224no—
588C2×D4—1224no—
589C2×D4—1224no—
590C2×D4—1221no—
591C2×D4—1221no—
592C2×D4—1221no—
593C2×D4C2×C4×D6112yes—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—1224no—
611C22×C4—1224no—
612C22×C4—1224no—
613C22×C4—1221no—
614C22×C4—1224no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1224no—
618C22×C4—2442no—
619C22×C4—2442no—
620C22×C4—2442no—
621C22×C4—2442no—
622C22×C4C2×C4×D6112yes—
623C22×C4#1175822212yes—
624C22×C4C2×C22⋊D6111yescharacteristic
625C22×C4C2×C22⋊D6111yescharacteristic
626C22×C4C2×C22⋊D6111yescharacteristic
627C22×C4C2×C22⋊D6111yescharacteristic
628C22×C4C2×C22⋊D6111yescharacteristic
629C22×C4C23×D6111yescharacteristic
630SD16—1228no—
631D8—1228no—
632C2×C8—612no—
633C2×C8—612no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—612no—
651C4⋊C4—612no—
652C4⋊C4—1224no—
653C4⋊C4—1221no—
654C4⋊C4—1221no—
655C4⋊C4—1224no—
656C4⋊C4C2×C4×D6112yes—
657C22⋊C4—24no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—1224no—
663C22⋊C4—1224no—
664C22⋊C4—1224no—
665C42—21no—
666C42—21no—
667C42—22no—
668C42—22no—
669C42—42no—
670C42—1224no—
671C42—1224no—
672C42—1224no—
673C42D4×D6112yes—
674C42D4×D6112yes—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—22no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—2441no—
692C23—2441no—
693C23—2441no—
694C23—2441no—
695C23C4×C22⋊D6112yes—
696C23C22×C22⋊D6111yescharacteristic
697Q8—614no—
698Q8—1222no—
699Q8—1222no—
700Q8—1222no—
701D4—22no—
702D4—22no—
703D4—48no—
704D4—41no—
705D4—41no—
706D4—614no—
707D4—12216no—
708D4—1222no—
709D4—1222no—
710D4—1222no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—12216no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—1222no—
744C2×C4—2448no—
745C2×C4—2448no—
746C2×C4—2441no—
747C2×C4—2441no—
748C2×C4—2441no—
749C2×C4—2441no—
750C2×C4C4×C22⋊D6112yes—
751C2×C4#1451974512yes—
752C2×C4#1451974512yes—
753C2×C4#1451980312yes—
754C2×C4C22×C4×D6111yescharacteristic
755C2×C4C2×D4×D6111yescharacteristic
756C2×C4C2×D4×D6111yescharacteristic
757C2×C4#41×D6111yescharacteristic
758C2×C4#41×D6111yescharacteristic
759C2×C4C2×#1175822211yescharacteristic
760C8—1222no—
761C8—1222no—
762C8—2441no—
763C8—2441no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—1224no—
779C22—2442no—
780C22—2442no—
781C22—2442no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22C2×C4×C22⋊D6111yescharacteristic
786C22C2×#1451974511yescharacteristic
787C22#1684026911yescharacteristic
788C22C2×#1451980311yescharacteristic
789C22#1684056011yescharacteristic
790C22#1684056011yescharacteristic
791C22#1684056011yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—81no—
799C4—81no—
800C4—1224no—
801C4—2442no—
802C4—2442no—
803C4C4×D4×D6111yescharacteristic
804C4C4×D4×D6111yescharacteristic
805C4#1684027111yescharacteristic
806C4#1684027111yescharacteristic
807C2—42no—
808C2—82no—
809C2—2444no—
810C2C4×#1451974511yescharacteristic
811C2#2145461711yescharacteristic
812C2C4×#1451980311yescharacteristic
813C2#2145505911yescharacteristic
814C2#2145506911yescharacteristic
815C2#2145592211yescharacteristic
816C2#2145596411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#121×C61C2
socleC23×C61C22×D4
prime radicalC2×#16839905C2
cosocleC22×C4×C61C24
hypercenterC4×#121D61
hypocenterC61#21456
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758222C2semidirect
3. C2×#16839872C2semidirect
4. C2×#16839862C2semidirect
5. #21446177C2semidirect
6. #21446170C2semidirect
7. #21446142C2semidirect
8. #21446086C2semidirect
9. #21446065C2semidirect
10. #21446016C2semidirect
11. #21445757C2semidirect
12. #21445652C2semidirect
13. #21445647C2semidirect
14. #21445581C2semidirect
15. C4×#121×C61C2semidirect
30. #16839905C4semidirect
69. C2×#11758222C2×C4semidirect
78. C2×#11758200C2×C4semidirect
81. C2×#11758199C2×C4semidirect
89. C4×Dic122D4semidirect
93. C4×D244D4semidirect
114. #14519700C2×C4semidirect
119. #14519697C2×C4semidirect
121. C22⋊#92418C2×C4semidirect
131. #121×C61C2×C4semidirect
343. D244C4×D4semidirect
350. Dic122C4×D4semidirect
403. C4×#121D61semidirect
472. C61#21456semidirect
502. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582222
C2×#168399052
C2×#168398722
C2×#168398622
#214461772
#214461702
#214461422
#214460862
#214460652
#214460162
#214457572
#214456522
#214456472
#214455812
C4×#121×C612
#2145661