Finite Group Databasebeta

← #29689108

Subgroups — #29689108

Order 15616.

1518 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840329C211yesmaximal, characteristic
2C2×#16839727C211yesmaximal, characteristic, complemented
3#21448408C211yesmaximal, characteristic, complemented
4#21446254C211yesmaximal, characteristic, complemented
5#21446254C211yesmaximal, characteristic, complemented
6#21446244C211yesmaximal, characteristic, complemented
7#21446244C211yesmaximal, characteristic, complemented
8#21446138C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21446133C211yesmaximal, characteristic, complemented
12#21445915C211yesmaximal, characteristic, complemented
13#21445911C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C61×#1786C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×#11758189C2211yescharacteristic, complemented
18C22×C8×D61C2211yescharacteristic, complemented
19#16840329—24no—
20#16840329C418yescomplemented
21C2×#14519773—21no—
22C2×#14519764—21no—
23C2×#14519748C2211yescharacteristic
24C2×#14519748C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×#14519748C2211yescharacteristic
27C2×#14519746—21no—
28C2×#14519746—21no—
29C2×#14519736C2211yescharacteristic
30C2×#14519735C2211yescharacteristic, complemented
31C2×C4⋊C4×D61C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36#16839727—24no—
37C2×C22⋊#92418C2211yescharacteristic
38C2×#14519689C2211yescharacteristic, complemented
39C2×#14519689C2211yescharacteristic, complemented
40#16839666—21no—
41#16839662—21no—
42#16839640—21no—
43#16839638—21no—
44#16839622C2211yescharacteristic
45#16839619C2211yescharacteristic, complemented
46#16839619C2211yescharacteristic, complemented
47#16839525C2211yescharacteristic, complemented
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55C23×D4×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic
60C2×C22⋊C8×C61C2211yescharacteristic
61C61×#380C2211yescharacteristic
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222C2×C414yes—
67C2×#11758222D414yes—
68C22×Dic122D411yescharacteristic
69C22×D244D411yescharacteristic
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C22×C22⋊D61—21no—
73C22×C22⋊D61—21no—
74C22×C22⋊D61D411yescharacteristic
75C22×C22⋊D61D411yescharacteristic
76C22×C4×D61—21no—
77C22×C4×D61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C2×#11758189—22no—
80C2×#11758189—41no—
81C2×#11758189—41no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C8×D61—22no—
85C2×C8×D61—41no—
86C2×C8×D61—41no—
87#14519773—28no—
88#14519764—28no—
89#14519748—22no—
90#14519748—22no—
91#14519748—22no—
92#14519748—22no—
93#14519748C2×C414yes—
94#14519748C2×C414yes—
95#14519748C2×C414yescomplemented
96#14519748C2×C414yescomplemented
97#14519746—28no—
98#14519746—28no—
99#14519736—22no—
100#14519736C2×C414yescomplemented
101#14519735—41no—
102#14519735—41no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C4⋊C4×D61—41no—
109C4⋊C4×D61—41no—
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×C22⋊Dic61—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121#14519698—41no—
122#14519698—41no—
123#14519698—41no—
124#14519698—41no—
125C22⋊#92418—22no—
126#14519689—22no—
127#14519689—22no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C25×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—22no—
134C22×D4×C61—41no—
135C22×D4×C61—41no—
136C22×D4×C61—41no—
137C22×D4×C61—41no—
138C22×D4×C61C2×C414yescomplemented
139C22×D4×C61C2311yescharacteristic
140C22×D4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C22⋊C4×C61—21no—
147#102×C61—41no—
148#102×C61—41no—
149#102×C61—41no—
150#102×C61—41no—
151C22⋊C8×C61—22no—
152#95×C61—21no—
153C24×C61—21no—
154C24×C61—21no—
155C24×C61—24no—
156C24×C61—42no—
157C24×C61—42no—
158C24×C61—81no—
159C24×C61—81no—
160C24×C61—81no—
161C24×C61—81no—
162C24×C61C2×D411yescharacteristic
163C23×D61C2×D411yescharacteristic
164C23×D61C2×D411yescharacteristic
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—44no—
177C2×D4×C61—44no—
178C2×D4×C61—42no—
179C2×D4×C61—42no—
180C2×D4×C61—44no—
181C2×D4×C61—44no—
182C2×D4×C61C22×C412yes—
183C2×D4×C61C22×C412yes—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61C22×C412yes—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D412yes—
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—24no—
196C2×C22⋊D61—24no—
197C2×C22⋊D61—24no—
198C2×C22⋊D61—41no—
199C2×C22⋊D61—41no—
200C2×C22⋊D61—41no—
201C2×C22⋊D61—41no—
202C2×C22⋊D61—81no—
203C2×C22⋊D61—81no—
204C2×C22⋊D61—81no—
205C2×C22⋊D61—81no—
206C2×C22⋊D61—81no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61C22⋊C414yes—
211C2×C22⋊D61C22⋊C414yes—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—21no—
216C22×Dic61C2×D411yescharacteristic
217C22×Dic61C2×D411yescharacteristic
218#11758222—44no—
219#11758222—44no—
220#11758222—44no—
221#11758222—44no—
222C2×D244—41no—
223C2×D244—41no—
224C2×D244C22⋊C414yes—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—42no—
234C2×C4×D61—81no—
235C2×C4×D61—81no—
236C2×C4×D61C22×C412yes—
237C2×C4×D61C22×C412yes—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2×D412yes—
240C2×Dic122—41no—
241C2×Dic122—41no—
242C2×Dic122C22⋊C414yes—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C22⋊C4×C61—81no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—24no—
258C22⋊Dic61—24no—
259C22⋊Dic61—81no—
260#11758198—42no—
261#11758198—81no—
262#11758198—81no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61C22×C412yes—
270C4⋊Dic61C22×C412yes—
271#11758196—42no—
272C4×Dic61—24no—
273C4×Dic61—42no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280#11758189—44no—
281C8×D61—44no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—22no—
289C23×C61—22no—
290C23×C61—48no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—84no—
304C23×C61—84no—
305C23×C61—84no—
306C23×C61—84no—
307C23×C61—84no—
308C23×C61—84no—
309C23×C61C2×C22⋊C412yes—
310C23×C61C22×D411yescharacteristic
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61C2×C22⋊C412yes—
324C22×D61C2×C22⋊C412yes—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—48no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—41no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61C2×C22⋊C412yes—
347C2×C4×C61C23×C411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61H(5,𝔽2)11yescharacteristic
350C2×C4×C61H(5,𝔽2)11yescharacteristic
351C2×C4×C61H(5,𝔽2)11yescharacteristic
352C2×C4×C61H(5,𝔽2)11yescharacteristic
353C22⋊D61—44no—
354C22⋊D61—44no—
355C22⋊D61—84no—
356C22⋊D61—84no—
357C22⋊D61—84no—
358C22⋊D61—84no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—22no—
364C2×Dic61—22no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61C2×C22⋊C412yes—
376C2×Dic61C2×C22⋊C412yes—
377D244—44no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—84no—
387Dic122—44no—
388C8×C61—41no—
389C8×C61—41no—
390#92418—41no—
391#92418—41no—
392#21770—611nomaximal, Sylow
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61—816no—
407C22×C61—81no—
408C22×C61—81no—
409C22×C61—81no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61—81no—
413C22×C61—81no—
414C22×C61—81no—
415C22×C61C22×C22⋊C411yescharacteristic
416C22×C61#53411yescharacteristic
417C22×C61#53411yescharacteristic
418C22×C61#57611yescharacteristic
419C22×C61#57611yescharacteristic
420C22×C61#57711yescharacteristic
421C22×C61#57711yescharacteristic
422C2×D61—22no—
423C2×D61—22no—
424C2×D61—22no—
425C2×D61—22no—
426C2×D61—22no—
427C2×D61—22no—
428C2×D61—41no—
429C2×D61—41no—
430C2×D61—41no—
431C2×D61—41no—
432C2×D61—41no—
433C2×D61—41no—
434C2×D61—41no—
435C2×D61—41no—
436C4×C61—22no—
437C4×C61—81no—
438C4×C61—81no—
439C4×C61#51811yescharacteristic
440C4×C61#51811yescharacteristic
441C4×C61#53411yescharacteristic
442C4×C61#53411yescharacteristic
443Dic61—22no—
444Dic61—22no—
445Dic61—42no—
446Dic61—42no—
447Dic61—81no—
448Dic61—81no—
449C2×#535—611no—
450C2×#408—611no—
451#2311—611no—
452#1895—611no—
453#1895—611no—
454#1893—611no—
455#1893—611no—
456#1875—611no—
457#1875—611no—
458#1874—611no—
459#1874—611no—
460#1825—611no—
461#1825—611no—
462#1786—611no—
463#1786D6111yescharacteristic, complemented
464C2×C61—42no—
465C2×C61—82no—
466C2×C61—82no—
467C2×C61#230811yescharacteristic
468C2×C61#289711yescharacteristic
469C2×C61#289711yescharacteristic
470C2×C61#319811yescharacteristic
471C2×C61#319811yescharacteristic
472C2×C61#319911yescharacteristic
473C2×C61#320011yescharacteristic
474D61—42no—
475D61—42no—
476C22×#41—611no—
477C23×D4C2×D6111yescharacteristic
478C22×M16—611no—
479C23×C8—611no—
480#535—618no—
481#535—1224no—
482C2×#127—1221no—
483C2×#124—1221no—
484C2×#121—611no—
485C2×#121—611no—
486C2×#121—611no—
487C2×#121—611no—
488C2×#120—1221no—
489C2×#120—1221no—
490C2×#117—611no—
491C2×#117—611no—
492C22×C4⋊C4—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102C2×D6111yescharacteristic
498C2×#102C2×D6111yescharacteristic
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501#408—1224no—
502C2×C22⋊C8—611no—
503C2×C22⋊C8—611no—
504C2×C22⋊C8—611no—
505C2×C22⋊C8C2×D6111yescharacteristic
506#391—1221no—
507#390—1221no—
508#386—1221no—
509#386—1221no—
510#380—611no—
511#380—611no—
512#380—611no—
513#380C2×D6111yescharacteristic
514#340—611no—
515#340—611no—
516#340—611no—
517#340—611no—
518#340—611no—
519#340—611no—
520#340—611no—
521#340—611no—
522C61#2177011yescharacteristic, complemented, Sylow
523C25—21no—
524C2×#41—614no—
525C2×#41—614no—
526C2×#41—2441no—
527C2×#41—2441no—
528C2×#41—2441no—
529C2×#41—2441no—
530C22×Q8—611no—
531C22×D4—21no—
532C22×D4—22no—
533C22×D4—41no—
534C22×D4—41no—
535C22×D4—41no—
536C22×D4—41no—
537C22×D4—611no—
538C22×D4—611no—
539C22×D4—611no—
540C22×D4—1221no—
541C22×D4—1221no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4C4×D6114yescomplemented
545C22×D4C22×D6111yescharacteristic
546C22×D4C22×D6111yescharacteristic
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—1221no—
550C23×C4C22×D6111yescharacteristic
551C2×M16—1222no—
552C2×M16—2441no—
553C2×M16—2441no—
554C22×C8—611no—
555C22×C8—611no—
556C22×C8—1222no—
557C22×C8—2441no—
558C22×C8—2441no—
559C22×C8C22×D6111yescharacteristic
560C22×C8C22×D6111yescharacteristic
561#127—1228no—
562#124—1228no—
563#121—614no—
564#121—614no—
565#121—614no—
566#121—614no—
567#121—1222no—
568#121—1222no—
569#121—1222no—
570#121—1222no—
571#120—1228no—
572#120—1228no—
573#117—614no—
574#117—1222no—
575#117—2441no—
576#117—2441no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—1221no—
582C2×C4⋊C4—2441no—
583C2×C4⋊C4—2441no—
584C2×C4⋊C4C22×D6111yescharacteristic
585C2×C4⋊C4C22×D6111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—1221no—
595C2×C22⋊C4—1221no—
596C2×C42—1221no—
597C2×C42—1221no—
598#102—41no—
599#102—41no—
600#102—41no—
601#102—41no—
602#102—2441no—
603#102—2441no—
604#102—2441no—
605#102—2441no—
606C22⋊C8—22no—
607C22⋊C8—1222no—
608C22⋊C8—1222no—
609C22⋊C8—1222no—
610#95—21no—
611#95—1221no—
612#95—1221no—
613#95—1221no—
614C24—21no—
615C24—21no—
616C24—24no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24—81no—
622C24—81no—
623C24—611no—
624C24—611no—
625C24D4×D6111yescharacteristic
626#41—2444no—
627#41—2444no—
628#41—2444no—
629#41—2444no—
630C2×Q8—614no—
631C2×Q8—2441no—
632C2×Q8—2441no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—24no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—614no—
651C2×D4—614no—
652C2×D4—614no—
653C2×D4—1224no—
654C2×D4—1224no—
655C2×D4—1224no—
656C2×D4—1224no—
657C2×D4—4881no—
658C2×D4—4881no—
659C2×D4—4881no—
660C2×D4—4881no—
661C2×D4—4881no—
662C2×D4—4881no—
663C2×D4—4881no—
664C2×D4—4881no—
665C2×D4—2441no—
666C2×D4—2441no—
667C2×D4—2441no—
668C2×D4—2441no—
669C2×D4—2441no—
670C2×D4—2441no—
671C2×D4C2×C4×D6112yes—
672C2×D4C2×C4×D6112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—612no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—4881no—
698C22×C4—4881no—
699C22×C4—2442no—
700C22×C4C2×C4×D6112yes—
701C22×C4D4×D6112yes—
702C22×C4D4×D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704M16—2444no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—2444no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—612no—
723C4⋊C4—612no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—2442no—
731C22⋊C4—81no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C22⋊C4—4881no—
738C22⋊C4—4881no—
739C22⋊C4—4881no—
740C22⋊C4—2442no—
741C42—1224no—
742C42—2442no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—22no—
751C23—48no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—612no—
771C23—612no—
772C23—1221no—
773C23—1221no—
774C23—1221no—
775C23—1221no—
776C23—1221no—
777C23—1221no—
778C23—1221no—
779C23—1221no—
780C23—1221no—
781C23—1221no—
782C23—1221no—
783C23—1221no—
784C23C22⋊C4×D6112yes—
785C23C2×D4×D6111yescharacteristic
786Q8—2444no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—4884no—
797D4—4884no—
798D4—4884no—
799D4—4884no—
800D4—2444no—
801D4—2444no—
802D4—2444no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—612no—
816C2×C4—612no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1222no—
822C2×C4—1222no—
823C2×C4—1222no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—4884no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4C22⋊C4×D6112yes—
843C2×C4C22×C4×D6111yescharacteristic
844C2×C4C2×D4×D6111yescharacteristic
845C2×C4#1451982211yescharacteristic
846C2×C4#1451982211yescharacteristic
847C2×C4#1451982211yescharacteristic
848C2×C4#1451982211yescharacteristic
849C8—41no—
850C8—41no—
851C8—2441no—
852C8—2441no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—816no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—1222no—
876C22—1222no—
877C22—1222no—
878C22—1222no—
879C22—1222no—
880C22—1222no—
881C22—2441no—
882C22—2441no—
883C22—2441no—
884C22—2441no—
885C22—2441no—
886C22—2441no—
887C22—2441no—
888C22—2441no—
889C22C2×C22⋊C4×D6111yescharacteristic
890C22#1684032211yescharacteristic
891C22#1684032211yescharacteristic
892C22#1684056311yescharacteristic
893C22#1684056611yescharacteristic
894C22#1684056811yescharacteristic
895C22#1684057211yescharacteristic
896C4—22no—
897C4—81no—
898C4—81no—
899C4—1222no—
900C4—1222no—
901C4—4881no—
902C4—4881no—
903C4—2442no—
904C4—2442no—
905C4#1684023511yescharacteristic
906C4#1684023511yescharacteristic
907C4#1684032211yescharacteristic
908C4#1684032211yescharacteristic
909C2—42no—
910C2—82no—
911C2—82no—
912C2—2442no—
913C2—2442no—
914C2#2144839511yescharacteristic
915C2#2145434011yescharacteristic
916C2#2145434411yescharacteristic
917C2#2145666711yescharacteristic
918C2#2145667511yescharacteristic
919C2#2145668211yescharacteristic
920C2#2145668811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1786C2
socleC23×C61C22×D4
prime radicalC2×#16840329C2
cosocleC22×C4×C61C24
hypercenter#1786D61
hypocenterC61#21770
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#16839727C2semidirect
3. #21448408C2semidirect
4. #21446254C2semidirect
5. #21446254C2semidirect
6. #21446244C2semidirect
7. #21446244C2semidirect
8. #21446138C2semidirect
9. #21446138C2semidirect
10. #21446133C2semidirect
11. #21446133C2semidirect
12. #21445915C2semidirect
13. #21445911C2semidirect
14. #21445750C2semidirect
15. C61×#1786C2semidirect
17. C22×#11758189C22semidirect
18. C22×C8×D61C22semidirect
20. #16840329C4semidirect
30. C2×#14519735C22semidirect
31. C2×C4⋊C4×D61C22semidirect
38. C2×#14519689C22semidirect
39. C2×#14519689C22semidirect
45. #16839619C22semidirect
46. #16839619C22semidirect
47. #16839525C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
95. #14519748C2×C4semidirect
96. #14519748C2×C4semidirect
100. #14519736C2×C4semidirect
138. C22×D4×C61C2×C4semidirect
463. #1786D61semidirect
522. C61#21770semidirect
544. C22×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403292
C2×#168397272
#214484082
#214462542
#214462442
#214461382
#214461332
#214459152
#214459112
#214457502
C61×#17862
#2177061