Finite Group Databasebeta

← #29700470

Subgroups — #29700470

Order 15616.

1106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839926C211yesmaximal, characteristic
2C2×#16839870C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic
4#21448822C211yesmaximal, characteristic, complemented
5#21448659C211yesmaximal, characteristic
6#21446673C211yesmaximal, characteristic, complemented
7#21446516C211yesmaximal, characteristic, complemented
8#21446447C211yesmaximal, characteristic, complemented
9#21446252C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21446159C211yesmaximal, characteristic, complemented
12#21446090C211yesmaximal, characteristic, complemented
13#21446014C211yesmaximal, characteristic, complemented
14C4×#14519702C211yesmaximal, characteristic, complemented
15C61×#1753C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24#16839926C418yescomplemented
25#16839870—24no—
26C2×#14519709C2211yescharacteristic
27C2×#14519709C2211yescharacteristic
28#16839764—24no—
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519702C2211yescharacteristic
32C2×#14519702C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519699C2211yescharacteristic
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37#16839668C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839664C2211yescharacteristic
40#16839662—21no—
41#16839662—21no—
42#16839660C2211yescharacteristic
43#16839659—21no—
44#16839649—21no—
45#16839634—21no—
46#16839622C2211yescharacteristic
47#16839621—21no—
48C4×C4⋊Dic61C2211yescharacteristic
49C22⋊C4×Dic61—21no—
50#16839609—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839525C2211yescharacteristic
54#16839525C2211yescharacteristic
55C22×M16×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C2×C4×C8×C61C2211yescharacteristic
59C4×C22⋊C4×C61C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C2×#11758222—22no—
63C2×#11758222—22no—
64C2×#11758222—22no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yes—
68C22×Dic122C2311yescharacteristic
69C22×Dic122C2311yescharacteristic
70C22×D244C2311yescharacteristic
71C22×C22⋊D61—21no—
72C23×Dic61—21no—
73C22×C4×D61—21no—
74C2×Dic244—22no—
75C2×Dic244—22no—
76C2×Dic244C2×C414yescomplemented
77C2×#11758190—41no—
78C2×#11758190—41no—
79C2×#11758190C2×C414yescomplemented
80#14519756—22no—
81#14519756C2×C414yes—
82C4×Dic122—22no—
83C4×Dic122—22no—
84C4×Dic122—22no—
85C4×Dic122—41no—
86C4×Dic122—41no—
87C4×Dic122—41no—
88C2×C4⋊Dic61—22no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—41no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×C22⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—21no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×#11758198—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61—21no—
111#14519709—22no—
112#14519709—41no—
113#14519702—22no—
114#14519702—22no—
115#14519702—41no—
116#14519702C2×C414yescomplemented
117#14519702D414yes—
118#14519699—22no—
119#14519699—22no—
120#14519699C2×C414yescomplemented
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125#14519684—21no—
126C23×C4×C61C2311yescharacteristic
127C2×M16×C61—22no—
128C2×M16×C61—22no—
129C2×M16×C61—41no—
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C22×C8×C61C2311yescharacteristic
134C2×C22⋊C4×C61D411yescharacteristic
135C2×C22⋊C4×C61D411yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C22⋊C8×C61C2×C414yes—
139#97×C61—22no—
140C4×C8×C61—41no—
141#95×C61D411yescharacteristic
142#95×C61D411yescharacteristic
143C24×C61C2×D411yescharacteristic
144C23×D61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61C22×C412yes—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61#4112yes—
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—24no—
158C2×C22⋊D61—42no—
159C2×C22⋊D61—42no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—42no—
168C22×Dic61—42no—
169C22×Dic61—81no—
170#11758222—28no—
171#11758222—44no—
172#11758222—44no—
173#11758222—44no—
174C2×D244—21no—
175C2×D244—21no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244C22×C412yes—
180C2×C4×D61—24no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122C22×C412yes—
192C2×Dic122C22×C412yes—
193C2×Dic122C2×D412yes—
194C2×Dic122#4112yes—
195M16×C61—44no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61C22×C412yes—
206C2×C8×C61C22×C412yes—
207C2×C8×C61C2×D412yes—
208C22⋊C4×C61—22no—
209C22⋊C4×C61—41no—
210C42×C61—21no—
211C42×C61—21no—
212C42×C61—21no—
213C42×C61—21no—
214C22⋊Dic61—24no—
215C22⋊Dic61—81no—
216#11758198—42no—
217#11758198—42no—
218#11758198—81no—
219#11758198—81no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—42no—
229C4⋊Dic61C22×C412yes—
230C4⋊Dic61C2×D412yes—
231#11758196—24no—
232#11758196—42no—
233#11758196—42no—
234#11758196—42no—
235#11758196—81no—
236C4×Dic61—42no—
237C4×Dic61—42no—
238C4×Dic61—42no—
239C4×Dic61—81no—
240Dic244—28no—
241#11758190—44no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61C4×D412yes—
249C23×C61C22×D411yescharacteristic
250C22×D61—22no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—41no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61C4×D412yes—
275C2×C4×C61#13712yes—
276C2×C4×C61C23×C411yescharacteristic
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C61H(5,𝔽2)11yescharacteristic
281C2×C4×C61H(5,𝔽2)11yescharacteristic
282C22⋊D61—48no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—22no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—84no—
305D244—22no—
306D244—22no—
307D244—41no—
308D244—41no—
309C4×D61—48no—
310Dic122—22no—
311Dic122—22no—
312Dic122—22no—
313Dic122—22no—
314Dic122—22no—
315Dic122—41no—
316Dic122—41no—
317Dic122C4×D414yes—
318C8×C61—22no—
319C8×C61—22no—
320C8×C61—22no—
321C8×C61—41no—
322#22867—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61C2×C4×D411yescharacteristic
331C22×C61D4211yescharacteristic
332C22×C61#54611yescharacteristic
333C22×C61C2×#13711yescharacteristic
334C22×C61#57511yescharacteristic
335C22×C61#57711yescharacteristic
336C22×C61#57711yescharacteristic
337C2×D61—42no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—81no—
341C2×D61—81no—
342C2×D61—81no—
343C2×D61—81no—
344C4×C61—22no—
345C4×C61—22no—
346C4×C61—41no—
347C4×C61—41no—
348C4×C61—41no—
349C4×C61C2×C4×D411yescharacteristic
350C4×C61#51811yescharacteristic
351C4×C61#54611yescharacteristic
352C4×C61#55111yescharacteristic
353Dic61—24no—
354Dic61—42no—
355Dic61—42no—
356Dic61—42no—
357Dic61—81no—
358Dic61—81no—
359Dic61—81no—
360C2×#452—611no—
361C2×#441—611no—
362C2×#417—611no—
363#2360—611no—
364#2341—611no—
365#1968—611no—
366#1936—611no—
367#1926—611no—
368#1894—611no—
369#1880—611no—
370#1878—611no—
371#1865—611no—
372#1853—611no—
373C4×#103—611no—
374#1753D6111yescharacteristic, complemented
375C2×C61—42no—
376C2×C61#235811yescharacteristic
377C2×C61C4×#13711yescharacteristic
378C2×C61#295211yescharacteristic
379C2×C61#327511yescharacteristic
380C2×C61#327811yescharacteristic
381C2×C61#331611yescharacteristic
382C2×C61#331711yescharacteristic
383D61—82no—
384C22×#41—611no—
385C22×Q16—611no—
386C22×SD16—611no—
387C22×M16C2×D6111yescharacteristic
388C2×C22⋊Q8—611no—
389C2×C4×Q8—611no—
390C2×C4×Q8—611no—
391C2×C4×Q8—611no—
392C22×C4⋊C4—611no—
393#452—618no—
394#441—1224no—
395C2×#106—611no—
396C2×#106—611no—
397#417—1224no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#102—611no—
404C2×#102—611no—
405C2×#102—611no—
406C2×C22⋊C8C2×D6111yescharacteristic
407C2×#97C2×D6111yescharacteristic
408C2×C4×C8C2×D6111yescharacteristic
409#391—611no—
410#390—611no—
411#390—611no—
412#390—1221no—
413#390—1221no—
414#389—611no—
415#389—1221no—
416#387—1221no—
417#385—1221no—
418#380—611no—
419#380—1221no—
420C4×C4⋊C4—611no—
421C4×C22⋊C4—1221no—
422C4×C22⋊C4—1221no—
423C4×C22⋊C4C2×D6111yescharacteristic
424#340—611no—
425#340—611no—
426#340—611no—
427#340—611no—
428#336C2×D6111yescharacteristic
429#336C2×D6111yescharacteristic
430C61#2286711yescharacteristic, complemented, Sylow
431C2×#41—614no—
432C2×#41—1222no—
433C2×#41—1222no—
434C2×#41—1222no—
435C2×#41—2441no—
436C2×#41—2441no—
437C22×Q8—611no—
438C22×Q8—611no—
439C22×D4—611no—
440C22×D4—1221no—
441C23×C4—1221no—
442C23×C4—1221no—
443C23×C4C22×D6111yescharacteristic
444C2×Q16—614no—
445C2×Q16—1222no—
446C2×Q16—1222no—
447C2×SD16—614no—
448C2×SD16—2441no—
449C2×SD16—2441no—
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—41no—
453C22×C8C22×D6111yescharacteristic
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C22×C8C22×D6111yescharacteristic
457C22⋊Q8—614no—
458C22⋊Q8—1222no—
459C4×Q8—1222no—
460C4×Q8—1222no—
461C4×Q8—1222no—
462C4×Q8—2441no—
463C4×Q8—2441no—
464C4×Q8—2441no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—1222no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—2441no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—1221no—
484C2×C22⋊C4D24411yescharacteristic
485C2×C22⋊C4D24411yescharacteristic
486C2×C42—1221no—
487C2×C42—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42C22×D6111yescharacteristic
491C2×C42C22×D6111yescharacteristic
492#106—1222no—
493#106—2441no—
494#103—614no—
495#103—614no—
496#103—1222no—
497#103—1222no—
498#103—2441no—
499#102—614no—
500#102—1222no—
501#102—1222no—
502C22⋊C8C4×D6114yes—
503#97—22no—
504C4×C8—41no—
505#95—1221no—
506#95—1221no—
507#95—1221no—
508#95—1221no—
509#95—1221no—
510#95D24411yescharacteristic
511#95D24411yescharacteristic
512C24—1221no—
513C24C2×D24411yescharacteristic
514#41—1228no—
515#41—2444no—
516#41—2444no—
517#41—2444no—
518C2×Q8—612no—
519C2×Q8—612no—
520C2×Q8—612no—
521C2×Q8—612no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8—1221no—
529C2×Q8—1221no—
530C2×D4—612no—
531C2×D4—1224no—
532C2×D4—1221no—
533C2×D4—1221no—
534C2×D4—1221no—
535C2×D4—1221no—
536C2×D4—1221no—
537C2×D4—2442no—
538C2×D4—2442no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1224no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—4881no—
552C22×C4—2442no—
553C22×C4—2442no—
554C22×C4—2442no—
555C22×C4—2442no—
556C22×C4C2×C4×D6112yes—
557C22×C4C2×D24411yescharacteristic
558C22×C4C2×D24411yescharacteristic
559C22×C4C2×D24411yescharacteristic
560C22×C4C2×D24411yescharacteristic
561C22×C4C2×D24411yescharacteristic
562C22×C4#1175822212yes—
563C22×C4C23×D6111yescharacteristic
564Q16—1228no—
565SD16—2444no—
566M16—44no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8C2×C4×D6112yes—
577C2×C8C2×C4×D6112yes—
578C2×C8D4×D6112yes—
579C4⋊C4—612no—
580C4⋊C4—612no—
581C4⋊C4—1221no—
582C4⋊C4—1221no—
583C4⋊C4—1224no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—4881no—
591C4⋊C4—2442no—
592C4⋊C4—2442no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C22⋊C4—22no—
596C22⋊C4—41no—
597C22⋊C4—1224no—
598C22⋊C4—4881no—
599C22⋊C4—4881no—
600C22⋊C4—4881no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C42—21no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—4881no—
608C42—2442no—
609C42—2442no—
610C42—2442no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—1222no—
618C23—2441no—
619C23—2441no—
620C23—2441no—
621C23—2441no—
622C23—2441no—
623C23—2441no—
624C23C4×D24412yes—
625C23C22×D24411yescharacteristic
626Q8—614no—
627Q8—1222no—
628Q8—1222no—
629Q8—1222no—
630Q8—1222no—
631Q8—1222no—
632Q8—2441no—
633Q8—2441no—
634D4—1222no—
635D4—1222no—
636D4—2448no—
637D4—2441no—
638D4—2441no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—4884no—
663C2×C4—2448no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2441no—
670C2×C4—2441no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4C4×D24412yes—
680C2×C4#1451981012yes—
681C2×C4C22×C4×D6111yescharacteristic
682C2×C4C2×D4×D6111yescharacteristic
683C2×C4#41×D6111yescharacteristic
684C2×C4C2×#1175822211yescharacteristic
685C2×C4#1451982211yescharacteristic
686C2×C4#1451982311yescharacteristic
687C8—22no—
688C8—22no—
689C8—22no—
690C8—41no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—4881no—
699C22—4881no—
700C22—4881no—
701C22—4881no—
702C22—2442no—
703C22—2442no—
704C22—2442no—
705C22C2×C4×D24411yescharacteristic
706C22D4×D24411yescharacteristic
707C22#1684040711yescharacteristic
708C22C2×#1451981011yescharacteristic
709C22#1684056211yescharacteristic
710C22#1684057411yescharacteristic
711C22#1684057411yescharacteristic
712C4—22no—
713C4—22no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—1224no—
718C4—4881no—
719C4—4881no—
720C4—4881no—
721C4—2442no—
722C4—2442no—
723C4—2442no—
724C4C4×D4×D6111yescharacteristic
725C4#1684023411yescharacteristic
726C4#1684040211yescharacteristic
727C4#1684043611yescharacteristic
728C2—42no—
729C2—4882no—
730C2#2144880111yescharacteristic
731C2C4×#1451981011yescharacteristic
732C2#2145470411yescharacteristic
733C2#2145745511yescharacteristic
734C2#2145748711yescharacteristic
735C2#2145793211yescharacteristic
736C2#2145794711yescharacteristic
subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1753C2
socleC23×C61C22×D4
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1753D61
hypocenterC61#22867
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#16839870C2semidirect
4. #21448822C2semidirect
6. #21446673C2semidirect
7. #21446516C2semidirect
8. #21446447C2semidirect
9. #21446252C2semidirect
10. #21446173C2semidirect
11. #21446159C2semidirect
12. #21446090C2semidirect
13. #21446014C2semidirect
14. C4×#14519702C2semidirect
15. C61×#1753C2semidirect
24. #16839926C4semidirect
76. C2×Dic244C2×C4semidirect
79. C2×#11758190C2×C4semidirect
116. #14519702C2×C4semidirect
120. #14519699C2×C4semidirect
374. #1753D61semidirect
430. C61#22867semidirect

Maximal subgroups

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

subgroupindex
C2×#168399262
C2×#168398702
C2×#168397642
#214488222
#214486592
#214466732
#214465162
#214464472
#214462522
#214461732
#214461592
#214460902
#214460142
C4×#145197022
C61×#17532
#2286761