Finite Group Databasebeta

← #29779544

Subgroups — #29779544

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454170C211yesmaximal, characteristic, complemented
2#390×D61C211yesmaximal, characteristic
3#21447226C211yesmaximal, characteristic, complemented
4#21447225C211yesmaximal, characteristic, complemented
5#21446954C211yesmaximal, characteristic, complemented
6#21446953C211yesmaximal, characteristic, complemented
7#21446519C211yesmaximal, characteristic, complemented
8#21446516C211yesmaximal, characteristic, complemented
9#21446515C211yesmaximal, characteristic, complemented
10#21445908C211yesmaximal, characteristic, complemented
11#21445908C211yesmaximal, characteristic, complemented
12#21445748C211yesmaximal, characteristic
13#21445748C211yesmaximal, characteristic
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1936C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17C2×#14519776C2211yescharacteristic, complemented
18C2×#14519755—21no—
19C2×C4⋊C4×D61C2211yescharacteristic
20C2×C22⋊C4×D61—21no—
21C2×C22⋊C4×D61—21no—
22C2×C42×D61C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519688C2211yescharacteristic, complemented
32#16839666—21no—
33#16839665C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839663C2211yescharacteristic
36#16839662—21no—
37#16839662—21no—
38#16839660C2211yescharacteristic, complemented
39#16839657—21no—
40#16839631C2211yescharacteristic, complemented
41#16839621—21no—
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44#16839525C2211yescharacteristic, complemented
45#16839525C2211yescharacteristic, complemented
46#16839524C2211yescharacteristic, complemented
47#16839524C2211yescharacteristic, complemented
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839516C2211yescharacteristic, complemented
51#16839516C2211yescharacteristic, complemented
52C2×#102×C61C2211yescharacteristic
53C2×#102×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic, complemented
55C61×#390C2211yescharacteristic
56C61×#389C2211yescharacteristic, complemented
57C61×#340C2211yescharacteristic, complemented
58C61×#340C2211yescharacteristic, complemented
59C24×D61—21no—
60C22×Dic122—21no—
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C2×D4×D61—22no—
64C2×D4×D61—22no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—41no—
68C2×D4×D61—41no—
69C22×C4×D61—21no—
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519776—41no—
76#14519776—41no—
77#14519755—44no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C4⋊C4×D61—22no—
87C4⋊C4×D61—22no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C22⋊C4×D61—44no—
97C22⋊C4×D61—44no—
98C2×C4×Dic61D411yescharacteristic
99C2×C4×Dic61D411yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C42×D61—41no—
102C42×D61—41no—
103#14519699—22no—
104#14519699—41no—
105#14519698—22no—
106#14519698—41no—
107#14519697—22no—
108#14519697—41no—
109#14519689—22no—
110#14519689—22no—
111#14519688—41no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×D4×C61C2311yescharacteristic
116C22×C8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C42×C61C2311yescharacteristic
125#102×C61—22no—
126#102×C61—41no—
127#97×C61—41no—
128#95×C61—21no—
129C24×C61—21no—
130C23×D61—24no—
131C23×D61—21no—
132C23×D61—42no—
133C23×D61—42no—
134C23×D61—42no—
135C23×D61—42no—
136C23×D61—42no—
137C23×D61—42no—
138C23×D61C2×D411yescharacteristic
139C2×D4×C61—21no—
140C2×D4×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61#4112yes—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—24no—
152C2×C22⋊D61—42no—
153C2×C22⋊D61—42no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61C2×D411yescharacteristic
158C22×Dic61C2×D411yescharacteristic
159C22×Dic61C2×D411yescharacteristic
160D4×D61—44no—
161D4×D61—44no—
162D4×D61—44no—
163D4×D61—44no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244—21no—
168C2×D244—21no—
169C2×D244#4112yes—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—41no—
179C2×C4×D61—41no—
180C2×C4×D61—42no—
181C2×C4×D61—42no—
182C2×C4×D61—42no—
183C2×C4×D61#4112yes—
184C2×C4×D61#4112yes—
185C2×Dic122—42no—
186C2×Dic122—42no—
187C2×Dic122—42no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61—21no—
197C4⋊C4×C61—21no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—42no—
201C22⋊C4×C61—42no—
202C22⋊C4×C61—42no—
203C42×C61—21no—
204C42×C61—21no—
205C22⋊Dic61—42no—
206C22⋊Dic61—42no—
207#11758198—42no—
208#11758198—42no—
209#11758198—42no—
210#11758198—42no—
211#11758198—42no—
212#11758198—42no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219#11758196—42no—
220#11758196—42no—
221#11758196—42no—
222#11758196—42no—
223#11758196—42no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—41no—
227C4×Dic61—41no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C23×C61—22no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61—41no—
240C23×C61—41no—
241C23×C61C22×D411yescharacteristic
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—22no—
247C22×D61—48no—
248C22×D61—48no—
249C22×D61—48no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61—41no—
254C22×D61—41no—
255C22×D61—41no—
256C22×D61—84no—
257C22×D61—84no—
258C22×D61—84no—
259C22×D61—84no—
260C22×D61#12412yes—
261C22×D61AGL(1,ℤ/8)12yes—
262C22×D61#13712yes—
263D4×C61—22no—
264D4×C61—22no—
265D4×C61—41no—
266D4×C61—41no—
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—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×C4×C61C2×#4111yescharacteristic
285C2×C4×C61C2×#4111yescharacteristic
286C2×C4×C61H(5,𝔽2)11yescharacteristic
287C2×C4×C61H(5,𝔽2)11yescharacteristic
288C22⋊D61—48no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
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#12412yes—
305C2×Dic61AGL(1,ℤ/8)12yes—
306C2×Dic61AGL(1,ℤ/8)12yes—
307D244—22no—
308D244—22no—
309D244—41no—
310D244—41no—
311C4×D61—22no—
312C4×D61—22no—
313C4×D61—22no—
314C4×D61—22no—
315C4×D61—44no—
316C4×D61—44no—
317C4×D61—84no—
318Dic122—84no—
319C8×C61—41no—
320C8×C61—41no—
321#92418—41no—
322#92418—41no—
323#29109—611nomaximal, Sylow
324C22×C61—42no—
325C22×C61—42no—
326C22×C61—42no—
327C22×C61—81no—
328C22×C61—81no—
329C22×C61—81no—
330C22×C61—81no—
331C22×C61#52511yescharacteristic
332C22×C61C2×#12411yescharacteristic
333C22×C61#53411yescharacteristic
334C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
336C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C61C2×#13711yescharacteristic
338C2×D61—22no—
339C2×D61—22no—
340C2×D61—22no—
341C2×D61—22no—
342C2×D61—22no—
343C2×D61—22no—
344C2×D61—42no—
345C2×D61—42no—
346C2×D61—42no—
347C2×D61—816no—
348C2×D61—81no—
349C2×D61—81no—
350C2×D61—81no—
351C2×D61—81no—
352C2×D61#48914yes—
353C4×C61—41no—
354C4×C61—41no—
355C4×C61—81no—
356C4×C61—81no—
357C4×C61—81no—
358C4×C61#55111yescharacteristic
359C4×C61#55111yescharacteristic
360C4×C61#55111yescharacteristic
361C4×C61#55111yescharacteristic
362Dic61—22no—
363Dic61—22no—
364Dic61—22no—
365Dic61—81no—
366Dic61—81no—
367Dic61—81no—
368#2857—611no—
369C2×#390—611no—
370#2071—611no—
371#2071—611no—
372#2023—611no—
373#2023—611no—
374#1936—611no—
375#1936—611no—
376#1936—611no—
377#1936D6111yescharacteristic, complemented
378#1824—611no—
379#1824—611no—
380#1786—611no—
381#1786—611no—
382#1749—611no—
383C2×C61—82no—
384C2×C61#256111yescharacteristic
385C2×C61#310911yescharacteristic
386C2×C61#311011yescharacteristic
387C2×C61C2×#48911yescharacteristic
388C2×C61#313811yescharacteristic
389C2×C61#319211yescharacteristic
390C2×C61#319311yescharacteristic
391D61—24no—
392D61—82no—
393C23×D4—611no—
394C2×C4⋊Q8—611no—
395C2×C22⋊Q8—1221no—
396C22×C4⋊C4—611no—
397C22×C22⋊C4—1221no—
398C22×C22⋊C4—1221no—
399C22×C42—611no—
400C2×#102—611no—
401C2×#102—611no—
402C2×#102—611no—
403C2×#102—611no—
404C2×#102—611no—
405C2×#102—611no—
406C2×#102C2×D6111yescharacteristic
407C2×#102C2×D6111yescharacteristic
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×#97—611no—
411C2×#97C2×D6111yescharacteristic, complemented
412#391—1221no—
413#390—611no—
414#390—611no—
415#390—611no—
416#390—1221no—
417#390—1221no—
418#390C2×D6111yescharacteristic
419#389—611no—
420#389—1221no—
421#389C2×D6111yescharacteristic, complemented
422#384—611no—
423#380—611no—
424#380—611no—
425#380—1221no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340C2×D6111yescharacteristic, complemented
433#340C2×D6111yescharacteristic, complemented
434#336—611no—
435#336—611no—
436C61#2910911yescharacteristic, complemented, Sylow
437C25—1221no—
438C22×Q8—1221no—
439C22×D4—611no—
440C22×D4—1222no—
441C22×D4—1222no—
442C22×D4—1221no—
443C22×D4—1222no—
444C22×D4—1222no—
445C22×D4—2441no—
446C22×D4—2441no—
447C22×D4C22×D6111yescharacteristic
448C23×C4—611no—
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—1221no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C4⋊Q8—2441no—
457C4⋊Q8—2441no—
458C22⋊Q8—2444no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—1222no—
464C2×C4⋊C4—1222no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C4⋊C4C22×D6111yescharacteristic
472C2×C4⋊C4C22×D6111yescharacteristic
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C22⋊C4—2444no—
484C2×C22⋊C4—2444no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—611no—
488C2×C42—2441no—
489C2×C42—2441no—
490C2×C42C22×D6111yescharacteristic
491#102—22no—
492#102—41no—
493#102—1222no—
494#102—1222no—
495#102—1222no—
496#102—2441no—
497#102—2441no—
498#102—2441no—
499C22⋊C8—1222no—
500C22⋊C8—1222no—
501#97—41no—
502#97—2441no—
503#95—21no—
504#95—1221no—
505#95—1221no—
506#95—1221no—
507C24—21no—
508C24—611no—
509C24—1224no—
510C24—1221no—
511C24—2442no—
512C24—2442no—
513C24—2442no—
514C24—2442no—
515C24—2442no—
516C24—2442no—
517C2×Q8—2442no—
518C2×Q8—2442no—
519C2×Q8—2442no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—612no—
526C2×D4—1224no—
527C2×D4—1221no—
528C2×D4—1221no—
529C2×D4—1221no—
530C2×D4—1221no—
531C2×D4—1221no—
532C2×D4—2442no—
533C2×D4—2444no—
534C2×D4—2444no—
535C2×D4—2444no—
536C2×D4—2444no—
537C2×D4—2442no—
538C2×D4#1175822212yes—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—611no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1222no—
551C22×C4—1221no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—1221no—
557C22×C4—1221no—
558C22×C4—2441no—
559C22×C4—2441no—
560C22×C4—2442no—
561C22×C4—2442no—
562C22×C4—2442no—
563C22×C4D4×D6111yescharacteristic
564C22×C4D4×D6111yescharacteristic
565C22×C4C23×D6111yescharacteristic
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—2442no—
592C4⋊C4—2442no—
593C4⋊C4—2442no—
594C4⋊C4—2442no—
595C4⋊C4—2442no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—2442no—
599C22⋊C4—2442no—
600C22⋊C4—2442no—
601C22⋊C4—2442no—
602C22⋊C4—2442no—
603C22⋊C4—2442no—
604C22⋊C4—2442no—
605C22⋊C4—2442no—
606C42—21no—
607C42—21no—
608C42—1221no—
609C42—1221no—
610C42—2441no—
611C42—2441no—
612C23—22no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—612no—
620C23—612no—
621C23—612no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23—1222no—
627C23—4884no—
628C23—4884no—
629C23—4884no—
630C23—4884no—
631C23—2448no—
632C23—2448no—
633C23—2448no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23—2441no—
640C23C2×D4×D6111yescharacteristic
641Q8—4884no—
642D4—22no—
643D4—22no—
644D4—41no—
645D4—41no—
646D4—1222no—
647D4—1222no—
648D4—2448no—
649D4—2441no—
650D4—2441no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—612no—
667C2×C4—612no—
668C2×C4—612no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—1221no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1222no—
679C2×C4—4884no—
680C2×C4—2444no—
681C2×C4—2444no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4—2441no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4#41×D6111yescharacteristic
692C2×C4#41×D6111yescharacteristic
693C2×C4#41×D6111yescharacteristic
694C2×C4C2×#1175822211yescharacteristic
695C2×C4#1451982211yescharacteristic
696C2×C4#1451982311yescharacteristic
697C8—41no—
698C8—41no—
699C8—2441no—
700C8—2441no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—614no—
709C22—1222no—
710C22—1222no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—48816no—
716C22—4881no—
717C22—4881no—
718C22—4881no—
719C22—4881no—
720C22—2442no—
721C22—2442no—
722C22—2442no—
723C22#1684027111yescharacteristic
724C22#124×D6111yescharacteristic
725C22#1684032011yescharacteristic
726C22AGL(1,ℤ/8)×D6111yescharacteristic
727C22AGL(1,ℤ/8)×D6111yescharacteristic
728C22AGL(1,ℤ/8)×D6111yescharacteristic
729C22#137×D6111yescharacteristic
730C4—41no—
731C4—41no—
732C4—81no—
733C4—81no—
734C4—81no—
735C4—1222no—
736C4—1222no—
737C4—1222no—
738C4—4881no—
739C4—4881no—
740C4—4881no—
741C4#1684043611yescharacteristic
742C4#1684043711yescharacteristic
743C4#1684044011yescharacteristic
744C4#1684044111yescharacteristic
745C2—82no—
746C2—1224no—
747C2—4882no—
748C2#2145097511yescharacteristic
749C2#2145590811yescharacteristic
750C2#2145591611yescharacteristic
751C2#489×D6111yescharacteristic
752C2#2145619211yescharacteristic
753C2#2145661511yescharacteristic
754C2#2145662011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1936C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenter#1936D61
hypocenterC61#29109
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
1. #21454170C2semidirect
3. #21447226C2semidirect
4. #21447225C2semidirect
5. #21446954C2semidirect
6. #21446953C2semidirect
7. #21446519C2semidirect
8. #21446516C2semidirect
9. #21446515C2semidirect
10. #21445908C2semidirect
11. #21445908C2semidirect
14. #21445582C2semidirect
15. C61×#1936C2semidirect
17. C2×#14519776C22semidirect
31. C2×#14519688C22semidirect
38. #16839660C22semidirect
40. #16839631C22semidirect
44. #16839525C22semidirect
45. #16839525C22semidirect
46. #16839524C22semidirect
47. #16839524C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839516C22semidirect
51. #16839516C22semidirect
54. C2×#97×C61C22semidirect
56. C61×#389C22semidirect
57. C61×#340C22semidirect
58. C61×#340C22semidirect
377. #1936D61semidirect
411. C2×#97C2×D61semidirect
421. #389C2×D61semidirect
432. #340C2×D61semidirect
433. #340C2×D61semidirect
436. C61#29109semidirect

Maximal subgroups

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

subgroupindex
#214541702
#390×D612
#214472262
#214472252
#214469542
#214469532
#214465192
#214465162
#214465152
#214459082
#214457482
#214455822
C61×#19362
#2910961