Finite Group Databasebeta

← #29690052

Subgroups — #29690052

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448305C211yesmaximal, characteristic
2#21446434C211yesmaximal, characteristic, complemented
3#21446432C211yesmaximal, characteristic, complemented
4#21446430C211yesmaximal, characteristic, complemented
5#21446428C211yesmaximal, characteristic, complemented
6#21446426C211yesmaximal, characteristic, complemented
7#21446424C211yesmaximal, characteristic, complemented
8#21446422C211yesmaximal, characteristic, complemented
9#21445802C211yesmaximal, characteristic, complemented
10#21445800C211yesmaximal, characteristic, complemented
11#21445730C211yesmaximal, characteristic
12#21445730C211yesmaximal, characteristic
13#21445582C211yesmaximal, characteristic, complemented
14#21445576C211yesmaximal, characteristic, complemented
15C61×#1924C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C2×#14519734C2211yescharacteristic
18C2×C42×D61C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519706C2211yescharacteristic
21C2×#14519706C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×#14519689C2211yescharacteristic
25C2×#14519689C2211yescharacteristic
26C2×#14519689C2211yescharacteristic
27C2×#14519689C2211yescharacteristic
28C2×#14519689C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519688C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34C2×C8×Dic61C2211yescharacteristic
35#16839666C411yescharacteristic
36#16839666C411yescharacteristic
37#16839662C411yescharacteristic
38#16839662C411yescharacteristic
39#16839640C411yescharacteristic
40#16839640C411yescharacteristic
41#16839638C411yescharacteristic
42#16839638C411yescharacteristic
43C4×#11758198C2211yescharacteristic
44C4×#11758198C2211yescharacteristic
45C4×C22⋊Dic61C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839516C2211yescharacteristic
49#16839516C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C2×C22⋊C8×C61C2211yescharacteristic
55C2×#97×C61C2211yescharacteristic
56C4×C22⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C2×#11758222—22no—
60C2×#11758222—22no—
61C2×#11758222—41no—
62C2×#11758222—41no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C22×Dic122C2×C411yescharacteristic
66C22×D244C2×C411yescharacteristic
67C22×C22⋊D61C2×C411yescharacteristic
68C22×C22⋊D61C2×C411yescharacteristic
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2311yescharacteristic
72C22×C4×D61C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519734—41no—
78#14519734—41no—
79C2×#11758196C2×C411yescharacteristic
80C2×#11758196C2×C411yescharacteristic
81C2×C22⋊Dic61C2×C411yescharacteristic
82C2×C22⋊Dic61C2×C411yescharacteristic
83C2×#11758198C2×C411yescharacteristic
84C2×#11758198C2×C411yescharacteristic
85C2×#11758198C2×C411yescharacteristic
86C2×#11758198C2×C411yescharacteristic
87C2×#11758198C2×C411yescharacteristic
88C2×#11758198C2×C411yescharacteristic
89C2×C4×Dic61C2×C411yescharacteristic
90C2×C4×Dic61C2×C411yescharacteristic
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93C42×D61—41no—
94C42×D61—41no—
95C4⋊#92418—41no—
96#14519706—41no—
97#14519706—41no—
98C22⋊#92418—41no—
99C22⋊#92418—41no—
100#14519689—22no—
101#14519689—22no—
102#14519689—22no—
103#14519689—22no—
104#14519689—41no—
105#14519689—41no—
106#14519689—41no—
107#14519689—41no—
108#14519688—41no—
109C8×Dic61—41no—
110C8×Dic61—41no—
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C2×C22⋊C4×C61C2×C411yescharacteristic
123C2×C22⋊C4×C61C2×C411yescharacteristic
124C2×C42×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126C4⋊C8×C61—41no—
127C22⋊C8×C61—41no—
128C22⋊C8×C61—41no—
129#97×C61—41no—
130#95×C61C2×C411yescharacteristic
131#95×C61C2×C411yescharacteristic
132C24×C61C22×C411yescharacteristic
133C23×D61C22×C411yescharacteristic
134C23×D61C22×C411yescharacteristic
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—41no—
150C2×C22⋊D61—41no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61—41no—
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159#11758222—44no—
160#11758222—44no—
161#11758222—44no—
162#11758222—44no—
163C2×D244—22no—
164C2×D244—41no—
165C2×D244—41no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—41no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181C2×C4×D61—41no—
182C2×C4×D61#4112yes—
183C2×C4×D61#4112yes—
184C2×Dic122—22no—
185C2×Dic122—41no—
186C2×Dic122—41no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C22⋊C4×C61—41no—
200C22⋊C4×C61—41no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61—21no—
205C22⋊Dic61—22no—
206C22⋊Dic61—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198—41no—
210#11758198—41no—
211#11758198—41no—
212#11758198—41no—
213#11758196—41no—
214#11758196—41no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—41no—
220C4×Dic61—41no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61C23×C411yescharacteristic
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61—21no—
254C22×D61#11712yes—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61C2×#4111yescharacteristic
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61H(5,𝔽2)11yescharacteristic
277C2×C4×C61H(5,𝔽2)11yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C61H(5,𝔽2)11yescharacteristic
280C22⋊D61—44no—
281C22⋊D61—44no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61#11712yes—
298C2×Dic61#13112yes—
299C2×Dic61#13112yes—
300D244—44no—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—44no—
306C4×D61—44no—
307C4×D61—41no—
308C4×D61—41no—
309C4×D61—41no—
310C4×D61—41no—
311Dic122—44no—
312C8×C61—41no—
313C8×C61—41no—
314C8×C61—41no—
315C8×C61—41no—
316#92418—41no—
317#92418—41no—
318#92418—41no—
319#92418—41no—
320#21905—611nomaximal, Sylow
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61C2×#11711yescharacteristic
329C22×C61#51811yescharacteristic
330C22×C61#51811yescharacteristic
331C22×C61C2×#13111yescharacteristic
332C22×C61C2×#13111yescharacteristic
333C22×C61#56811yescharacteristic
334C22×C61#56811yescharacteristic
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61—41no—
341C2×D61—41no—
342C2×D61—41no—
343C2×D61—41no—
344C2×D61—41no—
345C2×D61—41no—
346C2×D61—41no—
347C2×D61—41no—
348C2×D61—41no—
349C4×C61—41no—
350C4×C61—41no—
351C4×C61—41no—
352C4×C61—41no—
353C4×C61—41no—
354C4×C61#53811yescharacteristic
355C4×C61#53811yescharacteristic
356C4×C61#53811yescharacteristic
357C4×C61#53811yescharacteristic
358Dic61—22no—
359Dic61—22no—
360Dic61—22no—
361Dic61—41no—
362Dic61—41no—
363Dic61—41no—
364#2297—611no—
365#1924—611no—
366#1924—611no—
367#1924—611no—
368#1924D6111yescharacteristic, complemented
369#1923—611no—
370#1923—611no—
371#1923—611no—
372#1923—611no—
373#1798—611no—
374#1798—611no—
375#1780—611no—
376#1780—611no—
377#1749—611no—
378C4×C22⋊C8—611no—
379C2×C61—81no—
380C2×C61#231211yescharacteristic
381C2×C61#292211yescharacteristic
382C2×C61#292311yescharacteristic
383C2×C61#297611yescharacteristic
384C2×C61#297611yescharacteristic
385C2×C61#298111yescharacteristic
386C2×C61#298111yescharacteristic
387D61—42no—
388D61—81no—
389C22×#41—611no—
390C2×#117—611no—
391C22×C42—611no—
392C2×C4⋊C8—611no—
393C2×C4⋊C8—611no—
394C2×C4⋊C8—611no—
395C2×C4⋊C8C2×D6111yescharacteristic
396C2×C22⋊C8—611no—
397C2×C22⋊C8—611no—
398C2×C22⋊C8—611no—
399C2×C22⋊C8—611no—
400C2×C22⋊C8—611no—
401C2×C22⋊C8—611no—
402C2×C22⋊C8—611no—
403C2×C22⋊C8—611no—
404C2×C22⋊C8—611no—
405C2×C22⋊C8—611no—
406C2×C22⋊C8C2×D6111yescharacteristic
407C2×C22⋊C8C2×D6111yescharacteristic
408C2×#97—611no—
409C2×#97C2×D6111yescharacteristic
410C2×C4×C8—611no—
411C2×C4×C8—611no—
412#391—611no—
413#391—611no—
414#390—611no—
415#390—611no—
416#386—611no—
417#386—611no—
418#386—611no—
419#386—611no—
420C4×C22⋊C4—611no—
421C4×C22⋊C4—611no—
422C4×C22⋊C4—611no—
423C4×C22⋊C4C2×D6111yescharacteristic
424#336—611no—
425#336—611no—
426#336—611no—
427#336—611no—
428#336—611no—
429#336—611no—
430#336C2×D6111yescharacteristic
431#336C2×D6111yescharacteristic
432C61#2190511yescharacteristic, complemented, Sylow
433C2×#41—1222no—
434C2×#41—1222no—
435C2×#41—2441no—
436C2×#41—2441no—
437C2×#41—2441no—
438C2×#41—2441no—
439C22×Q8—611no—
440C22×D4—611no—
441C22×D4—611no—
442C22×D4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—611no—
446C23×C4—611no—
447C23×C4C22×D6111yescharacteristic
448C22×C8—611no—
449C22×C8—611no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8C22×D6111yescharacteristic
453C22×C8C22×D6111yescharacteristic
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456#117—2441no—
457#117—2441no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C22⋊C4—611no—
461C2×C22⋊C4—611no—
462C2×C22⋊C4—611no—
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4C4×D6111yescharacteristic
469C2×C22⋊C4C4×D6111yescharacteristic
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—2441no—
475C2×C42—2441no—
476C2×C42C22×D6111yescharacteristic
477C2×C42C22×D6111yescharacteristic
478C4⋊C8—41no—
479C4⋊C8—2441no—
480C4⋊C8—2441no—
481C4⋊C8—2441no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—1222no—
485C22⋊C8—1222no—
486C22⋊C8—1222no—
487C22⋊C8—1222no—
488C22⋊C8—2441no—
489C22⋊C8—2441no—
490C22⋊C8—2441no—
491C22⋊C8—2441no—
492C22⋊C8—2441no—
493C22⋊C8—2441no—
494#97—41no—
495#97—2441no—
496C4×C8—2441no—
497C4×C8—2441no—
498#95—611no—
499#95—611no—
500#95—611no—
501#95—611no—
502#95—611no—
503#95—611no—
504#95C4×D6111yescharacteristic
505#95C4×D6111yescharacteristic
506C24—611no—
507C24—611no—
508C24C2×C4×D6111yescharacteristic
509#41—2444no—
510#41—2444no—
511#41—2444no—
512#41—2444no—
513C2×Q8—1222no—
514C2×Q8—2441no—
515C2×Q8—2441no—
516C2×D4—1222no—
517C2×D4—1222no—
518C2×D4—1222no—
519C2×D4—2441no—
520C2×D4—2441no—
521C2×D4—2441no—
522C2×D4—2441no—
523C2×D4—2441no—
524C2×D4—2441no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—612no—
535C22×C4—612no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—1222no—
540C22×C4—1222no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—2441no—
552C22×C4—2441no—
553C22×C4—2441no—
554C22×C4—2441no—
555C22×C4C2×C4×D6111yescharacteristic
556C22×C4C2×C4×D6111yescharacteristic
557C22×C4C2×C4×D6111yescharacteristic
558C22×C4C2×C4×D6111yescharacteristic
559C22×C4C2×C4×D6111yescharacteristic
560C22×C4C23×D6111yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C4⋊C4—2441no—
586C4⋊C4—2441no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—1222no—
590C22⋊C4—1222no—
591C22⋊C4—1222no—
592C22⋊C4—1222no—
593C22⋊C4—2441no—
594C22⋊C4—2441no—
595C22⋊C4—2441no—
596C22⋊C4—2441no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—1221no—
602C42—1221no—
603C42—1221no—
604C42—1221no—
605C42—2441no—
606C42—2441no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—612no—
615C23—1221no—
616C23—1221no—
617C23—1221no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23—1221no—
626C23—1221no—
627C23—1221no—
628C23C22×C4×D6111yescharacteristic
629Q8—2444no—
630D4—2444no—
631D4—2444no—
632D4—2444no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—612no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1221no—
659C2×C4—1221no—
660C2×C4—1221no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1221no—
666C2×C4—1221no—
667C2×C4—1221no—
668C2×C4—1221no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—1221no—
673C2×C4—1221no—
674C2×C4—2444no—
675C2×C4—2444no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4#41×D6111yescharacteristic
681C2×C4#41×D6111yescharacteristic
682C2×C4#1451982211yescharacteristic
683C2×C4#1451982211yescharacteristic
684C2×C4#1451982311yescharacteristic
685C2×C4#1451982311yescharacteristic
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—2441no—
691C8—2441no—
692C8—2441no—
693C8—2441no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—2441no—
705C22—2441no—
706C22—2441no—
707C22—2441no—
708C22—2441no—
709C22—2441no—
710C22—2441no—
711C22—2441no—
712C22—2441no—
713C22—2441no—
714C22—2441no—
715C22#117×D6111yescharacteristic
716C22#1684023411yescharacteristic
717C22#1684023411yescharacteristic
718C22#131×D6111yescharacteristic
719C22#131×D6111yescharacteristic
720C22#1684052811yescharacteristic
721C22#1684052811yescharacteristic
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—1222no—
728C4—1222no—
729C4—1222no—
730C4—2441no—
731C4—2441no—
732C4—2441no—
733C4#1684034411yescharacteristic
734C4#1684034611yescharacteristic
735C4#1684034811yescharacteristic
736C4#1684035111yescharacteristic
737C2—81no—
738C2—4881no—
739C2—2442no—
740C2#2144841311yescharacteristic
741C2#2145446011yescharacteristic
742C2#2145446511yescharacteristic
743C2#2145486311yescharacteristic
744C2#2145486611yescharacteristic
745C2#2145489111yescharacteristic
746C2#2145489111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1924C2
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenter#1924D61
hypocenterC61#21905
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
2. #21446434C2semidirect
3. #21446432C2semidirect
4. #21446430C2semidirect
5. #21446428C2semidirect
6. #21446426C2semidirect
7. #21446424C2semidirect
8. #21446422C2semidirect
9. #21445802C2semidirect
10. #21445800C2semidirect
13. #21445582C2semidirect
14. #21445576C2semidirect
15. C61×#1924C2semidirect
368. #1924D61semidirect
432. C61#21905semidirect

Maximal subgroups

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

subgroupindex
#214483052
#214464342
#214464322
#214464302
#214464282
#214464262
#214464242
#214464222
#214458022
#214458002
#214457302
#214455822
#214455762
C61×#19242
#2190561