Finite Group Databasebeta

← #21456067

Subgroups — #21456067

Order 7808.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840372C211yesmaximal, characteristic, complemented
2#16840236C211yesmaximal, characteristic
3#16840103C211yesmaximal, characteristic, complemented
4#16840065C211yesmaximal, characteristic, complemented
5#16840061C211yesmaximal, characteristic, complemented
6#16839966C211yesmaximal, characteristic, complemented
7#16839966C211yesmaximal, characteristic, complemented
8#16839915C211yesmaximal, characteristic
9#16839912C211yesmaximal, characteristic
10#16839865C211yesmaximal, characteristic, complemented
11#16839861C211yesmaximal, characteristic, complemented
12#16839849C211yesmaximal, characteristic, complemented
13#16839847C211yesmaximal, characteristic, complemented
14#16839820C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21#14519775C2211yescharacteristic, complemented
22#14519770—21no—
23#14519770—21no—
24#14519768—21no—
25#14519768C2211yescharacteristic, complemented
26#14519767—21no—
27#14519756C2211yescharacteristic
28Q8×Dic61C2211yescharacteristic, complemented
29#14519742C2211yescharacteristic, complemented
30C4×D244—21no—
31C4×D244—21no—
32#14519739C2211yescharacteristic
33#14519739C2211yescharacteristic
34#14519739C2211yescharacteristic
35#14519739C2211yescharacteristic
36#14519736C2211yescharacteristic
37C22⋊C4×D61—21no—
38C22⋊C4×D61—21no—
39#14519710C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519700C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C2×D244—21no—
63C2×D244—22no—
64C2×D244—22no—
65C2×D244C2311yescharacteristic
66C2×D244C2311yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×Dic122C2311yescharacteristic
72C2×C8×C61C2311yescharacteristic
73C2×C8×C61C2311yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61C2311yescharacteristic
76C4⋊C4×C61C2311yescharacteristic
77C4⋊C4×C61C2311yescharacteristic
78C22⋊C4×C61—21no—
79C22⋊C4×C61—21no—
80C42×C61—21no—
81C22⋊Dic61—21no—
82C22⋊Dic61D411yescharacteristic
83C22⋊Dic61D411yescharacteristic
84#11758201—22no—
85#11758201—22no—
86#11758198—21no—
87#11758198—21no—
88#11758198—21no—
89#11758198—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61D411yescharacteristic
93C4⋊Dic61D411yescharacteristic
94C4⋊Dic61C2311yescharacteristic
95#11758196—21no—
96#11758196—21no—
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61C2311yescharacteristic
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106#11758190—22no—
107#11758190—22no—
108C23×C61C2×D411yescharacteristic
109C22×D61—21no—
110C22×D61—21no—
111C22×D61—24no—
112C22×D61—81no—
113C22×D61—81no—
114Q8×C61—21no—
115Q8×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130D244—24no—
131D244—21no—
132D244—21no—
133D244#4112yes—
134D244#4112yes—
135C4×D61—81no—
136C4×D61—81no—
137C4×D61—81no—
138C4×D61—81no—
139Dic122—21no—
140Dic122—21no—
141C8×C61—21no—
142C8×C61—21no—
143#92418—21no—
144#92418—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—21no—
148C22×C61C22×D411yescharacteristic
149C2×D61—22no—
150C2×D61—22no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C2×D61—84no—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61C2×#4111yescharacteristic
162C4×C61C2×#4111yescharacteristic
163Dic61—21no—
164Dic61—21no—
165Dic61—21no—
166Dic61—21no—
167Dic61—41no—
168Dic61—41no—
169#3123—611nomaximal, Sylow
170C2×C61—41no—
171C2×C61#52511yescharacteristic
172C2×C61#57711yescharacteristic
173C2×C61#57711yescharacteristic
174D61—42no—
175D61—42no—
176#541—611no—
177#518—611no—
178#485—611no—
179#485D6111yescharacteristic, complemented
180#478—611no—
181#478—611no—
182#461—611no—
183#461—611no—
184#450—611no—
185#450—611no—
186#440—611no—
187#440—611no—
188C4×SD16—611no—
189C4×SD16—611no—
190#433—611no—
191C61#312311yescharacteristic, complemented, Sylow
192C22×D4—611no—
193C2×SD16—611no—
194C2×SD16—611no—
195C2×SD16—611no—
196C2×SD16—611no—
197C4⋊Q8—611no—
198#126—1221no—
199#126—1221no—
200#125—611no—
201#125—1221no—
202#125—1221no—
203C22⋊Q8—611no—
204C22⋊Q8C2×D6111yescharacteristic
205C4×Q8—611no—
206C4×Q8—611no—
207C4×D4—611no—
208C4×D4—611no—
209C4×D4—611no—
210C4×D4—611no—
211C4×D4—1221no—
212C4×D4—1221no—
213#117—611no—
214#117C2×D6111yescharacteristic
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217#107—611no—
218#107C2×D6111yescharacteristic, complemented
219#106—611no—
220#106C2×D6111yescharacteristic, complemented
221C4⋊C8—611no—
222C4⋊C8—611no—
223#103—611no—
224#103—611no—
225#103C2×D6111yescharacteristic, complemented
226#103C2×D6111yescharacteristic, complemented
227#102—611no—
228#102—611no—
229#102—611no—
230#102—611no—
231C22⋊C8—611no—
232C22⋊C8C2×D6111yescharacteristic
233#97—611no—
234C4×C8—611no—
235C24—1221no—
236C2×Q8—611no—
237C2×Q8C22×D6111yescharacteristic
238C2×D4—611no—
239C2×D4—611no—
240C2×D4—1222no—
241C2×D4—1222no—
242C2×D4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4C22×D6111yescharacteristic
248SD16—1222no—
249SD16—1222no—
250SD16—1222no—
251SD16—1222no—
252C2×C8—611no—
253C2×C8—611no—
254C2×C8C22×D6111yescharacteristic
255C2×C8C22×D6111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—611no—
258C4⋊C4—611no—
259C4⋊C4—611no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4C22×D6111yescharacteristic
268C4⋊C4C22×D6111yescharacteristic
269C4⋊C4C22×D6111yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—611no—
273C22⋊C4—611no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4—1221no—
277C22⋊C4—1221no—
278C22⋊C4—1221no—
279C42—21no—
280C42—611no—
281C42—611no—
282C42—1221no—
283C42—1221no—
284C23—1224no—
285C23—1221no—
286C23—1221no—
287C23—4881no—
288C23—4881no—
289C23D4×D6111yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—1221no—
293Q8—1221no—
294D4—612no—
295D4—612no—
296D4—1224no—
297D4—1221no—
298D4—1221no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—4881no—
314C2×C4—4881no—
315C2×C4D4×D6111yescharacteristic
316C2×C4C23×D6111yescharacteristic
317C8—21no—
318C8—21no—
319C8—1221no—
320C8—1221no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—1222no—
325C22—1222no—
326C22—4884no—
327C22—2441no—
328C22—2441no—
329C22—2441no—
330C22—2441no—
331C22C2×D4×D6111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1221no—
338C4—1221no—
339C4—1221no—
340C4—1221no—
341C4—2441no—
342C4—2441no—
343C4#41×D6111yescharacteristic
344C4#41×D6111yescharacteristic
345C2—41no—
346C2—2442no—
347C2—2442no—
348C2#1684027011yescharacteristic
349C2#1684056911yescharacteristic
350C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3123
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #16840372C2semidirect
3. #16840103C2semidirect
4. #16840065C2semidirect
5. #16840061C2semidirect
6. #16839966C2semidirect
7. #16839966C2semidirect
10. #16839865C2semidirect
11. #16839861C2semidirect
12. #16839849C2semidirect
13. #16839847C2semidirect
14. #16839820C2semidirect
15. C61×#485C2semidirect
21. #14519775C22semidirect
25. #14519768C22semidirect
28. Q8×Dic61C22semidirect
29. #14519742C22semidirect
39. #14519710C22semidirect
40. #14519708C22semidirect
41. #14519706C22semidirect
42. #14519706C22semidirect
43. #14519700C22semidirect
44. #14519700C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. #103×C61C22semidirect
57. #103×C61C22semidirect
179. #485D61semidirect
191. C61#3123semidirect
218. #107C2×D61semidirect
220. #106C2×D61semidirect
225. #103C2×D61semidirect
226. #103C2×D61semidirect