Finite Group Databasebeta

← #21434890

Subgroups — #21434890

Order 7552.

424 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837915C212yesmaximal, complemented
2#16837742C212yesmaximal, complemented
3#16837729C212yesmaximal, complemented
4#16837638C211yesmaximal, characteristic, complemented
5#16837633C212yesmaximal, complemented
6#16837563C212yesmaximal, complemented
7#16837550C212yesmaximal, complemented
8C2×(C2×D59)⋊C8C211yesmaximal, characteristic, complemented
9C59×#467C211yesmaximal, characteristic, complemented
10C2×#11745689C2212yes—
11C22×C4×D59C2211yescharacteristic
12C2×#11745671C2212yescomplemented
13C2×D472C2211yescharacteristic, complemented
14C22×C59⋊C8C2211yescharacteristic
15#14273712—22no—
16#14273703C2212yes—
17#14273702C2212yes—
18#14273701C2212yes—
19#14273697—22no—
20#14273689—22no—
21(C22⋊D59)⋊C4—22no—
22#14273685C2212yes—
23#14273661C2211yescharacteristic, complemented
24#14273658C2212yescomplemented
25#14273651C2212yescomplemented
26#14273649C2212yescomplemented
27#14273647C2212yescomplemented
28(C2×D59)⋊C8C2212yes—
29(C2×D59)⋊C8C2212yes—
30C2×Q16×C59C2211yescharacteristic, complemented
31C22×C8×C59C2211yescharacteristic
32C22⋊Q8×C59C2212yes—
33#107×C59C2211yescharacteristic, complemented
34#103×C59C2212yescomplemented
35C23×D59D411yescharacteristic
36C2×Q8×C59C2312yes—
37C22×C4×C59C2311yescharacteristic
38C2×C22⋊D59—22no—
39C22×Dic59D411yescharacteristic
40#11745689—42no—
41#11745689—42no—
42C2×D236—22no—
43C2×D236—22no—
44C2×D236C2312yes—
45C2×C4×D59—22no—
46C2×C4×D59—41no—
47C2×C4×D59—41no—
48C2×C4×D59D412yes—
49C2×C4×D59C2312yes—
50Q16×C59—41no—
51C2×C8×C59—41no—
52C2×C8×C59C2311yescharacteristic
53C2×C8×C59C2311yescharacteristic
54C4⋊C4×C59—22no—
55C4⋊C4×C59C2312yes—
56C22⋊C4×C59—22no—
57#11745671—42no—
58(C2×D59)⋊C4—22no—
59(C2×D59)⋊C4—22no—
60(C2×D59)⋊C4—22no—
61(C2×D59)⋊C4—22no—
62C4⋊Dic59C2312yes—
63Dic59⋊C4—22no—
64C4×Dic59—22no—
65C2×C59⋊C8—41no—
66C2×C59⋊C8C2312yes—
67D472—41no—
68C23×C59C2×D411yescharacteristic
69C22×D59—22no—
70C22×D59—22no—
71C22×D59—41no—
72C22×D59—41no—
73C22×D59C2×D412yes—
74Q8×C59—22no—
75Q8×C59—22no—
76C2×C4×C59—21no—
77C2×C4×C59—21no—
78C2×C4×C59—22no—
79C2×C4×C59—22no—
80C2×C4×C59C2×D411yescharacteristic
81C2×C4×C59C2411yescharacteristic
82C22⋊D59—44no—
83C2×Dic59—22no—
84C2×Dic59—41no—
85C2×Dic59C2×D412yes—
86D236—22no—
87D236—22no—
88D236—44no—
89D236—44no—
90C4×D59—22no—
91C4×D59—22no—
92C4×D59—42no—
93C4×D59—44no—
94C8×C59—21no—
95C8×C59—21no—
96C59⋊C8—22no—
97C22×C59—21no—
98C22×C59—21no—
99C22×C59#13512yes—
100C22×C59C22×D411yescharacteristic
101C2×D59—22no—
102C2×D59—22no—
103C2×D59—22no—
104C2×D59—44no—
105C2×D59—42no—
106C2×D59—42no—
107C2×D59—42no—
108C4×C59—21no—
109C4×C59—42no—
110C4×C59—42no—
111C4×C59H(5,𝔽2)11yescharacteristic
112C4×C59H(5,𝔽2)11yescharacteristic
113Dic59—22no—
114Dic59—42no—
115#3191—591nomaximal, Sylow
116C2×C59—22no—
117C2×C59#53411yescharacteristic
118C2×C59C2×#13511yescharacteristic
119C2×C59#57511yescharacteristic
120D59—42no—
121D59—82no—
122#525—592no—
123#485—592no—
124#482—592no—
125#467D5911yescharacteristic, complemented
126#466—591no—
127#465—592no—
128#452—592no—
129#449—592no—
130C2×C22⋊C8—591no—
131C59#319111yescharacteristic, complemented, Sylow
132C2×#41—592no—
133C23×C4—591no—
134C2×Q16C2×D5911yescharacteristic, complemented
135C2×SD16—592no—
136C2×D8—591no—
137C22×C8—591no—
138C22×C8C2×D5911yescharacteristic
139#123—1182no—
140C22⋊Q8—592no—
141C22⋊Q8C2×D5912yes—
142#121—592no—
143#121—592no—
144#120—1182no—
145C4×D4—1182no—
146C4×D4—1182no—
147#117—592no—
148#107—591no—
149#107C2×D5911yescharacteristic, complemented
150#106—592no—
151#103—592no—
152#103C2×D5912yescomplemented
153#102—592no—
154#102—592no—
155C22⋊C8—592no—
156C22⋊C8—592no—
157C24—591no—
158#41—2362no—
159#41—2362no—
160C2×Q8C22×D5912yes—
161C2×D4—592no—
162C2×D4—1182no—
163C2×D4—1182no—
164C2×D4—1182no—
165C22×C4—591no—
166C22×C4—592no—
167C22×C4—592no—
168C22×C4—1182no—
169C22×C4—2361no—
170C22×C4—2361no—
171C22×C4C22×D5911yescharacteristic
172Q16—41no—
173SD16—2362no—
174D8—2361no—
175C2×C8—41no—
176C2×C8—592no—
177C2×C8—2361no—
178C2×C8C22×D5911yescharacteristic
179C2×C8C22×D5911yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—592no—
182C4⋊C4—1182no—
183C4⋊C4C22×D5912yes—
184C22⋊C4—22no—
185C22⋊C4—1182no—
186C22⋊C4—1182no—
187C22⋊C4—1182no—
188C22⋊C4—1182no—
189C42—1182no—
190C23—592no—
191C23—1182no—
192C23—1182no—
193C23—2361no—
194C23—2361no—
195C23D4×D5911yescharacteristic
196Q8—22no—
197Q8—22no—
198D4—1182no—
199D4—1182no—
200D4—2364no—
201D4—2364no—
202D4—2364no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—592no—
208C2×C4—1182no—
209C2×C4—1182no—
210C2×C4—1182no—
211C2×C4—2362no—
212C2×C4—2364no—
213C2×C4—2361no—
214C2×C4D4×D5911yescharacteristic
215C2×C4C23×D5911yescharacteristic
216C8—21no—
217C8—21no—
218C8—1182no—
219C22—21no—
220C22—21no—
221C22—1182no—
222C22—1182no—
223C22—1182no—
224C22—2364no—
225C22—2362no—
226C22—2362no—
227C22—2362no—
228C22#1427375012yes—
229C22C2×D4×D5911yescharacteristic
230C4—21no—
231C4—42no—
232C4—42no—
233C4—1182no—
234C4—2362no—
235C4#1427377211yescharacteristic
236C4#1427377311yescharacteristic
237C2—22no—
238C2—4722no—
239C2—2362no—
240C2#1683796011yescharacteristic
241C2C2×#1427375011yescharacteristic
242C2#1683819911yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#467C2
socleC22×C59C22×D4
hypercenter#467D59
hypocenterC59#3191
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #16837915C2semidirect
2. #16837742C2semidirect
3. #16837729C2semidirect
4. #16837638C2semidirect
5. #16837633C2semidirect
6. #16837563C2semidirect
7. #16837550C2semidirect
8. C2×(C2×D59)⋊C8C2semidirect
9. C59×#467C2semidirect
12. C2×#11745671C22semidirect
13. C2×D472C22semidirect
23. #14273661C22semidirect
24. #14273658C22semidirect
25. #14273651C22semidirect
26. #14273649C22semidirect
27. #14273647C22semidirect
30. C2×Q16×C59C22semidirect
33. #107×C59C22semidirect
34. #103×C59C22semidirect
125. #467D59semidirect
131. C59#3191semidirect
134. C2×Q16C2×D59semidirect
149. #107C2×D59semidirect
152. #103C2×D59semidirect