Finite Group Databasebeta

← #21434469

Subgroups — #21434469

Order 7552.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#16837958C211yesmaximal, characteristic, complemented
2#127×D59C211yesmaximal, characteristic
3#16837768C211yesmaximal, characteristic, complemented
4#16837767C211yesmaximal, characteristic, complemented
5#16837766C211yesmaximal, characteristic, complemented
6#16837747C214yesmaximal, complemented
7#16837405C214yesmaximal, complemented
8#16837354C211yesmaximal, characteristic, complemented
9C59×#490C211yesmaximal, characteristic, complemented
10C2×D4×D59—22no—
11C2×D4×D59C2212yes—
12C2×#11745659C2212yes—
13#14273726C2212yescomplemented
14#14273724C2211yescharacteristic
15#14273723—22no—
16#14273723C2212yes—
17#14273719C2211yescharacteristic, complemented
18#14273705—22no—
19#14273692—22no—
20#14273685C2212yes—
21C42×D59C2211yescharacteristic
22#14273649C2214yescomplemented
23#14273648C2214yescomplemented
24#14273647C2214yescomplemented
25#14273638C2211yescharacteristic, complemented
26C8×Dic59C2212yescomplemented
27#127×C59C2211yescharacteristic
28#125×C59C2211yescharacteristic, complemented
29#102×C59C2214yescomplemented
30#97×C59C2211yescharacteristic, complemented
31C23×D59—22no—
32C2×D4×C59—22no—
33C2×D4×C59C2312yes—
34C2×C22⋊D59—22no—
35C2×C22⋊D59—24no—
36D4×D59—28no—
37D4×D59—48no—
38C2×D236—22no—
39C2×D236C2312yes—
40C2×C4×D59D412yes—
41C2×C4×D59C2311yescharacteristic
42C2×Dic118—22no—
43C2×C8×C59C2312yes—
44C4⋊C4×C59—22no—
45C4⋊C4×C59C2312yes—
46C42×C59C2311yescharacteristic
47(C2×D59)⋊C4—22no—
48C4⋊Dic59C2312yes—
49Dic59⋊C4—22no—
50Dic59⋊C4—22no—
51C4×Dic59—22no—
52C4×Dic59D412yes—
53C4×Dic59C2311yescharacteristic
54C2×C59⋊C8C2312yes—
55#11745659—24no—
56C23×C59—22no—
57C22×D59—22no—
58C22×D59—48no—
59C22×D59—44no—
60C22×D59C2×D411yescharacteristic
61D4×C59—24no—
62D4×C59—44no—
63C2×C4×C59—22no—
64C2×C4×C59C2×D412yes—
65C2×C4×C59C2411yescharacteristic
66C22⋊D59—44no—
67C22⋊D59—48no—
68C2×Dic59—22no—
69C2×Dic59C2×D411yescharacteristic
70C2×Dic59C2×D412yes—
71D236—24no—
72D236—44no—
73C4×D59—24no—
74C4×D59#4114yes—
75Dic118—44no—
76C8×C59—22no—
77C59⋊C8—22no—
78C22×C59—42no—
79C22×C59—44no—
80C22×C59C22×D411yescharacteristic
81C2×D59—22no—
82C2×D59—42no—
83C2×D59—44no—
84C2×D59—88no—
85C2×D59#12412yes—
86C4×C59—22no—
87C4×C59—42no—
88C4×C59C2×#4112yes—
89Dic59—42no—
90Dic59#12412yes—
91Dic59AGL(1,ℤ/8)14yes—
92#3138—591nomaximal, Sylow
93C2×C59—82no—
94C2×C59C2×#12411yescharacteristic
95C2×C59C2×AGL(1,ℤ/8)12yes—
96D59—22no—
97D59—82no—
98#533—591no—
99C2×#127—591no—
100#490—591no—
101#490—591no—
102#490—591no—
103#490D5911yescharacteristic, complemented
104#486—594no—
105#418—594no—
106C4×M16—591no—
107C59#313811yescharacteristic, complemented, Sylow
108C22×D4—592no—
109C22×D4—1182no—
110C2×M16—592no—
111C4⋊Q8—592no—
112#127—592no—
113#127—591no—
114#127—1182no—
115#127C2×D5911yescharacteristic
116#125—591no—
117#125C2×D5911yescharacteristic, complemented
118C22⋊Q8—1182no—
119C4×Q8—1182no—
120#117—592no—
121C2×C42—591no—
122#102—594no—
123#102—594no—
124#102—594no—
125#102C2×D5914yescomplemented
126#97—591no—
127#97C2×D5911yescharacteristic, complemented
128C4×C8—592no—
129C24—1182no—
130C2×Q8—1182no—
131C2×D4—22no—
132C2×D4—592no—
133C2×D4—1188no—
134C2×D4—1184no—
135C2×D4—1182no—
136C2×D4—1182no—
137C2×D4—2368no—
138C2×D4C22×D5912yes—
139C22×C4—591no—
140C22×C4—592no—
141M16—1184no—
142C2×C8—592no—
143C2×C8C22×D5912yes—
144C4⋊C4—22no—
145C4⋊C4—592no—
146C4⋊C4—1182no—
147C4⋊C4—1182no—
148C4⋊C4C22×D5912yes—
149C22⋊C4—1182no—
150C42—592no—
151C42—591no—
152C42—1182no—
153C42C22×D5911yescharacteristic
154C23—22no—
155C23—591no—
156C23—1182no—
157C23—2364no—
158C23—2368no—
159Q8—2364no—
160D4—24no—
161D4—44no—
162D4—1184no—
163D4—2364no—
164D4—2364no—
165D4—2368no—
166C2×C4—22no—
167C2×C4—591no—
168C2×C4—592no—
169C2×C4—594no—
170C2×C4—1184no—
171C2×C4—1182no—
172C2×C4D4×D5912yes—
173C2×C4C23×D5911yescharacteristic
174C8—22no—
175C8—1182no—
176C22—42no—
177C22—44no—
178C22—592no—
179C22—1182no—
180C22—4728no—
181C22—2362no—
182C22—2364no—
183C22C2×D4×D5911yescharacteristic
184C4—22no—
185C4—42no—
186C4—592no—
187C4—594no—
188C4—2362no—
189C4#41×D5912yes—
190C2—82no—
191C2—1182no—
192C2—4722no—
193C2#124×D5911yescharacteristic
194C2AGL(1,ℤ/8)×D5912yes—
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#490C2
socleC22×C59C22×D4
hypercenter#490D59
hypocenterC59#3138
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #16837958C2semidirect
3. #16837768C2semidirect
4. #16837767C2semidirect
5. #16837766C2semidirect
6. #16837747C2semidirect
7. #16837405C2semidirect
8. #16837354C2semidirect
9. C59×#490C2semidirect
13. #14273726C22semidirect
17. #14273719C22semidirect
22. #14273649C22semidirect
23. #14273648C22semidirect
24. #14273647C22semidirect
25. #14273638C22semidirect
26. C8×Dic59C22semidirect
28. #125×C59C22semidirect
29. #102×C59C22semidirect
30. #97×C59C22semidirect
103. #490D59semidirect
107. C59#3138semidirect
117. #125C2×D59semidirect
125. #102C2×D59semidirect
127. #97C2×D59semidirect