Finite Group Databasebeta

← #21422567

Subgroups — #21422567

Order 7552.

202 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 65 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#16837956C211yesmaximal, characteristic
2#16837458C211yesmaximal, characteristic
3#16837453C211yesmaximal, characteristic
4#16837134C211yesmaximal, characteristic, complemented
5Q8⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837132C211yesmaximal, characteristic, complemented
7C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8#14273726C411yescharacteristic
9#14273725C411yescharacteristic
10#14273717—21no—
11#14273707C411yescharacteristic
12#14273705—21no—
13#14273703C411yescharacteristic
14C4×Dic118—21no—
15C4×Dic118C2211yescharacteristic
16#14273684—21no—
17C42×D59C2211yescharacteristic
18C4⋊(C59⋊C8)C2211yescharacteristic
19Dic59⋊C8—21no—
20(C2×D59)⋊C8—21no—
21(C2×D59)⋊C8—21no—
22#14273637—21no—
23C4×C59⋊C8C2211yescharacteristic
24C4×Q8×C59C2211yescharacteristic
25C4⋊C8×C59C2211yescharacteristic
26C4×C8×C59C2211yescharacteristic
27C2×Q8×C59C2×C411yescharacteristic
28C2×C4×D59C2×C411yescharacteristic
29C2×C4×D59D411yescharacteristic
30C2×C4×D59D411yescharacteristic
31C2×Dic118—21no—
32C2×Dic118C2×C411yescharacteristic
33C2×C8×C59—21no—
34C2×C8×C59—21no—
35C4⋊C4×C59—21no—
36C4⋊C4×C59C2×C411yescharacteristic
37C42×C59—21no—
38C42×C59C2311yescharacteristic
39(C2×D59)⋊C4—21no—
40(C2×D59)⋊C4—21no—
41C4⋊Dic59—21no—
42C4⋊Dic59C2×C411yescharacteristic
43Dic59⋊C4—21no—
44Dic59⋊C4—21no—
45Dic59⋊C4—21no—
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48C4×Dic59—21no—
49C4×Dic59C2×C411yescharacteristic
50C4×Dic59D411yescharacteristic
51C4×Dic59D411yescharacteristic
52C2×C59⋊C8—21no—
53C2×C59⋊C8—21no—
54C22×D59C22⋊C411yescharacteristic
55Q8×C59—21no—
56Q8×C59—21no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59C22×C411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×Dic59—21no—
63C2×Dic59—21no—
64C2×Dic59C22⋊C411yescharacteristic
65C2×Dic59C22⋊C411yescharacteristic
66C2×Dic59C22⋊C411yescharacteristic
67C4×D59—21no—
68C4×D59—21no—
69C4×D59—21no—
70C4×D59—21no—
71C4×D59—41no—
72Dic118—21no—
73Dic118—21no—
74Dic118—42no—
75C8×C59—41no—
76C8×C59—41no—
77C59⋊C8—41no—
78C59⋊C8—41no—
79C22×C59C2×C22⋊C411yescharacteristic
80C2×D59—21no—
81C2×D59—21no—
82C2×D59—21no—
83C4×C59—21no—
84C4×C59—41no—
85C4×C59—41no—
86C4×C59#13111yescharacteristic
87C4×C59#13111yescharacteristic
88C4×C59#13711yescharacteristic
89C4×C59#13711yescharacteristic
90Dic59—21no—
91Dic59—21no—
92Dic59—21no—
93Dic59—41no—
94Dic59—41no—
95#1497—591nomaximal, Sylow
96C2×C59#40811yescharacteristic
97C2×C59#41911yescharacteristic
98C2×C59#42111yescharacteristic
99D59—41no—
100#533—591no—
101#432—591no—
102#431—591no—
103Q8⋊C8—591no—
104Q8⋊C8—591no—
105Q8⋊C8—591no—
106Q8⋊C8D5911yescharacteristic, complemented
107C59#149711yescharacteristic, complemented, Sylow
108C4⋊Q8—591no—
109C4⋊Q8—591no—
110#125—1181no—
111C22⋊Q8—591no—
112C22⋊Q8—591no—
113C22⋊Q8—1181no—
114C4×Q8—591no—
115C4×Q8—1181no—
116C4×Q8C2×D5911yescharacteristic
117#117—1181no—
118C2×C42—591no—
119C4⋊C8—591no—
120C4⋊C8—1181no—
121C4⋊C8C2×D5911yescharacteristic
122C22⋊C8—1181no—
123C22⋊C8—1181no—
124#97—1181no—
125C4×C8—591no—
126C4×C8C2×D5911yescharacteristic
127C2×Q8—591no—
128C2×Q8—1181no—
129C2×Q8C4×D5911yescharacteristic
130C22×C4—591no—
131C22×C4—591no—
132C22×C4—591no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—1181no—
136C2×C8—1181no—
137C4⋊C4—21no—
138C4⋊C4—591no—
139C4⋊C4—1181no—
140C4⋊C4—1181no—
141C4⋊C4—1181no—
142C4⋊C4—1181no—
143C4⋊C4—1181no—
144C4⋊C4—1181no—
145C4⋊C4C4×D5911yescharacteristic
146C22⋊C4—1181no—
147C22⋊C4—1181no—
148C42—21no—
149C42—591no—
150C42—591no—
151C42—591no—
152C42—1181no—
153C42C22×D5911yescharacteristic
154C23—591no—
155Q8—21no—
156Q8—21no—
157Q8—1181no—
158Q8—1181no—
159Q8—2362no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—591no—
163C2×C4—591no—
164C2×C4—591no—
165C2×C4—1181no—
166C2×C4—1181no—
167C2×C4—1181no—
168C2×C4—1181no—
169C2×C4—1181no—
170C2×C4—1181no—
171C2×C4—2361no—
172C2×C4C2×C4×D5911yescharacteristic
173C2×C4D4×D5911yescharacteristic
174C2×C4D4×D5911yescharacteristic
175C8—41no—
176C8—41no—
177C8—2361no—
178C8—2361no—
179C22—1181no—
180C22—1181no—
181C22—1181no—
182C22C22⋊C4×D5911yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—1181no—
187C4—1181no—
188C4—1181no—
189C4—2361no—
190C4—2361no—
191C4#1427373311yescharacteristic
192C4#1427373511yescharacteristic
193C4#1427375611yescharacteristic
194C4#1427375911yescharacteristic
195C2—2361no—
196C2#1683736711yescharacteristic
197C2#1683740911yescharacteristic
198C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×Q8⋊C8C2
socleC22×C59C2×C22⋊C4
hypercenterQ8⋊C8D59
hypocenterC59#1497
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. #16837134C2semidirect
5. Q8⋊(C59⋊C8)C2semidirect
6. #16837132C2semidirect
7. C59×Q8⋊C8C2semidirect
106. Q8⋊C8D59semidirect
107. C59#1497semidirect