Finite Group Databasebeta

← #21422503

Subgroups — #21422503

Order 7552.

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

normal subgroups only

This group has 212 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#16837939C211yesmaximal, characteristic
2#16837454C211yesmaximal, characteristic, complemented
3#16837453C211yesmaximal, characteristic, complemented
4Q8⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
5#16837131C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8#14273722—21no—
9#14273718C411yescharacteristic
10#14273716C411yescharacteristic
11#14273712—21no—
12#14273703C411yescharacteristic
13#14273702C411yescharacteristic
14C4×D236—21no—
15C4×D236C2211yescharacteristic
16#14273684—21no—
17C42×D59C2211yescharacteristic
18C4⋊(C59⋊C8)C2211yescharacteristic
19Dic59⋊C8—21no—
20(C2×D59)⋊C8—21no—
21(C2×D59)⋊C8—21no—
22C4×C59⋊C8C2211yescharacteristic
23C8×Dic59—21no—
24C4×Q8×C59C2211yescharacteristic
25C4⋊C8×C59C2211yescharacteristic
26C4×C8×C59C2211yescharacteristic
27C2×Q8×C59C2×C411yescharacteristic
28C2×D236—21no—
29C2×D236C2×C411yescharacteristic
30C2×C4×D59—21no—
31C2×C4×D59C2×C411yescharacteristic
32C2×C4×D59D411yescharacteristic
33C2×C4×D59D411yescharacteristic
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C4⋊C4×C59—21no—
37C4⋊C4×C59C2×C411yescharacteristic
38C42×C59—21no—
39C42×C59C2311yescharacteristic
40(C2×D59)⋊C4—21no—
41(C2×D59)⋊C4—21no—
42(C2×D59)⋊C4—21no—
43(C2×D59)⋊C4—21no—
44(C2×D59)⋊C4—21no—
45C4⋊Dic59—21no—
46C4⋊Dic59C2×C411yescharacteristic
47Dic59⋊C4—21no—
48Dic59⋊C4—21no—
49C4×Dic59C2×C411yescharacteristic
50C4×Dic59D411yescharacteristic
51C4×Dic59D411yescharacteristic
52C2×C59⋊C8—21no—
53C2×C59⋊C8—21no—
54C22×D59—21no—
55C22×D59C22⋊C411yescharacteristic
56Q8×C59—21no—
57Q8×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59C22×C411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×Dic59—21no—
64C2×Dic59C22⋊C411yescharacteristic
65C2×Dic59C22⋊C411yescharacteristic
66C2×Dic59C22⋊C411yescharacteristic
67D236—21no—
68D236—21no—
69D236—42no—
70C4×D59—21no—
71C4×D59—21no—
72C4×D59—21no—
73C4×D59—21no—
74C4×D59—41no—
75C4×D59—41no—
76C4×D59—41no—
77C8×C59—41no—
78C8×C59—41no—
79C59⋊C8—41no—
80C59⋊C8—41no—
81C22×C59C2×C22⋊C411yescharacteristic
82C2×D59—21no—
83C2×D59—21no—
84C2×D59—21no—
85C2×D59—41no—
86C2×D59—41no—
87C2×D59—41no—
88C4×C59—21no—
89C4×C59—41no—
90C4×C59—41no—
91C4×C59#13111yescharacteristic
92C4×C59#13111yescharacteristic
93C4×C59#13511yescharacteristic
94C4×C59#13511yescharacteristic
95Dic59—21no—
96Dic59—21no—
97Dic59—21no—
98Dic59—41no—
99#1482—591nomaximal, Sylow
100C2×C59#40811yescharacteristic
101C2×C59#41611yescharacteristic
102C2×C59#42111yescharacteristic
103D59—41no—
104D59—81no—
105#529—591no—
106#431—591no—
107#431—591no—
108Q8⋊C8—591no—
109Q8⋊C8D5911yescharacteristic, complemented
110D4⋊C8—591no—
111D4⋊C8—591no—
112C59#148211yescharacteristic, complemented, Sylow
113#126—1181no—
114#125—591no—
115#124—591no—
116#123—1181no—
117C22⋊Q8—591no—
118#121—591no—
119C4×Q8C2×D5911yescharacteristic
120C4×D4—591no—
121C4×D4—1181no—
122#117—1181no—
123C2×C42—591no—
124C4⋊C8—591no—
125C4⋊C8—1181no—
126C4⋊C8C2×D5911yescharacteristic
127C22⋊C8—1181no—
128C22⋊C8—1181no—
129C4×C8—591no—
130C4×C8—1181no—
131C4×C8C2×D5911yescharacteristic
132C2×Q8C4×D5911yescharacteristic
133C2×D4—591no—
134C2×D4—1181no—
135C22×C4—591no—
136C22×C4—591no—
137C22×C4—591no—
138C22×C4—1181no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—1181no—
142C2×C8—1181no—
143C4⋊C4—21no—
144C4⋊C4—591no—
145C4⋊C4—1181no—
146C4⋊C4—1181no—
147C4⋊C4—1181no—
148C4⋊C4C4×D5911yescharacteristic
149C22⋊C4—1181no—
150C22⋊C4—1181no—
151C22⋊C4—1181no—
152C22⋊C4—1181no—
153C22⋊C4—1181no—
154C42—21no—
155C42—591no—
156C42—591no—
157C42—591no—
158C42C22×D5911yescharacteristic
159C23—591no—
160C23—1181no—
161Q8—21no—
162Q8—21no—
163D4—1181no—
164D4—1181no—
165D4—2362no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—591no—
169C2×C4—591no—
170C2×C4—591no—
171C2×C4—1181no—
172C2×C4—1181no—
173C2×C4—1181no—
174C2×C4—1181no—
175C2×C4—1181no—
176C2×C4—2361no—
177C2×C4—2361no—
178C2×C4—2361no—
179C2×C4C2×C4×D5911yescharacteristic
180C2×C4D4×D5911yescharacteristic
181C2×C4D4×D5911yescharacteristic
182C8—41no—
183C8—41no—
184C8—2361no—
185C8—2361no—
186C22—1181no—
187C22—1181no—
188C22—1181no—
189C22—2361no—
190C22—2361no—
191C22—2361no—
192C22C22⋊C4×D5911yescharacteristic
193C4—21no—
194C4—41no—
195C4—41no—
196C4—1181no—
197C4—1181no—
198C4—1181no—
199C4—2361no—
200C4#1427373311yescharacteristic
201C4#1427373511yescharacteristic
202C4#1427374811yescharacteristic
203C4#1427375011yescharacteristic
204C2—4721no—
205C2—2361no—
206C2#1683736711yescharacteristic
207C2#1683739711yescharacteristic
208C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×Q8⋊C8C2
socleC22×C59C2×C22⋊C4
hypercenterQ8⋊C8D59
hypocenterC59#1482
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
2. #16837454C2semidirect
3. #16837453C2semidirect
4. Q8⋊(C59⋊C8)C2semidirect
5. #16837131C2semidirect
6. #16837129C2semidirect
7. C59×Q8⋊C8C2semidirect
109. Q8⋊C8D59semidirect
112. C59#1482semidirect