Finite Group Databasebeta

← #21422560

Subgroups — #21422560

Order 7552.

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

normal subgroups only

This group has 216 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#16837453C211yesmaximal, characteristic, complemented
3#16837424C211yesmaximal, characteristic, complemented
4Q8⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
5#16837131C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11745659—21no—
9#14273722—21no—
10#14273718C411yescharacteristic
11#14273716C411yescharacteristic
12#14273712—21no—
13#14273703C411yescharacteristic
14#14273702C411yescharacteristic
15C4×D236—21no—
16C4×D236C2211yescharacteristic
17#14273684—21no—
18C42×D59C2211yescharacteristic
19C4⋊(C59⋊C8)C2211yescharacteristic
20Dic59⋊C8—21no—
21Dic59⋊C8—21no—
22(C2×D59)⋊C8—21no—
23C4×C59⋊C8C2211yescharacteristic
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—
54#11745659—42no—
55C22×D59—21no—
56C22×D59C22⋊C411yescharacteristic
57Q8×C59—21no—
58Q8×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59C22×C411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59C2×D411yescharacteristic
64C2×Dic59—21no—
65C2×Dic59C22⋊C411yescharacteristic
66C2×Dic59C22⋊C411yescharacteristic
67C2×Dic59C22⋊C411yescharacteristic
68D236—21no—
69D236—21no—
70D236—42no—
71C4×D59—21no—
72C4×D59—21no—
73C4×D59—21no—
74C4×D59—21no—
75C4×D59—41no—
76C4×D59—41no—
77C4×D59—41no—
78C8×C59—41no—
79C8×C59—41no—
80C59⋊C8—41no—
81C59⋊C8—41no—
82C22×C59C2×C22⋊C411yescharacteristic
83C2×D59—21no—
84C2×D59—21no—
85C2×D59—21no—
86C2×D59—41no—
87C2×D59—41no—
88C2×D59—41no—
89C4×C59—21no—
90C4×C59—41no—
91C4×C59—41no—
92C4×C59#13111yescharacteristic
93C4×C59#13111yescharacteristic
94C4×C59AGL(1,ℤ/8)11yescharacteristic
95C4×C59#13711yescharacteristic
96Dic59—21no—
97Dic59—21no—
98Dic59—21no—
99Dic59—41no—
100#1495—591nomaximal, Sylow
101C2×C59#40811yescharacteristic
102C2×C59#41711yescharacteristic
103C2×C59#42111yescharacteristic
104D59—41no—
105D59—81no—
106#529—591no—
107#431—591no—
108#423—591no—
109Q8⋊C8—591no—
110Q8⋊C8D5911yescharacteristic, complemented
111D4⋊C8—591no—
112D4⋊C8—591no—
113C59#149511yescharacteristic, complemented, Sylow
114C2×M16—1181no—
115#126—1181no—
116#125—591no—
117#124—591no—
118#123—1181no—
119C22⋊Q8—591no—
120#121—591no—
121C4×Q8C2×D5911yescharacteristic
122C4×D4—591no—
123C4×D4—1181no—
124#117—1181no—
125C2×C42—591no—
126C4⋊C8—591no—
127C4⋊C8—1181no—
128C4⋊C8—1181no—
129C4⋊C8C2×D5911yescharacteristic
130C22⋊C8—1181no—
131C4×C8—591no—
132C4×C8C2×D5911yescharacteristic
133C2×Q8C4×D5911yescharacteristic
134C2×D4—591no—
135C2×D4—1181no—
136C22×C4—591no—
137C22×C4—591no—
138C22×C4—591no—
139C22×C4—1181no—
140M16—2362no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—1181no—
144C2×C8—1181no—
145C4⋊C4—21no—
146C4⋊C4—591no—
147C4⋊C4—1181no—
148C4⋊C4—1181no—
149C4⋊C4—1181no—
150C4⋊C4C4×D5911yescharacteristic
151C22⋊C4—1181no—
152C22⋊C4—1181no—
153C22⋊C4—1181no—
154C22⋊C4—1181no—
155C22⋊C4—1181no—
156C42—21no—
157C42—591no—
158C42—591no—
159C42—591no—
160C42C22×D5911yescharacteristic
161C23—591no—
162C23—1181no—
163Q8—21no—
164Q8—21no—
165D4—1181no—
166D4—1181no—
167D4—2362no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—591no—
171C2×C4—591no—
172C2×C4—591no—
173C2×C4—1181no—
174C2×C4—1181no—
175C2×C4—1181no—
176C2×C4—1181no—
177C2×C4—1181no—
178C2×C4—2361no—
179C2×C4—2361no—
180C2×C4—2361no—
181C2×C4C2×C4×D5911yescharacteristic
182C2×C4D4×D5911yescharacteristic
183C2×C4D4×D5911yescharacteristic
184C8—41no—
185C8—41no—
186C8—2361no—
187C8—2361no—
188C22—1181no—
189C22—1181no—
190C22—1181no—
191C22—2361no—
192C22—2361no—
193C22—2361no—
194C22C22⋊C4×D5911yescharacteristic
195C4—21no—
196C4—41no—
197C4—41no—
198C4—1181no—
199C4—1181no—
200C4—1181no—
201C4—2361no—
202C4#1427373311yescharacteristic
203C4#1427373511yescharacteristic
204C4#1427375411yescharacteristic
205C4#1427375911yescharacteristic
206C2—4721no—
207C2—2361no—
208C2#1683736711yescharacteristic
209C2#1683740211yescharacteristic
210C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×Q8⋊C8C2
socleC22×C59C2×C22⋊C4
hypercenterQ8⋊C8D59
hypocenterC59#1495
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. #16837453C2semidirect
3. #16837424C2semidirect
4. Q8⋊(C59⋊C8)C2semidirect
5. #16837131C2semidirect
6. #16837129C2semidirect
7. C59×Q8⋊C8C2semidirect
110. Q8⋊C8D59semidirect
113. C59#1495semidirect