Finite Group Databasebeta

← #21422537

Subgroups — #21422537

Order 7552.

316 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C4×D4×D59C211yesmaximal, characteristic
2#16837458C211yesmaximal, characteristic, complemented
3C4×#11745659C211yesmaximal, characteristic, complemented
4#16837131C211yesmaximal, characteristic, complemented
5D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837129C211yesmaximal, characteristic, complemented
7C59×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×D4×D59C411yescharacteristic
9C22×C4×D59—21no—
10C2×#11745659—21no—
11C4×D236C2211yescharacteristic
12D4×Dic59C411yescharacteristic
13#14273689C411yescharacteristic
14C4×C22⋊D59—21no—
15(C22⋊D59)⋊C4—21no—
16C4⋊C4×D59C411yescharacteristic
17C22⋊C4×D59—21no—
18C42×D59C2211yescharacteristic
19C4⋊(C59⋊C8)C2211yescharacteristic, complemented
20(C2×D59)⋊C8—21no—
21#14273637—21no—
22#14273637—21no—
23C4×C59⋊C8C2211yescharacteristic, complemented
24C4×D4×C59C2211yescharacteristic
25C4⋊C8×C59C2211yescharacteristic, complemented
26C4×C8×C59C2211yescharacteristic, complemented
27C23×D59—21no—
28C2×D4×C59C2×C411yescharacteristic
29C22×C4×C59—21no—
30C2×C22⋊D59—21no—
31C22×Dic59—21no—
32D4×D59—22no—
33D4×D59—22no—
34C2×D236C2×C411yescharacteristic
35C2×C4×D59—21no—
36C2×C4×D59—21no—
37C2×C4×D59—21no—
38C2×C4×D59—42no—
39C2×C4×D59—42no—
40C2×C4×D59C2×C411yescharacteristic
41C2×C4×D59D411yescharacteristic
42C2×C4×D59D411yescharacteristic
43C2×C8×C59—21no—
44C2×C8×C59—21no—
45C4⋊C4×C59C2×C411yescharacteristic
46C22⋊C4×C59—21no—
47C42×C59C2311yescharacteristic
48C22⋊Dic59—21no—
49(C2×D59)⋊C4—21no—
50(C2×D59)⋊C4—21no—
51C4⋊Dic59C2×C411yescharacteristic
52Dic59⋊C4—21no—
53C4×Dic59C2×C411yescharacteristic
54C4×Dic59D411yescharacteristic
55C4×Dic59D411yescharacteristic
56C2×C59⋊C8—21no—
57C2×C59⋊C8—21no—
58#11745659—24no—
59C23×C59—21no—
60C22×D59—24no—
61C22×D59—21no—
62C22×D59—42no—
63C22×D59—42no—
64C22×D59C22⋊C411yescharacteristic
65D4×C59—21no—
66D4×C59M1612yescomplemented
67C2×C4×C59—21no—
68C2×C4×C59—41no—
69C2×C4×C59—41no—
70C2×C4×C59C22×C411yescharacteristic
71C2×C4×C59C2×D411yescharacteristic
72C2×C4×C59C2×D411yescharacteristic
73C22⋊D59—24no—
74C2×Dic59—21no—
75C2×Dic59—42no—
76C2×Dic59C22⋊C411yescharacteristic
77C2×Dic59C22⋊C411yescharacteristic
78C2×Dic59C22⋊C411yescharacteristic
79D236—21no—
80D236M1612yescomplemented
81C4×D59—22no—
82C4×D59—21no—
83C4×D59—21no—
84C4×D59—21no—
85C4×D59—21no—
86C4×D59—42no—
87C4×D59—42no—
88C4×D59—41no—
89C4×D59—41no—
90C8×C59—22no—
91C8×C59—41no—
92C59⋊C8—22no—
93C59⋊C8—41no—
94C22×C59—22no—
95C22×C59—41no—
96C22×C59—41no—
97C22×C59C2×C22⋊C411yescharacteristic
98C2×D59—21no—
99C2×D59—21no—
100C2×D59—22no—
101C2×D59—48no—
102C2×D59—41no—
103C2×D59—41no—
104C2×D59#10412yes—
105C4×C59—21no—
106C4×C59—41no—
107C4×C59C2×M1611yescharacteristic
108C4×C59C2×M1611yescharacteristic
109C4×C59AGL(1,ℤ/8)11yescharacteristic
110C4×C59AGL(1,ℤ/8)11yescharacteristic
111Dic59—21no—
112Dic59—21no—
113Dic59—21no—
114Dic59—41no—
115#1490—591nomaximal, Sylow
116C2×C59—42no—
117C2×C59#40711yescharacteristic
118C2×C59#41811yescharacteristic
119C2×C59C2×#10411yescharacteristic
120D59—22no—
121D59—42no—
122C2×C4×D4—591no—
123#432—591no—
124C4×M16—591no—
125D4⋊C8—591no—
126D4⋊C8—591no—
127D4⋊C8—591no—
128D4⋊C8D5911yescharacteristic, complemented
129C59#149011yescharacteristic, complemented, Sylow
130C22×D4—591no—
131C23×C4—1181no—
132C2×M16—1181no—
133C4×D4—591no—
134C4×D4—591no—
135C4×D4—591no—
136C4×D4—1181no—
137C4×D4—1181no—
138C4×D4C2×D5911yescharacteristic
139C2×C4⋊C4—591no—
140C2×C22⋊C4—1181no—
141C2×C42—591no—
142C4⋊C8—591no—
143C4⋊C8C2×D5911yescharacteristic, complemented
144C22⋊C8—1181no—
145#97—1181no—
146#97—1181no—
147C4×C8—591no—
148C4×C8C2×D5911yescharacteristic, complemented
149C24—1181no—
150C2×D4—591no—
151C2×D4—1181no—
152C2×D4—1182no—
153C2×D4—1182no—
154C2×D4C4×D5911yescharacteristic
155C22×C4—21no—
156C22×C4—591no—
157C22×C4—591no—
158C22×C4—591no—
159C22×C4—1181no—
160C22×C4—1181no—
161C22×C4—1181no—
162C22×C4—1181no—
163C22×C4—2362no—
164C22×C4—2362no—
165M16—1184no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—1181no—
169C2×C8—1181no—
170C4⋊C4—591no—
171C4⋊C4—1181no—
172C4⋊C4C4×D5911yescharacteristic
173C22⋊C4—21no—
174C22⋊C4—1181no—
175C22⋊C4—1181no—
176C22⋊C4—1181no—
177C42—591no—
178C42—591no—
179C42—591no—
180C42C22×D5911yescharacteristic
181C23—21no—
182C23—591no—
183C23—1184no—
184C23—1181no—
185C23—2362no—
186C23—2362no—
187D4—21no—
188D4—592no—
189D4—1184no—
190D4—1181no—
191D4#1174565912yescomplemented
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—591no—
196C2×C4—591no—
197C2×C4—591no—
198C2×C4—1182no—
199C2×C4—1181no—
200C2×C4—1181no—
201C2×C4—1181no—
202C2×C4—1181no—
203C2×C4—1181no—
204C2×C4—2362no—
205C2×C4—2362no—
206C2×C4—2362no—
207C2×C4—2361no—
208C2×C4—2361no—
209C2×C4C2×C4×D5911yescharacteristic
210C2×C4D4×D5911yescharacteristic
211C2×C4D4×D5911yescharacteristic
212C8—22no—
213C8—41no—
214C8—1182no—
215C8—2361no—
216C22—22no—
217C22—41no—
218C22—41no—
219C22—592no—
220C22—1181no—
221C22—1181no—
222C22—1182no—
223C22—2368no—
224C22—2361no—
225C22—2361no—
226C22C22⋊C4×D5911yescharacteristic
227C4—21no—
228C4—41no—
229C4—1181no—
230C4—1181no—
231C4—1181no—
232C4—2361no—
233C4M16×D5911yescharacteristic
234C4C2×#1174565911yescharacteristic
235C4#1427375111yescharacteristic
236C4#1427375411yescharacteristic
237C2—42no—
238C2—1182no—
239C2—2362no—
240C2#1683736411yescharacteristic
241C2#1683740511yescharacteristic
242C2#104×D5911yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×D4⋊C8C2
socleC22×C59C2×C22⋊C4
hypercenterD4⋊C8D59
hypocenterC59#1490
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16837458C2semidirect
3. C4×#11745659C2semidirect
4. #16837131C2semidirect
5. D4⋊(C59⋊C8)C2semidirect
6. #16837129C2semidirect
7. C59×D4⋊C8C2semidirect
19. C4⋊(C59⋊C8)C22semidirect
23. C4×C59⋊C8C22semidirect
25. C4⋊C8×C59C22semidirect
26. C4×C8×C59C22semidirect
66. D4×C59M16semidirect
80. D236M16semidirect
128. D4⋊C8D59semidirect
129. C59#1490semidirect
143. C4⋊C8C2×D59semidirect
148. C4×C8C2×D59semidirect
191. D4#11745659semidirect