Finite Group Databasebeta

← #21422501

Subgroups — #21422501

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#16837934C211yesmaximal, characteristic
2#16837454C211yesmaximal, characteristic, complemented
3#16837453C211yesmaximal, characteristic, complemented
4#16837134C211yesmaximal, characteristic, complemented
5#16837132C211yesmaximal, characteristic, complemented
6D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
7C59×D4⋊C8C211yesmaximal, characteristic, complemented
8#14273720—21no—
9#14273718C411yescharacteristic
10#14273714C411yescharacteristic
11#14273709—21no—
12#14273707C411yescharacteristic
13#14273698C411yescharacteristic
14C4×Dic118C2211yescharacteristic
15C4×C22⋊D59—21no—
16#14273686—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×D4×C59C2211yescharacteristic
25C4⋊C8×C59C2211yescharacteristic
26C4×C8×C59C2211yescharacteristic
27C2×D4×C59C2×C411yescharacteristic
28C22×C4×C59—21no—
29C2×C22⋊D59—21no—
30C2×C4×D59C2×C411yescharacteristic
31C2×C4×D59D411yescharacteristic
32C2×C4×D59D411yescharacteristic
33C2×Dic118C2×C411yescharacteristic
34C2×C8×C59—21no—
35C2×C8×C59—21no—
36C4⋊C4×C59C2×C411yescharacteristic
37C22⋊C4×C59—21no—
38C42×C59C2311yescharacteristic
39C22⋊Dic59—21no—
40C22⋊Dic59—21no—
41C22⋊Dic59—21no—
42(C2×D59)⋊C4—21no—
43C4⋊Dic59—21no—
44C4⋊Dic59—21no—
45C4⋊Dic59C2×C411yescharacteristic
46Dic59⋊C4—21no—
47Dic59⋊C4—21no—
48C4×Dic59—21no—
49C4×Dic59C2×C411yescharacteristic
50C4×Dic59D411yescharacteristic
51C4×Dic59D411yescharacteristic
52C2×C59⋊C8—21no—
53C2×C59⋊C8—21no—
54C23×C59—21no—
55C22×D59C22⋊C411yescharacteristic
56D4×C59—21no—
57D4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—41no—
60C2×C4×C59—41no—
61C2×C4×C59C22×C411yescharacteristic
62C2×C4×C59C2×D411yescharacteristic
63C2×C4×C59C2×D411yescharacteristic
64C22⋊D59—42no—
65C2×Dic59—21no—
66C2×Dic59—21no—
67C2×Dic59C22⋊C411yescharacteristic
68C2×Dic59C22⋊C411yescharacteristic
69C2×Dic59C22⋊C411yescharacteristic
70C4×D59—21no—
71C4×D59—21no—
72C4×D59—21no—
73C4×D59—21no—
74C4×D59—41no—
75Dic118—21no—
76Dic118—21no—
77C8×C59—41no—
78C8×C59—41no—
79C59⋊C8—41no—
80C59⋊C8—41no—
81C22×C59—41no—
82C22×C59—41no—
83C22×C59—41no—
84C22×C59C2×C22⋊C411yescharacteristic
85C2×D59—21no—
86C2×D59—21no—
87C2×D59—21no—
88C4×C59—21no—
89C4×C59—41no—
90C4×C59#13111yescharacteristic
91C4×C59#13111yescharacteristic
92C4×C59#13511yescharacteristic
93C4×C59#13511yescharacteristic
94Dic59—21no—
95Dic59—21no—
96Dic59—21no—
97Dic59—41no—
98Dic59—41no—
99#1482—591nomaximal, Sylow
100C2×C59—81no—
101C2×C59#40811yescharacteristic
102C2×C59#41611yescharacteristic
103C2×C59#42111yescharacteristic
104D59—41no—
105#529—591no—
106#431—591no—
107#431—591no—
108Q8⋊C8—591no—
109Q8⋊C8—591no—
110D4⋊C8—591no—
111D4⋊C8D5911yescharacteristic, complemented
112C59#148211yescharacteristic, complemented, Sylow
113#126—1181no—
114#125—591no—
115#124—591no—
116#123—1181no—
117C22⋊Q8—591no—
118#121—591no—
119C4×Q8—591no—
120C4×D4—1181no—
121C4×D4C2×D5911yescharacteristic
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×Q8—591no—
133C2×D4—1181no—
134C2×D4C4×D5911yescharacteristic
135C22×C4—21no—
136C22×C4—591no—
137C22×C4—591no—
138C22×C4—591no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—1181no—
142C2×C8—1181no—
143C4⋊C4—591no—
144C4⋊C4—1181no—
145C4⋊C4—1181no—
146C4⋊C4—1181no—
147C4⋊C4—1181no—
148C4⋊C4C4×D5911yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—1181no—
151C22⋊C4—1181no—
152C22⋊C4—1181no—
153C22⋊C4—1181no—
154C42—591no—
155C42—591no—
156C42—591no—
157C42—1181no—
158C42C22×D5911yescharacteristic
159C23—21no—
160C23—591no—
161Q8—1181no—
162Q8—1181no—
163D4—21no—
164D4—21no—
165D4—2362no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—591no—
170C2×C4—591no—
171C2×C4—591no—
172C2×C4—1181no—
173C2×C4—1181no—
174C2×C4—1181no—
175C2×C4—1181no—
176C2×C4—1181no—
177C2×C4—1181no—
178C2×C4—2361no—
179C2×C4C2×C4×D5911yescharacteristic
180C2×C4D4×D5911yescharacteristic
181C2×C4D4×D5911yescharacteristic
182C8—41no—
183C8—41no—
184C8—2361no—
185C8—2361no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—1181no—
190C22—1181no—
191C22—1181no—
192C22C22⋊C4×D5911yescharacteristic
193C4—21no—
194C4—41no—
195C4—1181no—
196C4—1181no—
197C4—1181no—
198C4—2361no—
199C4—2361no—
200C4#1427373311yescharacteristic
201C4#1427373511yescharacteristic
202C4#1427374611yescharacteristic
203C4#1427374811yescharacteristic
204C2—81no—
205C2—2361no—
206C2#1683736711yescharacteristic
207C2#1683739511yescharacteristic
208C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×D4⋊C8C2
socleC22×C59C2×C22⋊C4
hypercenterD4⋊C8D59
hypocenterC59#1482
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. #16837454C2semidirect
3. #16837453C2semidirect
4. #16837134C2semidirect
5. #16837132C2semidirect
6. D4⋊(C59⋊C8)C2semidirect
7. C59×D4⋊C8C2semidirect
111. D4⋊C8D59semidirect
112. C59#1482semidirect