Finite Group Databasebeta

← #21422497

Subgroups — #21422497

Order 7552.

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

normal subgroups only

This group has 216 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
1#16837956C211yesmaximal, characteristic
2#16837453C211yesmaximal, characteristic
3C4⋊C8×D59C211yesmaximal, characteristic
4#16837134C211yesmaximal, characteristic, complemented
5Q8⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#16837132C211yesmaximal, characteristic, complemented
7C59×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×C8×D59—21no—
9#14273726C411yescharacteristic
10#14273725C411yescharacteristic
11#14273717—21no—
12#14273707C411yescharacteristic
13#14273705—21no—
14#14273703C411yescharacteristic
15C4×Dic118—21no—
16C4×Dic118C2211yescharacteristic
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×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—
54C8×D59—42no—
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×Dic59—21no—
65C2×Dic59C22⋊C411yescharacteristic
66C2×Dic59C22⋊C411yescharacteristic
67C2×Dic59C22⋊C411yescharacteristic
68C4×D59—21no—
69C4×D59—21no—
70C4×D59—41no—
71C4×D59SD1612yes—
72C4×D59Q1612yes—
73Dic118—21no—
74Dic118—21no—
75Dic118—42no—
76C8×C59—41no—
77C8×C59—41no—
78C59⋊C8—41no—
79C59⋊C8—41no—
80C22×C59C2×C22⋊C411yescharacteristic
81C2×D59—21no—
82C2×D59—21no—
83C2×D59#10312yes—
84C4×C59—21no—
85C4×C59—41no—
86C4×C59—41no—
87C4×C59#13111yescharacteristic
88C4×C59#13111yescharacteristic
89C4×C59C2×SD1611yescharacteristic
90C4×C59C2×Q1611yescharacteristic
91Dic59—21no—
92Dic59—21no—
93Dic59—41no—
94Dic59—41no—
95Dic59#10312yes—
96#1481—591nomaximal, Sylow
97C2×C59#40811yescharacteristic
98C2×C59C2×#10311yescharacteristic
99C2×C59#42111yescharacteristic
100D59—22no—
101#533—591no—
102#431—591no—
103C2×C4⋊C8—591no—
104Q8⋊C8—591no—
105Q8⋊C8—591no—
106Q8⋊C8—591no—
107Q8⋊C8D5911yescharacteristic, complemented
108C59#148111yescharacteristic, complemented, Sylow
109C22×C8—1181no—
110C4⋊Q8—591no—
111C4⋊Q8—591no—
112#125—1181no—
113C22⋊Q8—591no—
114C22⋊Q8—591no—
115C22⋊Q8—1181no—
116C4×Q8—591no—
117C4×Q8—1181no—
118C4×Q8C2×D5911yescharacteristic
119#117—1181no—
120C2×C42—591no—
121C4⋊C8—591no—
122C4⋊C8—1181no—
123C4⋊C8—1181no—
124C4⋊C8C2×D5911yescharacteristic
125C22⋊C8—1181no—
126C4×C8—591no—
127C4×C8C2×D5911yescharacteristic
128C2×Q8—591no—
129C2×Q8—1181no—
130C2×Q8C4×D5911yescharacteristic
131C22×C4—591no—
132C22×C4—591no—
133C22×C4—591no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1181no—
137C2×C8—1181no—
138C2×C8—2362no—
139C4⋊C4—21no—
140C4⋊C4—591no—
141C4⋊C4—1181no—
142C4⋊C4—1181no—
143C4⋊C4—1181no—
144C4⋊C4—1181no—
145C4⋊C4—1181no—
146C4⋊C4—1181no—
147C4⋊C4C4×D5911yescharacteristic
148C22⋊C4—1181no—
149C22⋊C4—1181no—
150C42—21no—
151C42—591no—
152C42—591no—
153C42—591no—
154C42—1181no—
155C42C22×D5911yescharacteristic
156C23—591no—
157Q8—21no—
158Q8—21no—
159Q8—1181no—
160Q8—1181no—
161Q8—2362no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—591no—
165C2×C4—592no—
166C2×C4—592no—
167C2×C4—591no—
168C2×C4—591no—
169C2×C4—1181no—
170C2×C4—1181no—
171C2×C4—1181no—
172C2×C4—1181no—
173C2×C4—2361no—
174C2×C4C2×C4×D5911yescharacteristic
175C2×C4D4×D5911yescharacteristic
176C2×C4D4×D5911yescharacteristic
177C8—41no—
178C8—41no—
179C8—2361no—
180C8—2361no—
181C22—592no—
182C22—1181no—
183C22—1181no—
184C22C22⋊C4×D5911yescharacteristic
185C4—21no—
186C4—41no—
187C4—41no—
188C4—592no—
189C4—1181no—
190C4—1181no—
191C4—2361no—
192C4—2361no—
193C4#1427373311yescharacteristic
194C4#1427373511yescharacteristic
195C4SD16×D5911yescharacteristic
196C4Q16×D5911yescharacteristic
197C2—1182no—
198C2#1683736711yescharacteristic
199C2#103×D5911yescharacteristic
200C2#1683741711yescharacteristic
subgroupG/H
centerC2×C4D4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×Q8⋊C8C2
socleC22×C59C2×C22⋊C4
hypercenterQ8⋊C8D59
hypocenterC59#1481
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
107. Q8⋊C8D59semidirect
108. C59#1481semidirect