Finite Group Databasebeta

← #21422702

Subgroups — #21422702

Order 7552.

216 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 59 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#16837937C211yesmaximal, characteristic
2#16837457C211yesmaximal, characteristic, complemented
3#16837354C211yesmaximal, characteristic, complemented
4#16837144C211yesmaximal, characteristic, complemented
5#16837141C211yesmaximal, characteristic, complemented
6#16837141C211yesmaximal, characteristic, complemented
7C59×#330C211yesmaximal, characteristic, complemented
8C2×#11745659—21no—
9#14273722—21no—
10#14273715C2211yescharacteristic
11#14273712—21no—
12#14273707C411yescharacteristic
13#14273702C411yescharacteristic
14#14273692C411yescharacteristic
15#14273689—21no—
16#14273689C411yescharacteristic
17#14273685—21no—
18C42×D59C2211yescharacteristic
19Dic59⋊C8—21no—
20(C2×D59)⋊C8—21no—
21#14273638C2211yescharacteristic
22#14273638C2211yescharacteristic
23C8×Dic59—21no—
24#125×C59C2211yescharacteristic
25#97×C59C2211yescharacteristic
26#97×C59C2211yescharacteristic
27C2×D236—21no—
28C2×D236C2×C411yescharacteristic
29C2×C4×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×C59—21no—
37C4⋊C4×C59—21no—
38C4⋊C4×C59C2×C411yescharacteristic
39C4⋊C4×C59C2×C411yescharacteristic
40C42×C59C2311yescharacteristic
41(C2×D59)⋊C4—21no—
42(C2×D59)⋊C4—21no—
43(C2×D59)⋊C4—21no—
44(C2×D59)⋊C4—21no—
45(C2×D59)⋊C4—21no—
46C4⋊Dic59—21no—
47Dic59⋊C4—21no—
48C4×Dic59—21no—
49C4×Dic59C2×C411yescharacteristic
50C4×Dic59D411yescharacteristic
51C4×Dic59D411yescharacteristic
52C2×C59⋊C8—21no—
53C2×C59⋊C8—21no—
54#11745659—24no—
55C22×D59—21no—
56C22×D59C22⋊C411yescharacteristic
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59C22×C411yescharacteristic
60C2×C4×C59C2×D411yescharacteristic
61C2×C4×C59C2×D411yescharacteristic
62C2×Dic59—21no—
63C2×Dic59C22⋊C411yescharacteristic
64C2×Dic59C22⋊C411yescharacteristic
65C2×Dic59C22⋊C411yescharacteristic
66D236—41no—
67D236—42no—
68C4×D59—22no—
69C4×D59—41no—
70C4×D59—41no—
71C4×D59—42no—
72Dic118—41no—
73C8×C59—22no—
74C8×C59—41no—
75C59⋊C8—22no—
76C59⋊C8—41no—
77C22×C59C2×C22⋊C411yescharacteristic
78C2×D59—21no—
79C2×D59—21no—
80C2×D59—21no—
81C2×D59—41no—
82C2×D59—41no—
83C2×D59—41no—
84C4×C59—21no—
85C4×C59—21no—
86C4×C59—21no—
87C4×C59—41no—
88C4×C59—41no—
89Dic59—21no—
90Dic59—21no—
91Dic59—41no—
92Dic59#10412yes—
93#1529—591nomaximal, Sylow
94C2×C59#41311yescharacteristic
95C2×C59C2×#10411yescharacteristic
96C2×C59#42111yescharacteristic
97D59—41no—
98D59—81no—
99#529—591no—
100#432—591no—
101C4×M16—591no—
102#330—591no—
103#330D5911yescharacteristic, complemented
104#329—591no—
105#329—591no—
106C59#152911yescharacteristic, complemented, Sylow
107C2×M16—1181no—
108#126—1181no—
109#125C2×D5911yescharacteristic
110#124—591no—
111#123—1181no—
112C22⋊Q8—591no—
113#121—591no—
114C4×Q8—591no—
115C4×D4—591no—
116C4×D4—1181no—
117#117—1181no—
118C2×C42—591no—
119C4⋊C8—1181no—
120C22⋊C8—1181no—
121#97—591no—
122#97—591no—
123#97C2×D5911yescharacteristic
124#97C2×D5911yescharacteristic
125C4×C8—1181no—
126C2×Q8—591no—
127C2×D4—591no—
128C2×D4—1181no—
129C22×C4—591no—
130C22×C4—591no—
131C22×C4—591no—
132C22×C4—1181no—
133M16—1184no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1181no—
137C2×C8—1181no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—1181no—
141C4⋊C4—1181no—
142C4⋊C4C4×D5911yescharacteristic
143C4⋊C4C4×D5911yescharacteristic
144C22⋊C4—1181no—
145C22⋊C4—1181no—
146C22⋊C4—1181no—
147C22⋊C4—1181no—
148C22⋊C4—1181no—
149C42—591no—
150C42—591no—
151C42—591no—
152C42—1181no—
153C42C22×D5911yescharacteristic
154C23—591no—
155C23—1181no—
156Q8—2361no—
157D4—2361no—
158D4—2362no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—591no—
162C2×C4—591no—
163C2×C4—591no—
164C2×C4—1182no—
165C2×C4—1181no—
166C2×C4—2361no—
167C2×C4—2361no—
168C2×C4—2362no—
169C2×C4C2×C4×D5911yescharacteristic
170C2×C4D4×D5911yescharacteristic
171C2×C4D4×D5911yescharacteristic
172C8—22no—
173C8—41no—
174C8—1182no—
175C8—2361no—
176C22—1181no—
177C22—1181no—
178C22—1181no—
179C22—2361no—
180C22—2361no—
181C22—2361no—
182C22C22⋊C4×D5911yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—592no—
189C4—1181no—
190C4—1181no—
191C4—2361no—
192C2—4721no—
193C2—2361no—
194C2#1683738511yescharacteristic
195C2#104×D5911yescharacteristic
196C2#1683741711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D59
commutatorC2×C4×C59C22×C4
FrattiniC42C22×D59
FittingC59×#330C2
socleC22×C59C2×C22⋊C4
hypercenter#330D59
hypocenterC59#1529
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #16837457C2semidirect
3. #16837354C2semidirect
4. #16837144C2semidirect
5. #16837141C2semidirect
6. #16837141C2semidirect
7. C59×#330C2semidirect
103. #330D59semidirect
106. C59#1529semidirect