Finite Group Databasebeta

← #38767463

Subgroups — #38767463

Order 25472.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#27164574C211yesmaximal, characteristic
2#27164073C211yesmaximal, characteristic
3#97×D199C211yesmaximal, characteristic
4#27163760C211yesmaximal, characteristic, complemented
5#27163759C211yesmaximal, characteristic, complemented
6#27163759C211yesmaximal, characteristic, complemented
7#330×C199C211yesmaximal, characteristic, complemented
8C2×C8×D199—21no—
9#20263954C411yescharacteristic
10#20263954C411yescharacteristic
11#20263947C2211yescharacteristic
12#20263933—21no—
13#20263933—21no—
14#20263920—21no—
15#20263920—21no—
16#20263913C411yescharacteristic
17#20263913C411yescharacteristic
18C42×D199C2211yescharacteristic
19Dic199⋊C8—21no—
20(C2×D199)⋊C8—21no—
21#20263866C2211yescharacteristic
22#20263866C2211yescharacteristic
23#20263865—21no—
24#125×C199C2211yescharacteristic
25#97×C199C2211yescharacteristic
26#97×C199C2211yescharacteristic
27C2×Dic398—21no—
28C2×Dic398—21no—
29C2×C4×D199C2×C411yescharacteristic
30C2×C4×D199D411yescharacteristic
31C2×C4×D199D411yescharacteristic
32C2×C199⋊C8—21no—
33C2×C199⋊C8—21no—
34C8×D199—24no—
35C4⋊Dic199C2×C411yescharacteristic
36C4⋊Dic199C2×C411yescharacteristic
37Dic199⋊C4—21no—
38Dic199⋊C4—21no—
39Dic199⋊C4—21no—
40Dic199⋊C4—21no—
41(C2×D199)⋊C4—21no—
42(C2×D199)⋊C4—21no—
43C4×Dic199—21no—
44C4×Dic199—21no—
45C4×Dic199C2×C411yescharacteristic
46C4×Dic199D411yescharacteristic
47C4×Dic199D411yescharacteristic
48C2×C8×C199—21no—
49C2×C8×C199—21no—
50C4⋊C4×C199—21no—
51C4⋊C4×C199—21no—
52C4⋊C4×C199C2×C411yescharacteristic
53C4⋊C4×C199C2×C411yescharacteristic
54C42×C199C2311yescharacteristic
55C22×D199C22⋊C411yescharacteristic
56Dic398—42no—
57Dic398—42no—
58C2×Dic199—21no—
59C2×Dic199—21no—
60C2×Dic199C22⋊C411yescharacteristic
61C2×Dic199C22⋊C411yescharacteristic
62C2×Dic199C22⋊C411yescharacteristic
63C4×D199—22no—
64C4×D199—22no—
65C4×D199—41no—
66C199⋊C8—22no—
67C199⋊C8—41no—
68C2×C4×C199—21no—
69C2×C4×C199—21no—
70C2×C4×C199C22×C411yescharacteristic
71C2×C4×C199C2×D411yescharacteristic
72C2×C4×C199C2×D411yescharacteristic
73C8×C199—22no—
74C8×C199—41no—
75C22×C199C2×C22⋊C411yescharacteristic
76C2×D199—21no—
77C2×D199—21no—
78C2×D199#10112yes—
79C4×C199—21no—
80C4×C199—21no—
81C4×C199—21no—
82C4×C199—41no—
83C4×C199—41no—
84Dic199—21no—
85Dic199—21no—
86Dic199—41no—
87Dic199—41no—
88Dic199#10412yes—
89C2×C199C2×#10111yescharacteristic
90C2×C199C2×#10411yescharacteristic
91C2×C199#42111yescharacteristic
92D199—22no—
93C199#153111yescharacteristic, complemented, Sylow
94#1531—1991nomaximal, Sylow
95#533—1991no—
96#432—1991no—
97C2×#97—1991no—
98#330—1991no—
99#330—1991no—
100#330—1991no—
101#330D19911yescharacteristic, complemented
102C22×C8—3981no—
103C4⋊Q8—1991no—
104C4⋊Q8—1991no—
105#125—1991no—
106#125C2×D19911yescharacteristic
107C22⋊Q8—3981no—
108C22⋊Q8—3981no—
109C4×Q8—3981no—
110C4×Q8—3981no—
111#117—1991no—
112#117—1991no—
113C2×C42—1991no—
114C4⋊C8—3981no—
115C22⋊C8—3981no—
116#97—3981no—
117#97—1991no—
118#97—1991no—
119#97C2×D19911yescharacteristic
120#97C2×D19911yescharacteristic
121C2×Q8—3981no—
122C2×Q8—3981no—
123C22×C4—1991no—
124C22×C4—1991no—
125C22×C4—1991no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—3984no—
129C2×C8—3981no—
130C2×C8—3981no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—3981no—
134C4⋊C4—3981no—
135C4⋊C4—3981no—
136C4⋊C4—3981no—
137C4⋊C4—1991no—
138C4⋊C4—1991no—
139C4⋊C4C4×D19911yescharacteristic
140C4⋊C4C4×D19911yescharacteristic
141C22⋊C4—3981no—
142C22⋊C4—3981no—
143C42—3981no—
144C42—3981no—
145C42—1991no—
146C42—1991no—
147C42—1991no—
148C42C22×D19911yescharacteristic
149C23—1991no—
150Q8—7962no—
151Q8—7962no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—7961no—
155C2×C4—3982no—
156C2×C4—3982no—
157C2×C4—3981no—
158C2×C4—3981no—
159C2×C4—1991no—
160C2×C4—1991no—
161C2×C4—1991no—
162C2×C4C2×C4×D19911yescharacteristic
163C2×C4D4×D19911yescharacteristic
164C2×C4D4×D19911yescharacteristic
165C8—22no—
166C8—41no—
167C8—7961no—
168C8—3982no—
169C22—3981no—
170C22—3981no—
171C22—1992no—
172C22C22⋊C4×D19911yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—7961no—
179C4—7961no—
180C4—3981no—
181C4—3981no—
182C4—1992no—
183C2—3982no—
184C2#101×D19911yescharacteristic
185C2#104×D19911yescharacteristic
186C2#2716403311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#330×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC22×D199C22⋊C4
cosocleC42×C199C23
hypercenter#330D199
hypocenterC199#1531
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #27163760C2semidirect
5. #27163759C2semidirect
6. #27163759C2semidirect
7. #330×C199C2semidirect
93. C199#1531semidirect
101. #330D199semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#271645742
#271640732
#97×D1992
#271637602
#271637592
#330×C1992
#1531199