Finite Group Databasebeta

← #38767542

Subgroups — #38767542

Order 25472.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#27164566C211yesmaximal, characteristic
2#27164074C211yesmaximal, characteristic, complemented
3C4⋊C8×D199C211yesmaximal, characteristic, complemented
4#27163766C211yesmaximal, characteristic, complemented
5#27163766C211yesmaximal, characteristic, complemented
6#27163762C211yesmaximal, characteristic, complemented
7#331×C199C211yesmaximal, characteristic, complemented
8C2×#15691885C412yes—
9C2×C8×D199—21no—
10#20263955C2211yescharacteristic
11#20263942C412yes—
12#20263926—21no—
13#20263926—21no—
14D4×Dic199—21no—
15D4×Dic199—21no—
16C42×D199C2211yescharacteristic
17C4⋊(C199⋊C8)C2211yescharacteristic
18C4⋊(C199⋊C8)C2211yescharacteristic
19Dic199⋊C8—21no—
20(C2×D199)⋊C8—21no—
21#20263865—21no—
22#127×C199C2211yescharacteristic
23C4⋊C8×C199C2211yescharacteristic
24C4⋊C8×C199C2211yescharacteristic
25#15691885—44no—
26C2×Dic398C2×C412yes—
27C2×C22⋊D199—22no—
28C22×Dic199—22no—
29C2×C4×D199C2×C411yescharacteristic
30C2×C4×D199D411yescharacteristic
31C2×C4×D199D411yescharacteristic
32C2×C199⋊C8—21no—
33C2×C199⋊C8—21no—
34C8×D199—42no—
35C4⋊Dic199—21no—
36C4⋊Dic199—21no—
37C22⋊Dic199—22no—
38C22⋊Dic199—22no—
39C4×Dic199C2×C411yescharacteristic
40C4×Dic199D411yescharacteristic
41C4×Dic199D411yescharacteristic
42C2×D4×C199—21no—
43C2×D4×C199—21no—
44C2×D4×C199C2×C412yes—
45C2×C8×C199—21no—
46C2×C8×C199—21no—
47C42×C199C2311yescharacteristic
48C22×D199C22⋊C411yescharacteristic
49Dic398—42no—
50C22⋊D199—44no—
51C2×Dic199—22no—
52C2×Dic199—44no—
53C2×Dic199C22⋊C411yescharacteristic
54C2×Dic199C22⋊C411yescharacteristic
55C2×Dic199C22⋊C411yescharacteristic
56C4×D199—22no—
57C4×D199—21no—
58C4×D199—21no—
59C4×D199—21no—
60C4×D199—21no—
61C199⋊C8—41no—
62C199⋊C8—41no—
63C23×C199—22no—
64D4×C199—42no—
65D4×C199—41no—
66D4×C199—41no—
67D4×C199—41no—
68D4×C199—41no—
69C2×C4×C199C22×C411yescharacteristic
70C2×C4×C199C2×D411yescharacteristic
71C2×C4×C199C2×D411yescharacteristic
72C8×C199—41no—
73C8×C199—41no—
74C22×C199—42no—
75C22×C199—42no—
76C22×C199—42no—
77C22×C199C2×C22⋊C411yescharacteristic
78C2×D199—21no—
79C2×D199—21no—
80C2×D199#10012yes—
81C4×C199—21no—
82C4×C199#13511yescharacteristic
83C4×C199#13511yescharacteristic
84C4×C199AGL(1,ℤ/8)11yescharacteristic
85C4×C199#13711yescharacteristic
86Dic199—21no—
87Dic199—21no—
88Dic199—21no—
89Dic199—42no—
90C2×C199—82no—
91C2×C199C2×#10011yescharacteristic
92C2×C199#41611yescharacteristic
93C2×C199#41711yescharacteristic
94D199—22no—
95C199#155111yescharacteristic, complemented, Sylow
96#1551—1991nomaximal, Sylow
97#532—1991no—
98#432—1991no—
99C2×C4⋊C8—1991no—
100#333—1991no—
101#333—1991no—
102#331—1991no—
103#331D19911yescharacteristic, complemented
104C2×#41—1992no—
105C22×C8—3981no—
106C4⋊Q8—1991no—
107#127C2×D19911yescharacteristic
108#124—1992no—
109#121—3981no—
110#121—3981no—
111C4×D4—3981no—
112C4×D4—3981no—
113C2×C42—1991no—
114C4⋊C8—3981no—
115C4⋊C8—1991no—
116C4⋊C8—1991no—
117C4⋊C8C2×D19911yescharacteristic
118C4⋊C8C2×D19911yescharacteristic
119C22⋊C8—3981no—
120#97—3981no—
121#41—7964no—
122C2×Q8—1992no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—3982no—
126C2×D4C4×D19912yes—
127C22×C4—3982no—
128C22×C4—1991no—
129C22×C4—1991no—
130C22×C4—1991no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—7962no—
134C2×C8—3981no—
135C2×C8—3981no—
136C4⋊C4—3981no—
137C4⋊C4—3981no—
138C22⋊C4—3982no—
139C22⋊C4—3982no—
140C42—1991no—
141C42—1991no—
142C42—1991no—
143C42C22×D19911yescharacteristic
144C23—22no—
145C23—1991no—
146Q8—7962no—
147D4—42no—
148D4—41no—
149D4—41no—
150D4—41no—
151D4—41no—
152D4—7964no—
153C2×C4—7964no—
154C2×C4—3982no—
155C2×C4—3982no—
156C2×C4—3981no—
157C2×C4—3981no—
158C2×C4—3981no—
159C2×C4—3981no—
160C2×C4—1991no—
161C2×C4—1991no—
162C2×C4—1991no—
163C2×C4C2×C4×D19911yescharacteristic
164C2×C4D4×D19911yescharacteristic
165C2×C4D4×D19911yescharacteristic
166C8—41no—
167C8—41no—
168C8—7961no—
169C8—7961no—
170C22—42no—
171C22—42no—
172C22—42no—
173C22—3981no—
174C22—3981no—
175C22—1992no—
176C22C22⋊C4×D19911yescharacteristic
177C4—21no—
178C4—7962no—
179C4—3981no—
180C4—3981no—
181C4—3981no—
182C4#2026397411yescharacteristic
183C4#2026397611yescharacteristic
184C4#2026397911yescharacteristic
185C4#2026398411yescharacteristic
186C2—82no—
187C2—3982no—
188C2#100×D19911yescharacteristic
189C2#2716401111yescharacteristic
190C2#2716401611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#331×C199C2
socleC22×C199C2×C22⋊C4
prime radical#27164566C2
cosocleC42×C199C23
hypercenter#331D199
hypocenterC199#1551
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #27164074C2semidirect
3. C4⋊C8×D199C2semidirect
4. #27163766C2semidirect
5. #27163766C2semidirect
6. #27163762C2semidirect
7. #331×C199C2semidirect
95. C199#1551semidirect
103. #331D199semidirect

Maximal subgroups

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

subgroupindex
#271645662
#271640742
C4⋊C8×D1992
#271637662
#271637622
#331×C1992
#1551199