Finite Group Databasebeta

← #38767456

Subgroups — #38767456

Order 25472.

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#27164553C211yesmaximal, characteristic
2#27164073C211yesmaximal, characteristic, complemented
3#27163970C211yesmaximal, characteristic, complemented
4#27163760C211yesmaximal, characteristic, complemented
5#27163757C211yesmaximal, characteristic, complemented
6#27163757C211yesmaximal, characteristic, complemented
7#330×C199C211yesmaximal, characteristic, complemented
8C2×#15691869—21no—
9#20263950—21no—
10#20263943C2211yescharacteristic
11#20263940—21no—
12#20263935C411yescharacteristic
13#20263930C411yescharacteristic
14#20263920C411yescharacteristic
15#20263917—21no—
16#20263917C411yescharacteristic
17#20263913—21no—
18C42×D199C2211yescharacteristic
19Dic199⋊C8—21no—
20(C2×D199)⋊C8—21no—
21#20263866C2211yescharacteristic
22#20263866C2211yescharacteristic
23C8×Dic199—21no—
24#125×C199C2211yescharacteristic
25#97×C199C2211yescharacteristic
26#97×C199C2211yescharacteristic
27C2×Dic398C2×C411yescharacteristic
28C2×D796—21no—
29C2×D796C2×C411yescharacteristic
30C2×C4×D199—21no—
31C2×C4×D199C2×C411yescharacteristic
32C2×C4×D199D411yescharacteristic
33C2×C4×D199D411yescharacteristic
34#15691869—24no—
35C2×C199⋊C8—21no—
36C2×C199⋊C8—21no—
37C4⋊Dic199—21no—
38Dic199⋊C4—21no—
39(C2×D199)⋊C4—21no—
40(C2×D199)⋊C4—21no—
41(C2×D199)⋊C4—21no—
42(C2×D199)⋊C4—21no—
43(C2×D199)⋊C4—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×D199—21no—
56C22×D199C22⋊C411yescharacteristic
57Dic398—41no—
58D796—41no—
59D796—42no—
60C2×Dic199—21no—
61C2×Dic199C22⋊C411yescharacteristic
62C2×Dic199C22⋊C411yescharacteristic
63C2×Dic199C22⋊C411yescharacteristic
64C4×D199—22no—
65C4×D199—41no—
66C4×D199—41no—
67C4×D199—42no—
68C199⋊C8—22no—
69C199⋊C8—41no—
70C2×C4×C199—21no—
71C2×C4×C199—21no—
72C2×C4×C199C22×C411yescharacteristic
73C2×C4×C199C2×D411yescharacteristic
74C2×C4×C199C2×D411yescharacteristic
75C8×C199—22no—
76C8×C199—41no—
77C22×C199C2×C22⋊C411yescharacteristic
78C2×D199—21no—
79C2×D199—21no—
80C2×D199—21no—
81C2×D199—41no—
82C2×D199—41no—
83C2×D199—41no—
84C4×C199—21no—
85C4×C199—21no—
86C4×C199—21no—
87C4×C199—41no—
88C4×C199—41no—
89Dic199—21no—
90Dic199—21no—
91Dic199—41no—
92Dic199#10412yes—
93C2×C199#41311yescharacteristic
94C2×C199C2×#10411yescharacteristic
95C2×C199#42111yescharacteristic
96D199—41no—
97D199—81no—
98C199#152911yescharacteristic, complemented, Sylow
99#1529—1991nomaximal, Sylow
100#529—1991no—
101#432—1991no—
102C4×M16—1991no—
103#330—1991no—
104#330D19911yescharacteristic, complemented
105#329—1991no—
106#329—1991no—
107C2×M16—3981no—
108#126—3981no—
109#125C2×D19911yescharacteristic
110#124—1991no—
111#123—3981no—
112C22⋊Q8—1991no—
113#121—1991no—
114C4×Q8—1991no—
115C4×D4—3981no—
116C4×D4—1991no—
117#117—3981no—
118C2×C42—1991no—
119C4⋊C8—3981no—
120C22⋊C8—3981no—
121#97—1991no—
122#97—1991no—
123#97C2×D19911yescharacteristic
124#97C2×D19911yescharacteristic
125C4×C8—3981no—
126C2×Q8—1991no—
127C2×D4—3981no—
128C2×D4—1991no—
129C22×C4—3981no—
130C22×C4—1991no—
131C22×C4—1991no—
132C22×C4—1991no—
133M16—3984no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—3981no—
137C2×C8—3981no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—3981no—
141C4⋊C4—3981no—
142C4⋊C4C4×D19911yescharacteristic
143C4⋊C4C4×D19911yescharacteristic
144C22⋊C4—3981no—
145C22⋊C4—3981no—
146C22⋊C4—3981no—
147C22⋊C4—3981no—
148C22⋊C4—3981no—
149C42—3981no—
150C42—1991no—
151C42—1991no—
152C42—1991no—
153C42C22×D19911yescharacteristic
154C23—3981no—
155C23—1991no—
156Q8—7961no—
157D4—7961no—
158D4—7962no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—7961no—
162C2×C4—7961no—
163C2×C4—7962no—
164C2×C4—3982no—
165C2×C4—3981no—
166C2×C4—1991no—
167C2×C4—1991no—
168C2×C4—1991no—
169C2×C4C2×C4×D19911yescharacteristic
170C2×C4D4×D19911yescharacteristic
171C2×C4D4×D19911yescharacteristic
172C8—22no—
173C8—41no—
174C8—7961no—
175C8—3982no—
176C22—7961no—
177C22—7961no—
178C22—7961no—
179C22—3981no—
180C22—3981no—
181C22—3981no—
182C22C22⋊C4×D19911yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—7961no—
189C4—3981no—
190C4—3981no—
191C4—1992no—
192C2—7961no—
193C2—15921no—
194C2#2716400111yescharacteristic
195C2#104×D19911yescharacteristic
196C2#2716403311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#330×C199C2
socleC22×C199C2×C22⋊C4
prime radical#20263930C4
cosocleC42×C199C23
hypercenter#330D199
hypocenterC199#1529
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
2. #27164073C2semidirect
3. #27163970C2semidirect
4. #27163760C2semidirect
5. #27163757C2semidirect
6. #27163757C2semidirect
7. #330×C199C2semidirect
98. C199#1529semidirect
104. #330D199semidirect

Maximal subgroups

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

subgroupindex
#271645532
#271640732
#271639702
#271637602
#271637572
#330×C1992
#1529199