Finite Group Databasebeta

← #38767360

Subgroups — #38767360

Order 25472.

228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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#27164570C211yesmaximal, characteristic
2#27164072C211yesmaximal, characteristic
3#27163863C211yesmaximal, characteristic
4#27163756C211yesmaximal, characteristic
5#27163755C211yesmaximal, characteristic
6#27163754C211yesmaximal, characteristic
7#328×C199C211yesmaximal, characteristic
8#20263954C411yescharacteristic, complemented
9#20263953C411yescharacteristic, complemented
10#20263945—21no—
11#20263934C2211yescharacteristic
12#20263932—21no—
13Q8×Dic199C411yescharacteristic, complemented
14#20263920—21no—
15#20263920C411yescharacteristic, complemented
16#20263911—21no—
17C2×C4×Dic199—21no—
18C2×C4×Dic199C2211yescharacteristic
19Dic199⋊C8—21no—
20C22⋊(C199⋊C8)C2211yescharacteristic
21#20263865—21no—
22C199⋊#95—21no—
23C199⋊#95C2211yescharacteristic
24C22⋊Q8×C199C2211yescharacteristic
25C22⋊C8×C199C2211yescharacteristic
26#95×C199C2211yescharacteristic
27C2×Dic398—21no—
28C2×Dic398C2×C411yescharacteristic
29C22×Dic199—21no—
30C22×Dic199D411yescharacteristic
31C22×Dic199D411yescharacteristic
32C2×C199⋊C8—21no—
33C4⋊Dic199—21no—
34C4⋊Dic199C2×C411yescharacteristic
35Dic199⋊C4—21no—
36Dic199⋊C4—21no—
37Dic199⋊C4—21no—
38Dic199⋊C4—21no—
39Dic199⋊C4—21no—
40C22⋊Dic199—21no—
41C4×Dic199—24no—
42C4×Dic199—21no—
43C4×Dic199—21no—
44C4×Dic199C2×C411yescharacteristic
45C4×Dic199C2×C411yescharacteristic
46C4×Dic199D411yescharacteristic
47C4×Dic199D411yescharacteristic
48C2×Q8×C199C2×C411yescharacteristic
49C22×C4×C199—21no—
50C22×C4×C199C2311yescharacteristic
51C2×C8×C199—21no—
52C4⋊C4×C199—21no—
53C4⋊C4×C199C2×C411yescharacteristic
54C22⋊C4×C199—21no—
55Dic398—42no—
56Dic398—41no—
57C2×Dic199—21no—
58C2×Dic199—21no—
59C2×Dic199—22no—
60C2×Dic199—22no—
61C2×Dic199—21no—
62C2×Dic199—21no—
63C2×Dic199—41no—
64C2×Dic199—41no—
65C2×Dic199C22⋊C411yescharacteristic
66C2×Dic199C22⋊C411yescharacteristic
67C2×Dic199C22⋊C411yescharacteristic
68C2×Dic199C22⋊C411yescharacteristic
69C199⋊C8—41no—
70C23×C199C2×D411yescharacteristic
71Q8×C199—41no—
72C2×C4×C199—22no—
73C2×C4×C199—21no—
74C2×C4×C199—21no—
75C2×C4×C199—41no—
76C2×C4×C199—41no—
77C2×C4×C199—41no—
78C2×C4×C199C22×C411yescharacteristic
79C2×C4×C199C2×D411yescharacteristic
80C8×C199—41no—
81C22×C199—21no—
82C22×C199—21no—
83C22×C199C2×C22⋊C411yescharacteristic
84C22×C199#13711yescharacteristic
85C22×C199#13711yescharacteristic
86C4×C199—21no—
87C4×C199—21no—
88C4×C199—42no—
89C4×C199—41no—
90C4×C199—41no—
91Dic199—21no—
92Dic199—21no—
93Dic199—21no—
94Dic199—42no—
95Dic199—41no—
96Dic199—41no—
97Dic199#10412yes—
98C2×C199—21no—
99C2×C199—21no—
100C2×C199#41011yescharacteristic
101C2×C199#41911yescharacteristic
102C2×C199C2×#10411yescharacteristic
103C199#150611yescharacteristic, complemented, Sylow
104#1506—1991nomaximal, Sylow
105#533—1991no—
106#432—1991no—
107#376—1991no—
108#328—1991no—
109#328—1991no—
110#328—1991no—
111#328D19911yescharacteristic
112C4⋊Q8—1991no—
113C4⋊Q8—1991no—
114#125—3981no—
115C22⋊Q8—3981no—
116C22⋊Q8—1991no—
117C22⋊Q8C2×D19911yescharacteristic
118C4×Q8—3981no—
119C4×Q8—1991no—
120C4×Q8—1991no—
121#117—3981no—
122C2×C42—3981no—
123C2×C42—1991no—
124C4⋊C8—3981no—
125C22⋊C8—1991no—
126C22⋊C8C2×D19911yescharacteristic
127#97—3981no—
128#95—3981no—
129#95—1991no—
130#95C2×D19911yescharacteristic
131C2×Q8—3981no—
132C2×Q8—1991no—
133C2×Q8C4×D19911yescharacteristic
134C22×C4—21no—
135C22×C4—3981no—
136C22×C4—1991no—
137C22×C4—1991no—
138C22×C4C22×D19911yescharacteristic
139C2×C8—21no—
140C2×C8—3981no—
141C4⋊C4—21no—
142C4⋊C4—3981no—
143C4⋊C4—3981no—
144C4⋊C4—3981no—
145C4⋊C4—3981no—
146C4⋊C4—3981no—
147C4⋊C4—3981no—
148C4⋊C4—1991no—
149C4⋊C4C4×D19911yescharacteristic
150C22⋊C4—21no—
151C22⋊C4—3981no—
152C42—3984no—
153C42—3981no—
154C42—3981no—
155C42—1991no—
156C42—1991no—
157C42—1991no—
158C42—1991no—
159C23D4×D19911yescharacteristic
160Q8—41no—
161Q8—7961no—
162Q8—7962no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—7961no—
170C2×C4—7961no—
171C2×C4—3982no—
172C2×C4—3981no—
173C2×C4—3981no—
174C2×C4—3981no—
175C2×C4—3981no—
176C2×C4—3982no—
177C2×C4—1991no—
178C2×C4—1991no—
179C2×C4—1991no—
180C2×C4—1991no—
181C2×C4C2×C4×D19911yescharacteristic
182C2×C4D4×D19911yescharacteristic
183C8—41no—
184C8—7961no—
185C22—21no—
186C22—21no—
187C22C22⋊C4×D19911yescharacteristic
188C22#2026398411yescharacteristic
189C22#2026398711yescharacteristic
190C4—21no—
191C4—21no—
192C4—42no—
193C4—41no—
194C4—41no—
195C4—7962no—
196C4—7961no—
197C4—7961no—
198C4—3981no—
199C4—3981no—
200C4—3981no—
201C4—1992no—
202C2—21no—
203C2—21no—
204C2#2716399011yescharacteristic
205C2#2716402511yescharacteristic
206C2#104×D19911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC22×C4C22×D199
Fitting#328×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC23×C199C2×D4
cosocleC22×C4×C199C23
hypercenter#328D199
hypocenterC199#1506
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #20263954C4semidirect
9. #20263953C4semidirect
13. Q8×Dic199C4semidirect
15. #20263920C4semidirect
103. C199#1506semidirect

Maximal subgroups

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

subgroupindex
#271645702
#271640722
#271638632
#271637562
#271637552
#271637542
#328×C1992
#1506199