Finite Group Databasebeta

← #38767440

Subgroups — #38767440

Order 25472.

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

normal subgroups only

This group has 270 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#27164567C211yesmaximal, characteristic
2#27163970C212yesmaximal, complemented
3#27163758C211yesmaximal, characteristic, complemented
4#27163757C212yesmaximal, complemented
5#329×C199C211yesmaximal, characteristic, complemented
6C2×#15691887C411yescharacteristic
7C2×#15691885C411yescharacteristic
8C2×#15691869—22no—
9#20263953C411yescharacteristic
10#20263951C411yescharacteristic
11#20263943C2211yescharacteristic
12#20263928—22no—
13(C22⋊D199)⋊C4—22no—
14C42×D199C2211yescharacteristic
15#20263866C2212yes—
16C8×Dic199—22no—
17#124×C199C2211yescharacteristic
18#97×C199C2212yes—
19#15691887—42no—
20#15691885—42no—
21C2×Dic398C2×C411yescharacteristic
22C2×D796—21no—
23C2×D796C2×C411yescharacteristic
24C2×C22⋊D199—21no—
25C2×C22⋊D199—22no—
26C22×Dic199—21no—
27C2×C4×D199—21no—
28C2×C4×D199C2×C411yescharacteristic
29C2×C4×D199D412yes—
30#15691869—28no—
31C2×C199⋊C8—22no—
32Dic199⋊C4—22no—
33(C2×D199)⋊C4—22no—
34C4×Dic199C2×C411yescharacteristic
35C4×Dic199D412yes—
36C2×Q8×C199C2×C411yescharacteristic
37C2×D4×C199C2×C411yescharacteristic
38C2×C8×C199—22no—
39C22⋊C4×C199—22no—
40C42×C199C2311yescharacteristic
41C22×D199—21no—
42C22×D199C22⋊C411yescharacteristic
43Dic398—41no—
44D796—41no—
45D796—42no—
46C22⋊D199—42no—
47C22⋊D199—44no—
48C2×Dic199—21no—
49C2×Dic199—42no—
50C2×Dic199C22⋊C411yescharacteristic
51C2×Dic199C22⋊C412yes—
52C4×D199—22no—
53C4×D199—24no—
54C4×D199—42no—
55C199⋊C8—24no—
56C23×C199—21no—
57Q8×C199—41no—
58D4×C199—41no—
59C2×C4×C199—21no—
60C2×C4×C199C22×C411yescharacteristic
61C2×C4×C199C2×D412yes—
62C8×C199—24no—
63C22×C199—41no—
64C22×C199—42no—
65C22×C199C2×C22⋊C411yescharacteristic
66C2×D199—21no—
67C2×D199—22no—
68C2×D199—41no—
69C2×D199—42no—
70C4×C199—21no—
71C4×C199—22no—
72C4×C199—41no—
73Dic199—41no—
74Dic199#10012yes—
75Dic199#10414yes—
76C2×C199—81no—
77C2×C199C2×#10011yescharacteristic
78C2×C199C2×#10412yes—
79D199—41no—
80D199—81no—
81C199#152511yescharacteristic, complemented, Sylow
82#1525—1991nomaximal, Sylow
83#532—1991no—
84C4×M16—1992no—
85#329—1991no—
86#329—1992no—
87#329D19911yescharacteristic, complemented
88C2×#41—1991no—
89C2×#41—1991no—
90C2×M16—3982no—
91C4⋊Q8—1991no—
92#127—1991no—
93#124—1991no—
94#124C2×D19911yescharacteristic
95#121—3982no—
96C4×D4—3982no—
97C2×C42—1991no—
98#97—1992no—
99#97C2×D19912yes—
100C4×C8—3982no—
101#41—7962no—
102#41—7962no—
103C2×Q8—1991no—
104C2×Q8C4×D19911yescharacteristic
105C2×D4—3981no—
106C2×D4—3981no—
107C2×D4—3982no—
108C2×D4—1991no—
109C2×D4C4×D19911yescharacteristic
110C22×C4—3981no—
111C22×C4—3981no—
112C22×C4—1991no—
113C22×C4—1992no—
114M16—3988no—
115C2×C8—22no—
116C2×C8—3982no—
117C4⋊C4—3982no—
118C22⋊C4—22no—
119C22⋊C4—3982no—
120C42—1991no—
121C42—1992no—
122C42C22×D19911yescharacteristic
123C23—21no—
124C23—3981no—
125C23—1991no—
126Q8—41no—
127Q8—7961no—
128D4—41no—
129D4—7961no—
130D4—7962no—
131D4—7962no—
132D4—7964no—
133C2×C4—21no—
134C2×C4—7962no—
135C2×C4—7962no—
136C2×C4—3984no—
137C2×C4—3982no—
138C2×C4—3981no—
139C2×C4—1992no—
140C2×C4—1991no—
141C2×C4C2×C4×D19911yescharacteristic
142C2×C4D4×D19912yes—
143C8—24no—
144C8—3984no—
145C22—41no—
146C22—42no—
147C22—7961no—
148C22—7962no—
149C22—3981no—
150C22—3982no—
151C22C22⋊C4×D19911yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—7961no—
156C4—1992no—
157C4—1994no—
158C2—81no—
159C2—7961no—
160C2—15921no—
161C2#100×D19911yescharacteristic
162C2#104×D19912yes—
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#329×C199C2
socleC22×C199C2×C22⋊C4
prime radical#27164567C2
cosocleC42×C199C23
hypercenter#329D199
hypocenterC199#1525
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #27163970C2semidirect
3. #27163758C2semidirect
4. #27163757C2semidirect
5. #329×C199C2semidirect
81. C199#1525semidirect
87. #329D199semidirect

Maximal subgroups

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

subgroupindex
#271645672
#271639702
#271637582
#271637572
#329×C1992
#1525199