Finite Group Databasebeta

← #38767472

Subgroups — #38767472

Order 25472.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 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#124×D199C211yesmaximal, characteristic
2#27164073C212yesmaximal, complemented
3#27163758C211yesmaximal, characteristic, complemented
4#27163757C212yesmaximal, complemented
5#329×C199C211yesmaximal, characteristic, complemented
6C2×Q8×D199C411yescharacteristic
7C2×D4×D199C411yescharacteristic
8#20263944C411yescharacteristic
9#20263943C2211yescharacteristic
10#20263942C411yescharacteristic
11#20263941—22no—
12C22⋊C4×D199—22no—
13C42×D199C2211yescharacteristic
14Dic199⋊C8—22no—
15(C2×D199)⋊C8—22no—
16#20263866C2212yescomplemented
17#124×C199C2211yescharacteristic
18#97×C199C2212yescomplemented
19C23×D199—21no—
20C2×Dic398—21no—
21C2×Dic398C2×C411yescharacteristic
22Q8×D199—42no—
23C2×D796C2×C411yescharacteristic
24C2×C22⋊D199—21no—
25D4×D199—42no—
26C2×C4×D199—21no—
27C2×C4×D199C2×C411yescharacteristic
28C2×C4×D199D412yes—
29C2×C199⋊C8—22no—
30C22⋊Dic199—22no—
31(C2×D199)⋊C4—22no—
32(C2×D199)⋊C4—22no—
33C4×Dic199C2×C411yescharacteristic
34C4×Dic199D412yes—
35C2×Q8×C199C2×C411yescharacteristic
36C2×D4×C199C2×C411yescharacteristic
37C2×C8×C199—22no—
38C22⋊C4×C199—22no—
39C42×C199C2311yescharacteristic
40C22×D199—21no—
41C22×D199—44no—
42C22×D199—42no—
43C22×D199C22⋊C411yescharacteristic
44Dic398—42no—
45Dic398—41no—
46D796—41no—
47C22⋊D199—42no—
48C2×Dic199—21no—
49C2×Dic199C22⋊C412yes—
50C2×Dic199C22⋊C411yescharacteristic
51C4×D199—22no—
52C4×D199—42no—
53C4×D199—42no—
54C199⋊C8—42no—
55C23×C199—21no—
56Q8×C199—41no—
57D4×C199—41no—
58C2×C4×C199—21no—
59C2×C4×C199C22×C411yescharacteristic
60C2×C4×C199C2×D412yes—
61C8×C199—42no—
62C22×C199—41no—
63C22×C199—42no—
64C22×C199C2×C22⋊C411yescharacteristic
65C2×D199—22no—
66C2×D199—41no—
67C2×D199—42no—
68C2×D199—84no—
69C2×D199#10012yes—
70C4×C199—21no—
71C4×C199—22no—
72C4×C199—41no—
73Dic199—21no—
74Dic199—22no—
75Dic199—41no—
76C2×C199—81no—
77C2×C199C2×#10011yescharacteristic
78C2×C199#42112yes—
79D199—22no—
80D199—81no—
81C199#153311yescharacteristic, complemented, Sylow
82#1533—1991nomaximal, Sylow
83C2×#124—1991no—
84#432—1992no—
85#329—1991no—
86#329—1992no—
87#329D19911yescharacteristic, complemented
88C22×Q8—1991no—
89C22×D4—1991no—
90#124—3982no—
91#124—1991no—
92#124—1991no—
93#124—1991no—
94#124C2×D19911yescharacteristic
95C2×C22⋊C4—3982no—
96C2×C42—1991no—
97C4⋊C8—3982no—
98C22⋊C8—3982no—
99#97—1992no—
100#97C2×D19912yescomplemented
101C24—3981no—
102C2×Q8—7962no—
103C2×Q8—3981no—
104C2×Q8—1991no—
105C2×Q8C4×D19911yescharacteristic
106C2×D4—7962no—
107C2×D4—3981no—
108C2×D4—1991no—
109C2×D4C4×D19911yescharacteristic
110C22×C4—3981no—
111C22×C4—1992no—
112C22×C4—1991no—
113C2×C8—22no—
114C2×C8—3982no—
115C22⋊C4—22no—
116C22⋊C4—3982no—
117C22⋊C4—3982no—
118C22⋊C4—3982no—
119C42—1991no—
120C42—1992no—
121C42C22×D19911yescharacteristic
122C23—21no—
123C23—7964no—
124C23—7962no—
125C23—3981no—
126C23—1991no—
127Q8—41no—
128Q8—7961no—
129Q8—7962no—
130D4—41no—
131D4—7961no—
132D4—7962no—
133C2×C4—21no—
134C2×C4—7962no—
135C2×C4—7962no—
136C2×C4—3982no—
137C2×C4—3981no—
138C2×C4—1992no—
139C2×C4—1991no—
140C2×C4C2×C4×D19911yescharacteristic
141C2×C4D4×D19912yes—
142C8—42no—
143C8—7962no—
144C22—41no—
145C22—42no—
146C22—7961no—
147C22—7962no—
148C22—15924no—
149C22—3982no—
150C22—1992no—
151C22C22⋊C4×D19911yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—7961no—
156C4—3981no—
157C4—3982no—
158C2—81no—
159C2—15921no—
160C2—3982no—
161C2#100×D19911yescharacteristic
162C2#2716403312yes—
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#329×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC2×D4×D199C4
cosocleC42×C199C23
hypercenter#329D199
hypocenterC199#1533
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. #27164073C2semidirect
3. #27163758C2semidirect
4. #27163757C2semidirect
5. #329×C199C2semidirect
16. #20263866C22semidirect
18. #97×C199C22semidirect
81. C199#1533semidirect
87. #329D199semidirect
100. #97C2×D199semidirect

Maximal subgroups

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

subgroupindex
#124×D1992
#271640732
#271637582
#271637572
#329×C1992
#1533199