Finite Group Databasebeta

← #38767483

Subgroups — #38767483

Order 25472.

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

normal subgroups only

This group has 238 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#27164567C211yesmaximal, characteristic
2#27164073C212yesmaximal, complemented
3#27163758C211yesmaximal, characteristic, complemented
4#27163757C212yesmaximal, complemented
5#329×C199C211yesmaximal, characteristic, complemented
6C2×#15691887C411yescharacteristic
7C2×#15691885C411yescharacteristic
8#20263953C411yescharacteristic
9#20263951C411yescharacteristic
10#20263943C2211yescharacteristic
11#20263928—22no—
12(C22⋊D199)⋊C4—22no—
13C42×D199C2211yescharacteristic
14Dic199⋊C8—22no—
15(C2×D199)⋊C8—22no—
16#20263866C2212yes—
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—
30C2×C199⋊C8—22no—
31Dic199⋊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×D199C22⋊C411yescharacteristic
42Dic398—41no—
43D796—41no—
44D796—42no—
45C22⋊D199—44no—
46C22⋊D199—42no—
47C2×Dic199—21no—
48C2×Dic199—42no—
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—21no—
66C2×D199—22no—
67C2×D199—41no—
68C2×D199—42no—
69C4×C199—21no—
70C4×C199—22no—
71C4×C199—41no—
72Dic199—22no—
73Dic199—41no—
74Dic199#10012yes—
75C2×C199—81no—
76C2×C199C2×#10011yescharacteristic
77C2×C199#42112yes—
78D199—41no—
79D199—81no—
80C199#153611yescharacteristic, complemented, Sylow
81#1536—1991nomaximal, Sylow
82#532—1991no—
83#432—1992no—
84#329—1991no—
85#329—1992no—
86#329D19911yescharacteristic, complemented
87C2×#41—1991no—
88C2×#41—1991no—
89C4⋊Q8—1991no—
90#127—1991no—
91#124—1991no—
92#124C2×D19911yescharacteristic
93#121—3982no—
94C4×D4—3982no—
95C2×C42—1991no—
96C4⋊C8—3982no—
97C22⋊C8—3982no—
98#97—1992no—
99#97C2×D19912yes—
100#41—7962no—
101#41—7962no—
102C2×Q8—1991no—
103C2×Q8C4×D19911yescharacteristic
104C2×D4—3981no—
105C2×D4—3981no—
106C2×D4—3982no—
107C2×D4—1991no—
108C2×D4C4×D19911yescharacteristic
109C22×C4—3981no—
110C22×C4—3981no—
111C22×C4—1992no—
112C22×C4—1991no—
113C2×C8—22no—
114C2×C8—3982no—
115C4⋊C4—3982no—
116C22⋊C4—22no—
117C22⋊C4—3982no—
118C42—1991no—
119C42—1992no—
120C42C22×D19911yescharacteristic
121C23—21no—
122C23—3981no—
123C23—1991no—
124Q8—41no—
125Q8—7961no—
126D4—41no—
127D4—7961no—
128D4—7962no—
129D4—7962no—
130D4—7964no—
131C2×C4—21no—
132C2×C4—7962no—
133C2×C4—7962no—
134C2×C4—7962no—
135C2×C4—3982no—
136C2×C4—3981no—
137C2×C4—1992no—
138C2×C4—1991no—
139C2×C4C2×C4×D19911yescharacteristic
140C2×C4D4×D19912yes—
141C8—42no—
142C8—7962no—
143C22—41no—
144C22—42no—
145C22—7961no—
146C22—7962no—
147C22—3981no—
148C22—3982no—
149C22C22⋊C4×D19911yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—7961no—
154C4—3982no—
155C4—1992no—
156C2—81no—
157C2—7961no—
158C2—15921no—
159C2#100×D19911yescharacteristic
160C2#2716403312yes—
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#1536
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
80. C199#1536semidirect
86. #329D199semidirect

Maximal subgroups

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

subgroupindex
#271645672
#271640732
#271637582
#271637572
#329×C1992
#1536199