Finite Group Databasebeta

← #38767482

Subgroups — #38767482

Order 25472.

200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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#27164552C211yesmaximal, characteristic
2#27164075C211yesmaximal, characteristic, complemented
3#27163759C212yesmaximal, complemented
4#27163757C212yesmaximal, complemented
5#432×C199C211yesmaximal, characteristic, complemented
6#20263949—21no—
7#20263947C2211yescharacteristic
8#20263943C2211yescharacteristic
9#20263938—21no—
10#20263934C411yescharacteristic
11#20263929C411yescharacteristic
12C4×Dic398C411yescharacteristic
13C4×D796C411yescharacteristic
14C4×C22⋊D199—21no—
15#20263912—21no—
16C4⋊(C199⋊C8)—21no—
17C22⋊(C199⋊C8)—21no—
18#20263866C2212yes—
19C2×C42×C199C2211yescharacteristic
20C4⋊C8×C199—21no—
21C22⋊C8×C199—21no—
22#97×C199C2212yes—
23C2×Dic398C2×C411yescharacteristic
24C2×D796C2×C411yescharacteristic
25C2×C22⋊D199—21no—
26C2×C4×D199—21no—
27C2×C199⋊C8—22no—
28C4⋊Dic199C2×C411yescharacteristic
29C4⋊Dic199C2×C411yescharacteristic
30Dic199⋊C4—21no—
31Dic199⋊C4—21no—
32Dic199⋊C4—21no—
33Dic199⋊C4—21no—
34C22⋊Dic199—21no—
35(C2×D199)⋊C4—21no—
36(C2×D199)⋊C4—21no—
37(C2×D199)⋊C4—21no—
38(C2×D199)⋊C4—21no—
39C4×Dic199—21no—
40C22×C4×C199C2×C411yescharacteristic
41C22×C4×C199D411yescharacteristic
42C22×C4×C199D411yescharacteristic
43C2×C8×C199—22no—
44C42×C199C2×C411yescharacteristic
45C42×C199D411yescharacteristic
46C42×C199D411yescharacteristic
47C42×C199C2311yescharacteristic
48C22×D199—21no—
49Dic398—41no—
50D796—41no—
51C22⋊D199—42no—
52C2×Dic199—21no—
53C2×Dic199—21no—
54C2×Dic199—21no—
55C4×D199—42no—
56C199⋊C8—42no—
57C23×C199C22⋊C411yescharacteristic
58C2×C4×C199—41no—
59C2×C4×C199—41no—
60C2×C4×C199—41no—
61C2×C4×C199C22⋊C411yescharacteristic
62C2×C4×C199C22⋊C411yescharacteristic
63C2×C4×C199C22⋊C411yescharacteristic
64C2×C4×C199C22×C411yescharacteristic
65C2×C4×C199C2×D411yescharacteristic
66C2×C4×C199C2×D411yescharacteristic
67C8×C199—42no—
68C22×C199—21no—
69C22×C199—21no—
70C22×C199—21no—
71C22×C199C2×C22⋊C411yescharacteristic
72C2×D199—41no—
73C2×D199—41no—
74C2×D199—41no—
75C4×C199—21no—
76C4×C199—21no—
77C4×C199—21no—
78C4×C199—21no—
79C4×C199—21no—
80C4×C199—21no—
81Dic199—41no—
82Dic199—41no—
83Dic199—41no—
84C2×C199—41no—
85C2×C199#41311yescharacteristic
86C2×C199#42111yescharacteristic
87C2×C199#42111yescharacteristic
88D199—81no—
89C199#153511yescharacteristic, complemented, Sylow
90#1535—1991nomaximal, Sylow
91#529—1991no—
92#432—1991no—
93#432D19911yescharacteristic, complemented
94#330—1992no—
95#329—1992no—
96#126—3981no—
97#125—1991no—
98#124—1991no—
99#123—3981no—
100C22⋊Q8—1991no—
101#121—1991no—
102C4×Q8—1991no—
103C4×D4—3981no—
104C4×D4—1991no—
105#117—3981no—
106C2×C42C2×D19911yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—3981no—
109C22⋊C8—21no—
110C22⋊C8—3981no—
111#97—1992no—
112#97C2×D19912yes—
113C2×Q8—1991no—
114C2×D4—3981no—
115C2×D4—1991no—
116C22×C4—3981no—
117C22×C4C4×D19911yescharacteristic
118C22×C4C22⋊D19911yescharacteristic
119C22×C4D79611yescharacteristic
120C2×C8—22no—
121C2×C8—3982no—
122C4⋊C4—3981no—
123C4⋊C4—3981no—
124C4⋊C4—3981no—
125C4⋊C4—3981no—
126C4⋊C4—1991no—
127C4⋊C4—1991no—
128C22⋊C4—3981no—
129C22⋊C4—3981no—
130C22⋊C4—3981no—
131C22⋊C4—3981no—
132C22⋊C4—3981no—
133C42—3981no—
134C42C4×D19911yescharacteristic
135C42C22⋊D19911yescharacteristic
136C42D79611yescharacteristic
137C42C22×D19911yescharacteristic
138C23—3981no—
139C23(C2×D199)⋊C411yescharacteristic
140Q8—7961no—
141D4—7961no—
142D4—7962no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—7962no—
147C2×C4—3981no—
148C2×C4—3981no—
149C2×C4—3981no—
150C2×C4(C2×D199)⋊C411yescharacteristic
151C2×C4(C2×D199)⋊C411yescharacteristic
152C2×C4(C2×D199)⋊C411yescharacteristic
153C2×C4C2×C4×D19911yescharacteristic
154C2×C4C2×C22⋊D19911yescharacteristic
155C2×C4C2×D79611yescharacteristic
156C8—42no—
157C8—7962no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—7961no—
162C22—7961no—
163C22—7961no—
164C22C2×(C2×D199)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—7961no—
172C4—7961no—
173C4—7961no—
174C2—41no—
175C2—15921no—
176C2#2716400011yescharacteristic
177C2#2716403411yescharacteristic
178C2#2716403611yescharacteristic
subgroupG/H
centerC22C2×(C2×D199)⋊C4
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#432×C199C2
socleC22×C199C2×C22⋊C4
prime radical#20263929C4
cosocleC42×C199C23
hypercenter#432D199
hypocenterC199#1535
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #27164075C2semidirect
3. #27163759C2semidirect
4. #27163757C2semidirect
5. #432×C199C2semidirect
89. C199#1535semidirect
93. #432D199semidirect

Maximal subgroups

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

subgroupindex
#271645522
#271640752
#271637592
#271637572
#432×C1992
#1535199