Finite Group Databasebeta

← #38770524

Subgroups — #38770524

Order 25472.

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

normal subgroups only

This group has 238 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#27164589C211yesmaximal, characteristic
2#27163992C211yesmaximal, characteristic
3#27163812C214yesmaximal, complemented
4#410×C199C211yesmaximal, characteristic
5C22×Dic398C411yescharacteristic, complemented
6#20263953C412yescomplemented
7#20263942C2212yes—
8#20263936—21no—
9#20263936—21no—
10#20263934—21no—
11#20263934—21no—
12#20263914—21no—
13#20263914C411yescharacteristic, complemented
14#20263870—21no—
15#20263870C2212yes—
16C2×#41×C199C2211yescharacteristic
17#117×C199—21no—
18#99×C199—21no—
19#99×C199C2212yes—
20C2×Dic398—21no—
21C2×Dic398—41no—
22C2×Dic398—41no—
23C2×Dic398C2×C412yes—
24C22×Dic199—21no—
25C4⋊Dic199—21no—
26C4⋊Dic199—41no—
27Dic199⋊C4—22no—
28Dic199⋊C4—22no—
29C22⋊Dic199—21no—
30C22⋊Dic199—22no—
31C22⋊Dic199—22no—
32C22⋊Dic199—22no—
33C4×Dic199—41no—
34C4×Dic199C2×C412yes—
35#41×C199—41no—
36#41×C199—41no—
37C2×Q8×C199C2×C411yescharacteristic
38C2×D4×C199D411yescharacteristic
39C2×D4×C199D411yescharacteristic
40C2×D4×C199C2311yescharacteristic
41C22×C4×C199C2×C411yescharacteristic
42C22×C4×C199D411yescharacteristic
43C22×C4×C199D411yescharacteristic
44C4⋊C4×C199—41no—
45C22⋊C4×C199—22no—
46C42×C199—41no—
47Dic398—41no—
48Dic398—41no—
49Dic398—42no—
50C2×Dic199—22no—
51C2×Dic199—22no—
52C2×Dic199—42no—
53C2×Dic199—42no—
54C23×C199C22⋊C411yescharacteristic
55C23×C199C2×D411yescharacteristic
56C23×C199C2×D411yescharacteristic
57Q8×C199—41no—
58D4×C199—41no—
59D4×C199—41no—
60D4×C199—41no—
61C2×C4×C199—21no—
62C2×C4×C199—21no—
63C2×C4×C199—21no—
64C2×C4×C199—21no—
65C2×C4×C199—21no—
66C2×C4×C199—21no—
67C2×C4×C199—42no—
68C2×C4×C199C22⋊C411yescharacteristic
69C2×C4×C199C22⋊C411yescharacteristic
70C2×C4×C199C22⋊C411yescharacteristic
71C2×C4×C199C22×C411yescharacteristic
72C22×C199—21no—
73C22×C199—21no—
74C22×C199—21no—
75C22×C199—41no—
76C22×C199—41no—
77C22×C199—41no—
78C22×C199C2×C22⋊C411yescharacteristic
79C4×C199—21no—
80C4×C199—21no—
81C4×C199—21no—
82C4×C199—82no—
83C4×C199#9911yescharacteristic
84C4×C199#9911yescharacteristic
85Dic199—42no—
86Dic199—42no—
87Dic199—82no—
88C2×C199—21no—
89C2×C199—41no—
90C2×C199—41no—
91C2×C199—41no—
92C2×C199C2×#9911yescharacteristic
93C199#212911yescharacteristic, complemented, Sylow
94#2129—1991nomaximal, Sylow
95#536—1991no—
96#410—1991no—
97#410D19911yescharacteristic
98#354—1994no—
99C2×#41C2×D19911yescharacteristic
100C22×Q8—1991no—
101C4⋊Q8—1992no—
102#124—1992no—
103#123—3981no—
104#123—3981no—
105C22⋊Q8—3981no—
106C22⋊Q8—3981no—
107#117—21no—
108#117—3981no—
109#117—1991no—
110#99—21no—
111#99—3981no—
112#99—1992no—
113#99C2×D19912yes—
114#41—41no—
115#41—41no—
116C2×Q8—7961no—
117C2×Q8—7961no—
118C2×Q8—3981no—
119C2×Q8—1992no—
120C2×Q8C4×D19911yescharacteristic
121C2×D4C22⋊D19911yescharacteristic
122C2×D4D79611yescharacteristic
123C2×D4C22×D19911yescharacteristic
124C22×C4—3981no—
125C22×C4C4×D19911yescharacteristic
126C22×C4C22⋊D19911yescharacteristic
127C22×C4D79611yescharacteristic
128C4⋊C4—41no—
129C4⋊C4—7961no—
130C4⋊C4—3982no—
131C4⋊C4—3982no—
132C4⋊C4—3981no—
133C22⋊C4—22no—
134C22⋊C4—3982no—
135C22⋊C4—3981no—
136C22⋊C4—3982no—
137C22⋊C4—3982no—
138C42—41no—
139C42—7961no—
140C42—1992no—
141C23(C2×D199)⋊C411yescharacteristic
142C23C2×C22⋊D19911yescharacteristic
143C23C2×D79611yescharacteristic
144Q8—41no—
145Q8—7962no—
146Q8—7961no—
147Q8—7961no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—42no—
158C2×C4—7962no—
159C2×C4—7962no—
160C2×C4—3982no—
161C2×C4—3982no—
162C2×C4(C2×D199)⋊C411yescharacteristic
163C2×C4(C2×D199)⋊C411yescharacteristic
164C2×C4(C2×D199)⋊C411yescharacteristic
165C2×C4C2×C4×D19911yescharacteristic
166C22—21no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22C2×(C2×D199)⋊C411yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—82no—
177C4—7962no—
178C4—7962no—
179C4—15922no—
180C4#2026386911yescharacteristic
181C4#2026386911yescharacteristic
182C2—21no—
183C2—41no—
184C2—41no—
185C2—41no—
186C2C2×#2026386911yescharacteristic
subgroupG/H
centerC2C2×#20263869
commutatorC2×C4×C199C22×C4
FrattiniC2×D4C22×D199
Fitting#410×C199C2
socleC2×C199C2×#99
prime radicalC2×#41×C199C22
cosocleC2×D4×C199C23
hypercenter#410D199
hypocenterC199#2129
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #27163812C2semidirect
5. C22×Dic398C4semidirect
6. #20263953C4semidirect
13. #20263914C4semidirect
93. C199#2129semidirect

Maximal subgroups

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

subgroupindex
#271645892
#271639922
#271638122
#410×C1992
#2129199