Finite Group Databasebeta

← #38769242

Subgroups — #38769242

Order 25472.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#20263955C211yesmaximal, characteristic
2#27164495C211yesmaximal, characteristic
3#27164028C211yesmaximal, characteristic
4#27164026C211yesmaximal, characteristic
5C2×#20263873C211yesmaximal, characteristic
6#27163778C211yesmaximal, characteristic
7#339×C199C211yesmaximal, characteristic
8C22×Dic398C2211yescharacteristic
9C22×Dic398C2211yescharacteristic
10C2×#15691870C2211yescharacteristic
11#20263955—22no—
12#20263955C414yescomplemented
13C4×Dic398—22no—
14#20263920—22no—
15#20263914C2211yescharacteristic
16#20263911—22no—
17C2×C4⋊Dic199—22no—
18#20263880—22no—
19#20263878—22no—
20#20263873—22no—
21C2×M16×C199C2211yescharacteristic
22#117×C199C2211yescharacteristic
23C2×C42×C199C2211yescharacteristic
24C2×Dic398—21no—
25C2×Dic398—21no—
26C2×Dic398—21no—
27C2×Dic398—21no—
28C2×Dic398—21no—
29C2×Dic398—21no—
30C2×Dic398—21no—
31C2×Dic398—21no—
32C2×Dic398—21no—
33C2×Dic398C2×C412yes—
34C2×Dic398C2×C412yes—
35C2×Dic398D412yes—
36C22×Dic199—21no—
37C22×Dic199D412yes—
38#15691870—21no—
39#15691870—21no—
40C2×C199⋊C8—21no—
41C4⋊Dic199—28no—
42C4⋊Dic199D412yes—
43Dic199⋊C4—24no—
44C22⋊Dic199—21no—
45C4×Dic199—24no—
46C4×Dic199—21no—
47C22×C4×C199—21no—
48C22×C4×C199C2311yescharacteristic
49M16×C199—21no—
50M16×C199—21no—
51C2×C8×C199—21no—
52C4⋊C4×C199D412yes—
53C22⋊C4×C199—21no—
54C42×C199—21no—
55C42×C199—21no—
56C42×C199C2×C412yes—
57Dic398—22no—
58Dic398—22no—
59Dic398—22no—
60Dic398—22no—
61Dic398—22no—
62Dic398—22no—
63Dic398—41no—
64Dic398—41no—
65C2×Dic199—22no—
66C2×Dic199—22no—
67C2×Dic199—22no—
68C2×Dic199—22no—
69C2×Dic199—41no—
70C2×Dic199—41no—
71C2×Dic199C22⋊C414yes—
72C199⋊C8—41no—
73C23×C199C2×D411yescharacteristic
74C2×C4×C199—24no—
75C2×C4×C199—22no—
76C2×C4×C199—22no—
77C2×C4×C199C22×C411yescharacteristic
78C2×C4×C199C2×D411yescharacteristic
79C2×C4×C199C2×D411yescharacteristic
80C2×C4×C199C2×D411yescharacteristic
81C2×C4×C199#4111yescharacteristic
82C2×C4×C199#4111yescharacteristic
83C8×C199—41no—
84C22×C199—22no—
85C22×C199C2×C22⋊C411yescharacteristic
86C22×C199#12011yescharacteristic
87C22×C199#12311yescharacteristic
88C4×C199—24no—
89C4×C199—42no—
90C4×C199C4×D411yescharacteristic
91C4×C199C4×D411yescharacteristic
92C4×C199#12111yescharacteristic
93C4×C199#12111yescharacteristic
94Dic199—24no—
95Dic199—42no—
96Dic199—42no—
97C2×C199—21no—
98C2×C199—21no—
99C2×C199#38611yescharacteristic
100C2×C199#45612yes—
101C199#188611yescharacteristic, complemented, Sylow
102#1886—1991nomaximal, Sylow
103C2×C4⋊Q8—1991no—
104#519—1991no—
105#419—1991no—
106#419—1991no—
107C2×#101—1991no—
108#339—1991no—
109#339D19911yescharacteristic
110C22×Q8—1991no—
111C22×Q8—1991no—
112C2×M16—1991no—
113C2×M16C2×D19911yescharacteristic
114C4⋊Q8—3982no—
115C4⋊Q8—1994no—
116C4×Q8—3982no—
117C4×Q8—3982no—
118#117—3982no—
119#117—1991no—
120#117C2×D19911yescharacteristic
121C2×C4⋊C4—3982no—
122C2×C42C2×D19911yescharacteristic
123#103—3982no—
124#103—3982no—
125#101—3982no—
126C2×Q8—3981no—
127C2×Q8—3981no—
128C2×Q8—3981no—
129C2×Q8—3981no—
130C2×Q8—3981no—
131C2×Q8—3981no—
132C2×Q8—3981no—
133C2×Q8—3981no—
134C2×Q8—3981no—
135C2×Q8—1992no—
136C2×Q8—1992no—
137C2×Q8—1992no—
138C22×C4—21no—
139C22×C4—3981no—
140C22×C4—1992no—
141C22×C4C22×D19911yescharacteristic
142M16—21no—
143M16—21no—
144M16—3981no—
145M16—3981no—
146C2×C8—21no—
147C2×C8—3981no—
148C4⋊C4—3984no—
149C4⋊C4—3988no—
150C4⋊C4—1992no—
151C4⋊C4D79612yes—
152C22⋊C4—21no—
153C22⋊C4—3981no—
154C42—21no—
155C42—21no—
156C42—3984no—
157C42—3981no—
158C42C4×D19912yes—
159C23D4×D19911yescharacteristic
160Q8—7961no—
161Q8—7961no—
162Q8—3982no—
163Q8—3982no—
164Q8—3982no—
165Q8—3982no—
166Q8—3982no—
167Q8—3982no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—7961no—
172C2×C4—7961no—
173C2×C4—3982no—
174C2×C4—3982no—
175C2×C4—3982no—
176C2×C4—3982no—
177C2×C4—1994no—
178C2×C4C2×C4×D19911yescharacteristic
179C2×C4D4×D19911yescharacteristic
180C2×C4D4×D19911yescharacteristic
181C2×C4C2×D79611yescharacteristic
182C2×C4#1569188611yescharacteristic
183C2×C4#1569188711yescharacteristic
184C8—41no—
185C8—7961no—
186C22—22no—
187C22C22⋊C4×D19911yescharacteristic
188C22#2026392511yescharacteristic
189C22#2026394011yescharacteristic
190C4—24no—
191C4—42no—
192C4—7962no—
193C4—7962no—
194C4—3984no—
195C4#2026391711yescharacteristic
196C4C4×D79611yescharacteristic
197C4#2026392811yescharacteristic
198C4#2026393011yescharacteristic
199C2—21no—
200C2—21no—
201C2#2716389611yescharacteristic
202C2#2716420212yes—
subgroupG/H
centerC22#20263925
commutatorC2×C4×C199C22×C4
FrattiniC22×C4C22×D199
Fitting#339×C199C2
socleC22×C199#120
prime radicalC23×C199C2×D4
cosocleC22×C4×C199C23
hypercenter#339D199
hypocenterC199#1886
LCSG ▷ C2×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
12. #20263955C4semidirect
101. C199#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#202639552
#271644952
#271640282
#271640262
C2×#202638732
#271637782
#339×C1992
#1886199