Finite Group Databasebeta

← #38767437

Subgroups — #38767437

Order 25472.

234 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 61 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#27164553C211yesmaximal, characteristic
2#27163970C211yesmaximal, characteristic, complemented
3#97×D199C211yesmaximal, characteristic, complemented
4#27163760C211yesmaximal, characteristic, complemented
5#27163757C211yesmaximal, characteristic, complemented
6#27163757C211yesmaximal, characteristic, complemented
7#330×C199C211yesmaximal, characteristic, complemented
8C2×#15691869—21no—
9C2×C8×D199—21no—
10#20263950—21no—
11#20263943C2211yescharacteristic
12#20263940—21no—
13#20263935C411yescharacteristic
14#20263930C411yescharacteristic
15#20263920C411yescharacteristic
16#20263917—21no—
17#20263917C411yescharacteristic
18#20263913—21no—
19C42×D199C2211yescharacteristic
20#20263866C2211yescharacteristic
21#20263866C2211yescharacteristic
22#20263865—21no—
23C8×Dic199—21no—
24#125×C199C2211yescharacteristic
25#97×C199C2211yescharacteristic
26#97×C199C2211yescharacteristic
27C2×Dic398C2×C411yescharacteristic
28C2×D796—21no—
29C2×D796C2×C411yescharacteristic
30C2×C4×D199—21no—
31C2×C4×D199C2×C411yescharacteristic
32C2×C4×D199D411yescharacteristic
33C2×C4×D199D411yescharacteristic
34#15691869—24no—
35C2×C199⋊C8—21no—
36C2×C199⋊C8—21no—
37C8×D199—24no—
38C4⋊Dic199—21no—
39Dic199⋊C4—21no—
40(C2×D199)⋊C4—21no—
41(C2×D199)⋊C4—21no—
42(C2×D199)⋊C4—21no—
43(C2×D199)⋊C4—21no—
44(C2×D199)⋊C4—21no—
45C4×Dic199—21no—
46C4×Dic199C2×C411yescharacteristic
47C4×Dic199D411yescharacteristic
48C4×Dic199D411yescharacteristic
49C2×C8×C199—21no—
50C2×C8×C199—21no—
51C4⋊C4×C199—21no—
52C4⋊C4×C199—21no—
53C4⋊C4×C199C2×C411yescharacteristic
54C4⋊C4×C199C2×C411yescharacteristic
55C42×C199C2311yescharacteristic
56C22×D199—21no—
57C22×D199C22⋊C411yescharacteristic
58Dic398—41no—
59D796—41no—
60D796—42no—
61C2×Dic199—21no—
62C2×Dic199C22⋊C411yescharacteristic
63C2×Dic199C22⋊C411yescharacteristic
64C2×Dic199C22⋊C411yescharacteristic
65C4×D199—22no—
66C4×D199—22no—
67C4×D199—41no—
68C4×D199—42no—
69C199⋊C8—22no—
70C199⋊C8—22no—
71C2×C4×C199—21no—
72C2×C4×C199—21no—
73C2×C4×C199C22×C411yescharacteristic
74C2×C4×C199C2×D411yescharacteristic
75C2×C4×C199C2×D411yescharacteristic
76C8×C199—22no—
77C8×C199—22no—
78C22×C199C2×C22⋊C411yescharacteristic
79C2×D199—21no—
80C2×D199—21no—
81C2×D199—41no—
82C2×D199—41no—
83C2×D199—41no—
84C2×D199#10412yes—
85C4×C199—21no—
86C4×C199—21no—
87C4×C199—21no—
88C4×C199—41no—
89C4×C199—41no—
90Dic199—21no—
91Dic199—21no—
92Dic199—41no—
93Dic199#10412yes—
94C2×C199#41311yescharacteristic
95C2×C199C2×#10411yescharacteristic
96C2×C199C2×#10411yescharacteristic
97D199—22no—
98D199—81no—
99C199#152411yescharacteristic, complemented, Sylow
100#1524—1991nomaximal, Sylow
101#529—1991no—
102C4×M16—1991no—
103C2×#97—1991no—
104#330—1991no—
105#330D19911yescharacteristic, complemented
106#329—1991no—
107#329—1991no—
108C2×M16—3981no—
109C22×C8—3981no—
110#126—3981no—
111#125C2×D19911yescharacteristic
112#124—1991no—
113#123—3981no—
114C22⋊Q8—1991no—
115#121—1991no—
116C4×Q8—1991no—
117C4×D4—3981no—
118C4×D4—1991no—
119#117—3981no—
120C2×C42—1991no—
121#97—3981no—
122#97—1991no—
123#97—1991no—
124#97C2×D19911yescharacteristic
125#97C2×D19911yescharacteristic
126C4×C8—3981no—
127C2×Q8—1991no—
128C2×D4—3981no—
129C2×D4—1991no—
130C22×C4—3981no—
131C22×C4—1991no—
132C22×C4—1991no—
133C22×C4—1991no—
134M16—3984no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—3984no—
138C2×C8—3981no—
139C2×C8—3981no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—3981no—
143C4⋊C4—3981no—
144C4⋊C4C4×D19911yescharacteristic
145C4⋊C4C4×D19911yescharacteristic
146C22⋊C4—3981no—
147C22⋊C4—3981no—
148C22⋊C4—3981no—
149C22⋊C4—3981no—
150C22⋊C4—3981no—
151C42—3981no—
152C42—1991no—
153C42—1991no—
154C42—1991no—
155C42C22×D19911yescharacteristic
156C23—3981no—
157C23—1991no—
158Q8—7961no—
159D4—7961no—
160D4—7962no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—7961no—
164C2×C4—7962no—
165C2×C4—3982no—
166C2×C4—3982no—
167C2×C4—3981no—
168C2×C4—1991no—
169C2×C4—1991no—
170C2×C4—1991no—
171C2×C4C2×C4×D19911yescharacteristic
172C2×C4D4×D19911yescharacteristic
173C2×C4D4×D19911yescharacteristic
174C8—22no—
175C8—22no—
176C8—3982no—
177C8—3982no—
178C22—7961no—
179C22—7961no—
180C22—7961no—
181C22—3981no—
182C22—3981no—
183C22—1992no—
184C22C22⋊C4×D19911yescharacteristic
185C4—21no—
186C4—21no—
187C4—21no—
188C4—41no—
189C4—41no—
190C4—7961no—
191C4—3981no—
192C4—3981no—
193C4—1992no—
194C2—15921no—
195C2—3982no—
196C2#2716400111yescharacteristic
197C2#104×D19911yescharacteristic
198C2#104×D19911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#330×C199C2
socleC22×C199C2×C22⋊C4
prime radical#20263930C4
cosocleC42×C199C23
hypercenter#330D199
hypocenterC199#1524
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #27163970C2semidirect
3. #97×D199C2semidirect
4. #27163760C2semidirect
5. #27163757C2semidirect
6. #27163757C2semidirect
7. #330×C199C2semidirect
99. C199#1524semidirect
105. #330D199semidirect

Maximal subgroups

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

subgroupindex
#271645532
#271639702
#97×D1992
#271637602
#271637572
#330×C1992
#1524199