Finite Group Databasebeta

← #38767480

Subgroups — #38767480

Order 25472.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#27164073C211yesmaximal, characteristic, complemented
3#27164073C211yesmaximal, characteristic, complemented
4#27163760C211yesmaximal, characteristic, complemented
5#27163757C211yesmaximal, characteristic, complemented
6#27163757C211yesmaximal, characteristic, complemented
7#330×C199C211yesmaximal, characteristic, complemented
8#20263950—21no—
9#20263943C2211yescharacteristic
10#20263940—21no—
11#20263935C411yescharacteristic
12#20263930C411yescharacteristic
13#20263920C411yescharacteristic
14#20263917—21no—
15#20263917C411yescharacteristic
16#20263913—21no—
17C42×D199C2211yescharacteristic
18Dic199⋊C8—21no—
19Dic199⋊C8—21no—
20(C2×D199)⋊C8—21no—
21(C2×D199)⋊C8—21no—
22#20263866C2211yescharacteristic
23#20263866C2211yescharacteristic
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
34C2×C199⋊C8—21no—
35C2×C199⋊C8—21no—
36C4⋊Dic199—21no—
37Dic199⋊C4—21no—
38(C2×D199)⋊C4—21no—
39(C2×D199)⋊C4—21no—
40(C2×D199)⋊C4—21no—
41(C2×D199)⋊C4—21no—
42(C2×D199)⋊C4—21no—
43C4×Dic199—21no—
44C4×Dic199C2×C411yescharacteristic
45C4×Dic199D411yescharacteristic
46C4×Dic199D411yescharacteristic
47C2×C8×C199—21no—
48C2×C8×C199—21no—
49C4⋊C4×C199—21no—
50C4⋊C4×C199—21no—
51C4⋊C4×C199C2×C411yescharacteristic
52C4⋊C4×C199C2×C411yescharacteristic
53C42×C199C2311yescharacteristic
54C22×D199—21no—
55C22×D199C22⋊C411yescharacteristic
56Dic398—41no—
57D796—41no—
58D796—42no—
59C2×Dic199—21no—
60C2×Dic199C22⋊C411yescharacteristic
61C2×Dic199C22⋊C411yescharacteristic
62C2×Dic199C22⋊C411yescharacteristic
63C4×D199—41no—
64C4×D199—41no—
65C4×D199—41no—
66C4×D199—42no—
67C199⋊C8—41no—
68C199⋊C8—41no—
69C2×C4×C199—21no—
70C2×C4×C199—21no—
71C2×C4×C199C22×C411yescharacteristic
72C2×C4×C199C2×D411yescharacteristic
73C2×C4×C199C2×D411yescharacteristic
74C8×C199—41no—
75C8×C199—41no—
76C22×C199C2×C22⋊C411yescharacteristic
77C2×D199—21no—
78C2×D199—21no—
79C2×D199—21no—
80C2×D199—41no—
81C2×D199—41no—
82C2×D199—41no—
83C4×C199—21no—
84C4×C199—21no—
85C4×C199—21no—
86C4×C199—41no—
87C4×C199—41no—
88Dic199—21no—
89Dic199—21no—
90Dic199—21no—
91Dic199—41no—
92C2×C199#41311yescharacteristic
93C2×C199#42111yescharacteristic
94C2×C199#42111yescharacteristic
95D199—41no—
96D199—81no—
97C199#153511yescharacteristic, complemented, Sylow
98#1535—1991nomaximal, Sylow
99#529—1991no—
100#432—1991no—
101#432—1991no—
102#330—1991no—
103#330D19911yescharacteristic, complemented
104#329—1991no—
105#329—1991no—
106#126—3981no—
107#125C2×D19911yescharacteristic
108#124—1991no—
109#123—3981no—
110C22⋊Q8—1991no—
111#121—1991no—
112C4×Q8—1991no—
113C4×D4—3981no—
114C4×D4—1991no—
115#117—3981no—
116C2×C42—1991no—
117C4⋊C8—3981no—
118C4⋊C8—3981no—
119C22⋊C8—3981no—
120C22⋊C8—3981no—
121#97—1991no—
122#97—1991no—
123#97C2×D19911yescharacteristic
124#97C2×D19911yescharacteristic
125C2×Q8—1991no—
126C2×D4—3981no—
127C2×D4—1991no—
128C22×C4—3981no—
129C22×C4—1991no—
130C22×C4—1991no—
131C22×C4—1991no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—3981no—
135C2×C8—3981no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3981no—
139C4⋊C4—3981no—
140C4⋊C4C4×D19911yescharacteristic
141C4⋊C4C4×D19911yescharacteristic
142C22⋊C4—3981no—
143C22⋊C4—3981no—
144C22⋊C4—3981no—
145C22⋊C4—3981no—
146C22⋊C4—3981no—
147C42—3981no—
148C42—1991no—
149C42—1991no—
150C42—1991no—
151C42C22×D19911yescharacteristic
152C23—3981no—
153C23—1991no—
154Q8—7961no—
155D4—7961no—
156D4—7962no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—7961no—
160C2×C4—7961no—
161C2×C4—7961no—
162C2×C4—7962no—
163C2×C4—3981no—
164C2×C4—1991no—
165C2×C4—1991no—
166C2×C4—1991no—
167C2×C4C2×C4×D19911yescharacteristic
168C2×C4D4×D19911yescharacteristic
169C2×C4D4×D19911yescharacteristic
170C8—41no—
171C8—41no—
172C8—7961no—
173C8—7961no—
174C22—7961no—
175C22—7961no—
176C22—7961no—
177C22—3981no—
178C22—3981no—
179C22—3981no—
180C22C22⋊C4×D19911yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—7961no—
187C4—3981no—
188C4—3981no—
189C4—3981no—
190C2—7961no—
191C2—15921no—
192C2#2716400111yescharacteristic
193C2#2716403311yescharacteristic
194C2#2716403311yescharacteristic
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#1535
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. #27164073C2semidirect
3. #27164073C2semidirect
4. #27163760C2semidirect
5. #27163757C2semidirect
6. #27163757C2semidirect
7. #330×C199C2semidirect
97. C199#1535semidirect
103. #330D199semidirect

Maximal subgroups

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

subgroupindex
#271645532
#271640732
#271637602
#271637572
#330×C1992
#1535199