Finite Group Databasebeta

← #38768150

Subgroups — #38768150

Order 25472.

206 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 45 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#27164772C211yesmaximal, characteristic, complemented
2#27164407C211yesmaximal, characteristic
3#27164384C211yesmaximal, characteristic, complemented
4#27164383C211yesmaximal, characteristic, complemented
5#27163759C211yesmaximal, characteristic, complemented
6#27163757C211yesmaximal, characteristic, complemented
7#330×C199C211yesmaximal, characteristic, complemented
8C2×#15691875—21no—
9C2×D1592—21no—
10#20263954—21no—
11#20263952C2211yescharacteristic
12#20263950—21no—
13#20263950—21no—
14#20263947C2211yescharacteristic
15#20263943C2211yescharacteristic
16#20263940—21no—
17#20263935—21no—
18#20263933—21no—
19#20263877—21no—
20#20263877—21no—
21#20263875—21no—
22#20263875—21no—
23#20263866C2211yescharacteristic
24#125×C199C2211yescharacteristic
25#97×C199C2211yescharacteristic
26#97×C199C2211yescharacteristic
27C2×Dic398—21no—
28C2×Dic398D411yescharacteristic
29C2×D796—21no—
30C2×D796—21no—
31C2×D796—21no—
32C2×D796D411yescharacteristic
33C2×C4×D199—21no—
34#15691875—42no—
35D1592—42no—
36C2×C199⋊C8—21no—
37C4⋊Dic199—21no—
38C4⋊Dic199D411yescharacteristic
39C4⋊Dic199D411yescharacteristic
40Dic199⋊C4—21no—
41Dic199⋊C4—21no—
42Dic199⋊C4—21no—
43(C2×D199)⋊C4—21no—
44(C2×D199)⋊C4—21no—
45(C2×D199)⋊C4—21no—
46(C2×D199)⋊C4—21no—
47(C2×D199)⋊C4—21no—
48C4×Dic199—21no—
49C2×C8×C199—21no—
50C2×C8×C199—21no—
51C4⋊C4×C199—21no—
52C4⋊C4×C199—21no—
53C4⋊C4×C199D411yescharacteristic
54C4⋊C4×C199D411yescharacteristic
55C42×C199C2311yescharacteristic
56C22×D199—21no—
57C22×D199—41no—
58Dic398—41no—
59Dic398—81no—
60D796—41no—
61D796—41no—
62D796—41no—
63D796—42no—
64D796—42no—
65C2×Dic199—21no—
66C2×Dic199—21no—
67C2×Dic199—21no—
68C4×D199—81no—
69C199⋊C8—41no—
70C2×C4×C199—21no—
71C2×C4×C199—21no—
72C2×C4×C199C2×D411yescharacteristic
73C2×C4×C199C2×D411yescharacteristic
74C2×C4×C199C2×D411yescharacteristic
75C8×C199—22no—
76C8×C199—41no—
77C22×C199#12011yescharacteristic
78C2×D199—41no—
79C2×D199—41no—
80C2×D199—41no—
81C2×D199—81no—
82C2×D199—81no—
83C2×D199—81no—
84C4×C199—21no—
85C4×C199—21no—
86C4×C199—21no—
87C4×C199—41no—
88C4×C199—41no—
89Dic199—41no—
90Dic199—41no—
91Dic199—41no—
92C2×C199#45311yescharacteristic
93C2×C199#45411yescharacteristic
94C2×C199#45411yescharacteristic
95D199—81no—
96D199—161no—
97C199#165711yescharacteristic, complemented, Sylow
98#1657—1991nomaximal, Sylow
99#563—1991no—
100#496—1991no—
101#490—1991no—
102#490—1991no—
103#330—1991no—
104#330D19911yescharacteristic, complemented
105#329—1991no—
106C2×SD16—3981no—
107C2×D8—3981no—
108C4⋊Q8—3981no—
109#127—1991no—
110#126—3981no—
111#126—3981no—
112#125—1991no—
113#125C2×D19911yescharacteristic
114#124—1991no—
115#123—3981no—
116C22⋊Q8—3981no—
117C22⋊Q8—3981no—
118#102—3981no—
119#102—3981no—
120#102—3981no—
121#102—3981no—
122#97—1991no—
123#97C2×D19911yescharacteristic
124#97C2×D19911yescharacteristic
125C2×Q8—3981no—
126C2×Q8—1991no—
127C2×D4—3981no—
128C2×D4—3981no—
129C2×D4—3981no—
130C2×D4—1991no—
131C22×C4—3981no—
132SD16—7962no—
133D8—7962no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—3981no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—3981no—
140C4⋊C4—3981no—
141C4⋊C4—3981no—
142C4⋊C4—3981no—
143C4⋊C4—1991no—
144C4⋊C4—1991no—
145C4⋊C4D79611yescharacteristic
146C4⋊C4D79611yescharacteristic
147C22⋊C4—3981no—
148C22⋊C4—3981no—
149C22⋊C4—3981no—
150C22⋊C4—3981no—
151C22⋊C4—3981no—
152C42—3981no—
153C42C22×D19911yescharacteristic
154C23—7961no—
155C23—3981no—
156Q8—7961no—
157Q8—15921no—
158D4—7961no—
159D4—7961no—
160D4—7961no—
161D4—7962no—
162D4—7962no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—15921no—
166C2×C4—3981no—
167C2×C4—3981no—
168C2×C4—3981no—
169C2×C4D4×D19911yescharacteristic
170C2×C4D4×D19911yescharacteristic
171C2×C4C2×D79611yescharacteristic
172C8—22no—
173C8—41no—
174C8—7961no—
175C22—7961no—
176C22—7961no—
177C22—7961no—
178C22—15921no—
179C22—15921no—
180C22—15921no—
181C22#2026392511yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—7961no—
188C4—7961no—
189C4—7961no—
190C2—15921no—
191C2—31841no—
192C2#2716418711yescharacteristic
193C2#2716419211yescharacteristic
194C2#2716419311yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#330×C199C2
socleC22×C199#120
prime radical#27164407C2
hypercenter#330D199
hypocenterC199#1657
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #27164772C2semidirect
3. #27164384C2semidirect
4. #27164383C2semidirect
5. #27163759C2semidirect
6. #27163757C2semidirect
7. #330×C199C2semidirect
97. C199#1657semidirect
104. #330D199semidirect

Maximal subgroups

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

subgroupindex
#271647722
#271644072
#271643842
#271643832
#271637592
#271637572
#330×C1992
#1657199