Finite Group Databasebeta

← #38767923

Subgroups — #38767923

Order 25472.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#27164729C211yesmaximal, characteristic, complemented
2#27164392C211yesmaximal, characteristic, complemented
3#27164219C211yesmaximal, characteristic, complemented
4#27164214C211yesmaximal, characteristic
5#27163748C211yesmaximal, characteristic, complemented
6#27163745C211yesmaximal, characteristic, complemented
7#333×C199C211yesmaximal, characteristic, complemented
8C2×#15691875—21no—
9C2×#15691873—22no—
10C2×D1592—21no—
11#20263952C2211yescharacteristic
12#20263946—21no—
13#20263935—21no—
14#20263931—22no—
15C4×Dic398C2211yescharacteristic
16C4×D796C2211yescharacteristic
17#20263917—21no—
18C4⋊C4×D199—21no—
19#20263877—21no—
20#20263877—21no—
21C4×C199⋊C8C2211yescharacteristic
22C4⋊Q8×C199C2211yescharacteristic
23C4⋊C8×C199C2211yescharacteristic
24C4⋊C8×C199C2211yescharacteristic
25C2×Dic398D411yescharacteristic
26C2×D796—21no—
27C2×D796—21no—
28C2×D796—21no—
29C2×D796D411yescharacteristic
30C2×C4×D199—22no—
31C2×C4×D199—21no—
32#15691875—42no—
33#15691873—44no—
34D1592—42no—
35C2×C199⋊C8—21no—
36C4⋊Dic199—22no—
37C4⋊Dic199D411yescharacteristic
38C4⋊Dic199D411yescharacteristic
39Dic199⋊C4—22no—
40Dic199⋊C4—21no—
41(C2×D199)⋊C4—22no—
42(C2×D199)⋊C4—21no—
43C4×Dic199—21no—
44C2×Q8×C199D412yes—
45C2×C8×C199—21no—
46C2×C8×C199—21no—
47C4⋊C4×C199—21no—
48C4⋊C4×C199—21no—
49C42×C199C2311yescharacteristic
50C22×D199—21no—
51C22×D199—41no—
52Dic398—21no—
53Dic398—21no—
54D796—21no—
55D796—42no—
56D796—41no—
57D796—41no—
58D796—41no—
59D796—41no—
60D796SD1612yescomplemented
61C2×Dic199—21no—
62C2×Dic199—21no—
63C2×Dic199—21no—
64C4×D199—41no—
65C4×D199—41no—
66C4×D199—82no—
67C199⋊C8—22no—
68Q8×C199—42no—
69C2×C4×C199—22no—
70C2×C4×C199C2×D411yescharacteristic
71C2×C4×C199C2×D411yescharacteristic
72C2×C4×C199C2×D411yescharacteristic
73C8×C199—41no—
74C8×C199—41no—
75C22×C199#12011yescharacteristic
76C2×D199—22no—
77C2×D199—41no—
78C2×D199—41no—
79C2×D199—81no—
80C2×D199—81no—
81C2×D199—81no—
82C4×C199—21no—
83C4×C199—42no—
84C4×C199C2×SD1611yescharacteristic
85C4×C199#13511yescharacteristic
86C4×C199AGL(1,ℤ/8)11yescharacteristic
87C4×C199#13711yescharacteristic
88Dic199—41no—
89Dic199—41no—
90Dic199—41no—
91C2×C199#44811yescharacteristic
92C2×C199#44911yescharacteristic
93C2×C199#45311yescharacteristic
94D199—42no—
95D199—161no—
96C199#162211yescharacteristic, complemented, Sylow
97#1622—1991nomaximal, Sylow
98#554—1991no—
99#492—1991no—
100#460—1991no—
101#459—1991no—
102#333D19911yescharacteristic, complemented
103Q8⋊C8—1991no—
104D4⋊C8—1991no—
105C2×SD16—3981no—
106C2×SD16—3982no—
107C2×D8—3981no—
108C4⋊Q8C2×D19911yescharacteristic
109#127—1991no—
110#125—3981no—
111C22⋊Q8—3981no—
112C22⋊Q8—3982no—
113C4×Q8—1991no—
114C4×D4—3981no—
115C4×D4—1991no—
116C2×C4⋊C4—3981no—
117C4⋊C8C2×D19911yescharacteristic
118C4⋊C8C2×D19911yescharacteristic
119#102—3981no—
120#102—3981no—
121C4×C8—1991no—
122C2×Q8—1991no—
123C2×Q8D79612yes—
124C2×D4—3981no—
125C2×D4—3981no—
126C2×D4—3981no—
127C2×D4—1991no—
128C22×C4—3982no—
129C22×C4—3981no—
130SD16—7962no—
131SD16—7964no—
132D8—7962no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—3981no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3982no—
139C4⋊C4—3982no—
140C4⋊C4—3981no—
141C4⋊C4—1991no—
142C4⋊C4—1991no—
143C22⋊C4—3982no—
144C22⋊C4—3981no—
145C42—3981no—
146C42C22×D19911yescharacteristic
147C23—7961no—
148C23—3981no—
149Q8—42no—
150Q8—3981no—
151Q8—3981no—
152D4—7962no—
153D4—7961no—
154D4—7961no—
155D4—7961no—
156D4—7961no—
157D4—3981no—
158D4—1992no—
159C2×C4—22no—
160C2×C4—7961no—
161C2×C4—7961no—
162C2×C4—15922no—
163C2×C4—3981no—
164C2×C4—3981no—
165C2×C4—3981no—
166C2×C4D4×D19911yescharacteristic
167C2×C4D4×D19911yescharacteristic
168C2×C4C2×D79611yescharacteristic
169C8—41no—
170C8—41no—
171C8—3982no—
172C22—7961no—
173C22—7961no—
174C22—15921no—
175C22—15921no—
176C22—15921no—
177C22—3982no—
178C22#2026392511yescharacteristic
179C4—21no—
180C4—42no—
181C4—7961no—
182C4—7961no—
183C4—7961no—
184C4SD16×D19911yescharacteristic
185C4#2026397811yescharacteristic
186C4#2026398211yescharacteristic
187C4#2026398711yescharacteristic
188C2—7962no—
189C2—31841no—
190C2#2716415811yescharacteristic
191C2#2716416611yescharacteristic
192C2#2716418811yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#333×C199C2
socleC22×C199#120
prime radical#27164214C2
hypercenter#333D199
hypocenterC199#1622
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #27164729C2semidirect
2. #27164392C2semidirect
3. #27164219C2semidirect
5. #27163748C2semidirect
6. #27163745C2semidirect
7. #333×C199C2semidirect
60. D796SD16semidirect
96. C199#1622semidirect
102. #333D199semidirect

Maximal subgroups

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

subgroupindex
#271647292
#271643922
#271642192
#271642142
#271637482
#271637452
#333×C1992
#1622199