Finite Group Databasebeta

← #38767848

Subgroups — #38767848

Order 25472.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#27164613C211yesmaximal, characteristic
2#27164349C211yesmaximal, characteristic, complemented
3#27164329C211yesmaximal, characteristic
4#27163950C211yesmaximal, characteristic, complemented
5#27163754C211yesmaximal, characteristic, complemented
6#27163743C211yesmaximal, characteristic, complemented
7#327×C199C211yesmaximal, characteristic
8#20263948—21no—
9#20263945—21no—
10#20263936—21no—
11#20263936—21no—
12#20263934C2211yescharacteristic
13#20263932—21no—
14D4×Dic199—21no—
15C2×C4⋊Dic199—21no—
16C2×C4⋊Dic199C2211yescharacteristic
17C2×Dic199⋊C4C2211yescharacteristic
18#20263888—21no—
19#20263887—21no—
20#20263880—21no—
21#20263876—21no—
22C22⋊(C199⋊C8)C2211yescharacteristic
23C199⋊#95—21no—
24#121×C199C2211yescharacteristic
25C22⋊C8×C199C2211yescharacteristic
26#95×C199C2211yescharacteristic
27C2×Dic398D411yescharacteristic
28C22×Dic199—21no—
29C22×Dic199—21no—
30C22×Dic199D411yescharacteristic
31C22×Dic199D411yescharacteristic
32C2×C199⋊C8—21no—
33C4⋊Dic199—21no—
34C4⋊Dic199—21no—
35C4⋊Dic199—21no—
36C4⋊Dic199—42no—
37C4⋊Dic199D411yescharacteristic
38Dic199⋊C4—21no—
39Dic199⋊C4—21no—
40Dic199⋊C4—21no—
41Dic199⋊C4—21no—
42Dic199⋊C4—21no—
43C22⋊Dic199—21no—
44C22⋊Dic199—21no—
45C22⋊Dic199—21no—
46C22⋊Dic199—21no—
47C4×Dic199—21no—
48C2×D4×C199—21no—
49C2×D4×C199D411yescharacteristic
50C22×C4×C199—21no—
51C22×C4×C199C2311yescharacteristic
52C2×C8×C199—21no—
53C4⋊C4×C199D411yescharacteristic
54C22⋊C4×C199—21no—
55Dic398—41no—
56C2×Dic199—21no—
57C2×Dic199—21no—
58C2×Dic199—21no—
59C2×Dic199—21no—
60C2×Dic199—21no—
61C2×Dic199—21no—
62C2×Dic199—41no—
63C2×Dic199—41no—
64C2×Dic199—41no—
65C2×Dic199—41no—
66C2×Dic199—81no—
67C199⋊C8—41no—
68C23×C199—21no—
69C23×C199C2×D411yescharacteristic
70D4×C199—41no—
71D4×C199—41no—
72D4×C199—41no—
73C2×C4×C199—22no—
74C2×C4×C199—21no—
75C2×C4×C199—41no—
76C2×C4×C199—41no—
77C2×C4×C199—41no—
78C2×C4×C199C2×D411yescharacteristic
79C2×C4×C199C2×D411yescharacteristic
80C8×C199—41no—
81C22×C199—21no—
82C22×C199—21no—
83C22×C199—41no—
84C22×C199—41no—
85C22×C199—41no—
86C22×C199#12011yescharacteristic
87C22×C199#13511yescharacteristic
88C22×C199AGL(1,ℤ/8)11yescharacteristic
89C4×C199—21no—
90C4×C199—21no—
91C4×C199—42no—
92C4×C199—41no—
93Dic199—41no—
94Dic199—41no—
95Dic199—41no—
96Dic199—41no—
97Dic199—81no—
98C2×C199—21no—
99C2×C199—21no—
100C2×C199—81no—
101C2×C199#44911yescharacteristic
102C2×C199#45611yescharacteristic
103C2×C199#45811yescharacteristic
104C199#160911yescharacteristic, complemented, Sylow
105#1609—1991nomaximal, Sylow
106#539—1991no—
107#483—1991no—
108#480—1991no—
109#398—1991no—
110#328—1991no—
111#327D19911yescharacteristic
112#324—1991no—
113#126—3981no—
114#125—3981no—
115#123—3981no—
116#123—3981no—
117C22⋊Q8—3981no—
118C22⋊Q8—1991no—
119#121C2×D19911yescharacteristic
120C4×D4—3981no—
121C2×C4⋊C4—3981no—
122C2×C4⋊C4—1991no—
123C2×C4⋊C4—1991no—
124#107—3981no—
125#106—3981no—
126#103—3981no—
127#102—3981no—
128C22⋊C8—1991no—
129C22⋊C8C2×D19911yescharacteristic
130#95—3981no—
131#95C2×D19911yescharacteristic
132C2×Q8—1991no—
133C2×D4—21no—
134C2×D4D79611yescharacteristic
135C22×C4—21no—
136C22×C4—3981no—
137C22×C4—3981no—
138C22×C4—1991no—
139C22×C4—1991no—
140C22×C4C22×D19911yescharacteristic
141C2×C8—21no—
142C2×C8—3981no—
143C4⋊C4—7962no—
144C4⋊C4—3981no—
145C4⋊C4—3981no—
146C4⋊C4—3981no—
147C4⋊C4—3981no—
148C4⋊C4—3981no—
149C4⋊C4—3981no—
150C4⋊C4—3981no—
151C4⋊C4—3981no—
152C4⋊C4—1991no—
153C4⋊C4D79611yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—3981no—
156C22⋊C4—3981no—
157C22⋊C4—3981no—
158C22⋊C4—3981no—
159C42—3981no—
160C23—21no—
161C23D4×D19911yescharacteristic
162Q8—7961no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—7961no—
172C2×C4—7961no—
173C2×C4—7961no—
174C2×C4—7961no—
175C2×C4—15921no—
176C2×C4—3981no—
177C2×C4—3981no—
178C2×C4—3981no—
179C2×C4—3981no—
180C2×C4—3981no—
181C2×C4—3981no—
182C2×C4D4×D19911yescharacteristic
183C2×C4C2×D79611yescharacteristic
184C8—41no—
185C8—7961no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#2026392511yescharacteristic
192C22#2026397611yescharacteristic
193C22#2026397911yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—7961no—
199C4—7961no—
200C4—7961no—
201C4—7961no—
202C4—15921no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#2716416411yescharacteristic
207C2#2716420211yescharacteristic
208C2#2716420911yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#327×C199C2
socleC22×C199#120
prime radical#121×C199C22
hypercenter#327D199
hypocenterC199#1609
LCSG ▷ C22×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #27164349C2semidirect
4. #27163950C2semidirect
5. #27163754C2semidirect
6. #27163743C2semidirect
104. C199#1609semidirect

Maximal subgroups

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

subgroupindex
#271646132
#271643492
#271643292
#271639502
#271637542
#271637432
#327×C1992
#1609199