Finite Group Databasebeta

← #38767845

Subgroups — #38767845

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#27164615C211yesmaximal, characteristic
2#27164348C211yesmaximal, characteristic, complemented
3#27164331C211yesmaximal, characteristic
4#27163754C211yesmaximal, characteristic, complemented
5#27163751C211yesmaximal, characteristic
6#27163744C211yesmaximal, characteristic, complemented
7#398×C199C211yesmaximal, characteristic, complemented
8#20263950—21no—
9#20263945—21no—
10#20263940—21no—
11#20263938—21no—
12#20263934C2211yescharacteristic
13#20263933—21no—
14#20263929C2211yescharacteristic
15C4×C22⋊D199—21no—
16#20263888—21no—
17#20263886—21no—
18#20263878—21no—
19#20263875—21no—
20C22⋊(C199⋊C8)C2211yescharacteristic
21C22⋊(C199⋊C8)C2211yescharacteristic
22C2×C4⋊C4×C199—21no—
23C2×C4⋊C4×C199C2211yescharacteristic
24C2×C4⋊C4×C199C2211yescharacteristic
25#95×C199—21no—
26#95×C199C2211yescharacteristic
27C2×Dic398D411yescharacteristic
28C2×D796D411yescharacteristic
29C2×C22⋊D199—21no—
30C2×C4×D199—21no—
31C2×C199⋊C8—21no—
32C2×C199⋊C8—21no—
33C4⋊Dic199D411yescharacteristic
34C4⋊Dic199D411yescharacteristic
35Dic199⋊C4—21no—
36Dic199⋊C4—21no—
37Dic199⋊C4—21no—
38Dic199⋊C4—21no—
39C22⋊Dic199—21no—
40(C2×D199)⋊C4—21no—
41(C2×D199)⋊C4—21no—
42(C2×D199)⋊C4—21no—
43(C2×D199)⋊C4—21no—
44C4×Dic199—21no—
45C22×C4×C199—21no—
46C22×C4×C199—21no—
47C22×C4×C199D411yescharacteristic
48C22×C4×C199D411yescharacteristic
49C22×C4×C199C2311yescharacteristic
50C4⋊C4×C199—21no—
51C4⋊C4×C199—21no—
52C4⋊C4×C199—21no—
53C4⋊C4×C199—21no—
54C4⋊C4×C199—42no—
55C22×D199—21no—
56Dic398—41no—
57D796—41no—
58C22⋊D199—41no—
59C22⋊D199—41no—
60C2×Dic199—21no—
61C2×Dic199—21no—
62C2×Dic199—21no—
63C4×D199—81no—
64C199⋊C8—41no—
65C199⋊C8—41no—
66C23×C199C2×D411yescharacteristic
67C2×C4×C199—22no—
68C2×C4×C199—21no—
69C2×C4×C199—21no—
70C2×C4×C199—21no—
71C2×C4×C199—21no—
72C2×C4×C199—41no—
73C2×C4×C199—41no—
74C2×C4×C199—41no—
75C2×C4×C199—41no—
76C2×C4×C199—41no—
77C2×C4×C199—41no—
78C2×C4×C199—41no—
79C2×C4×C199C2×D411yescharacteristic
80C2×C4×C199C2×D411yescharacteristic
81C22×C199—21no—
82C22×C199—21no—
83C22×C199#12011yescharacteristic
84C22×C199#13511yescharacteristic
85C22×C199AGL(1,ℤ/8)11yescharacteristic
86C2×D199—41no—
87C2×D199—41no—
88C2×D199—41no—
89C4×C199—21no—
90C4×C199—21no—
91C4×C199—42no—
92C4×C199—41no—
93C4×C199—41no—
94C4×C199—81no—
95Dic199—41no—
96Dic199—41no—
97Dic199—41no—
98C2×C199—21no—
99C2×C199—21no—
100C2×C199#44911yescharacteristic
101C2×C199#45611yescharacteristic
102C2×C199#45811yescharacteristic
103D199—81no—
104C199#160911yescharacteristic, complemented, Sylow
105#1609—1991nomaximal, Sylow
106#539—1991no—
107#483—1991no—
108#480—1991no—
109#398D19911yescharacteristic, complemented
110#328—1991no—
111#327—1991no—
112#324—1991no—
113#126—3981no—
114#125—3981no—
115#123—3981no—
116#123—3981no—
117C22⋊Q8—3981no—
118C22⋊Q8—1991no—
119#121—1991no—
120C4×D4—3981no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4C2×D19911yescharacteristic
123C2×C4⋊C4C2×D19911yescharacteristic
124#107—3981no—
125#106—3981no—
126#103—3981no—
127#102—3981no—
128C22⋊C8—1991no—
129C22⋊C8—1991no—
130#95—21no—
131#95C2×D19911yescharacteristic
132C2×Q8—1991no—
133C2×D4—3981no—
134C2×D4—1991no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—3981no—
138C22×C4C22⋊D19911yescharacteristic
139C22×C4C22⋊D19911yescharacteristic
140C22×C4C22×D19911yescharacteristic
141C2×C8—3981no—
142C2×C8—3981no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—21no—
146C4⋊C4—21no—
147C4⋊C4—42no—
148C4⋊C4—3981no—
149C4⋊C4—3981no—
150C4⋊C4—3981no—
151C4⋊C4—3981no—
152C4⋊C4—1991no—
153C4⋊C4—1991no—
154C22⋊C4—3981no—
155C22⋊C4—3981no—
156C22⋊C4—3981no—
157C22⋊C4—3981no—
158C22⋊C4—3981no—
159C42—3981no—
160C23—3981no—
161C23C2×C22⋊D19911yescharacteristic
162Q8—7961no—
163D4—7961no—
164D4—7961no—
165D4—7961no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—15921no—
179C2×C4—3981no—
180C2×C4—3981no—
181C2×C4—3981no—
182C2×C4D4×D19911yescharacteristic
183C2×C4D4×D19911yescharacteristic
184C8—7961no—
185C8—7961no—
186C22—21no—
187C22—21no—
188C22—7961no—
189C22—7961no—
190C22—7961no—
191C22#2026392311yescharacteristic
192C22#2026397511yescharacteristic
193C22#2026398111yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—81no—
200C4—7961no—
201C4—7961no—
202C4—7961no—
203C2—21no—
204C2—21no—
205C2—15921no—
206C2#2716416111yescharacteristic
207C2#2716420011yescharacteristic
208C2#2716420711yescharacteristic
subgroupG/H
centerC22#20263923
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#398×C199C2
socleC22×C199#120
prime radical#20263929C22
hypercenter#398D199
hypocenterC199#1609
LCSG ▷ C22×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #27164348C2semidirect
4. #27163754C2semidirect
6. #27163744C2semidirect
7. #398×C199C2semidirect
104. C199#1609semidirect
109. #398D199semidirect

Maximal subgroups

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

subgroupindex
#271646152
#271643482
#271643312
#271637542
#271637512
#271637442
#398×C1992
#1609199