Finite Group Databasebeta

← #38767859

Subgroups — #38767859

Order 25472.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#27164647C211yesmaximal, characteristic
2#27164349C211yesmaximal, characteristic
3#27164346C211yesmaximal, characteristic
4#27163950C211yesmaximal, characteristic
5#27163754C211yesmaximal, characteristic
6#27163743C211yesmaximal, characteristic
7#328×C199C211yesmaximal, characteristic
8#20263954—21no—
9#20263953—21no—
10#20263945—21no—
11#20263945—21no—
12#20263934C2211yescharacteristic
13#20263932—21no—
14#20263911—21no—
15C2×C4⋊Dic199—21no—
16C2×C4⋊Dic199C2211yescharacteristic
17C2×Dic199⋊C4C2211yescharacteristic
18#20263887—21no—
19#20263886—21no—
20#20263880—21no—
21#20263879—21no—
22C22⋊(C199⋊C8)C2211yescharacteristic
23C199⋊#95—21no—
24C22⋊Q8×C199C2211yescharacteristic
25C22⋊C8×C199C2211yescharacteristic
26#95×C199C2211yescharacteristic
27C2×Dic398—21no—
28C2×Dic398D411yescharacteristic
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—
43Dic199⋊C4—21no—
44Dic199⋊C4—21no—
45C22⋊Dic199—21no—
46C4×Dic199—21no—
47C4×Dic199—21no—
48C2×Q8×C199D411yescharacteristic
49C22×C4×C199—21no—
50C22×C4×C199C2311yescharacteristic
51C2×C8×C199—21no—
52C4⋊C4×C199—21no—
53C4⋊C4×C199D411yescharacteristic
54C22⋊C4×C199—21no—
55Dic398—41no—
56Dic398—81no—
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×Dic199SD1612yes—
67C199⋊C8—41no—
68C23×C199C2×D411yescharacteristic
69Q8×C199—41no—
70C2×C4×C199—22no—
71C2×C4×C199—21no—
72C2×C4×C199—21no—
73C2×C4×C199—41no—
74C2×C4×C199—41no—
75C2×C4×C199—41no—
76C2×C4×C199C2×D411yescharacteristic
77C2×C4×C199C2×D411yescharacteristic
78C8×C199—41no—
79C22×C199—21no—
80C22×C199—21no—
81C22×C199#12011yescharacteristic
82C22×C199C2×SD1611yescharacteristic
83C22×C199#13711yescharacteristic
84C4×C199—21no—
85C4×C199—21no—
86C4×C199—42no—
87C4×C199—41no—
88C4×C199—41no—
89Dic199—22no—
90Dic199—41no—
91Dic199—41no—
92Dic199—41no—
93Dic199—81no—
94C2×C199—21no—
95C2×C199—21no—
96C2×C199#44811yescharacteristic
97C2×C199#45611yescharacteristic
98C2×C199#45811yescharacteristic
99C199#161111yescharacteristic, complemented, Sylow
100#1611—1991nomaximal, Sylow
101#544—1991no—
102#483—1991no—
103#483—1991no—
104#398—1991no—
105#328—1991no—
106#328D19911yescharacteristic
107#324—1991no—
108C4⋊Q8—3981no—
109C4⋊Q8—3981no—
110#125—3981no—
111#125—3981no—
112C22⋊Q8—3981no—
113C22⋊Q8—1991no—
114C22⋊Q8C2×D19911yescharacteristic
115#117—3981no—
116C2×C4⋊C4—3981no—
117C2×C4⋊C4—1991no—
118C2×C4⋊C4—1991no—
119#106—3981no—
120#106—3981no—
121#103—3981no—
122#103—3981no—
123C22⋊C8—1991no—
124C22⋊C8C2×D19911yescharacteristic
125#95—3981no—
126#95C2×D19911yescharacteristic
127C2×Q8—3981no—
128C2×Q8—1991no—
129C2×Q8D79611yescharacteristic
130C22×C4—21no—
131C22×C4—3981no—
132C22×C4—1991no—
133C22×C4—1991no—
134C22×C4C22×D19911yescharacteristic
135C2×C8—21no—
136C2×C8—3981no—
137C4⋊C4—21no—
138C4⋊C4—7962no—
139C4⋊C4—3981no—
140C4⋊C4—3981no—
141C4⋊C4—3981no—
142C4⋊C4—3981no—
143C4⋊C4—3981no—
144C4⋊C4—3981no—
145C4⋊C4—3981no—
146C4⋊C4—3981no—
147C4⋊C4—3981no—
148C4⋊C4—3981no—
149C4⋊C4—1991no—
150C4⋊C4D79611yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—3981no—
153C42—3981no—
154C42—3981no—
155C23D4×D19911yescharacteristic
156Q8—41no—
157Q8—7961no—
158Q8—15921no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—7961no—
166C2×C4—7961no—
167C2×C4—7961no—
168C2×C4—7961no—
169C2×C4—3981no—
170C2×C4—3981no—
171C2×C4—3981no—
172C2×C4—3981no—
173C2×C4—3981no—
174C2×C4—1992no—
175C2×C4D4×D19911yescharacteristic
176C2×C4C2×D79611yescharacteristic
177C8—41no—
178C8—7961no—
179C22—21no—
180C22—21no—
181C22#2026392511yescharacteristic
182C22SD16×D19911yescharacteristic
183C22#2026398711yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—7961no—
190C4—7961no—
191C4—7961no—
192C4—15921no—
193C4—3982no—
194C2—21no—
195C2—21no—
196C2#2716415811yescharacteristic
197C2#2716420211yescharacteristic
198C2#2716420911yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#328×C199C2
socleC22×C199#120
prime radicalC23×C199C2×D4
hypercenter#328D199
hypocenterC199#1611
LCSG ▷ C22×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
99. C199#1611semidirect

Maximal subgroups

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

subgroupindex
#271646472
#271643492
#271643462
#271639502
#271637542
#271637432
#328×C1992
#1611199