Finite Group Databasebeta

← #38769999

Subgroups — #38769999

Order 25472.

258 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#20263946C211yesmaximal, characteristic
2C2×#20263879C211yesmaximal, characteristic
3#27163925C211yesmaximal, characteristic
4#27163781C211yesmaximal, characteristic
5#27163780C211yesmaximal, characteristic
6#27163772C211yesmaximal, characteristic
7C2×#103×C199C211yesmaximal, characteristic
8C22×C199⋊C8C2211yescharacteristic
9#20263946—22no—
10#20263946—22no—
11C2×C4⋊Dic199—21no—
12C2×C4⋊Dic199C2211yescharacteristic
13C2×C4⋊Dic199C2211yescharacteristic
14C2×Dic199⋊C4—21no—
15C2×C4×Dic199C2211yescharacteristic
16#20263879—22no—
17C199⋊#95—21no—
18C199⋊#95—21no—
19C22×Q8×C199C2211yescharacteristic
20C22×C8×C199C2211yescharacteristic
21C2×C4⋊C4×C199C2211yescharacteristic
22#103×C199—22no—
23C22×Dic199—21no—
24C22×Dic199—21no—
25C22×Dic199D411yescharacteristic
26C22×Dic199D411yescharacteristic
27C2×C199⋊C8—21no—
28C2×C199⋊C8—21no—
29C2×C199⋊C8—21no—
30C4⋊Dic199—24no—
31C4⋊Dic199—21no—
32C4⋊Dic199—21no—
33C4⋊Dic199—21no—
34C4⋊Dic199D412yes—
35Dic199⋊C4—24no—
36C4×Dic199—21no—
37C4×Dic199—21no—
38C2×Q8×C199—21no—
39C2×Q8×C199—21no—
40C2×Q8×C199—21no—
41C2×Q8×C199—21no—
42C2×Q8×C199—21no—
43C2×Q8×C199Q812yes—
44C22×C4×C199—21no—
45C22×C4×C199—21no—
46C22×C4×C199C2311yescharacteristic
47C2×C8×C199—21no—
48C2×C8×C199—21no—
49C2×C8×C199—21no—
50C4⋊C4×C199—21no—
51C4⋊C4×C199D412yes—
52C2×Dic199—21no—
53C2×Dic199—21no—
54C2×Dic199—22no—
55C2×Dic199—21no—
56C2×Dic199—21no—
57C2×Dic199—21no—
58C2×Dic199—21no—
59C2×Dic199—41no—
60C2×Dic199—41no—
61C2×Dic199—41no—
62C2×Dic199—41no—
63C2×Dic199—41no—
64C199⋊C8—41no—
65C23×C199C2×D411yescharacteristic
66Q8×C199—22no—
67Q8×C199—22no—
68Q8×C199—41no—
69Q8×C199—41no—
70C2×C4×C199—22no—
71C2×C4×C199—22no—
72C2×C4×C199—41no—
73C2×C4×C199—41no—
74C2×C4×C199—41no—
75C2×C4×C199—41no—
76C2×C4×C199C2×D411yescharacteristic
77C2×C4×C199C2×D411yescharacteristic
78C2×C4×C199C2×Q811yescharacteristic
79C2×C4×C199#4111yescharacteristic
80C2×C4×C199#4111yescharacteristic
81C2×C4×C199#4111yescharacteristic
82C8×C199—41no—
83C22×C199#12011yescharacteristic
84C22×C199C22⋊Q811yescharacteristic
85C22×C199#12411yescharacteristic
86C22×C199#13511yescharacteristic
87C22×C199#13511yescharacteristic
88C22×C199#13711yescharacteristic
89C22×C199#13711yescharacteristic
90C4×C199—42no—
91C4×C199—42no—
92C4×C199C22⋊Q811yescharacteristic
93C4×C199C22⋊Q811yescharacteristic
94C4×C199#12411yescharacteristic
95C4×C199#12411yescharacteristic
96Dic199—41no—
97Dic199—41no—
98Dic199—42no—
99Dic199—81no—
100C2×C199#39311yescharacteristic
101C2×C199#45211yescharacteristic
102C2×C199#45211yescharacteristic
103C2×C199#47911yescharacteristic
104C2×C199#47911yescharacteristic
105C2×C199#48811yescharacteristic
106C2×C199#49111yescharacteristic
107C199#202611yescharacteristic, complemented, Sylow
108#2026—1991nomaximal, Sylow
109C2×#125—1991no—
110C2×#103—1991no—
111C2×#103D19911yescharacteristic
112#391—1991no—
113#340—1991no—
114#340—1991no—
115#336—1991no—
116C22×Q8C2×D19911yescharacteristic
117C22×C8—1991no—
118C22×C8C2×D19911yescharacteristic
119#125—3982no—
120#125—3982no—
121C2×C4⋊C4—3981no—
122C2×C4⋊C4—3981no—
123C2×C4⋊C4—1991no—
124C2×C4⋊C4—1991no—
125C2×C4⋊C4C2×D19911yescharacteristic
126C2×C42—1991no—
127#103—22no—
128#103—3982no—
129#95—3981no—
130#95—3981no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8Dic39812yes—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—3981no—
140C22×C4—3981no—
141C22×C4—1991no—
142C22×C4—1991no—
143C22×C4C22×D19911yescharacteristic
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—3981no—
148C2×C8—3981no—
149C2×C8—3981no—
150C4⋊C4—21no—
151C4⋊C4—3984no—
152C4⋊C4—3984no—
153C4⋊C4—3981no—
154C4⋊C4—3981no—
155C4⋊C4—3981no—
156C4⋊C4—1992no—
157C4⋊C4C22⋊D19912yes—
158C42—3981no—
159C42—3981no—
160C23D4×D19911yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—7961no—
172C2×C4—7961no—
173C2×C4—7961no—
174C2×C4—7961no—
175C2×C4—7961no—
176C2×C4—3981no—
177C2×C4—3981no—
178C2×C4—3981no—
179C2×C4—3981no—
180C2×C4—3981no—
181C2×C4—3981no—
182C2×C4—3982no—
183C2×C4D4×D19911yescharacteristic
184C2×C4C2×C22⋊D19911yescharacteristic
185C2×C4C2×Dic39811yescharacteristic
186C2×C4#1569188511yescharacteristic
187C2×C4#1569188511yescharacteristic
188C2×C4#1569188611yescharacteristic
189C8—41no—
190C8—7961no—
191C22#2026392311yescharacteristic
192C22#2026393211yescharacteristic
193C22#2026394111yescharacteristic
194C22#2026397611yescharacteristic
195C22#2026397811yescharacteristic
196C22#2026398411yescharacteristic
197C22#2026398711yescharacteristic
198C4—42no—
199C4—42no—
200C4—7961no—
201C4—7962no—
202C4—7961no—
203C4—15921no—
204C4#2026393211yescharacteristic
205C4#2026393411yescharacteristic
206C4#2026394111yescharacteristic
207C4#2026394211yescharacteristic
208C2#2716393011yescharacteristic
209C2#2716417711yescharacteristic
210C2#2716417911yescharacteristic
211C2#2716432311yescharacteristic
212C2#2716432711yescharacteristic
213C2#2716437411yescharacteristic
214C2#2716438511yescharacteristic
subgroupG/H
centerC23D4×D199
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
FittingC2×#103×C199C2
socle, prime radicalC23×C199C2×D4
hypercenterC2×#103D199
hypocenterC199#2026
LCSG ▷ C22×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
107. C199#2026semidirect

Maximal subgroups

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

subgroupindex
C2×#202639462
C2×#202638792
#271639252
#271637812
#271637802
#271637722
C2×#103×C1992
#2026199