Finite Group Databasebeta

← #38770390

Subgroups — #38770390

Order 25472.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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×#20263886C211yesmaximal, characteristic
2C2×#20263880C211yesmaximal, characteristic
3C2×#20263878C211yesmaximal, characteristic
4#27163923C211yesmaximal, characteristic
5#27163887C211yesmaximal, characteristic
6#27163772C211yesmaximal, characteristic
7C2×#106×C199C211yesmaximal, characteristic
8C22×Dic398C2211yescharacteristic
9C22×C199⋊C8C2211yescharacteristic
10C2×C4⋊Dic199C2211yescharacteristic
11C2×Dic199⋊C4—22no—
12C2×C4×Dic199C2211yescharacteristic
13#20263886—22no—
14#20263880—22no—
15#20263878—22no—
16C199⋊#95—22no—
17C22×C8×C199C2211yescharacteristic
18C2×C4⋊C4×C199C2211yescharacteristic
19C2×C4⋊C4×C199C2211yescharacteristic
20#106×C199—22no—
21C2×Dic398—21no—
22C2×Dic398—21no—
23C2×Dic398—21no—
24C2×Dic398—21no—
25C2×Dic398—21no—
26C2×Dic398Q812yes—
27C22×Dic199—21no—
28C22×Dic199—21no—
29C22×Dic199D412yes—
30C2×C199⋊C8—21no—
31C2×C199⋊C8—21no—
32C2×C199⋊C8D412yes—
33C4⋊Dic199—21no—
34C4⋊Dic199—21no—
35Dic199⋊C4—44no—
36C4×Dic199—21no—
37C4×Dic199—21no—
38C22×C4×C199—21no—
39C22×C4×C199—21no—
40C22×C4×C199C2311yescharacteristic
41C2×C8×C199—21no—
42C2×C8×C199—21no—
43C2×C8×C199D412yes—
44C4⋊C4×C199—21no—
45C4⋊C4×C199—21no—
46C4⋊C4×C199—21no—
47C4⋊C4×C199—21no—
48Dic398—22no—
49Dic398—22no—
50Dic398—41no—
51Dic398—41no—
52C2×Dic199—22no—
53C2×Dic199—22no—
54C2×Dic199—22no—
55C2×Dic199—41no—
56C2×Dic199—41no—
57C2×Dic199—41no—
58C2×Dic199—42no—
59C2×Dic199SD1614yes—
60C199⋊C8—22no—
61C23×C199C2×D411yescharacteristic
62C2×C4×C199—41no—
63C2×C4×C199—41no—
64C2×C4×C199—42no—
65C2×C4×C199—42no—
66C2×C4×C199C2×D411yescharacteristic
67C2×C4×C199C2×D411yescharacteristic
68C2×C4×C199C2×Q811yescharacteristic
69C2×C4×C199#4111yescharacteristic
70C2×C4×C199#4111yescharacteristic
71C2×C4×C199#4111yescharacteristic
72C8×C199—22no—
73C22×C199C22⋊Q811yescharacteristic
74C22×C199#12311yescharacteristic
75C22×C199#12711yescharacteristic
76C22×C199C2×SD1612yes—
77C22×C199#13712yes—
78C4×C199—81no—
79C4×C199—81no—
80C4×C199C22⋊Q811yescharacteristic
81C4×C199C22⋊Q811yescharacteristic
82C4×C199#12311yescharacteristic
83C4×C199#12311yescharacteristic
84Dic199—24no—
85Dic199—42no—
86Dic199—81no—
87C2×C199#39911yescharacteristic
88C2×C199#47512yes—
89C2×C199#48312yes—
90C2×C199#49211yescharacteristic
91C2×C199#49711yescharacteristic
92C199#209611yescharacteristic, complemented, Sylow
93#2096—1991nomaximal, Sylow
94C2×#106—1991no—
95C2×#106D19911yescharacteristic
96C2×#103—1991no—
97C2×#103—1991no—
98#391—1991no—
99#384—1991no—
100#336—1991no—
101C22×Q8—1991no—
102C22×C8—1991no—
103C22×C8C2×D19911yescharacteristic
104C2×C4⋊C4—3982no—
105C2×C4⋊C4—1991no—
106C2×C4⋊C4C2×D19911yescharacteristic
107C2×C4⋊C4C2×D19911yescharacteristic
108C2×C42—1991no—
109#106—22no—
110#106—3982no—
111#103—3982no—
112#103—3982no—
113#95—3982no—
114C2×Q8—3981no—
115C2×Q8—3981no—
116C2×Q8—3981no—
117C2×Q8—3981no—
118C2×Q8—3981no—
119C2×Q8—1992no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—3981no—
123C22×C4—3981no—
124C22×C4—1992no—
125C22×C4C22×D19911yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—3981no—
129C2×C8—3981no—
130C2×C8—1992no—
131C2×C8C22⋊D19912yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—7964no—
137C4⋊C4—3981no—
138C4⋊C4—3981no—
139C42—3981no—
140C42—3981no—
141C23D4×D19911yescharacteristic
142Q8—7961no—
143Q8—7961no—
144Q8—3982no—
145Q8—3982no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—7961no—
151C2×C4—7961no—
152C2×C4—7961no—
153C2×C4—7962no—
154C2×C4—3982no—
155C2×C4—3982no—
156C2×C4—3982no—
157C2×C4—1994no—
158C2×C4D4×D19911yescharacteristic
159C2×C4C2×C22⋊D19911yescharacteristic
160C2×C4Q8×D19911yescharacteristic
161C2×C4#1569188611yescharacteristic
162C2×C4#1569188611yescharacteristic
163C2×C4#1569188711yescharacteristic
164C8—22no—
165C8—3982no—
166C22#2026393311yescharacteristic
167C22#2026394011yescharacteristic
168C22#2026395111yescharacteristic
169C22SD16×D19912yes—
170C22#2026398412yes—
171C4—81no—
172C4—81no—
173C4—7962no—
174C4—15921no—
175C4—3984no—
176C4#2026393111yescharacteristic
177C4#2026393311yescharacteristic
178C4#2026393811yescharacteristic
179C4#2026394011yescharacteristic
180C2#2716395311yescharacteristic
181C2#2716430212yes—
182C2#2716435012yes—
183C2#2716438911yescharacteristic
184C2#2716440911yescharacteristic
subgroupG/H
centerC23D4×D199
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
FittingC2×#106×C199C2
socle, prime radicalC23×C199C2×D4
hypercenterC2×#106D199
hypocenterC199#2096
LCSG ▷ C22×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
92. C199#2096semidirect

Maximal subgroups

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

subgroupindex
C2×#202638862
C2×#202638802
C2×#202638782
#271639232
#271638872
#271637722
C2×#106×C1992
#2096199