Finite Group Databasebeta

← #38770544

Subgroups — #38770544

Order 25472.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#27164589C211yesmaximal, characteristic
2#27164002C211yesmaximal, characteristic
3#27163816C214yesmaximal, complemented
4#413×C199C211yesmaximal, characteristic
5C22×Dic398C411yescharacteristic
6C2×#15691870—21no—
7#20263953C2212yes—
8#20263942C412yes—
9#20263936—21no—
10#20263936—21no—
11#20263934—21no—
12#20263934—21no—
13#20263914C411yescharacteristic
14#20263874C2212yes—
15#20263872—21no—
16C2×#41×C199C2211yescharacteristic
17C2×M16×C199—21no—
18#101×C199C2212yes—
19#100×C199—21no—
20C2×Dic398—21no—
21C2×Dic398—41no—
22C2×Dic398—41no—
23C2×Dic398C2×C412yes—
24C22×Dic199—21no—
25#15691870—22no—
26#15691870—41no—
27C2×C199⋊C8—41no—
28C4⋊Dic199—21no—
29Dic199⋊C4—22no—
30Dic199⋊C4—22no—
31C22⋊Dic199—21no—
32C22⋊Dic199—22no—
33C22⋊Dic199—22no—
34C4×Dic199C2×C412yes—
35#41×C199—41no—
36#41×C199—41no—
37C2×Q8×C199C2311yescharacteristic
38C2×D4×C199C2×C411yescharacteristic
39C2×D4×C199D411yescharacteristic
40C2×D4×C199D411yescharacteristic
41C22×C4×C199C2×C411yescharacteristic
42C22×C4×C199D411yescharacteristic
43C22×C4×C199D411yescharacteristic
44M16×C199—22no—
45M16×C199—41no—
46C2×C8×C199—41no—
47Dic398—41no—
48Dic398—41no—
49Dic398—42no—
50C2×Dic199—22no—
51C2×Dic199—22no—
52C2×Dic199—42no—
53C199⋊C8—42no—
54C23×C199C22⋊C411yescharacteristic
55C23×C199C22⋊C411yescharacteristic
56C23×C199C22⋊C411yescharacteristic
57Q8×C199—41no—
58D4×C199—41no—
59D4×C199—41no—
60D4×C199—41no—
61C2×C4×C199—21no—
62C2×C4×C199—21no—
63C2×C4×C199—21no—
64C2×C4×C199—21no—
65C2×C4×C199—21no—
66C2×C4×C199—21no—
67C2×C4×C199C22⋊C411yescharacteristic
68C2×C4×C199C22×C411yescharacteristic
69C2×C4×C199C2×D411yescharacteristic
70C2×C4×C199C2×D411yescharacteristic
71C8×C199—42no—
72C22×C199—21no—
73C22×C199—21no—
74C22×C199—21no—
75C22×C199—41no—
76C22×C199—41no—
77C22×C199—41no—
78C22×C199C2×C22⋊C411yescharacteristic
79C4×C199—21no—
80C4×C199—21no—
81C4×C199—21no—
82C4×C199#9911yescharacteristic
83C4×C199#9911yescharacteristic
84Dic199—42no—
85Dic199—42no—
86C2×C199—21no—
87C2×C199—41no—
88C2×C199—41no—
89C2×C199—41no—
90C2×C199C2×#9911yescharacteristic
91C199#213511yescharacteristic, complemented, Sylow
92#2135—1991nomaximal, Sylow
93#536—1991no—
94#413—1991no—
95#413D19911yescharacteristic
96#356—1994no—
97C2×#41C2×D19911yescharacteristic
98C22×Q8—1991no—
99C2×M16—21no—
100C2×M16—3981no—
101C4⋊Q8—1992no—
102#124—1992no—
103#123—3981no—
104#123—3981no—
105C22⋊Q8—3981no—
106C22⋊Q8—3981no—
107#117—1991no—
108#101—1992no—
109#101C2×D19912yes—
110#100—21no—
111#100—3981no—
112#41—41no—
113#41—41no—
114C2×Q8—7961no—
115C2×Q8—7961no—
116C2×Q8—3981no—
117C2×Q8—1992no—
118C2×Q8C22×D19911yescharacteristic
119C2×D4C4×D19911yescharacteristic
120C2×D4C22⋊D19911yescharacteristic
121C2×D4D79611yescharacteristic
122C22×C4—3981no—
123C22×C4C4×D19911yescharacteristic
124C22×C4C22⋊D19911yescharacteristic
125C22×C4D79611yescharacteristic
126M16—22no—
127M16—41no—
128M16—7961no—
129M16—3982no—
130C2×C8—41no—
131C2×C8—7961no—
132C4⋊C4—3981no—
133C4⋊C4—3982no—
134C4⋊C4—3982no—
135C22⋊C4—3981no—
136C22⋊C4—3982no—
137C22⋊C4—3982no—
138C42—1992no—
139C23(C2×D199)⋊C411yescharacteristic
140C23(C2×D199)⋊C411yescharacteristic
141C23(C2×D199)⋊C411yescharacteristic
142Q8—41no—
143Q8—7962no—
144Q8—7961no—
145Q8—7961no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—7962no—
156C2×C4—3982no—
157C2×C4—3982no—
158C2×C4(C2×D199)⋊C411yescharacteristic
159C2×C4C2×C4×D19911yescharacteristic
160C2×C4C2×C22⋊D19911yescharacteristic
161C2×C4C2×D79611yescharacteristic
162C8—42no—
163C8—7962no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×(C2×D199)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—7962no—
175C4—7962no—
176C4#2026386911yescharacteristic
177C4#2026386911yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#2026386911yescharacteristic
subgroupG/H
centerC2C2×#20263869
commutatorC2×C4×C199C22×C4
FrattiniC2×Q8C22×D199
Fitting#413×C199C2
socleC2×C199C2×#99
prime radicalC2×#41×C199C22
cosocleC2×Q8×C199C23
hypercenter#413D199
hypocenterC199#2135
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #27163816C2semidirect
91. C199#2135semidirect

Maximal subgroups

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

subgroupindex
#271645892
#271640022
#271638162
#413×C1992
#2135199