Finite Group Databasebeta

← #38769914

Subgroups — #38769914

Order 25472.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#27164525C212yesmaximal, complemented
2#27164035C212yesmaximal, complemented
3#27163981C211yesmaximal, characteristic, complemented
4#27163775C211yesmaximal, characteristic, complemented
5#575×C199C211yesmaximal, characteristic, complemented
6C22×C4×D199C2211yescharacteristic
7C2×#15691870C2211yescharacteristic
8#20263936—22no—
9#20263931—22no—
10#20263926—22no—
11#20263923—22no—
12C4×C22⋊D199—24no—
13#20263914C2212yes—
14#20263882—24no—
15(C2×D199)⋊C8—22no—
16C2×#41×C199C2212yes—
17#137×C199—22no—
18AGL(1,ℤ/8)×C199—22no—
19#135×C199—22no—
20C2×M16×C199C2211yescharacteristic
21C23×D199D411yescharacteristic
22C2×C22⋊D199—24no—
23C22×Dic199D411yescharacteristic
24C2×C4×D199—21no—
25C2×C4×D199—22no—
26C2×C4×D199—22no—
27C2×C4×D199—21no—
28#15691870—22no—
29C2×C199⋊C8—21no—
30C4⋊Dic199—22no—
31Dic199⋊C4—24no—
32C22⋊Dic199—24no—
33C22⋊Dic199—22no—
34(C2×D199)⋊C4—24no—
35C4×Dic199D414yescomplemented
36#41×C199—22no—
37#41×C199—22no—
38#41×C199—22no—
39#41×C199—22no—
40C2×Q8×C199D412yescomplemented
41C2×D4×C199—22no—
42C2×D4×C199D412yescomplemented
43C22×C4×C199—22no—
44C22×C4×C199C2311yescharacteristic
45Q16×C199—22no—
46SD16×C199—24no—
47D8×C199—22no—
48M16×C199—22no—
49C2×C8×C199D412yescomplemented
50C22×D199—22no—
51C22×D199—21no—
52C22×D199—42no—
53C22⋊D199—48no—
54C2×Dic199—24no—
55C2×Dic199—22no—
56C2×Dic199—21no—
57C4×D199—41no—
58C4×D199—42no—
59C4×D199—41no—
60C199⋊C8—41no—
61C23×C199—22no—
62C23×C199C2×D411yescharacteristic
63Q8×C199—22no—
64Q8×C199—22no—
65D4×C199—22no—
66D4×C199—22no—
67D4×C199—42no—
68D4×C199—42no—
69C2×C4×C199—22no—
70C2×C4×C199—42no—
71C2×C4×C199—42no—
72C2×C4×C199C2×D412yes—
73C2×C4×C199C2×D412yes—
74C2×C4×C199C2×D411yescharacteristic
75C2×C4×C199#4111yescharacteristic
76C8×C199—22no—
77C22×C199—41no—
78C22×C199—44no—
79C22×C199—42no—
80C22×C199#12012yes—
81C22×C199#12111yescharacteristic
82C2×D199—24no—
83C2×D199—22no—
84C2×D199—42no—
85C2×D199—41no—
86C2×D199—41no—
87C4×C199—42no—
88C4×C199#12011yescharacteristic
89C4×C199#12112yes—
90C4×C199#12711yescharacteristic
91Dic199—44no—
92Dic199—41no—
93C2×C199—22no—
94C2×C199—21no—
95C2×C199—82no—
96C2×C199#39211yescharacteristic
97D199—42no—
98C199#201011yescharacteristic, complemented, Sylow
99#2010—1991nomaximal, Sylow
100#575D19911yescharacteristic, complemented
101#525—1992no—
102#421—1992no—
103#407—1991no—
104H(3,ℤ/4)—1991no—
105C2×#41C2×D19912yes—
106C23×C4—1991no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1991no—
111C2×M16C2×D19911yescharacteristic
112#123—3982no—
113C22⋊Q8—3982no—
114#121—3982no—
115#120—3982no—
116C4×D4—3984no—
117#117—1992no—
118#104—3984no—
119C22⋊C8—3982no—
120C24—1991no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D19912yescomplemented
126C2×D4—22no—
127C2×D4—3984no—
128C2×D4C22⋊D19912yescomplemented
129C22×C4—22no—
130C22×C4—3982no—
131C22×C4—3981no—
132C22×C4—3982no—
133C22×C4—3981no—
134C22×C4—1991no—
135C22×C4C22×D19911yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—3982no—
141C2×C8—3981no—
142C2×C8C22⋊D19912yescomplemented
143C4⋊C4—3984no—
144C4⋊C4—3982no—
145C22⋊C4—3984no—
146C22⋊C4—3984no—
147C22⋊C4—3982no—
148C42—1994no—
149C23—22no—
150C23—7962no—
151C23—3982no—
152C23—3981no—
153C23D4×D19911yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—7968no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—7961no—
165C2×C4—7961no—
166C2×C4—7962no—
167C2×C4—3984no—
168C2×C4—3982no—
169C2×C4—3981no—
170C2×C4D4×D19912yes—
171C2×C4C2×C22⋊D19911yescharacteristic
172C2×C4C2×C22⋊D19912yes—
173C2×C4#1569188511yescharacteristic
174C8—22no—
175C8—7961no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—7962no—
180C22—7961no—
181C22—7961no—
182C22—3984no—
183C22—3982no—
184C22#2026392312yes—
185C22#2026392611yescharacteristic
186C4—42no—
187C4—7964no—
188C4—7961no—
189C4#2026392411yescharacteristic
190C4#2026392712yes—
191C4#2026395111yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—7962no—
196C2#2716392611yescharacteristic
subgroupG/H
centerC4#20263951
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting#575×C199C2
socleC2×C199#392
hypercenter#575D199
hypocenterC199#2010
LCSG ▷ C22×C4×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #27164525C2semidirect
2. #27164035C2semidirect
3. #27163981C2semidirect
4. #27163775C2semidirect
5. #575×C199C2semidirect
35. C4×Dic199D4semidirect
40. C2×Q8×C199D4semidirect
42. C2×D4×C199D4semidirect
49. C2×C8×C199D4semidirect
98. C199#2010semidirect
100. #575D199semidirect
125. C2×Q8C22⋊D199semidirect
128. C2×D4C22⋊D199semidirect
142. C2×C8C22⋊D199semidirect

Maximal subgroups

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

subgroupindex
#271645252
#271640352
#271639812
#271637752
#575×C1992
#2010199