Finite Group Databasebeta

← #38767220

Subgroups — #38767220

Order 25472.

214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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×#20263949C211yesmaximal, characteristic
2#27164071C211yesmaximal, characteristic, complemented
3#27163743C212yesmaximal, complemented
4#27163741C212yesmaximal
5#432×C199C211yesmaximal, characteristic, complemented
6#20263949—21no—
7#20263949—21no—
8#20263949—21no—
9#20263949—21no—
10C2×Dic199⋊C4C411yescharacteristic
11C2×Dic199⋊C4C411yescharacteristic
12C2×Dic199⋊C4C2211yescharacteristic
13C2×(C2×D199)⋊C4C411yescharacteristic
14C2×(C2×D199)⋊C4C411yescharacteristic
15C2×(C2×D199)⋊C4C2211yescharacteristic
16C4⋊(C199⋊C8)—21no—
17C22⋊(C199⋊C8)C2212yes—
18C4×C199⋊C8—21no—
19C2×C42×C199C2211yescharacteristic
20C4⋊C8×C199—21no—
21C22⋊C8×C199C2212yes—
22#97×C199—21no—
23C23×D199C2×C411yescharacteristic
24C22×Dic199C2×C411yescharacteristic
25C22×Dic199C2×C411yescharacteristic
26C22×Dic199C2×C411yescharacteristic
27C2×C199⋊C8—22no—
28Dic199⋊C4—21no—
29Dic199⋊C4—21no—
30Dic199⋊C4—21no—
31Dic199⋊C4—21no—
32Dic199⋊C4—21no—
33Dic199⋊C4—21no—
34(C2×D199)⋊C4—21no—
35(C2×D199)⋊C4—21no—
36(C2×D199)⋊C4—21no—
37(C2×D199)⋊C4—21no—
38(C2×D199)⋊C4—21no—
39(C2×D199)⋊C4—21no—
40C22×C4×C199C2×C411yescharacteristic
41C22×C4×C199C2×C411yescharacteristic
42C22×C4×C199C2311yescharacteristic
43C2×C8×C199—22no—
44C42×C199D411yescharacteristic
45C42×C199D411yescharacteristic
46C42×C199D411yescharacteristic
47C42×C199D411yescharacteristic
48C22×D199—21no—
49C22×D199—22no—
50C22×D199—41no—
51C22×D199—41no—
52C2×Dic199—21no—
53C2×Dic199—21no—
54C2×Dic199—21no—
55C2×Dic199—22no—
56C2×Dic199—41no—
57C2×Dic199—41no—
58C199⋊C8—42no—
59C23×C199C22×C411yescharacteristic
60C2×C4×C199—22no—
61C2×C4×C199—41no—
62C2×C4×C199—41no—
63C2×C4×C199C22⋊C411yescharacteristic
64C2×C4×C199C22⋊C411yescharacteristic
65C2×C4×C199C22⋊C411yescharacteristic
66C2×C4×C199C22⋊C411yescharacteristic
67C2×C4×C199C2×D411yescharacteristic
68C2×C4×C199C2×D411yescharacteristic
69C8×C199—42no—
70C22×C199—21no—
71C22×C199—21no—
72C22×C199C2×C22⋊C411yescharacteristic
73C22×C199#13112yes—
74C2×D199—41no—
75C2×D199—41no—
76C2×D199—41no—
77C2×D199—82no—
78C4×C199—21no—
79C4×C199—21no—
80C4×C199—21no—
81C4×C199—21no—
82C4×C199—21no—
83C4×C199—21no—
84Dic199—41no—
85Dic199—41no—
86Dic199—41no—
87C2×C199—22no—
88C2×C199#40811yescharacteristic
89C2×C199#41011yescharacteristic
90C2×C199#41311yescharacteristic
91D199—81no—
92C199#147311yescharacteristic, complemented, Sylow
93#1473—1991nomaximal, Sylow
94C2×#126—1991no—
95#432D19911yescharacteristic, complemented
96#431—1991no—
97#324—1992no—
98#323—1992no—
99#126—3981no—
100#126—3981no—
101#126—3981no—
102#126—3981no—
103C2×C4⋊C4—1991no—
104C2×C4⋊C4—1991no—
105C2×C4⋊C4—1991no—
106C2×C22⋊C4—1991no—
107C2×C22⋊C4—1991no—
108C2×C22⋊C4—1991no—
109C2×C42C2×D19911yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—3981no—
112C22⋊C8—1992no—
113C22⋊C8C2×D19912yes—
114#97—21no—
115C4×C8—3981no—
116C24—1991no—
117C22×C4—1991no—
118C22×C4—1991no—
119C22×C4—1991no—
120C22×C4C4×D19911yescharacteristic
121C22×C4C4×D19911yescharacteristic
122C22×C4C22×D19911yescharacteristic
123C2×C8—22no—
124C2×C8—3982no—
125C4⋊C4—3981no—
126C4⋊C4—3981no—
127C4⋊C4—3981no—
128C4⋊C4—3981no—
129C4⋊C4—3981no—
130C4⋊C4—3981no—
131C22⋊C4—3981no—
132C22⋊C4—3981no—
133C22⋊C4—3981no—
134C22⋊C4—3981no—
135C22⋊C4—3981no—
136C22⋊C4—3981no—
137C42C22⋊D19911yescharacteristic
138C42C22⋊D19911yescharacteristic
139C42D79611yescharacteristic
140C42D79611yescharacteristic
141C23—7961no—
142C23—7961no—
143C23—3981no—
144C23—3982no—
145C23C2×C4×D19911yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—7961no—
150C2×C4—7961no—
151C2×C4—3982no—
152C2×C4—3981no—
153C2×C4—3981no—
154C2×C4—3981no—
155C2×C4(C2×D199)⋊C411yescharacteristic
156C2×C4(C2×D199)⋊C411yescharacteristic
157C2×C4(C2×D199)⋊C411yescharacteristic
158C2×C4(C2×D199)⋊C411yescharacteristic
159C2×C4C2×C22⋊D19911yescharacteristic
160C2×C4C2×D79611yescharacteristic
161C8—42no—
162C8—7962no—
163C22—21no—
164C22—21no—
165C22—7961no—
166C22—7961no—
167C22—7961no—
168C22—15922no—
169C22C2×(C2×D199)⋊C411yescharacteristic
170C22#2026396312yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—7961no—
178C4—7961no—
179C4—7961no—
180C2—22no—
181C2—15921no—
182C2#2716398611yescharacteristic
183C2#2716399111yescharacteristic
184C2#2716400011yescharacteristic
subgroupG/H
centerC22C2×(C2×D199)⋊C4
commutatorC23×C199C22×C4
FrattiniC22×C4C22×D199
Fitting#432×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC23×D199C2×C4
cosocleC22×C4×C199C23
hypercenter#432D199
hypocenterC199#1473
LCSG ▷ C23×C199 ▷ C2×C199 ▷ C199
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #27164071C2semidirect
3. #27163743C2semidirect
5. #432×C199C2semidirect
92. C199#1473semidirect
95. #432D199semidirect

Maximal subgroups

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

subgroupindex
C2×#202639492
#271640712
#271637432
#271637412
#432×C1992
#1473199