Finite Group Databasebeta

← #38767446

Subgroups — #38767446

Order 25472.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D199C211yesmaximal, characteristic
2#27164073C211yesmaximal, characteristic, complemented
3#27163970C211yesmaximal, characteristic, complemented
4#27163758C211yesmaximal, characteristic, complemented
5#27163757C211yesmaximal, characteristic, complemented
6#27163757C211yesmaximal, characteristic, complemented
7#329×C199C211yesmaximal, characteristic, complemented
8C2×Q8×D199C411yescharacteristic
9C2×D4×D199C411yescharacteristic
10C2×#15691869—21no—
11#20263944C411yescharacteristic
12#20263943C2211yescharacteristic
13#20263942C411yescharacteristic
14#20263941—21no—
15#20263941—21no—
16C22⋊C4×D199—21no—
17C22⋊C4×D199—21no—
18C42×D199C2211yescharacteristic
19Dic199⋊C8—21no—
20(C2×D199)⋊C8—21no—
21#20263866C2211yescharacteristic, complemented
22#20263866C2211yescharacteristic, complemented
23C8×Dic199—21no—
24#124×C199C2211yescharacteristic
25#97×C199C2211yescharacteristic, complemented
26#97×C199C2211yescharacteristic, complemented
27C23×D199—21no—
28C2×Dic398—21no—
29C2×Dic398C2×C411yescharacteristic
30Q8×D199—42no—
31C2×D796C2×C411yescharacteristic
32C2×C22⋊D199—21no—
33D4×D199—42no—
34C2×C4×D199—21no—
35C2×C4×D199C2×C411yescharacteristic
36C2×C4×D199D411yescharacteristic
37C2×C4×D199D411yescharacteristic
38#15691869—24no—
39C2×C199⋊C8—21no—
40C2×C199⋊C8—21no—
41C22⋊Dic199—21no—
42C22⋊Dic199—21no—
43(C2×D199)⋊C4—21no—
44(C2×D199)⋊C4—21no—
45(C2×D199)⋊C4—21no—
46(C2×D199)⋊C4—21no—
47C4×Dic199C2×C411yescharacteristic
48C4×Dic199D411yescharacteristic
49C4×Dic199D411yescharacteristic
50C2×Q8×C199C2×C411yescharacteristic
51C2×D4×C199C2×C411yescharacteristic
52C2×C8×C199—21no—
53C2×C8×C199—21no—
54C22⋊C4×C199—21no—
55C22⋊C4×C199—21no—
56C42×C199C2311yescharacteristic
57C22×D199—21no—
58C22×D199—42no—
59C22×D199—42no—
60C22×D199—42no—
61C22×D199C22⋊C411yescharacteristic
62Dic398—42no—
63Dic398—41no—
64D796—41no—
65C22⋊D199—42no—
66C2×Dic199—21no—
67C2×Dic199C22⋊C411yescharacteristic
68C2×Dic199C22⋊C411yescharacteristic
69C2×Dic199C22⋊C411yescharacteristic
70C4×D199—22no—
71C4×D199—22no—
72C4×D199—41no—
73C4×D199—42no—
74C199⋊C8—22no—
75C199⋊C8—41no—
76C23×C199—21no—
77Q8×C199—41no—
78D4×C199—41no—
79C2×C4×C199—21no—
80C2×C4×C199C22×C411yescharacteristic
81C2×C4×C199C2×D411yescharacteristic
82C2×C4×C199C2×D411yescharacteristic
83C8×C199—22no—
84C8×C199—41no—
85C22×C199—41no—
86C22×C199—41no—
87C22×C199—41no—
88C22×C199C2×C22⋊C411yescharacteristic
89C2×D199—21no—
90C2×D199—21no—
91C2×D199—41no—
92C2×D199—41no—
93C2×D199—41no—
94C2×D199—84no—
95C2×D199#10412yes—
96C4×C199—21no—
97C4×C199—21no—
98C4×C199—21no—
99C4×C199—41no—
100Dic199—21no—
101Dic199—21no—
102Dic199—41no—
103Dic199#10012yes—
104C2×C199—81no—
105C2×C199C2×#10011yescharacteristic
106C2×C199C2×#10411yescharacteristic
107C2×C199#42111yescharacteristic
108D199—22no—
109D199—81no—
110C199#152711yescharacteristic, complemented, Sylow
111#1527—1991nomaximal, Sylow
112C2×#124—1991no—
113#432—1991no—
114C4×M16—1991no—
115#329—1991no—
116#329—1991no—
117#329—1991no—
118#329D19911yescharacteristic, complemented
119C22×Q8—1991no—
120C22×D4—1991no—
121C2×M16—3981no—
122#124—3981no—
123#124—3981no—
124#124—1991no—
125#124—1991no—
126#124—1991no—
127#124C2×D19911yescharacteristic
128C2×C22⋊C4—3981no—
129C2×C22⋊C4—3981no—
130C2×C42—1991no—
131C4⋊C8—3981no—
132C22⋊C8—3981no—
133#97—1991no—
134#97—1991no—
135#97C2×D19911yescharacteristic, complemented
136#97C2×D19911yescharacteristic, complemented
137C4×C8—3981no—
138C24—3981no—
139C2×Q8—7962no—
140C2×Q8—3981no—
141C2×Q8—1991no—
142C2×Q8C4×D19911yescharacteristic
143C2×D4—7962no—
144C2×D4—3981no—
145C2×D4—1991no—
146C2×D4C4×D19911yescharacteristic
147C22×C4—3981no—
148C22×C4—1991no—
149C22×C4—1991no—
150C22×C4—1991no—
151M16—3984no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—3981no—
155C2×C8—3981no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—3981no—
159C22⋊C4—3981no—
160C22⋊C4—3981no—
161C22⋊C4—3981no—
162C22⋊C4—3981no—
163C22⋊C4—3981no—
164C42—1991no—
165C42—1991no—
166C42—1991no—
167C42C22×D19911yescharacteristic
168C23—21no—
169C23—7962no—
170C23—7962no—
171C23—7962no—
172C23—3981no—
173C23—1991no—
174Q8—41no—
175Q8—7961no—
176Q8—7962no—
177D4—41no—
178D4—7961no—
179D4—7962no—
180C2×C4—21no—
181C2×C4—7961no—
182C2×C4—7962no—
183C2×C4—3982no—
184C2×C4—3982no—
185C2×C4—3981no—
186C2×C4—1991no—
187C2×C4—1991no—
188C2×C4—1991no—
189C2×C4C2×C4×D19911yescharacteristic
190C2×C4D4×D19911yescharacteristic
191C2×C4D4×D19911yescharacteristic
192C8—22no—
193C8—41no—
194C8—7961no—
195C8—3982no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—7961no—
200C22—7961no—
201C22—7961no—
202C22—15924no—
203C22—3981no—
204C22—3981no—
205C22—1992no—
206C22C22⋊C4×D19911yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—7961no—
212C4—3981no—
213C4—3981no—
214C4—1992no—
215C2—81no—
216C2—15921no—
217C2—3982no—
218C2#100×D19911yescharacteristic
219C2#104×D19911yescharacteristic
220C2#2716403311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC42C22×D199
Fitting#329×C199C2
socleC22×C199C2×C22⋊C4
prime radicalC2×D4×D199C4
cosocleC42×C199C23
hypercenter#329D199
hypocenterC199#1527
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #27164073C2semidirect
3. #27163970C2semidirect
4. #27163758C2semidirect
5. #27163757C2semidirect
6. #27163757C2semidirect
7. #329×C199C2semidirect
21. #20263866C22semidirect
22. #20263866C22semidirect
25. #97×C199C22semidirect
26. #97×C199C22semidirect
110. C199#1527semidirect
118. #329D199semidirect
135. #97C2×D199semidirect
136. #97C2×D199semidirect

Maximal subgroups

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

subgroupindex
#124×D1992
#271640732
#271639702
#271637582
#271637572
#329×C1992
#1527199