Finite Group Databasebeta

← #38767426

Subgroups — #38767426

Order 25472.

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

normal subgroups only

This group has 218 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#27164554C211yesmaximal, characteristic
2#27164068C211yesmaximal, characteristic, complemented
3#27163885C211yesmaximal, characteristic, complemented
4#27163755C211yesmaximal, characteristic, complemented
5#27163753C211yesmaximal, characteristic
6#27163751C211yesmaximal, characteristic
7#328×C199C211yesmaximal, characteristic, complemented
8#20263950—21no—
9#20263946C411yescharacteristic, complemented
10#20263944C411yescharacteristic, complemented
11#20263939—21no—
12#20263929C2211yescharacteristic
13Q8×Dic199C411yescharacteristic, complemented
14#20263917C411yescharacteristic, complemented
15(C22⋊D199)⋊C4—21no—
16#20263913—21no—
17C2×C4×Dic199C2211yescharacteristic
18Dic199⋊C8—21no—
19C22⋊(C199⋊C8)C2211yescharacteristic
20C8×Dic199—21no—
21C199⋊#95—21no—
22C199⋊#95—21no—
23C199⋊#95C2211yescharacteristic
24C22⋊Q8×C199C2211yescharacteristic
25C22⋊C8×C199C2211yescharacteristic
26#95×C199C2211yescharacteristic
27C2×D796C2×C411yescharacteristic
28C2×C22⋊D199—21no—
29C22×Dic199—21no—
30C22×Dic199D411yescharacteristic
31C22×Dic199D411yescharacteristic
32C2×C4×D199—21no—
33C2×C199⋊C8—21no—
34C4⋊Dic199—21no—
35C4⋊Dic199—21no—
36C4⋊Dic199C2×C411yescharacteristic
37Dic199⋊C4—21no—
38(C2×D199)⋊C4—21no—
39(C2×D199)⋊C4—21no—
40(C2×D199)⋊C4—21no—
41(C2×D199)⋊C4—21no—
42C4×Dic199—21no—
43C4×Dic199C2×C411yescharacteristic
44C4×Dic199C2×C411yescharacteristic
45C4×Dic199D411yescharacteristic
46C4×Dic199D411yescharacteristic
47C2×Q8×C199C2×C411yescharacteristic
48C22×C4×C199—21no—
49C22×C4×C199C2311yescharacteristic
50C2×C8×C199—21no—
51C4⋊C4×C199—21no—
52C4⋊C4×C199C2×C411yescharacteristic
53C22⋊C4×C199—21no—
54C22×D199—21no—
55D796—41no—
56C22⋊D199—41no—
57C22⋊D199—41no—
58C2×Dic199—21no—
59C2×Dic199—21no—
60C2×Dic199—21no—
61C2×Dic199—41no—
62C2×Dic199—41no—
63C2×Dic199—41no—
64C2×Dic199—41no—
65C2×Dic199C22⋊C411yescharacteristic
66C2×Dic199C22⋊C411yescharacteristic
67C2×Dic199C22⋊C411yescharacteristic
68C2×Dic199C22⋊C411yescharacteristic
69C4×D199—42no—
70C199⋊C8—41no—
71C23×C199C2×D411yescharacteristic
72Q8×C199—41no—
73C2×C4×C199—21no—
74C2×C4×C199—21no—
75C2×C4×C199—41no—
76C2×C4×C199—41no—
77C2×C4×C199—41no—
78C2×C4×C199—41no—
79C2×C4×C199C22×C411yescharacteristic
80C2×C4×C199C2×D411yescharacteristic
81C8×C199—41no—
82C22×C199—21no—
83C22×C199—21no—
84C22×C199C2×C22⋊C411yescharacteristic
85C22×C199#13511yescharacteristic
86C22×C199#13511yescharacteristic
87C2×D199—41no—
88C2×D199—41no—
89C2×D199—41no—
90C4×C199—21no—
91C4×C199—21no—
92C4×C199—41no—
93C4×C199—41no—
94C4×C199—81no—
95Dic199—21no—
96Dic199—21no—
97Dic199—21no—
98Dic199—21no—
99Dic199—41no—
100Dic199—81no—
101C2×C199—21no—
102C2×C199—21no—
103C2×C199#41011yescharacteristic
104C2×C199#41611yescharacteristic
105C2×C199#42111yescharacteristic
106D199—81no—
107C199#152111yescharacteristic, complemented, Sylow
108#1521—1991nomaximal, Sylow
109#529—1991no—
110#431—1991no—
111#383—1991no—
112#328—1991no—
113#328D19911yescharacteristic, complemented
114#327—1991no—
115#327—1991no—
116#126—3981no—
117#125—1991no—
118#124—1991no—
119#123—3981no—
120C22⋊Q8C2×D19911yescharacteristic
121#121—1991no—
122C4×Q8—1991no—
123C4×D4—3981no—
124C4×D4—1991no—
125#117—3981no—
126C2×C42—1991no—
127C4⋊C8—3981no—
128C22⋊C8—1991no—
129C22⋊C8C2×D19911yescharacteristic
130C4×C8—3981no—
131#95—3981no—
132#95—3981no—
133#95—1991no—
134#95C2×D19911yescharacteristic
135C2×Q8C4×D19911yescharacteristic
136C2×D4—3981no—
137C2×D4—1991no—
138C22×C4—21no—
139C22×C4—3981no—
140C22×C4—3981no—
141C22×C4—1991no—
142C22×C4—1991no—
143C22×C4C22×D19911yescharacteristic
144C2×C8—21no—
145C2×C8—3981no—
146C4⋊C4—21no—
147C4⋊C4—3981no—
148C4⋊C4—3981no—
149C4⋊C4—3981no—
150C4⋊C4—1991no—
151C4⋊C4C4×D19911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3981no—
154C22⋊C4—3981no—
155C22⋊C4—3981no—
156C22⋊C4—3981no—
157C42—3981no—
158C42—1991no—
159C42—1991no—
160C42—1991no—
161C42—1991no—
162C23—3981no—
163C23D4×D19911yescharacteristic
164Q8—41no—
165D4—7961no—
166D4—7961no—
167D4—7961no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—7962no—
175C2×C4—7961no—
176C2×C4—7961no—
177C2×C4—7961no—
178C2×C4—7961no—
179C2×C4—3981no—
180C2×C4—3981no—
181C2×C4—3981no—
182C2×C4—1991no—
183C2×C4—1991no—
184C2×C4—1991no—
185C2×C4—1991no—
186C2×C4C2×C4×D19911yescharacteristic
187C2×C4D4×D19911yescharacteristic
188C8—41no—
189C8—7961no—
190C22—21no—
191C22—21no—
192C22—7961no—
193C22—7961no—
194C22—7961no—
195C22C22⋊C4×D19911yescharacteristic
196C22#2026397611yescharacteristic
197C22#2026397811yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—7961no—
204C4—15921no—
205C4—3981no—
206C4—3981no—
207C4—3981no—
208C4—3981no—
209C2—21no—
210C2—21no—
211C2—15921no—
212C2#2716399011yescharacteristic
213C2#2716401311yescharacteristic
214C2#2716403311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC22×C4C22×D199
Fitting#328×C199C2
socleC22×C199C2×C22⋊C4
prime radical#20263929C22
cosocleC22×C4×C199C23
hypercenter#328D199
hypocenterC199#1521
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #27164068C2semidirect
3. #27163885C2semidirect
4. #27163755C2semidirect
7. #328×C199C2semidirect
9. #20263946C4semidirect
10. #20263944C4semidirect
13. Q8×Dic199C4semidirect
14. #20263917C4semidirect
107. C199#1521semidirect
113. #328D199semidirect

Maximal subgroups

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

subgroupindex
#271645542
#271640682
#271638852
#271637552
#271637532
#271637512
#328×C1992
#1521199