Finite Group Databasebeta

← #38767424

Subgroups — #38767424

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#27164549C211yesmaximal, characteristic
2#27164068C211yesmaximal, characteristic, complemented
3#27163885C211yesmaximal, characteristic, complemented
4#27163756C211yesmaximal, characteristic, complemented
5#27163754C211yesmaximal, characteristic, complemented
6#27163752C211yesmaximal, characteristic
7#327×C199C211yesmaximal, characteristic
8#20263948—21no—
9#20263946C411yescharacteristic, complemented
10#20263942C411yescharacteristic, complemented
11#20263936—21no—
12#20263934C2211yescharacteristic
13#20263920C411yescharacteristic, complemented
14D4×Dic199—21no—
15D4×Dic199C411yescharacteristic, complemented
16#20263911—21no—
17C2×C4×Dic199C2211yescharacteristic
18Dic199⋊C8—21no—
19C22⋊(C199⋊C8)C2211yescharacteristic
20C8×Dic199—21no—
21C199⋊#95—21no—
22C199⋊#95—21no—
23C199⋊#95C2211yescharacteristic
24#121×C199C2211yescharacteristic
25C22⋊C8×C199C2211yescharacteristic
26#95×C199C2211yescharacteristic
27C2×Dic398C2×C411yescharacteristic
28C22×Dic199—21no—
29C22×Dic199—21no—
30C22×Dic199D411yescharacteristic
31C22×Dic199D411yescharacteristic
32C2×C199⋊C8—21no—
33C4⋊Dic199—21no—
34C4⋊Dic199C2×C411yescharacteristic
35Dic199⋊C4—21no—
36Dic199⋊C4—21no—
37Dic199⋊C4—21no—
38C22⋊Dic199—21no—
39C22⋊Dic199—21no—
40C22⋊Dic199—21no—
41C22⋊Dic199—21no—
42C4×Dic199—21no—
43C4×Dic199C2×C411yescharacteristic
44C4×Dic199C2×C411yescharacteristic
45C4×Dic199D411yescharacteristic
46C4×Dic199D411yescharacteristic
47C2×D4×C199—21no—
48C2×D4×C199C2×C411yescharacteristic
49C22×C4×C199—21no—
50C22×C4×C199C2311yescharacteristic
51C2×C8×C199—21no—
52C4⋊C4×C199C2×C411yescharacteristic
53C22⋊C4×C199—21no—
54Dic398—41no—
55C2×Dic199—21no—
56C2×Dic199—21no—
57C2×Dic199—21no—
58C2×Dic199—21no—
59C2×Dic199—41no—
60C2×Dic199—42no—
61C2×Dic199—41no—
62C2×Dic199—41no—
63C2×Dic199—41no—
64C2×Dic199C22⋊C411yescharacteristic
65C2×Dic199C22⋊C411yescharacteristic
66C2×Dic199C22⋊C411yescharacteristic
67C2×Dic199C22⋊C411yescharacteristic
68C199⋊C8—41no—
69C23×C199—21no—
70C23×C199C2×D411yescharacteristic
71D4×C199—41no—
72D4×C199—41no—
73D4×C199—41no—
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×C199—41no—
85C22×C199—41no—
86C22×C199—41no—
87C22×C199C2×C22⋊C411yescharacteristic
88C22×C199#13511yescharacteristic
89C22×C199#13511yescharacteristic
90C4×C199—21no—
91C4×C199—21no—
92C4×C199—41no—
93C4×C199—81no—
94Dic199—21no—
95Dic199—21no—
96Dic199—21no—
97Dic199—21no—
98Dic199—41no—
99Dic199—41no—
100Dic199—81no—
101C2×C199—21no—
102C2×C199—21no—
103C2×C199—81no—
104C2×C199#41011yescharacteristic
105C2×C199#41611yescharacteristic
106C2×C199#42111yescharacteristic
107C199#152111yescharacteristic, complemented, Sylow
108#1521—1991nomaximal, Sylow
109#529—1991no—
110#431—1991no—
111#383—1991no—
112#328—1991no—
113#328—1991no—
114#327—1991no—
115#327D19911yescharacteristic
116#126—3981no—
117#125—1991no—
118#124—1991no—
119#123—3981no—
120C22⋊Q8—1991no—
121#121C2×D19911yescharacteristic
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×Q8—1991no—
136C2×D4—21no—
137C2×D4C4×D19911yescharacteristic
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—3981no—
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—21no—
163C23D4×D19911yescharacteristic
164Q8—7961no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—7962no—
174C2×C4—7961no—
175C2×C4—7961no—
176C2×C4—7961no—
177C2×C4—7961no—
178C2×C4—3981no—
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—41no—
193C22—41no—
194C22—41no—
195C22C22⋊C4×D19911yescharacteristic
196C22#2026397411yescharacteristic
197C22#2026397611yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—81no—
202C4—7961no—
203C4—7961no—
204C4—15921no—
205C4—3981no—
206C4—3981no—
207C4—3981no—
208C4—3981no—
209C2—21no—
210C2—21no—
211C2—81no—
212C2#2716399011yescharacteristic
213C2#2716401111yescharacteristic
214C2#2716403311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D199
commutatorC2×C4×C199C22×C4
FrattiniC22×C4C22×D199
Fitting#327×C199C2
socleC22×C199C2×C22⋊C4
prime radical#121×C199C22
cosocleC22×C4×C199C23
hypercenter#327D199
hypocenterC199#1521
LCSG ▷ C2×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #27164068C2semidirect
3. #27163885C2semidirect
4. #27163756C2semidirect
5. #27163754C2semidirect
9. #20263946C4semidirect
10. #20263942C4semidirect
13. #20263920C4semidirect
15. D4×Dic199C4semidirect
107. C199#1521semidirect

Maximal subgroups

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

subgroupindex
#271645492
#271640682
#271638852
#271637562
#271637542
#271637522
#327×C1992
#1521199