Finite Group Databasebeta

← #38767864

Subgroups — #38767864

Order 25472.

232 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 53 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#27164346C211yesmaximal, characteristic, complemented
2#27164329C211yesmaximal, characteristic, complemented
3#27163943C211yesmaximal, characteristic, complemented
4#27163755C211yesmaximal, characteristic, complemented
5#27163752C211yesmaximal, characteristic, complemented
6#27163742C211yesmaximal, characteristic, complemented
7#538×C199C211yesmaximal, characteristic
8C2×C4⋊Dic199C2211yescharacteristic
9C2×C22⋊Dic199—21no—
10#20263888—21no—
11#20263886—21no—
12#20263879—21no—
13#20263876—21no—
14C22⋊(C199⋊C8)C2211yescharacteristic
15C22⋊(C199⋊C8)C2211yescharacteristic
16C199⋊#95—21no—
17C199⋊#95C2211yescharacteristic
18#126×C199—21no—
19#124×C199—21no—
20#123×C199—21no—
21C22⋊Q8×C199C2211yescharacteristic
22#121×C199—21no—
23#121×C199C2211yescharacteristic
24#120×C199—21no—
25C4×D4×C199—21no—
26C2×C22⋊C4×C199C2211yescharacteristic
27C22×Dic199—21no—
28C22×Dic199—21no—
29C2×C199⋊C8—21no—
30C2×C199⋊C8—21no—
31C4⋊Dic199—21no—
32C4⋊Dic199—21no—
33C22⋊Dic199—42no—
34C24×C199D411yescharacteristic
35C2×Q8×C199D411yescharacteristic
36C2×D4×C199—21no—
37C2×D4×C199—21no—
38C2×D4×C199—21no—
39C2×D4×C199D411yescharacteristic
40C22×C4×C199—21no—
41C22×C4×C199D411yescharacteristic
42C22×C4×C199C2311yescharacteristic
43C4⋊C4×C199—21no—
44C4⋊C4×C199—21no—
45C4⋊C4×C199D411yescharacteristic
46C4⋊C4×C199D411yescharacteristic
47C22⋊C4×C199—21no—
48C22⋊C4×C199—21no—
49C22⋊C4×C199—21no—
50C22⋊C4×C199—21no—
51C22⋊C4×C199—21no—
52C22⋊C4×C199—21no—
53C22⋊C4×C199—21no—
54C42×C199—21no—
55C2×Dic199—41no—
56C2×Dic199—41no—
57C2×Dic199—41no—
58C2×Dic199—41no—
59C2×Dic199—41no—
60C2×Dic199—41no—
61C199⋊C8—41no—
62C199⋊C8—41no—
63C23×C199—21no—
64C23×C199—21no—
65C23×C199—21no—
66C23×C199—21no—
67C23×C199—41no—
68C23×C199—41no—
69C23×C199C2×D411yescharacteristic
70Q8×C199—41no—
71D4×C199—41no—
72D4×C199—41no—
73D4×C199—41no—
74D4×C199—81no—
75D4×C199—81no—
76C2×C4×C199—21no—
77C2×C4×C199—21no—
78C2×C4×C199—21no—
79C2×C4×C199—21no—
80C2×C4×C199—41no—
81C2×C4×C199—41no—
82C2×C4×C199—81no—
83C2×C4×C199C2×D411yescharacteristic
84C2×C4×C199C2×D411yescharacteristic
85C22×C199—21no—
86C22×C199—21no—
87C22×C199—42no—
88C22×C199—41no—
89C22×C199—41no—
90C22×C199—41no—
91C22×C199—41no—
92C22×C199—41no—
93C22×C199—41no—
94C22×C199—81no—
95C22×C199#12011yescharacteristic
96C22×C199#13511yescharacteristic
97C22×C199AGL(1,ℤ/8)11yescharacteristic
98C4×C199—21no—
99C4×C199—21no—
100C4×C199—41no—
101C4×C199—41no—
102C4×C199—41no—
103C4×C199—41no—
104Dic199—81no—
105Dic199—81no—
106C2×C199—21no—
107C2×C199—21no—
108C2×C199—81no—
109C2×C199—81no—
110C2×C199#44911yescharacteristic
111C2×C199#45511yescharacteristic
112C2×C199#45811yescharacteristic
113C199#161211yescharacteristic, complemented, Sylow
114#1612—1991nomaximal, Sylow
115#538D19911yescharacteristic
116#483—1991no—
117#480—1991no—
118#397—1991no—
119#328—1991no—
120#327—1991no—
121#323—1991no—
122#126—21no—
123#124—21no—
124#123—21no—
125C22⋊Q8C2×D19911yescharacteristic
126#121—21no—
127#121C2×D19911yescharacteristic
128#120—21no—
129C4×D4—21no—
130C2×C4⋊C4—1991no—
131C2×C22⋊C4—3981no—
132C2×C22⋊C4C2×D19911yescharacteristic
133#107—3981no—
134#106—3981no—
135#103—3981no—
136#102—3981no—
137C22⋊C8—1991no—
138C22⋊C8—1991no—
139#95—3981no—
140#95—1991no—
141C24C22⋊D19911yescharacteristic
142C2×Q8C22⋊D19911yescharacteristic
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C22⋊D19911yescharacteristic
147C22×C4—21no—
148C22×C4—3981no—
149C22×C4—3981no—
150C22×C4C22⋊D19911yescharacteristic
151C22×C4C22×D19911yescharacteristic
152C2×C8—3981no—
153C2×C8—3981no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—3981no—
157C4⋊C4—3981no—
158C4⋊C4C22⋊D19911yescharacteristic
159C4⋊C4C22⋊D19911yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—7962no—
168C42—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23C2×C22⋊D19911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—81no—
181D4—81no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—7961no—
190C2×C4—7961no—
191C2×C4—7961no—
192C2×C4—7961no—
193C2×C4—7961no—
194C2×C4—7961no—
195C2×C4C2×C22⋊D19911yescharacteristic
196C2×C4C2×C22⋊D19911yescharacteristic
197C8—7961no—
198C8—7961no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22#2026392411yescharacteristic
210C22#2026397511yescharacteristic
211C22#2026398011yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—15921no—
219C4—15921no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—81no—
224C2#2716416311yescharacteristic
225C2#2716419611yescharacteristic
226C2#2716420811yescharacteristic
subgroupG/H
centerC22#20263924
commutator, cosocleC22×C4×C199C23
FrattiniC22×C4C22×D199
Fitting, prime radical#538×C199C2
socleC22×C199#120
hypercenter#538D199
hypocenterC199#1612
LCSG ▷ C22×C4×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #27164346C2semidirect
2. #27164329C2semidirect
3. #27163943C2semidirect
4. #27163755C2semidirect
5. #27163752C2semidirect
6. #27163742C2semidirect
113. C199#1612semidirect

Maximal subgroups

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

subgroupindex
#271643462
#271643292
#271639432
#271637552
#271637522
#271637422
#538×C1992
#1612199