Finite Group Databasebeta

← #37571531

Subgroups — #37571531

Order 24448.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#27133250C211yesmaximal, characteristic
2#27132993C211yesmaximal, characteristic, complemented
3#27132589C211yesmaximal, characteristic, complemented
4#27132401C211yesmaximal, characteristic, complemented
5#27132397C211yesmaximal, characteristic, complemented
6#27132386C211yesmaximal, characteristic, complemented
7#480×C191C211yesmaximal, characteristic, complemented
8#20259317—21no—
9#20259308—21no—
10#20259306—21no—
11#20259301C2211yescharacteristic
12#20259294—21no—
13#20259290—21no—
14D4×Dic191—21no—
15C2×(C2×D191)⋊C4—21no—
16C2×(C2×D191)⋊C4C2211yescharacteristic
17#20259253—21no—
18#20259245—21no—
19C22⋊(C191⋊C8)C2211yescharacteristic
20C191⋊#95—21no—
21C191⋊#95C2211yescharacteristic
22#121×C191C2211yescharacteristic
23C2×C4⋊C4×C191C2211yescharacteristic
24#107×C191—21no—
25#102×C191—21no—
26C22⋊C8×C191C2211yescharacteristic
27C23×D191D411yescharacteristic
28C2×Dic382D411yescharacteristic
29C2×C22⋊D191—21no—
30C2×C22⋊D191—21no—
31C22×Dic191—21no—
32C22×Dic191—21no—
33C22×Dic191D411yescharacteristic
34C2×C191⋊C8—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191D411yescharacteristic
37Dic191⋊C4—21no—
38C22⋊Dic191—21no—
39C22⋊Dic191—21no—
40(C2×D191)⋊C4—21no—
41(C2×D191)⋊C4—21no—
42(C2×D191)⋊C4—21no—
43(C2×D191)⋊C4—21no—
44(C2×D191)⋊C4—42no—
45C4×Dic191—21no—
46C2×D4×C191—21no—
47C2×D4×C191D411yescharacteristic
48C22×C4×C191—21no—
49C22×C4×C191C2311yescharacteristic
50C2×C8×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191—21no—
53C4⋊C4×C191D411yescharacteristic
54C22⋊C4×C191—21no—
55C22×D191—21no—
56C22×D191—21no—
57C22×D191—21no—
58C22×D191—41no—
59C22×D191—41no—
60Dic382—41no—
61C22⋊D191—81no—
62C22⋊D191—81no—
63C2×Dic191—21no—
64C2×Dic191—21no—
65C2×Dic191—21no—
66C2×Dic191—41no—
67C2×Dic191—41no—
68C2×Dic191—41no—
69C2×Dic191—41no—
70C2×Dic191—81no—
71C191⋊C8—41no—
72C23×C191—21no—
73C23×C191C2×D411yescharacteristic
74D4×C191—41no—
75D4×C191—41no—
76D4×C191—41no—
77C2×C4×C191—21no—
78C2×C4×C191—41no—
79C2×C4×C191—41no—
80C2×C4×C191—41no—
81C2×C4×C191—41no—
82C2×C4×C191C2×D411yescharacteristic
83C2×C4×C191C2×D411yescharacteristic
84C8×C191—41no—
85C22×C191—21no—
86C22×C191—21no—
87C22×C191—41no—
88C22×C191—41no—
89C22×C191—41no—
90C22×C191#12011yescharacteristic
91C22×C191#13511yescharacteristic
92C22×C191AGL(1,ℤ/8)11yescharacteristic
93C2×D191—42no—
94C2×D191—41no—
95C2×D191—41no—
96C2×D191—41no—
97C2×D191—81no—
98C4×C191—21no—
99C4×C191—21no—
100C4×C191—41no—
101C4×C191—81no—
102Dic191—41no—
103Dic191—41no—
104Dic191—41no—
105Dic191—81no—
106C2×C191—21no—
107C2×C191—21no—
108C2×C191—81no—
109C2×C191#44911yescharacteristic
110C2×C191#45511yescharacteristic
111C2×C191#45811yescharacteristic
112D191—81no—
113C191#161211yescharacteristic, complemented, Sylow
114#1612—1911nomaximal, Sylow
115#538—1911no—
116#483—1911no—
117#480D19111yescharacteristic, complemented
118#397—1911no—
119#328—1911no—
120#327—1911no—
121#323—1911no—
122#126—3821no—
123#124—3821no—
124#123—3821no—
125C22⋊Q8—1911no—
126#121—3821no—
127#121C2×D19111yescharacteristic
128#120—3821no—
129C4×D4—3821no—
130C2×C4⋊C4C2×D19111yescharacteristic
131C2×C22⋊C4—3821no—
132C2×C22⋊C4—1911no—
133#107—21no—
134#106—3821no—
135#103—3821no—
136#102—21no—
137C22⋊C8—1911no—
138C22⋊C8C2×D19111yescharacteristic
139#95—3821no—
140#95—1911no—
141C24—1911no—
142C2×Q8—1911no—
143C2×D4—21no—
144C2×D4—3821no—
145C2×D4—3821no—
146C2×D4C22⋊D19111yescharacteristic
147C22×C4—21no—
148C22×C4—3821no—
149C22×C4—3821no—
150C22×C4—1911no—
151C22×C4C22×D19111yescharacteristic
152C2×C8—21no—
153C2×C8—3821no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—3821no—
157C4⋊C4—3821no—
158C4⋊C4—1911no—
159C4⋊C4C22⋊D19111yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—3821no—
162C22⋊C4—3821no—
163C22⋊C4—3821no—
164C22⋊C4—3821no—
165C22⋊C4—3821no—
166C22⋊C4—3821no—
167C22⋊C4—7642no—
168C42—3821no—
169C23—21no—
170C23—3821no—
171C23—3821no—
172C23—3821no—
173C23—7641no—
174C23—7641no—
175C23D4×D19111yescharacteristic
176Q8—7641no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—15281no—
181D4—15281no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—3821no—
188C2×C4—3821no—
189C2×C4—3821no—
190C2×C4—15281no—
191C2×C4—7641no—
192C2×C4—7641no—
193C2×C4—7641no—
194C2×C4—7641no—
195C2×C4D4×D19111yescharacteristic
196C2×C4C2×C22⋊D19111yescharacteristic
197C8—41no—
198C8—7641no—
199C22—21no—
200C22—21no—
201C22—41no—
202C22—41no—
203C22—41no—
204C22—15281no—
205C22—7642no—
206C22—7641no—
207C22—7641no—
208C22—7641no—
209C22#2025929011yescharacteristic
210C22#2025934111yescharacteristic
211C22#2025934611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—15281no—
217C4—7641no—
218C4—7641no—
219C4—7641no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—15281no—
224C2#2713280511yescharacteristic
225C2#2713283911yescharacteristic
226C2#2713285211yescharacteristic
subgroupG/H
centerC22#20259290
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#480×C191C2
socleC22×C191#120
prime radical#27133250C2
hypercenter#480D191
hypocenterC191#1612
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #27132993C2semidirect
3. #27132589C2semidirect
4. #27132401C2semidirect
5. #27132397C2semidirect
6. #27132386C2semidirect
7. #480×C191C2semidirect
113. C191#1612semidirect
117. #480D191semidirect

Maximal subgroups

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

subgroupindex
#271332502
#271329932
#271325892
#271324012
#271323972
#271323862
#480×C1912
#1612191