Finite Group Databasebeta

← #37571536

Subgroups — #37571536

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#27133251C211yesmaximal, characteristic
2#27132994C211yesmaximal, characteristic, complemented
3#27132977C211yesmaximal, characteristic, complemented
4#27132588C211yesmaximal, characteristic, complemented
5#27132401C211yesmaximal, characteristic, complemented
6#27132398C211yesmaximal, characteristic, complemented
7#323×C191C211yesmaximal, characteristic, complemented
8#20259315—21no—
9#20259308—21no—
10#20259304—21no—
11#20259301C2211yescharacteristic
12#20259296C2211yescharacteristic
13#20259295—21no—
14#20259291—21no—
15C4×C22⋊D191—21no—
16C2×C4⋊Dic191C2211yescharacteristic
17C2×C22⋊Dic191—21no—
18#20259256—21no—
19#20259254—21no—
20#20259247—21no—
21#20259244—21no—
22C191⋊#95—21no—
23C191⋊#95C2211yescharacteristic
24C2×C22⋊C4×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26C22⋊C8×C191C2211yescharacteristic
27C2×Dic382D411yescharacteristic
28C2×D764D411yescharacteristic
29C2×C22⋊D191—21no—
30C2×C22⋊D191—21no—
31C2×C22⋊D191—21no—
32C22×Dic191—21no—
33C22×Dic191—21no—
34C2×C4×D191—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191—21no—
37C4⋊Dic191D411yescharacteristic
38C4⋊Dic191D411yescharacteristic
39Dic191⋊C4—21no—
40Dic191⋊C4—21no—
41C22⋊Dic191—21no—
42C22⋊Dic191—21no—
43C22⋊Dic191—21no—
44C22⋊Dic191—42no—
45(C2×D191)⋊C4—21no—
46(C2×D191)⋊C4—21no—
47C4×Dic191—21no—
48C24×C191D411yescharacteristic
49C22×C4×C191D411yescharacteristic
50C22×C4×C191C2311yescharacteristic
51C2×C8×C191—21no—
52C2×C8×C191—21no—
53C22⋊C4×C191—21no—
54C22⋊C4×C191—21no—
55C22×D191—21no—
56Dic382—41no—
57D764—41no—
58C22⋊D191—41no—
59C22⋊D191—41no—
60C22⋊D191—81no—
61C22⋊D191—81no—
62C2×Dic191—21no—
63C2×Dic191—21no—
64C2×Dic191—21no—
65C2×Dic191—41no—
66C2×Dic191—41no—
67C2×Dic191—41no—
68C2×Dic191—41no—
69C2×Dic191—41no—
70C2×Dic191—41no—
71C4×D191—81no—
72C23×C191—21no—
73C23×C191—21no—
74C23×C191—21no—
75C23×C191—41no—
76C23×C191—41no—
77C23×C191C2×D411yescharacteristic
78C2×C4×C191—21no—
79C2×C4×C191—41no—
80C2×C4×C191—41no—
81C2×C4×C191C2×D411yescharacteristic
82C2×C4×C191C2×D411yescharacteristic
83C8×C191—41no—
84C8×C191—41no—
85C22×C191—21no—
86C22×C191—21no—
87C22×C191—42no—
88C22×C191—41no—
89C22×C191—41no—
90C22×C191—41no—
91C22×C191—81no—
92C22×C191#12011yescharacteristic
93C22×C191#13511yescharacteristic
94C22×C191AGL(1,ℤ/8)11yescharacteristic
95C2×D191—41no—
96C2×D191—41no—
97C2×D191—41no—
98C4×C191—21no—
99C4×C191—21no—
100C4×C191—41no—
101Dic191—41no—
102Dic191—41no—
103Dic191—41no—
104Dic191—81no—
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#480—1911no—
118#397—1911no—
119#328—1911no—
120#327—1911no—
121#323D19111yescharacteristic, complemented
122#126—3821no—
123#124—3821no—
124#123—3821no—
125C22⋊Q8—1911no—
126#121—3821no—
127#121—1911no—
128#120—3821no—
129C4×D4—3821no—
130C2×C4⋊C4—1911no—
131C2×C22⋊C4—3821no—
132C2×C22⋊C4C2×D19111yescharacteristic
133#107—3821no—
134#106—3821no—
135#103—3821no—
136#102—3821no—
137C22⋊C8C2×D19111yescharacteristic
138C22⋊C8C2×D19111yescharacteristic
139#95—3821no—
140#95—1911no—
141C24D76411yescharacteristic
142C2×Q8—1911no—
143C2×D4—3821no—
144C2×D4—3821no—
145C2×D4—3821no—
146C2×D4—1911no—
147C22×C4—3821no—
148C22×C4—3821no—
149C22×C4—3821no—
150C22×C4D76411yescharacteristic
151C22×C4C22×D19111yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—3821no—
155C4⋊C4—3821no—
156C4⋊C4—3821no—
157C4⋊C4—3821no—
158C4⋊C4—1911no—
159C4⋊C4—1911no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—3821no—
163C22⋊C4—3821no—
164C22⋊C4—3821no—
165C22⋊C4—3821no—
166C22⋊C4—3821no—
167C22⋊C4—7642no—
168C42—3821no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—3821no—
175C23C2×D76411yescharacteristic
176Q8—7641no—
177D4—15281no—
178D4—15281no—
179D4—7641no—
180D4—7641no—
181D4—7641no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—3821no—
186C2×C4—3821no—
187C2×C4—3821no—
188C2×C4—15281no—
189C2×C4—7641no—
190C2×C4—7641no—
191C2×C4—7641no—
192C2×C4—7641no—
193C2×C4—7641no—
194C2×C4—7641no—
195C2×C4D4×D19111yescharacteristic
196C2×C4D4×D19111yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—7641no—
207C22—7641no—
208C22—7641no—
209C22#2025929211yescharacteristic
210C22#2025934411yescharacteristic
211C22#2025935011yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—15281no—
216C4—15281no—
217C4—7641no—
218C4—7641no—
219C4—7641no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—15281no—
224C2#2713281011yescharacteristic
225C2#2713284311yescharacteristic
226C2#2713285411yescharacteristic
subgroupG/H
centerC22#20259292
commutator, cosocleC22×C4×C191C23
FrattiniC22×C4C22×D191
Fitting#323×C191C2
socleC22×C191#120
prime radical#27133251C2
hypercenter#323D191
hypocenterC191#1612
LCSG ▷ C22×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #27132994C2semidirect
3. #27132977C2semidirect
4. #27132588C2semidirect
5. #27132401C2semidirect
6. #27132398C2semidirect
7. #323×C191C2semidirect
113. C191#1612semidirect
121. #323D191semidirect

Maximal subgroups

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

subgroupindex
#271332512
#271329942
#271329772
#271325882
#271324012
#271323982
#323×C1912
#1612191