Finite Group Databasebeta

← #37571096

Subgroups — #37571096

Order 24448.

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#27133199C211yesmaximal, characteristic
2#27132713C211yesmaximal, characteristic, complemented
3#27132530C211yesmaximal, characteristic, complemented
4#27132400C211yesmaximal, characteristic, complemented
5#27132398C211yesmaximal, characteristic
6#27132396C211yesmaximal, characteristic
7#328×C191C211yesmaximal, characteristic, complemented
8#20259317—21no—
9#20259313C411yescharacteristic, complemented
10#20259311C411yescharacteristic, complemented
11#20259306—21no—
12#20259296C2211yescharacteristic
13Q8×Dic191C411yescharacteristic, complemented
14#20259284C411yescharacteristic, complemented
15(C22⋊D191)⋊C4—21no—
16#20259280—21no—
17C2×C4×Dic191C2211yescharacteristic
18Dic191⋊C8—21no—
19C22⋊(C191⋊C8)C2211yescharacteristic
20C8×Dic191—21no—
21C191⋊#95—21no—
22C191⋊#95—21no—
23C191⋊#95C2211yescharacteristic
24C22⋊Q8×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27C2×D764C2×C411yescharacteristic
28C2×C22⋊D191—21no—
29C22×Dic191—21no—
30C22×Dic191D411yescharacteristic
31C22×Dic191D411yescharacteristic
32C2×C4×D191—21no—
33C2×C191⋊C8—21no—
34C4⋊Dic191—21no—
35C4⋊Dic191—21no—
36C4⋊Dic191C2×C411yescharacteristic
37Dic191⋊C4—21no—
38(C2×D191)⋊C4—21no—
39(C2×D191)⋊C4—21no—
40(C2×D191)⋊C4—21no—
41(C2×D191)⋊C4—21no—
42C4×Dic191—21no—
43C4×Dic191C2×C411yescharacteristic
44C4×Dic191C2×C411yescharacteristic
45C4×Dic191D411yescharacteristic
46C4×Dic191D411yescharacteristic
47C2×Q8×C191C2×C411yescharacteristic
48C22×C4×C191—21no—
49C22×C4×C191C2311yescharacteristic
50C2×C8×C191—21no—
51C4⋊C4×C191—21no—
52C4⋊C4×C191C2×C411yescharacteristic
53C22⋊C4×C191—21no—
54C22×D191—21no—
55D764—41no—
56C22⋊D191—41no—
57C22⋊D191—41no—
58C2×Dic191—21no—
59C2×Dic191—21no—
60C2×Dic191—21no—
61C2×Dic191—41no—
62C2×Dic191—41no—
63C2×Dic191—41no—
64C2×Dic191—41no—
65C2×Dic191C22⋊C411yescharacteristic
66C2×Dic191C22⋊C411yescharacteristic
67C2×Dic191C22⋊C411yescharacteristic
68C2×Dic191C22⋊C411yescharacteristic
69C4×D191—42no—
70C191⋊C8—41no—
71C23×C191C2×D411yescharacteristic
72Q8×C191—41no—
73C2×C4×C191—21no—
74C2×C4×C191—21no—
75C2×C4×C191—41no—
76C2×C4×C191—41no—
77C2×C4×C191—41no—
78C2×C4×C191—41no—
79C2×C4×C191C22×C411yescharacteristic
80C2×C4×C191C2×D411yescharacteristic
81C8×C191—41no—
82C22×C191—21no—
83C22×C191—21no—
84C22×C191C2×C22⋊C411yescharacteristic
85C22×C191#13511yescharacteristic
86C22×C191#13511yescharacteristic
87C2×D191—41no—
88C2×D191—41no—
89C2×D191—41no—
90C4×C191—21no—
91C4×C191—21no—
92C4×C191—41no—
93C4×C191—41no—
94C4×C191—81no—
95Dic191—21no—
96Dic191—21no—
97Dic191—21no—
98Dic191—21no—
99Dic191—41no—
100Dic191—81no—
101C2×C191—21no—
102C2×C191—21no—
103C2×C191#41011yescharacteristic
104C2×C191#41611yescharacteristic
105C2×C191#42111yescharacteristic
106D191—81no—
107C191#152111yescharacteristic, complemented, Sylow
108#1521—1911nomaximal, Sylow
109#529—1911no—
110#431—1911no—
111#383—1911no—
112#328—1911no—
113#328D19111yescharacteristic, complemented
114#327—1911no—
115#327—1911no—
116#126—3821no—
117#125—1911no—
118#124—1911no—
119#123—3821no—
120C22⋊Q8C2×D19111yescharacteristic
121#121—1911no—
122C4×Q8—1911no—
123C4×D4—3821no—
124C4×D4—1911no—
125#117—3821no—
126C2×C42—1911no—
127C4⋊C8—3821no—
128C22⋊C8—1911no—
129C22⋊C8C2×D19111yescharacteristic
130C4×C8—3821no—
131#95—3821no—
132#95—3821no—
133#95—1911no—
134#95C2×D19111yescharacteristic
135C2×Q8C4×D19111yescharacteristic
136C2×D4—3821no—
137C2×D4—1911no—
138C22×C4—21no—
139C22×C4—3821no—
140C22×C4—3821no—
141C22×C4—1911no—
142C22×C4—1911no—
143C22×C4C22×D19111yescharacteristic
144C2×C8—21no—
145C2×C8—3821no—
146C4⋊C4—21no—
147C4⋊C4—3821no—
148C4⋊C4—3821no—
149C4⋊C4—3821no—
150C4⋊C4—1911no—
151C4⋊C4C4×D19111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3821no—
154C22⋊C4—3821no—
155C22⋊C4—3821no—
156C22⋊C4—3821no—
157C42—3821no—
158C42—1911no—
159C42—1911no—
160C42—1911no—
161C42—1911no—
162C23—3821no—
163C23D4×D19111yescharacteristic
164Q8—41no—
165D4—7641no—
166D4—7641no—
167D4—7641no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3821no—
175C2×C4—3821no—
176C2×C4—3821no—
177C2×C4—1911no—
178C2×C4—1911no—
179C2×C4—1911no—
180C2×C4—1911no—
181C2×C4—7642no—
182C2×C4—7641no—
183C2×C4—7641no—
184C2×C4—7641no—
185C2×C4—7641no—
186C2×C4C2×C4×D19111yescharacteristic
187C2×C4D4×D19111yescharacteristic
188C8—41no—
189C8—7641no—
190C22—21no—
191C22—21no—
192C22—7641no—
193C22—7641no—
194C22—7641no—
195C22C22⋊C4×D19111yescharacteristic
196C22#2025934311yescharacteristic
197C22#2025934511yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—3821no—
204C4—3821no—
205C4—3821no—
206C4—3821no—
207C4—15281no—
208C4—7641no—
209C2—21no—
210C2—21no—
211C2—15281no—
212C2#2713263511yescharacteristic
213C2#2713265811yescharacteristic
214C2#2713267811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D191
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#328×C191C2
socleC22×C191C2×C22⋊C4
prime radical#20259296C22
cosocleC22×C4×C191C23
hypercenter#328D191
hypocenterC191#1521
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #27132713C2semidirect
3. #27132530C2semidirect
4. #27132400C2semidirect
7. #328×C191C2semidirect
9. #20259313C4semidirect
10. #20259311C4semidirect
13. Q8×Dic191C4semidirect
14. #20259284C4semidirect
107. C191#1521semidirect
113. #328D191semidirect

Maximal subgroups

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

subgroupindex
#271331992
#271327132
#271325302
#271324002
#271323982
#271323962
#328×C1912
#1521191