Finite Group Databasebeta

← #37571025

Subgroups — #37571025

Order 24448.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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#27133174C211yesmaximal, characteristic
2C2×C191⋊#95C211yesmaximal, characteristic, complemented
3#27132401C212yesmaximal, complemented
4#27132398C212yesmaximal, complemented
5#407×C191C211yesmaximal, characteristic, complemented
6C2×#15690287C411yescharacteristic, complemented
7C23×Dic191—21no—
8#20259305—21no—
9#20259301C411yescharacteristic, complemented
10#20259301C2211yescharacteristic
11#20259296C411yescharacteristic, complemented
12#20259296C2211yescharacteristic
13#20259291—21no—
14C4×C22⋊D191—21no—
15C4×C22⋊D191—21no—
16#20259281C411yescharacteristic, complemented
17C191⋊#95—21no—
18C191⋊#95C2212yes—
19C23×C4×C191C2211yescharacteristic
20C2×M16×C191—21no—
21C22⋊C8×C191—21no—
22C22⋊C8×C191C2212yes—
23#15690287—42no—
24C2×Dic382C2×C411yescharacteristic, complemented
25C2×D764C2×C411yescharacteristic, complemented
26C2×C22⋊D191—21no—
27C2×C22⋊D191—21no—
28C2×C22⋊D191—21no—
29C22×Dic191—24no—
30C22×Dic191—22no—
31C22×Dic191—42no—
32C22×Dic191—42no—
33C2×C4×D191—21no—
34C4⋊Dic191C2×C411yescharacteristic, complemented
35C4⋊Dic191C2×C411yescharacteristic, complemented
36Dic191⋊C4—21no—
37Dic191⋊C4—21no—
38C22⋊Dic191—21no—
39C22⋊Dic191—21no—
40C22⋊Dic191—21no—
41(C2×D191)⋊C4—21no—
42(C2×D191)⋊C4—21no—
43C4×Dic191—21no—
44C24×C191D411yescharacteristic
45C22×C4×C191—42no—
46C22×C4×C191C2×C411yescharacteristic
47C22×C4×C191C2×C411yescharacteristic
48C22×C4×C191D411yescharacteristic
49C22×C4×C191D411yescharacteristic
50C22×C4×C191D411yescharacteristic
51C22×C4×C191C2311yescharacteristic
52M16×C191—42no—
53C2×C8×C191—22no—
54C22×D191—21no—
55Dic382—41no—
56D764—41no—
57C22⋊D191—42no—
58C22⋊D191—42no—
59C22⋊D191—41no—
60C22⋊D191—41no—
61C2×Dic191—24no—
62C2×Dic191—21no—
63C2×Dic191—21no—
64C2×Dic191—21no—
65C2×Dic191—48no—
66C2×Dic191—42no—
67C2×Dic191—42no—
68C4×D191—42no—
69C23×C191—22no—
70C23×C191—22no—
71C23×C191—21no—
72C23×C191—21no—
73C23×C191C22⋊C411yescharacteristic
74C23×C191C22⋊C411yescharacteristic
75C23×C191C2×D411yescharacteristic
76C2×C4×C191—22no—
77C2×C4×C191—22no—
78C2×C4×C191—41no—
79C2×C4×C191—41no—
80C2×C4×C191—41no—
81C2×C4×C191—41no—
82C2×C4×C191C22⋊C411yescharacteristic
83C2×C4×C191C22⋊C411yescharacteristic
84C2×C4×C191C22×C411yescharacteristic
85C2×C4×C191C2×D411yescharacteristic
86C8×C191—42no—
87C22×C191—24no—
88C22×C191—24no—
89C22×C191—21no—
90C22×C191—21no—
91C22×C191—21no—
92C22×C191—21no—
93C22×C191—21no—
94C22×C191—21no—
95C22×C191#9912yes—
96C22×C191#10412yes—
97C22×C191C2×C22⋊C411yescharacteristic
98C22×C191AGL(1,ℤ/8)11yescharacteristic
99C22×C191#13711yescharacteristic
100C2×D191—41no—
101C2×D191—41no—
102C2×D191—41no—
103C4×C191—21no—
104C4×C191—21no—
105C4×C191—21no—
106C4×C191—21no—
107Dic191—44no—
108Dic191—41no—
109Dic191—41no—
110Dic191—41no—
111C2×C191—21no—
112C2×C191—22no—
113C2×C191—22no—
114C2×C191—21no—
115C2×C191C2×#9911yescharacteristic
116C2×C191#41711yescharacteristic
117C2×C191C2×#10411yescharacteristic
118D191—81no—
119C191#150411yescharacteristic, complemented, Sylow
120#1504—1911nomaximal, Sylow
121#525—1911no—
122#407D19111yescharacteristic, complemented
123C2×#95—1911no—
124#328—1912no—
125#327—1912no—
126C2×#41—1911no—
127C23×C4—3821no—
128C23×C4C2×D19111yescharacteristic
129C2×M16—21no—
130#123—3821no—
131C22⋊Q8—1911no—
132C22⋊Q8—1911no—
133#121—1911no—
134#121—1911no—
135#120—3821no—
136C4×D4—3821no—
137C4×D4—3821no—
138#117—1911no—
139C22⋊C8—21no—
140C22⋊C8C2×D19112yes—
141#95—3821no—
142#95—1912no—
143C24D76411yescharacteristic
144#41—7642no—
145C2×Q8—1911no—
146C2×D4—3821no—
147C2×D4—3821no—
148C2×D4—3821no—
149C2×D4—1911no—
150C22×C4—42no—
151C22×C4—3824no—
152C22×C4—3822no—
153C22×C4—3821no—
154C22×C4—7642no—
155C22×C4—7642no—
156C22×C4C4×D19111yescharacteristic
157C22×C4C4×D19111yescharacteristic
158C22×C4C22⋊D19111yescharacteristic
159C22×C4C22⋊D19111yescharacteristic
160C22×C4D76411yescharacteristic
161C22×C4C22×D19111yescharacteristic
162M16—42no—
163C2×C8—22no—
164C4⋊C4—3821no—
165C4⋊C4—3821no—
166C4⋊C4—1911no—
167C4⋊C4—1911no—
168C22⋊C4—3821no—
169C22⋊C4—3821no—
170C22⋊C4—3821no—
171C22⋊C4—3821no—
172C22⋊C4—3821no—
173C42—3821no—
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23—3821no—
179C23(C2×D191)⋊C411yescharacteristic
180C23(C2×D191)⋊C411yescharacteristic
181C23C2×D76411yescharacteristic
182Q8—7641no—
183D4—7641no—
184D4—7641no—
185D4—7641no—
186D4—7642no—
187D4—7642no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—3824no—
195C2×C4—3821no—
196C2×C4—3821no—
197C2×C4—3821no—
198C2×C4—7642no—
199C2×C4—7648no—
200C2×C4—7642no—
201C2×C4—7642no—
202C2×C4(C2×D191)⋊C411yescharacteristic
203C2×C4(C2×D191)⋊C411yescharacteristic
204C2×C4C2×C4×D19111yescharacteristic
205C2×C4C2×C22⋊D19111yescharacteristic
206C8—42no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—7641no—
216C22—7641no—
217C22—7641no—
218C22#2025923612yes—
219C22#2025924812yes—
220C22C2×(C2×D191)⋊C411yescharacteristic
221C22#2025935011yescharacteristic
222C22#2025935511yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—7644no—
228C4—7641no—
229C4—7641no—
230C4—7641no—
231C2—21no—
232C2—21no—
233C2—22no—
234C2—22no—
235C2—15281no—
236C2C2×#2025923611yescharacteristic
237C2#2713266511yescharacteristic
238C2C2×#2025924811yescharacteristic
subgroupG/H
centerC22C2×(C2×D191)⋊C4
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#407×C191C2
socleC22×C191C2×C22⋊C4
prime radical#27133174C2
cosocleC22×C4×C191C23
hypercenter#407D191
hypocenterC191#1504
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C191⋊#95C2semidirect
3. #27132401C2semidirect
4. #27132398C2semidirect
5. #407×C191C2semidirect
6. C2×#15690287C4semidirect
9. #20259301C4semidirect
11. #20259296C4semidirect
16. #20259281C4semidirect
24. C2×Dic382C2×C4semidirect
25. C2×D764C2×C4semidirect
34. C4⋊Dic191C2×C4semidirect
35. C4⋊Dic191C2×C4semidirect
119. C191#1504semidirect
122. #407D191semidirect

Maximal subgroups

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

subgroupindex
#271331742
C2×C191⋊#952
#271324012
#271323982
#407×C1912
#1504191