Finite Group Databasebeta

← #37571021

Subgroups — #37571021

Order 24448.

334 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 65 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#27133173C211yesmaximal, characteristic
2#27132625C211yesmaximal, characteristic, complemented
3#95×D191C211yesmaximal, characteristic, complemented
4#27132401C211yesmaximal, characteristic, complemented
5#27132399C211yesmaximal, characteristic, complemented
6#27132397C211yesmaximal, characteristic, complemented
7#327×C191C211yesmaximal, characteristic, complemented
8C2×#15690286C411yescharacteristic, complemented
9C22×C4×D191—21no—
10C22×C4×D191C2211yescharacteristic
11C2×#15690270—21no—
12#20259304—21no—
13#20259302C411yescharacteristic, complemented
14#20259301C2211yescharacteristic
15#20259293C411yescharacteristic, complemented
16#20259290—21no—
17D4×Dic191—21no—
18(C22⋊D191)⋊C4—21no—
19#20259280C411yescharacteristic, complemented
20C22⋊(C191⋊C8)C2211yescharacteristic
21(C2×D191)⋊C8—21no—
22C191⋊#95—21no—
23C191⋊#95C2211yescharacteristic
24#121×C191C2211yescharacteristic
25C22⋊C8×C191C2211yescharacteristic
26#95×C191C2211yescharacteristic
27C23×D191D411yescharacteristic
28#15690286—42no—
29C2×Dic382C2×C411yescharacteristic, complemented
30C2×C22⋊D191—21no—
31C2×C22⋊D191—21no—
32C22×Dic191—21no—
33C22×Dic191—21no—
34C22×Dic191D411yescharacteristic
35C2×C4×D191—24no—
36C2×C4×D191—42no—
37C2×C4×D191—42no—
38C2×C4×D191—42no—
39C2×C4×D191C2×C411yescharacteristic
40C2×C4×D191C2×C411yescharacteristic
41C2×C4×D191D411yescharacteristic
42C2×C4×D191D411yescharacteristic
43#15690270—42no—
44C2×C191⋊C8—21no—
45C4⋊Dic191—21no—
46C4⋊Dic191C2×C411yescharacteristic, complemented
47Dic191⋊C4—21no—
48C22⋊Dic191—21no—
49C22⋊Dic191—21no—
50(C2×D191)⋊C4—21no—
51(C2×D191)⋊C4—21no—
52C4×Dic191—21no—
53C2×D4×C191—21no—
54C2×D4×C191C2×C411yescharacteristic, complemented
55C22×C4×C191—21no—
56C22×C4×C191C2311yescharacteristic
57C2×C8×C191—21no—
58C4⋊C4×C191C2×C411yescharacteristic, complemented
59C22⋊C4×C191—21no—
60C22×D191—21no—
61C22×D191—21no—
62C22×D191—22no—
63C22×D191—22no—
64C22×D191C22⋊C411yescharacteristic
65C22×D191C22⋊C411yescharacteristic
66Dic382—41no—
67C22⋊D191—42no—
68C22⋊D191—42no—
69C2×Dic191—22no—
70C2×Dic191—21no—
71C2×Dic191—21no—
72C2×Dic191—41no—
73C2×Dic191—42no—
74C2×Dic191—41no—
75C2×Dic191—41no—
76C2×Dic191C22⋊C411yescharacteristic
77C2×Dic191C22⋊C411yescharacteristic
78C4×D191—22no—
79C4×D191—22no—
80C4×D191—41no—
81C4×D191—41no—
82C4×D191—48no—
83C191⋊C8—41no—
84C23×C191—21no—
85C23×C191C2×D411yescharacteristic
86D4×C191—41no—
87D4×C191—41no—
88D4×C191—41no—
89C2×C4×C191—22no—
90C2×C4×C191—21no—
91C2×C4×C191—41no—
92C2×C4×C191—41no—
93C2×C4×C191—41no—
94C2×C4×C191C22×C411yescharacteristic
95C2×C4×C191C2×D411yescharacteristic
96C8×C191—41no—
97C22×C191—21no—
98C22×C191—21no—
99C22×C191—41no—
100C22×C191—41no—
101C22×C191—41no—
102C22×C191C2×C22⋊C411yescharacteristic
103C22×C191AGL(1,ℤ/8)11yescharacteristic
104C22×C191#13711yescharacteristic
105C2×D191—24no—
106C2×D191—24no—
107C2×D191—21no—
108C2×D191—21no—
109C2×D191—21no—
110C2×D191—21no—
111C2×D191#9912yes—
112C2×D191#10412yes—
113C4×C191—21no—
114C4×C191—21no—
115C4×C191—42no—
116C4×C191—41no—
117Dic191—21no—
118Dic191—21no—
119Dic191—42no—
120Dic191—41no—
121Dic191—41no—
122C2×C191—21no—
123C2×C191—21no—
124C2×C191—81no—
125C2×C191C2×#9911yescharacteristic
126C2×C191#41711yescharacteristic
127C2×C191C2×#10411yescharacteristic
128D191—22no—
129D191—22no—
130C191#150411yescharacteristic, complemented, Sylow
131#1504—1911nomaximal, Sylow
132#525—1911no—
133#407—1911no—
134C2×#95—1911no—
135#328—1911no—
136#328—1911no—
137#327—1911no—
138#327D19111yescharacteristic, complemented
139C2×#41—1911no—
140C23×C4—3821no—
141C23×C4—1911no—
142C2×M16—3821no—
143#123—3821no—
144C22⋊Q8—1911no—
145C22⋊Q8—1911no—
146#121—1911no—
147#121C2×D19111yescharacteristic
148#120—3821no—
149C4×D4—3821no—
150C4×D4—3821no—
151#117—1911no—
152C22⋊C8—3821no—
153C22⋊C8—1911no—
154C22⋊C8C2×D19111yescharacteristic
155#95—3821no—
156#95—1911no—
157#95C2×D19111yescharacteristic
158C24—1911no—
159#41—7642no—
160C2×Q8—1911no—
161C2×D4—21no—
162C2×D4—3821no—
163C2×D4—3821no—
164C2×D4C4×D19111yescharacteristic, complemented
165C22×C4—21no—
166C22×C4—3824no—
167C22×C4—3821no—
168C22×C4—3821no—
169C22×C4—1911no—
170C22×C4—1911no—
171C22×C4—1911no—
172C22×C4—1911no—
173C22×C4—1911no—
174C22×C4—7642no—
175C22×C4—7642no—
176C22×C4—7642no—
177C22×C4C22×D19111yescharacteristic
178M16—7642no—
179C2×C8—21no—
180C2×C8—3821no—
181C4⋊C4—3821no—
182C4⋊C4—3821no—
183C4⋊C4—1911no—
184C4⋊C4C4×D19111yescharacteristic, complemented
185C22⋊C4—21no—
186C22⋊C4—3821no—
187C22⋊C4—3821no—
188C22⋊C4—3821no—
189C22⋊C4—3821no—
190C42—3821no—
191C23—21no—
192C23—3822no—
193C23—3822no—
194C23—3821no—
195C23—3821no—
196C23—1911no—
197C23—1911no—
198C23D4×D19111yescharacteristic
199Q8—7641no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—7642no—
204D4—7642no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—3822no—
211C2×C4—3822no—
212C2×C4—3822no—
213C2×C4—3821no—
214C2×C4—3821no—
215C2×C4—1911no—
216C2×C4—1911no—
217C2×C4—7641no—
218C2×C4—7641no—
219C2×C4—7648no—
220C2×C4—7641no—
221C2×C4—7642no—
222C2×C4—7641no—
223C2×C4—7641no—
224C2×C4C2×C4×D19111yescharacteristic
225C2×C4D4×D19111yescharacteristic
226C8—41no—
227C8—7641no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—3824no—
234C22—3824no—
235C22—3821no—
236C22—3821no—
237C22—3821no—
238C22—3821no—
239C22—1912no—
240C22—1912no—
241C22C22⋊C4×D19111yescharacteristic
242C22#2025934611yescharacteristic
243C22#2025935111yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—41no—
248C4—3821no—
249C4—3821no—
250C4—7642no—
251C4—7641no—
252C4—7641no—
253C2—21no—
254C2—21no—
255C2—81no—
256C2—3822no—
257C2—3822no—
258C2#99×D19111yescharacteristic
259C2#2713266111yescharacteristic
260C2#104×D19111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D191
commutatorC2×C4×C191C22×C4
FrattiniC22×C4C22×D191
Fitting#327×C191C2
socleC22×C191C2×C22⋊C4
prime radical#27133173C2
cosocleC22×C4×C191C23
hypercenter#327D191
hypocenterC191#1504
LCSG ▷ C2×C4×C191 ▷ C22×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #27132625C2semidirect
3. #95×D191C2semidirect
4. #27132401C2semidirect
5. #27132399C2semidirect
6. #27132397C2semidirect
7. #327×C191C2semidirect
8. C2×#15690286C4semidirect
13. #20259302C4semidirect
15. #20259293C4semidirect
19. #20259280C4semidirect
29. C2×Dic382C2×C4semidirect
46. C4⋊Dic191C2×C4semidirect
54. C2×D4×C191C2×C4semidirect
58. C4⋊C4×C191C2×C4semidirect
130. C191#1504semidirect
138. #327D191semidirect
164. C2×D4C4×D191semidirect
184. C4⋊C4C4×D191semidirect

Maximal subgroups

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

subgroupindex
#271331732
#271326252
#95×D1912
#271324012
#271323992
#271323972
#327×C1912
#1504191