Finite Group Databasebeta

← #37581999

Subgroups — #37581999

Order 24448.

584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#20259350C211yesmaximal, characteristic, complemented
2C2×#20259348C211yesmaximal, characteristic, complemented
3C2×#20259318C211yesmaximal, characteristic, complemented
4#27133131C211yesmaximal, characteristic, complemented
5#27132862C214yesmaximal, complemented
6#27132857C214yesmaximal, complemented
7#27132686C211yesmaximal, characteristic, complemented
8#27132667C211yesmaximal, characteristic, complemented
9#418×C191C211yesmaximal, characteristic, complemented
10C2×#15690287C2211yescharacteristic
11C22×D764C2211yescharacteristic
12C22×C22⋊D191—22no—
13#20259350—24no—
14#20259348—24no—
15C2×#15690276C2212yescomplemented
16C2×#15690275C2212yescomplemented
17C2×D1528C2212yescomplemented
18C2×#15690272C2212yescomplemented
19C2×#15690271C2211yescharacteristic
20#20259318—21no—
21#20259318—21no—
22#20259318C2214yes—
23#20259287C2212yescomplemented
24#20259284C2212yescomplemented
25(C22⋊D191)⋊C4—22no—
26#20259279—21no—
27C2×C4×Dic191C2211yescharacteristic
28C42×D191—21no—
29Dic191⋊C8C2214yescomplemented
30#20259242C2214yescomplemented
31C22×D4×C191C2211yescharacteristic
32C2×M16×C191C2211yescharacteristic
33#117×C191C2211yescharacteristic
34#102×C191C2214yescomplemented
35C23×D191—21no—
36#15690287—22no—
37#15690287D414yescomplemented
38C2×Dic382C2311yescharacteristic
39C2×D764—22no—
40C2×D764—21no—
41C2×D764—22no—
42C2×D764C2312yes—
43C2×D764C2311yescharacteristic
44C2×C22⋊D191—24no—
45C2×C22⋊D191—24no—
46C2×C22⋊D191—21no—
47C2×C22⋊D191—48no—
48C22×Dic191D412yes—
49C2×C4×D191—22no—
50C2×C4×D191—21no—
51#15690276—24no—
52#15690275—24no—
53D1528—24no—
54#15690272—24no—
55#15690271—22no—
56C2×C191⋊C8C2312yes—
57Dic191⋊C4—22no—
58(C2×D191)⋊C4—22no—
59C4×Dic191—22no—
60C4×Dic191D411yescharacteristic
61C4×Dic191D411yescharacteristic
62C4×Dic191C2312yes—
63C24×C191—21no—
64C2×D4×C191—22no—
65C2×D4×C191—21no—
66C2×D4×C191—22no—
67C2×D4×C191C2312yes—
68C22×C4×C191C2311yescharacteristic
69M16×C191—22no—
70C2×C8×C191C2312yes—
71C4⋊C4×C191C2312yes—
72C22⋊C4×C191—21no—
73C42×C191—21no—
74C22×D191—21no—
75C22×D191—22no—
76C22×D191—44no—
77C22×D191—42no—
78Dic382—21no—
79Dic382C2×D412yescomplemented
80D764—22no—
81D764—21no—
82D764—22no—
83D764—42no—
84D764C2×D412yescomplemented
85C22⋊D191—24no—
86C22⋊D191—48no—
87C22⋊D191—48no—
88C2×Dic191—21no—
89C2×Dic191—24no—
90C2×Dic191C2×D412yes—
91C2×Dic191C2×D412yes—
92C4×D191—24no—
93C4×D191—44no—
94C191⋊C8—22no—
95C23×C191—22no—
96C23×C191—44no—
97C23×C191—42no—
98C23×C191C2×D411yescharacteristic
99D4×C191—22no—
100D4×C191—22no—
101D4×C191—42no—
102C2×C4×C191—22no—
103C2×C4×C191C2×D411yescharacteristic
104C2×C4×C191C2×D412yes—
105C2×C4×C191#4112yes—
106C2×C4×C191C2411yescharacteristic
107C8×C191—22no—
108C22×C191—22no—
109C22×C191—42no—
110C22×C191—44no—
111C22×C191—84no—
112C22×C191#12112yes—
113C22×C191C22×D411yescharacteristic
114C2×D191—22no—
115C2×D191—42no—
116C2×D191—42no—
117C2×D191—44no—
118C2×D191—84no—
119C4×C191—42no—
120C4×C191#12112yes—
121C4×C191C22×D411yescharacteristic
122C4×C191C2×#4111yescharacteristic
123Dic191—22no—
124Dic191—22no—
125Dic191AGL(1,ℤ/8)14yescomplemented
126C2×C191—22no—
127C2×C191—82no—
128C2×C191C2×#12111yescharacteristic
129C2×C191C2×AGL(1,ℤ/8)12yes—
130D191—42no—
131D191—82no—
132C191#303811yescharacteristic, complemented, Sylow
133#3038—1911nomaximal, Sylow
134C2×AGL(1,ℤ/8)—1911no—
135C2×AGL(1,ℤ/8)—1911no—
136C2×#127—1911no—
137C4×#41—1911no—
138#460—1914no—
139#459—1914no—
140#423—1911no—
141#418—1911no—
142#418D19111yescharacteristic, complemented
143C2×#41—1911no—
144C22×D4—3822no—
145C22×D4—1911no—
146C22×D4C2×D19111yescharacteristic
147AGL(1,ℤ/8)—3824no—
148AGL(1,ℤ/8)—3824no—
149C2×SD16—1912no—
150C2×SD16—1912no—
151C2×D8—1912no—
152C2×D8—1912no—
153C2×M16—1911no—
154C2×M16C2×D19111yescharacteristic
155#127—3821no—
156#127—3821no—
157#127—1914no—
158C4×Q8—1912no—
159C4×D4—3822no—
160C4×D4—1912no—
161#117—3821no—
162#117C2×D19111yescharacteristic
163C2×C42—3821no—
164C2×C42—1911no—
165C4⋊C8—1914no—
166#102—1914no—
167#102C2×D19114yescomplemented
168C24—21no—
169C24—3821no—
170#41—3822no—
171#41—1914no—
172C2×Q8—1911no—
173C2×D4—22no—
174C2×D4—21no—
175C2×D4—22no—
176C2×D4—3821no—
177C2×D4—3824no—
178C2×D4—3824no—
179C2×D4—3822no—
180C2×D4—3821no—
181C2×D4—3822no—
182C2×D4—1912no—
183C2×D4—1911no—
184C2×D4—7648no—
185C2×D4C22×D19112yes—
186C22×C4—3822no—
187C22×C4—3821no—
188C22×C4—1912no—
189C22×C4C22×D19111yescharacteristic
190SD16—3824no—
191SD16—3824no—
192D8—3824no—
193D8—3824no—
194M16—22no—
195M16—3822no—
196C2×C8—1912no—
197C2×C8C22×D19112yes—
198C4⋊C4—3822no—
199C4⋊C4C22×D19112yes—
200C22⋊C4—21no—
201C22⋊C4—3822no—
202C42—21no—
203C42—3822no—
204C42—1911no—
205C42—1911no—
206C42—1912no—
207C23—22no—
208C23—44no—
209C23—42no—
210C23—3821no—
211C23—3822no—
212C23—7644no—
213C23—7642no—
214C23D4×D19111yescharacteristic
215Q8—3821no—
216Q8—1912no—
217D4—22no—
218D4—22no—
219D4—42no—
220D4—3824no—
221D4—3822no—
222D4—3821no—
223D4—3822no—
224D4—1912no—
225D4—7648no—
226D4—7648no—
227D4—7642no—
228C2×C4—22no—
229C2×C4—3821no—
230C2×C4—3824no—
231C2×C4—3824no—
232C2×C4—1912no—
233C2×C4—1912no—
234C2×C4—7644no—
235C2×C4D4×D19112yes—
236C2×C4D4×D19111yescharacteristic
237C2×C4#1569028712yes—
238C2×C4C23×D19111yescharacteristic
239C8—22no—
240C8—3822no—
241C22—22no—
242C22—44no—
243C22—42no—
244C22—84no—
245C22—3822no—
246C22—15284no—
247C22—7644no—
248C22—7642no—
249C22—7642no—
250C22#2025929512yes—
251C22C2×D4×D19111yescharacteristic
252C4—42no—
253C4—3822no—
254C4—3822no—
255C4—1914no—
256C4#2025929512yes—
257C4C2×D4×D19111yescharacteristic
258C4C2×#1569028711yescharacteristic
259C2—22no—
260C2—82no—
261C2—15282no—
262C2—7642no—
263C2C2×#2025929511yescharacteristic
264C2AGL(1,ℤ/8)×D19112yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#418×C191C2
socleC22×C191C22×D4
hypercenter#418D191
hypocenterC191#3038
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C2×#20259350C2semidirect
2. C2×#20259348C2semidirect
3. C2×#20259318C2semidirect
4. #27133131C2semidirect
5. #27132862C2semidirect
6. #27132857C2semidirect
7. #27132686C2semidirect
8. #27132667C2semidirect
9. #418×C191C2semidirect
15. C2×#15690276C22semidirect
16. C2×#15690275C22semidirect
17. C2×D1528C22semidirect
18. C2×#15690272C22semidirect
23. #20259287C22semidirect
24. #20259284C22semidirect
29. Dic191⋊C8C22semidirect
30. #20259242C22semidirect
34. #102×C191C22semidirect
37. #15690287D4semidirect
79. Dic382C2×D4semidirect
84. D764C2×D4semidirect
125. Dic191AGL(1,ℤ/8)semidirect
132. C191#3038semidirect
142. #418D191semidirect
167. #102C2×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593502
C2×#202593482
C2×#202593182
#271331312
#271328622
#271328572
#271326862
#271326672
#418×C1912
#3038191