Finite Group Databasebeta

← #486×D191 #37582823

Subgroups — #486×D191 #37582823

Order 24448.

528 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D191C211yesmaximal, characteristic, complemented
2#127×D191C211yesmaximal, characteristic
3#27133011C211yesmaximal, characteristic, complemented
4#27133010C211yesmaximal, characteristic, complemented
5#27133009C211yesmaximal, characteristic, complemented
6#27133008C214yesmaximal, complemented
7#102×D191C214yesmaximal, complemented
8C4×C8×D191C211yesmaximal, characteristic, complemented
9#486×C191C211yesmaximal, characteristic, complemented
10C2×Q8×D191—21no—
11C2×D4×D191—21no—
12C2×D4×D191—21no—
13C2×D4×D191C2212yes—
14C2×C8×D191C2212yes—
15#20259322C2211yescharacteristic, complemented
16#20259321—21no—
17#20259321C2212yescomplemented
18#20259320—21no—
19#20259319C2211yescharacteristic
20#20259318—21no—
21#20259318—21no—
22#20259318C2212yes—
23C4⋊C4×D191—21no—
24C4⋊C4×D191C2212yes—
25C42×D191C2211yescharacteristic
26#20259244C2214yescomplemented
27#20259243C2214yescomplemented
28#20259242C2214yescomplemented
29C4×C191⋊C8C2211yescharacteristic, complemented
30C8×Dic191C2212yescomplemented
31C4⋊Q8×C191C2211yescharacteristic, complemented
32#127×C191C2211yescharacteristic
33#102×C191C2214yescomplemented
34C4×C8×C191C2211yescharacteristic, complemented
35C23×D191—22no—
36C2×Dic382—22no—
37C2×Dic382—21no—
38Q8×D191—44no—
39C2×D764—21no—
40C2×D764—21no—
41C2×D764C2312yes—
42C2×C22⋊D191—22no—
43C2×C22⋊D191—22no—
44C2×C22⋊D191—22no—
45D4×D191—28no—
46D4×D191—44no—
47D4×D191—44no—
48C2×C4×D191—22no—
49C2×C4×D191D411yescharacteristic
50C2×C4×D191D411yescharacteristic
51C2×C4×D191C2311yescharacteristic
52C2×C191⋊C8C2312yes—
53C8×D191—24no—
54C4⋊Dic191—21no—
55C4⋊Dic191C2312yes—
56Dic191⋊C4—22no—
57Dic191⋊C4—22no—
58C4×Dic191D411yescharacteristic
59C4×Dic191D411yescharacteristic
60C4×Dic191C2311yescharacteristic
61C2×Q8×C191—21no—
62C2×D4×C191—21no—
63C2×D4×C191—21no—
64C2×D4×C191C2312yes—
65C2×C8×C191C2312yes—
66C4⋊C4×C191—21no—
67C4⋊C4×C191C2312yes—
68C42×C191C2311yescharacteristic
69C22×D191—22no—
70C22×D191—44no—
71C22×D191—44no—
72C22×D191—44no—
73C22×D191C2×D411yescharacteristic
74Dic382—42no—
75Dic382—44no—
76D764—24no—
77D764—42no—
78D764—42no—
79C22⋊D191—44no—
80C22⋊D191—44no—
81C22⋊D191—44no—
82C2×Dic191—22no—
83C2×Dic191C2×D411yescharacteristic
84C2×Dic191C2×D411yescharacteristic
85C2×Dic191C2×D411yescharacteristic
86C4×D191—44no—
87C4×D191D814yes—
88C4×D191SD1614yes—
89C4×D191#4114yes—
90C191⋊C8—22no—
91C23×C191—22no—
92Q8×C191—42no—
93D4×C191—24no—
94D4×C191—42no—
95D4×C191—42no—
96C2×C4×C191—22no—
97C2×C4×C191C2×D411yescharacteristic
98C2×C4×C191C2×D411yescharacteristic
99C2×C4×C191C2411yescharacteristic
100C8×C191—22no—
101C22×C191—42no—
102C22×C191—42no—
103C22×C191—42no—
104C22×C191C22×D411yescharacteristic
105C2×D191—42no—
106C2×D191—42no—
107C2×D191—42no—
108C2×D191—88no—
109C2×D191#12412yes—
110C2×D191C2×D812yes—
111C2×D191C2×SD1612yes—
112C4×C191—42no—
113C4×C191C2×D812yes—
114C4×C191C2×SD1612yes—
115C4×C191C2×#4112yes—
116Dic191—42no—
117Dic191#12412yes—
118Dic191C2×D812yes—
119Dic191C2×SD1612yes—
120C2×C191—82no—
121C2×C191C2×#12411yescharacteristic
122C2×C191C22×D811yescharacteristic
123C2×C191C22×SD1611yescharacteristic
124D191—82no—
125D191#48614yesdirect product factor
126C191C2×#48611yescharacteristic, complemented, Sylow
127C2×#486—1911nomaximal, Sylow
128C2×C4⋊Q8—1911no—
129C2×#127—1911no—
130#486—1911no—
131#486—1911no—
132#486—1914no—
133#486—1911no—
134#486D19111yescharacteristic, direct product factor
135C2×#102—1914no—
136C2×C4×C8—1911no—
137C22×Q8—3821no—
138C22×D4—3821no—
139C22×D4—3821no—
140C22×D4—1912no—
141C22×C8—1912no—
142C4⋊Q8—3821no—
143C4⋊Q8—3821no—
144C4⋊Q8—1912no—
145C4⋊Q8—1911no—
146C4⋊Q8C2×D19111yescharacteristic, complemented
147#127—3821no—
148#127—3821no—
149#127—1912no—
150#127—1911no—
151#127C2×D19111yescharacteristic
152C2×C4⋊C4—3821no—
153C2×C4⋊C4—1912no—
154C2×C42—1911no—
155#102—1914no—
156#102—1914no—
157#102—1914no—
158#102C2×D19114yescomplemented
159C4×C8—1912no—
160C4×C8—1911no—
161C4×C8C2×D19111yescharacteristic, complemented
162C24—3822no—
163C2×Q8—21no—
164C2×Q8—3822no—
165C2×Q8—3821no—
166C2×Q8—7644no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—3828no—
170C2×D4—3822no—
171C2×D4—3822no—
172C2×D4—3822no—
173C2×D4—3821no—
174C2×D4—3821no—
175C2×D4—1912no—
176C2×D4—7644no—
177C2×D4—7644no—
178C2×D4C22×D19112yes—
179C22×C4—3822no—
180C22×C4—1911no—
181C22×C4—1911no—
182C22×C4—1911no—
183C2×C8—3824no—
184C2×C8—1912no—
185C2×C8C22×D19112yes—
186C4⋊C4—21no—
187C4⋊C4—3822no—
188C4⋊C4—3822no—
189C4⋊C4—3821no—
190C4⋊C4—1912no—
191C4⋊C4C22×D19112yes—
192C42—1911no—
193C42—1911no—
194C42—1911no—
195C42C22×D19111yescharacteristic
196C23—22no—
197C23—3822no—
198C23—1911no—
199C23—7644no—
200C23—7644no—
201C23—7644no—
202Q8—42no—
203Q8—7644no—
204Q8—7642no—
205D4—24no—
206D4—42no—
207D4—42no—
208D4—3824no—
209D4—7644no—
210D4—7644no—
211D4—7644no—
212D4—7642no—
213D4—7642no—
214C2×C4—22no—
215C2×C4—3822no—
216C2×C4—1911no—
217C2×C4—1911no—
218C2×C4—1911no—
219C2×C4—1914no—
220C2×C4—1914no—
221C2×C4—1914no—
222C2×C4—7644no—
223C2×C4D4×D19111yescharacteristic
224C2×C4D4×D19111yescharacteristic
225C2×C4C23×D19111yescharacteristic
226C8—22no—
227C8—3822no—
228C22—42no—
229C22—42no—
230C22—42no—
231C22—1912no—
232C22—1912no—
233C22—1912no—
234C22—15288no—
235C22—7642no—
236C22—7642no—
237C22—7642no—
238C22C2×D4×D19111yescharacteristic
239C4—42no—
240C4—1912no—
241C4—1912no—
242C4—1912no—
243C4—7642no—
244C4D8×D19112yes—
245C4SD16×D19112yes—
246C4#41×D19112yes—
247C2—82no—
248C2—1914no—
249C2—15282no—
250C2#124×D19111yescharacteristic
251C2C2×D8×D19111yescharacteristic
252C2C2×SD16×D19111yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#486×C191C2
socleC22×C191C22×D4
prime radical#127×D191C2
hypercenter#486D191
hypocenterC191C2×#486
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D191C2semidirect
3. #27133011C2semidirect
4. #27133010C2semidirect
5. #27133009C2semidirect
6. #27133008C2semidirect
7. #102×D191C2semidirect
8. C4×C8×D191C2semidirect
9. #486×C191C2semidirect
15. #20259322C22semidirect
17. #20259321C22semidirect
26. #20259244C22semidirect
27. #20259243C22semidirect
28. #20259242C22semidirect
29. C4×C191⋊C8C22semidirect
30. C8×Dic191C22semidirect
31. C4⋊Q8×C191C22semidirect
33. #102×C191C22semidirect
34. C4×C8×C191C22semidirect
125. D191#486direct (N × H)
126. C191C2×#486semidirect
134. #486D191direct (N × H)
146. C4⋊Q8C2×D191semidirect
158. #102C2×D191semidirect
161. C4×C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1912
#127×D1912
#271330112
#271330102
#271330092
#271330082
#102×D1912
C4×C8×D1912
#486×C1912
C2×#486191