Finite Group Databasebeta

← C2×#27132803 #37581709

Subgroups — C2×#27132803 #37581709

Order 24448.

792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C22×Q8×D191C211yesmaximal, characteristic, complemented
2C22×#15690276C211yesmaximal, characteristic, complemented
3C22×#15690274C211yesmaximal, characteristic, complemented
4C2×#20259297C211yesmaximal, characteristic
5#27132803C218yesmaximal, direct product factor
6C2×#20259245C211yesmaximal, characteristic, complemented
7C2×(C2×D191)⋊C8C211yesmaximal, characteristic, complemented
8C2×#103×C191C211yesmaximal, characteristic, complemented
9C22×Dic382—21no—
10C22×Dic382C2211yescharacteristic
11C2×Q8×D191—24no—
12C2×Q8×D191—22no—
13C2×Q8×D191—24no—
14C2×Q8×D191C2214yescomplemented
15C22×D764—21no—
16C22×D764C2211yescharacteristic
17C22×C4×D191—21no—
18C22×C4×D191C2211yescharacteristic
19C2×#15690276—24no—
20C2×#15690276C2214yescomplemented
21C2×#15690274—24no—
22C2×#15690274C2214yescomplemented
23C22×C191⋊C8C2211yescharacteristic
24#20259297—22no—
25#20259297C2214yes—
26C2×(C2×D191)⋊C4—21no—
27#20259245C2214yescomplemented
28(C2×D191)⋊C8C2214yescomplemented
29C22×Q8×C191C2211yescharacteristic
30C22×C8×C191C2211yescharacteristic
31C2×C4⋊C4×C191C2211yescharacteristic
32#103×C191C2214yescomplemented
33C23×D191—21no—
34C23×D191D411yescharacteristic
35C2×Dic382—28no—
36C2×Dic382—24no—
37C2×Dic382—21no—
38C2×Dic382—22no—
39C2×Dic382D414yescomplemented
40C2×Dic382C2312yes—
41Q8×D191—216no—
42Q8×D191—28no—
43Q8×D191—28no—
44C2×D764—24no—
45C2×D764—22no—
46C2×D764—22no—
47C2×D764—21no—
48C2×D764—44no—
49C2×D764C2312yes—
50C22×Dic191—21no—
51C22×Dic191D411yescharacteristic
52C2×C4×D191—28no—
53C2×C4×D191—24no—
54C2×C4×D191—22no—
55C2×C4×D191—22no—
56C2×C4×D191D412yes—
57C2×C4×D191C2312yes—
58#15690276—28no—
59#15690274—28no—
60C2×C191⋊C8—22no—
61C2×C191⋊C8C2312yes—
62(C2×D191)⋊C4—24no—
63C2×Q8×C191—22no—
64C2×Q8×C191—21no—
65C2×Q8×C191D414yescomplemented
66C2×Q8×C191C2312yes—
67C22×C4×C191—21no—
68C22×C4×C191—21no—
69C22×C4×C191C2311yescharacteristic
70C2×C8×C191—22no—
71C2×C8×C191C2312yes—
72C4⋊C4×C191—21no—
73C4⋊C4×C191C2312yes—
74C22×D191—22no—
75C22×D191—22no—
76C22×D191—22no—
77C22×D191—42no—
78C22×D191—42no—
79C22×D191—42no—
80C22×D191SD1614yescomplemented
81C22×D191C2×D412yes—
82Dic382—216no—
83Dic382—24no—
84Dic382—22no—
85Dic382C2×D414yescomplemented
86D764—22no—
87D764—22no—
88D764—48no—
89D764—42no—
90C2×Dic191—24no—
91C2×Dic191—22no—
92C2×Dic191—22no—
93C2×Dic191C2×D412yes—
94C4×D191—216no—
95C4×D191—24no—
96C4×D191—22no—
97C4×D191—22no—
98C191⋊C8—22no—
99C23×C191C2×D411yescharacteristic
100Q8×C191—24no—
101Q8×C191—22no—
102Q8×C191C2×D414yescomplemented
103C2×C4×C191—24no—
104C2×C4×C191—22no—
105C2×C4×C191—22no—
106C2×C4×C191—42no—
107C2×C4×C191C2×D411yescharacteristic
108C2×C4×C191C2×D412yes—
109C2×C4×C191C2×D412yes—
110C2×C4×C191C2411yescharacteristic
111C8×C191—22no—
112C22×C191#12012yes—
113C22×C191C2×SD1612yes—
114C22×C191#13712yes—
115C22×C191C22×D411yescharacteristic
116C2×D191—22no—
117C2×D191—22no—
118C2×D191—28no—
119C2×D191—42no—
120C2×D191—42no—
121C2×D191—42no—
122C2×D191—84no—
123C2×D191C2×SD1614yescomplemented
124C4×C191—24no—
125C4×C191—42no—
126C4×C191#12012yes—
127C4×C191C22×D411yescharacteristic
128C4×C191C22×D411yescharacteristic
129Dic191—24no—
130Dic191—22no—
131C2×C191#44814yescomplemented
132C2×C191C2×#12011yescharacteristic
133C2×C191C22×SD1611yescharacteristic
134C2×C191C2×#13711yescharacteristic
135D191—24no—
136D191—82no—
137C191C2×#44811yescharacteristic, complemented, Sylow
138C2×#448—1911nomaximal, Sylow
139C23×Q8—1911no—
140C22×SD16—1911no—
141C22×SD16—1911no—
142C2×#121—1911no—
143#448—1918no—
144C2×#103—1911no—
145C2×#103D19111yescharacteristic, complemented
146C2×C22⋊C8—1911no—
147C22×Q8—3821no—
148C22×Q8—3824no—
149C22×Q8—3824no—
150C22×Q8—3822no—
151C22×Q8—1914no—
152C22×Q8—1911no—
153C22×Q8C2×D19111yescharacteristic
154C22×D4—3821no—
155C22×D4—1911no—
156C23×C4—3821no—
157C23×C4—1911no—
158C2×SD16—3824no—
159C2×SD16—3824no—
160C2×SD16—1914no—
161C2×SD16—1914no—
162C22×C8—1911no—
163C22×C8C2×D19111yescharacteristic
164#121—3822no—
165#121—1914no—
166C2×C4⋊C4C2×D19111yescharacteristic
167C2×C22⋊C4—3821no—
168#103—1914no—
169#103C2×D19114yescomplemented
170C22⋊C8—1914no—
171C24—3821no—
172C24—1911no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—3828no—
176C2×Q8—3824no—
177C2×Q8—38216no—
178C2×Q8—3828no—
179C2×Q8—3828no—
180C2×Q8—3821no—
181C2×Q8—3822no—
182C2×Q8—1914no—
183C2×Q8—1912no—
184C2×Q8D76414yescomplemented
185C2×Q8C22×D19112yes—
186C2×D4—3824no—
187C2×D4—3822no—
188C2×D4—3821no—
189C2×D4—3822no—
190C2×D4—1912no—
191C2×D4—7644no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—3828no—
195C22×C4—3824no—
196C22×C4—3821no—
197C22×C4—3822no—
198C22×C4—3822no—
199C22×C4—1911no—
200C22×C4—1912no—
201C22×C4—1912no—
202C22×C4C22×D19111yescharacteristic
203SD16—3828no—
204SD16—3828no—
205C2×C8—22no—
206C2×C8—3822no—
207C2×C8—1912no—
208C2×C8C22×D19112yes—
209C4⋊C4—21no—
210C4⋊C4C22×D19112yes—
211C22⋊C4—3824no—
212C23—3822no—
213C23—3822no—
214C23—3822no—
215C23—1914no—
216C23—1912no—
217C23—7642no—
218C23—7642no—
219C23—7642no—
220C23D4×D19111yescharacteristic
221Q8—22no—
222Q8—24no—
223Q8—38216no—
224Q8—3822no—
225Q8—3824no—
226Q8—1914no—
227Q8C2×D76414yescomplemented
228D4—3822no—
229D4—3822no—
230D4—7648no—
231D4—7642no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—38216no—
237C2×C4—3822no—
238C2×C4—3824no—
239C2×C4—3822no—
240C2×C4—3822no—
241C2×C4—3822no—
242C2×C4—3824no—
243C2×C4—1912no—
244C2×C4D4×D19112yes—
245C2×C4D4×D19111yescharacteristic
246C2×C4C2×D76412yes—
247C2×C4C23×D19111yescharacteristic
248C8—22no—
249C8—3822no—
250C22—3822no—
251C22—3828no—
252C22—3822no—
253C22—1914no—
254C22—15284no—
255C22—7642no—
256C22—7642no—
257C22—7642no—
258C22#2025929212yes—
259C22SD16×D19112yes—
260C22#2025935412yes—
261C22C2×D4×D19111yescharacteristic
262C4—24no—
263C4—42no—
264C4—3824no—
265C4—3822no—
266C4#2025929212yes—
267C4C2×D4×D19111yescharacteristic
268C4C22×D76411yescharacteristic
269C2—3824no—
270C2—15282no—
271C2#2713280314yesdirect product factor
272C2C2×#2025929211yescharacteristic
273C2C2×SD16×D19111yescharacteristic
274C2C2×#2025935411yescharacteristic
subgroupG/H
centerC23D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#103×C191C2
socleC23×C191C2×D4
prime radicalC2×#20259297C2
hypercenterC2×#103D191
hypocenterC191C2×#448
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D191C2semidirect
2. C22×#15690276C2semidirect
3. C22×#15690274C2semidirect
5. #27132803C2direct (N × H)
6. C2×#20259245C2semidirect
7. C2×(C2×D191)⋊C8C2semidirect
8. C2×#103×C191C2semidirect
14. C2×Q8×D191C22semidirect
20. C2×#15690276C22semidirect
22. C2×#15690274C22semidirect
27. #20259245C22semidirect
28. (C2×D191)⋊C8C22semidirect
32. #103×C191C22semidirect
39. C2×Dic382D4semidirect
65. C2×Q8×C191D4semidirect
80. C22×D191SD16semidirect
85. Dic382C2×D4semidirect
102. Q8×C191C2×D4semidirect
123. C2×D191C2×SD16semidirect
131. C2×C191#448semidirect
137. C191C2×#448semidirect
145. C2×#103D191semidirect
169. #103C2×D191semidirect
184. C2×Q8D764semidirect
227. Q8C2×D764semidirect
271. C2#27132803direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D1912
C22×#156902762
C22×#156902742
C2×#202592972
#271328032
C2×#202592452
C2×(C2×D191)⋊C82
C2×#103×C1912
C2×#448191