Finite Group Databasebeta

← #37581880

Subgroups — #37581880

Order 24448.

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

normal subgroups only

This group has 762 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
1C2×#20259367C211yesmaximal, characteristic, complemented
2#27133463C212yesmaximal, complemented
3#27133230C211yesmaximal, characteristic, complemented
4#27132843C214yesmaximal, complemented
5#27132833C214yesmaximal, complemented
6#27132679C212yesmaximal, complemented
7C2×#100×C191C211yesmaximal, characteristic, complemented
8#20259367—24no—
9#20259367—22no—
10#20259367C2214yes—
11C2×#15690287C2212yes—
12C2×#15690287C2211yescharacteristic, complemented
13C2×#15690286—22no—
14C22×C22⋊D191—22no—
15C2×D4×D191—22no—
16#20259355—22no—
17#20259355C2214yescomplemented
18#20259350—22no—
19#20259350C2214yescomplemented
20#20259344—24no—
21#20259318C2212yescomplemented
22#20259309C2212yescomplemented
23#20259293—22no—
24#20259291—22no—
25#20259281C2211yescharacteristic, complemented
26#20259248C2218yescomplemented
27C22×D4×C191C2211yescharacteristic
28C2×M16×C191C2212yescomplemented
29#100×C191C2214yescomplemented
30C23×D191—22no—
31#15690287—22no—
32#15690287—22no—
33#15690287—22no—
34#15690287—22no—
35#15690287D414yescomplemented
36#15690287C2314yes—
37#15690286—28no—
38#15690286—28no—
39C2×Dic382D412yescomplemented
40C2×Dic382C2311yescharacteristic, complemented
41C2×D764D412yescomplemented
42C2×D764C2311yescharacteristic, complemented
43C2×C22⋊D191—24no—
44C2×C22⋊D191—28no—
45C2×C22⋊D191—22no—
46C2×C22⋊D191—28no—
47C2×C22⋊D191—21no—
48C2×C22⋊D191—24no—
49D4×D191—28no—
50D4×D191—28no—
51C22×Dic191—22no—
52C2×C4×D191—22no—
53C2×C4×D191—21no—
54Dic764—24no—
55#15690276—24no—
56#15690276—24no—
57D1528—24no—
58C4⋊Dic191—21no—
59C22⋊Dic191—21no—
60C22⋊Dic191—24no—
61C4×Dic191C2312yescomplemented
62C24×C191D412yes—
63C2×D4×C191—22no—
64C2×D4×C191—22no—
65C2×D4×C191D412yes—
66C2×D4×C191C2312yes—
67C22×C4×C191C2311yescharacteristic
68M16×C191—22no—
69M16×C191C2314yescomplemented
70C2×C8×C191—22no—
71C22×D191—22no—
72C22×D191—28no—
73C22×D191—21no—
74C22×D191—84no—
75Dic382—22no—
76Dic382—22no—
77Dic382C2×D414yes—
78D764—22no—
79D764—22no—
80D764C2×D414yes—
81C22⋊D191—216no—
82C22⋊D191—24no—
83C22⋊D191—24no—
84C22⋊D191—41no—
85C22⋊D191—41no—
86C22⋊D191—84no—
87C2×Dic191—28no—
88C2×Dic191—22no—
89C2×Dic191—22no—
90C2×Dic191—21no—
91C4×D191—24no—
92C4×D191—24no—
93C4×D191—42no—
94C23×C191—22no—
95C23×C191—22no—
96C23×C191—82no—
97C23×C191C2×D414yes—
98C23×C191C2×D411yescharacteristic
99D4×C191—24no—
100D4×C191—24no—
101C2×C4×C191C2×D412yes—
102C2×C4×C191C2×D412yes—
103C2×C4×C191C2×D411yescharacteristic
104C2×C4×C191C2411yescharacteristic
105C8×C191—24no—
106C22×C191—24no—
107C22×C191—41no—
108C22×C191—44no—
109C22×C191—44no—
110C22×C191—82no—
111C22×C191#12011yescharacteristic
112C22×C191#12011yescharacteristic
113C22×C191C22×D411yescharacteristic
114C2×D191—24no—
115C2×D191—44no—
116C2×D191—42no—
117C2×D191—41no—
118C2×D191—88no—
119C4×C191#12012yes—
120C4×C191C22×D412yes—
121Dic191—24no—
122Dic191—42no—
123Dic191—41no—
124C2×C191—21no—
125C2×C191—21no—
126C2×C191—21no—
127C2×C191—44no—
128C2×C191C2×#12011yescharacteristic
129D191—44no—
130D191—81no—
131C191#301911yescharacteristic, complemented, Sylow
132#3019—1911nomaximal, Sylow
133C2×H(5,𝔽2)—1911no—
134#575—1912no—
135#535—1911no—
136#455—1914no—
137#453—1914no—
138#421—1912no—
139C2×#100D19111yescharacteristic, complemented
140H(5,𝔽2)—3824no—
141H(5,𝔽2)—3822no—
142H(5,𝔽2)—1914no—
143C2×#41—3822no—
144C2×#41—1911no—
145C2×#41—1912no—
146C22×D4—3822no—
147C22×D4—3822no—
148C22×D4C2×D19111yescharacteristic
149#137—3822no—
150#137—1914no—
151AGL(1,ℤ/8)—3822no—
152AGL(1,ℤ/8)—1914no—
153#135—3824no—
154C2×M16C2×D19112yescomplemented
155#127—1912no—
156#124—1912no—
157#121—3822no—
158#120—3822no—
159#117—1911no—
160#104—1918no—
161#100C2×D19114yescomplemented
162C24—3822no—
163C24D76412yes—
164#41—3828no—
165#41—3828no—
166#41—3822no—
167#41—3822no—
168#41—3822no—
169#41—3822no—
170#41—1914no—
171#41—1914no—
172C2×Q8—1912no—
173C2×Q8—1911no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—3828no—
177C2×D4—3828no—
178C2×D4—3824no—
179C2×D4—3828no—
180C2×D4—3822no—
181C2×D4—3828no—
182C2×D4—3824no—
183C2×D4—3821no—
184C2×D4—1912no—
185C2×D4—1911no—
186C2×D4D76412yes—
187C2×D4C22×D19112yes—
188C22×C4—3822no—
189C22×C4—3822no—
190C22×C4—3821no—
191C22×C4C22×D19111yescharacteristic
192Q16—3824no—
193SD16—3824no—
194SD16—3824no—
195D8—3824no—
196M16—22no—
197M16C22×D19114yescomplemented
198C2×C8—22no—
199C4⋊C4—3821no—
200C22⋊C4—3821no—
201C22⋊C4—3824no—
202C42—1912no—
203C23—22no—
204C23—22no—
205C23—82no—
206C23—3828no—
207C23—3822no—
208C23—3821no—
209C23—15284no—
210C23C2×D76414yes—
211C23C2×D76411yescharacteristic
212Q8—3822no—
213Q8—3822no—
214Q8—1914no—
215D4—24no—
216D4—24no—
217D4—38216no—
218D4—3824no—
219D4—3824no—
220D4—3822no—
221D4—3822no—
222D4—1914no—
223D4—15284no—
224D4—7641no—
225D4—7641no—
226C2×C4—3828no—
227C2×C4—3822no—
228C2×C4—3824no—
229C2×C4—3824no—
230C2×C4—3822no—
231C2×C4—3821no—
232C2×C4—7642no—
233C2×C4D4×D19112yes—
234C2×C4D4×D19112yes—
235C2×C4C2×D76411yescharacteristic
236C2×C4C23×D19111yescharacteristic
237C8—24no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—82no—
243C22—3824no—
244C22—15288no—
245C22—7642no—
246C22—7644no—
247C22—7641no—
248C22#2025929211yescharacteristic
249C22#2025929211yescharacteristic
250C22C22×D76411yescharacteristic
251C4—3824no—
252C4—7642no—
253C4—7641no—
254C4#2025929212yes—
255C4C2×D4×D19112yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—15281no—
261C2—7644no—
262C2C2×#2025929211yescharacteristic
subgroupG/H
centerC2C2×#20259292
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC2×#100×C191C2
socleC2×C191C2×#120
hypercenterC2×#100D191
hypocenterC191#3019
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#20259367C2semidirect
2. #27133463C2semidirect
3. #27133230C2semidirect
4. #27132843C2semidirect
5. #27132833C2semidirect
6. #27132679C2semidirect
7. C2×#100×C191C2semidirect
12. C2×#15690287C22semidirect
17. #20259355C22semidirect
19. #20259350C22semidirect
21. #20259318C22semidirect
22. #20259309C22semidirect
25. #20259281C22semidirect
26. #20259248C22semidirect
28. C2×M16×C191C22semidirect
29. #100×C191C22semidirect
35. #15690287D4semidirect
39. C2×Dic382D4semidirect
40. C2×Dic382C23semidirect
41. C2×D764D4semidirect
42. C2×D764C23semidirect
61. C4×Dic191C23semidirect
69. M16×C191C23semidirect
131. C191#3019semidirect
139. C2×#100D191semidirect
154. C2×M16C2×D191semidirect
161. #100C2×D191semidirect
197. M16C22×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593672
#271334632
#271332302
#271328432
#271328332
#271326792
C2×#100×C1912
#3019191