Finite Group Databasebeta

← C2×#23750013 #34055124

Subgroups — C2×#23750013 #34055124

Order 19072.

668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14558725C211yesmaximal, characteristic, complemented
2C22×#14558724C211yesmaximal, characteristic, complemented
3C22×#14558721C211yesmaximal, characteristic, complemented
4C2×#18011907C211yesmaximal, characteristic, complemented
5C2×#18011898C211yesmaximal, characteristic, complemented
6#23750013C218yesmaximal, direct product factor
7C2×#18011821C211yesmaximal, characteristic, complemented
8C22×D8×C149C211yesmaximal, characteristic, complemented
9C22×Dic298C2211yescharacteristic
10C22×D596C2211yescharacteristic
11C22×C22⋊D149—22no—
12C2×#14558725—24no—
13C2×#14558725C2214yescomplemented
14C2×#14558724—24no—
15C2×#14558724C2214yescomplemented
16C2×#14558721—24no—
17C2×#14558721C2214yescomplemented
18C22×#11924746C2211yescharacteristic
19#18011907—22no—
20#18011907C2214yescomplemented
21#18011898—22no—
22#18011898C2214yescomplemented
23C2×C22⋊Dic149—22no—
24C2×C4×Dic149C2211yescharacteristic
25#18011821C2214yescomplemented
26C22×D4×C149C2211yescharacteristic
27C22×D4×C149C2211yescharacteristic
28C2×D8×C149—24no—
29C2×D8×C149C2214yescomplemented
30C22×C8×C149C2211yescharacteristic
31C23×D149—21no—
32C2×Dic298—21no—
33C2×Dic298—22no—
34C2×Dic298—22no—
35C2×Dic298C2312yes—
36C2×D596—22no—
37C2×D596—22no—
38C2×D596—21no—
39C2×D596C2312yes—
40C2×C22⋊D149—28no—
41C2×C22⋊D149—48no—
42C22×Dic149—21no—
43C22×Dic149D412yes—
44#14558725—28no—
45#14558724—28no—
46#14558721—28no—
47C2×#11924746D414yescomplemented
48C2×#11924746C2312yes—
49C22⋊Dic149—28no—
50C4×Dic149D412yes—
51C4×Dic149C2312yes—
52C24×C149—21no—
53C24×C149—21no—
54C2×D4×C149—22no—
55C2×D4×C149—22no—
56C2×D4×C149—22no—
57C2×D4×C149—22no—
58C2×D4×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149C2312yes—
61C2×D4×C149C2312yes—
62C22×C4×C149C2311yescharacteristic
63D8×C149—28no—
64C2×C8×C149D414yescomplemented
65C2×C8×C149C2312yes—
66C22×D149—22no—
67C22×D149—42no—
68C22×D149—44no—
69Dic298—22no—
70Dic298—22no—
71Dic298—42no—
72D596—22no—
73D596—22no—
74D596—42no—
75C22⋊D149—416no—
76C2×Dic149—24no—
77C2×Dic149—22no—
78C2×Dic149—42no—
79C2×Dic149C2×D414yes—
80#11924746C2×D414yescomplemented
81C23×C149—22no—
82C23×C149—22no—
83C23×C149—42no—
84C23×C149—42no—
85C23×C149—44no—
86C23×C149—44no—
87C23×C149C2×D411yescharacteristic
88D4×C149—22no—
89D4×C149—22no—
90D4×C149—22no—
91D4×C149—22no—
92D4×C149—42no—
93D4×C149—42no—
94C2×C4×C149C2×D411yescharacteristic
95C2×C4×C149C2×D412yes—
96C2×C4×C149C2×D412yes—
97C2×C4×C149C2411yescharacteristic
98C8×C149C2×D414yescomplemented
99C22×C149—42no—
100C22×C149—42no—
101C22×C149—44no—
102C22×C149—44no—
103C22×C149—84no—
104C22×C149—84no—
105C22×C149#12712yes—
106C22×C149AGL(1,ℤ/8)14yes—
107C22×C149C22×D411yescharacteristic
108C2×D149—42no—
109C2×D149—44no—
110C2×D149—84no—
111C4×C149#12712yes—
112C4×C149C22×D411yescharacteristic
113C4×C149C22×D411yescharacteristic
114Dic149—24no—
115Dic149—42no—
116C2×C149—82no—
117C2×C149—82no—
118C2×C149#49614yescomplemented
119C2×C149C2×#12711yescharacteristic
120C2×C149C2×AGL(1,ℤ/8)12yes—
121D149—82no—
122C149C2×#49611yescharacteristic, complemented, Sylow
123C2×#496—1491nomaximal, Sylow
124C22×SD16—1491no—
125C22×SD16—1491no—
126C22×D8—1491no—
127C22×D8D14911yescharacteristic, complemented
128C2×#127—1491no—
129C2×#124—1491no—
130#496—1498no—
131C2×#97—1491no—
132C22×Q8—1491no—
133C22×D4—2982no—
134C22×D4—1491no—
135C22×D4C2×D14911yescharacteristic
136C22×D4C2×D14911yescharacteristic
137C2×SD16—2984no—
138C2×SD16—2984no—
139C2×SD16—1494no—
140C2×SD16—1494no—
141C2×D8—24no—
142C2×D8—2984no—
143C2×D8—1494no—
144C2×D8C2×D14914yescomplemented
145C22×C8—1491no—
146C22×C8C2×D14911yescharacteristic
147#127—2982no—
148#127—1494no—
149#124—2982no—
150#124—1494no—
151C2×C22⋊C4—2982no—
152C2×C42—1491no—
153#97—1494no—
154C24—21no—
155C24—21no—
156C24—2981no—
157C2×Q8—2981no—
158C2×Q8—2982no—
159C2×Q8—2982no—
160C2×Q8—1492no—
161C2×D4—22no—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—2988no—
168C2×D4—2982no—
169C2×D4—2981no—
170C2×D4—2982no—
171C2×D4—5968no—
172C2×D4—1492no—
173C2×D4C22×D14912yes—
174C2×D4C22×D14912yes—
175C22×C4—2981no—
176C22×C4—1492no—
177C22×C4C22×D14911yescharacteristic
178SD16—2988no—
179SD16—2988no—
180D8—28no—
181D8—2988no—
182C2×C8—1494no—
183C2×C8—1492no—
184C2×C8C22⋊D14914yescomplemented
185C2×C8C22×D14912yes—
186C22⋊C4—2988no—
187C42—1492no—
188C42—1492no—
189C23—22no—
190C23—22no—
191C23—42no—
192C23—42no—
193C23—44no—
194C23—44no—
195C23—2982no—
196C23—5962no—
197C23—5964no—
198C23D4×D14911yescharacteristic
199Q8—2982no—
200Q8—2982no—
201Q8—5962no—
202D4—22no—
203D4—22no—
204D4—22no—
205D4—22no—
206D4—42no—
207D4—42no—
208D4—2982no—
209D4—2982no—
210D4—59616no—
211D4—5962no—
212C2×C4—2984no—
213C2×C4—2982no—
214C2×C4—5962no—
215C2×C4—1494no—
216C2×C4D4×D14911yescharacteristic
217C2×C4D4×D14912yes—
218C2×C4C2×C22⋊D14912yes—
219C2×C4C23×D14911yescharacteristic
220C8—1494no—
221C8C2×C22⋊D14914yescomplemented
222C22—44no—
223C22—44no—
224C22—42no—
225C22—42no—
226C22—84no—
227C22—84no—
228C22—5964no—
229C22—5962no—
230C22—11924no—
231C22#1801190712yes—
232C22#1801193514yes—
233C22C2×D4×D14911yescharacteristic
234C4—2984no—
235C4—5962no—
236C4#1801190712yes—
237C4C2×D4×D14911yescharacteristic
238C4C22×C22⋊D14911yescharacteristic
239C2—82no—
240C2—82no—
241C2—11922no—
242C2#2375001314yesdirect product factor
243C2C2×#1801190711yescharacteristic
244C2C2×#1801193512yes—
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×D8×C149C2
socleC23×C149C2×D4
hypercenterC22×D8D149
hypocenterC149C2×#496
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#14558725C2semidirect
2. C22×#14558724C2semidirect
3. C22×#14558721C2semidirect
4. C2×#18011907C2semidirect
5. C2×#18011898C2semidirect
6. #23750013C2direct (N × H)
7. C2×#18011821C2semidirect
8. C22×D8×C149C2semidirect
13. C2×#14558725C22semidirect
15. C2×#14558724C22semidirect
17. C2×#14558721C22semidirect
20. #18011907C22semidirect
22. #18011898C22semidirect
25. #18011821C22semidirect
29. C2×D8×C149C22semidirect
47. C2×#11924746D4semidirect
64. C2×C8×C149D4semidirect
80. #11924746C2×D4semidirect
98. C8×C149C2×D4semidirect
118. C2×C149#496semidirect
122. C149C2×#496semidirect
127. C22×D8D149semidirect
144. C2×D8C2×D149semidirect
184. C2×C8C22⋊D149semidirect
221. C8C2×C22⋊D149semidirect
242. C2#23750013direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587252
C22×#145587242
C22×#145587212
C2×#180119072
C2×#180118982
#237500132
C2×#180118212
C22×D8×C1492
C2×#496149