Finite Group Databasebeta

← C2×#23749792 #34054014

Subgroups — C2×#23749792 #34054014

Order 19072.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18011956C211yesmaximal, characteristic, complemented
2C2×#18011937C212yesmaximal, complemented
3#23749792C218yesmaximal, direct product factor
4C2×#18011839C212yesmaximal, complemented
5C2×#18011828C211yesmaximal, characteristic, complemented
6C2×#127×C149C211yesmaximal, characteristic, complemented
7#18011956—22no—
8#18011956—24no—
9#18011956C2214yescomplemented
10C2×#14558736C2212yes—
11C2×#14558735—22no—
12C22×C22⋊D149—22no—
13C2×D4×D149—22no—
14#18011937—24no—
15#18011937C2218yescomplemented
16C2×#14558724—22no—
17C2×#14558721—22no—
18C2×#14558720C2212yescomplemented
19#18011839C2218yescomplemented
20#18011828C2214yescomplemented
21C22×D4×C149—22no—
22C22×D4×C149C2211yescharacteristic
23C22×D4×C149C2211yescharacteristic, complemented
24#127×C149—22no—
25#127×C149C2214yescomplemented
26C2×C42×C149C2211yescharacteristic, complemented
27C23×D149—22no—
28#14558736—22no—
29#14558736—22no—
30#14558736D414yescomplemented
31#14558736C2314yes—
32#14558735—28no—
33#14558735—28no—
34C2×Dic298D412yescomplemented
35C2×D596D412yescomplemented
36C2×C22⋊D149—24no—
37C2×C22⋊D149—28no—
38C2×C22⋊D149—22no—
39C2×C22⋊D149—28no—
40D4×D149—28no—
41D4×D149—28no—
42C22×Dic149—22no—
43C2×C4×D149—22no—
44#14558724—28no—
45#14558721—28no—
46#14558720—22no—
47#14558720C2314yescomplemented
48C2×#11924746—22no—
49C24×C149—21no—
50C24×C149D412yes—
51C2×D4×C149—28no—
52C2×D4×C149—22no—
53C2×D4×C149—22no—
54C2×D4×C149—22no—
55C2×D4×C149—22no—
56C2×D4×C149—21no—
57C2×D4×C149—48no—
58C2×D4×C149D412yes—
59C2×D4×C149C2312yes—
60C2×D4×C149C2312yescomplemented
61C22×C4×C149—21no—
62C22×C4×C149C2311yescharacteristic
63C42×C149—21no—
64C42×C149C2312yescomplemented
65C22×D149—22no—
66C22×D149—28no—
67C22×D149—84no—
68Dic298—22no—
69Dic298C2×D414yescomplemented
70D596—22no—
71D596C2×D414yescomplemented
72C22⋊D149—216no—
73C22⋊D149—24no—
74C22⋊D149—24no—
75C2×Dic149—28no—
76C2×Dic149—22no—
77C4×D149—24no—
78C4×D149—24no—
79#11924746—24no—
80C23×C149—22no—
81C23×C149—22no—
82C23×C149—22no—
83C23×C149—44no—
84C23×C149—44no—
85C23×C149—41no—
86C23×C149—41no—
87C23×C149C2×D411yescharacteristic
88C23×C149C2×D414yes—
89D4×C149—24no—
90D4×C149—24no—
91D4×C149—24no—
92D4×C149—416no—
93D4×C149—42no—
94C2×C4×C149—24no—
95C2×C4×C149—22no—
96C2×C4×C149C2×D412yes—
97C2×C4×C149C2×D412yes—
98C2×C4×C149C2×D411yescharacteristic
99C2×C4×C149C2411yescharacteristic
100C22×C149—22no—
101C22×C149—24no—
102C22×C149—44no—
103C22×C149—44no—
104C22×C149—44no—
105C22×C149—42no—
106C22×C149—82no—
107C22×C149—82no—
108C22×C149—82no—
109C22×C149#12011yescharacteristic
110C22×C149#12011yescharacteristic
111C22×C149C22×D411yescharacteristic
112C2×D149—24no—
113C2×D149—44no—
114C2×D149—88no—
115C4×C149—24no—
116C4×C149#12012yes—
117C4×C149C22×D412yes—
118Dic149—24no—
119C2×C149—21no—
120C2×C149—21no—
121C2×C149—44no—
122C2×C149—82no—
123C2×C149#45312yescomplemented
124C2×C149C2×#12011yescharacteristic
125D149—44no—
126C149C2×#45311yescharacteristic, complemented, Sylow
127C2×#453—1491nomaximal, Sylow
128C2×H(5,𝔽2)—1491no—
129C2×AGL(1,ℤ/8)—1492no—
130C2×#127D14911yescharacteristic, complemented
131#453—1498no—
132C2×#104—1492no—
133C2×#100—1491no—
134H(5,𝔽2)—2984no—
135H(5,𝔽2)—2982no—
136H(5,𝔽2)—1494no—
137C2×#41—2982no—
138C2×#41—1492no—
139C22×D4—22no—
140C22×D4—2982no—
141C22×D4—2982no—
142C22×D4C2×D14911yescharacteristic
143C22×D4C2×D14911yescharacteristic, complemented
144AGL(1,ℤ/8)—2984no—
145AGL(1,ℤ/8)—1498no—
146C2×SD16—2982no—
147C2×D8—2982no—
148C2×M16—1492no—
149#127—22no—
150#127C2×D14914yescomplemented
151C2×C42C2×D14911yescharacteristic, complemented
152#104—1498no—
153#100—1494no—
154C24—21no—
155C24—2982no—
156C24C22⋊D14912yes—
157#41—2988no—
158#41—2988no—
159#41—2982no—
160#41—2982no—
161#41—1494no—
162#41—1494no—
163C2×Q8—1492no—
164C2×D4—28no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—48no—
171C2×D4—2988no—
172C2×D4—2988no—
173C2×D4—2984no—
174C2×D4—2988no—
175C2×D4—2982no—
176C2×D4—2988no—
177C2×D4—1492no—
178C2×D4C22⋊D14912yes—
179C2×D4C22×D14912yes—
180C2×D4C22×D14912yescomplemented
181C22×C4—21no—
182C22×C4—2982no—
183C22×C4—2982no—
184C22×C4C22×D14911yescharacteristic
185SD16—2988no—
186D8—2988no—
187M16—2982no—
188M16—1494no—
189C2×C8—2982no—
190C42—21no—
191C42C22×D14912yescomplemented
192C23—22no—
193C23—22no—
194C23—22no—
195C23—44no—
196C23—44no—
197C23—41no—
198C23—41no—
199C23—2988no—
200C23—2982no—
201C23—11924no—
202C23C2×C22⋊D14911yescharacteristic
203C23C2×C22⋊D14914yes—
204Q8—2982no—
205Q8—1494no—
206D4—24no—
207D4—24no—
208D4—24no—
209D4—416no—
210D4—42no—
211D4—29816no—
212D4—2984no—
213D4—2984no—
214D4—2982no—
215D4—1494no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—2988no—
219C2×C4—2982no—
220C2×C4—2984no—
221C2×C4—2984no—
222C2×C4D4×D14912yes—
223C2×C4D4×D14912yes—
224C2×C4C2×C22⋊D14911yescharacteristic
225C2×C4C23×D14911yescharacteristic
226C8—2984no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—44no—
232C22—42no—
233C22—82no—
234C22—82no—
235C22—82no—
236C22—2984no—
237C22—5964no—
238C22—11928no—
239C22#1801187911yescharacteristic
240C22#1801187911yescharacteristic
241C22C22×C22⋊D14911yescharacteristic
242C4—24no—
243C4—2984no—
244C4#1801187912yes—
245C4C2×D4×D14912yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—82no—
250C2—5964no—
251C2#2374979212yesdirect product factor
252C2C2×#1801187911yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#127×C149C2
socleC22×C149#120
hypercenterC2×#127D149
hypocenterC149C2×#453
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#18011956C2semidirect
2. C2×#18011937C2semidirect
3. #23749792C2direct (N × H)
4. C2×#18011839C2semidirect
5. C2×#18011828C2semidirect
6. C2×#127×C149C2semidirect
9. #18011956C22semidirect
15. #18011937C22semidirect
18. C2×#14558720C22semidirect
19. #18011839C22semidirect
20. #18011828C22semidirect
23. C22×D4×C149C22semidirect
25. #127×C149C22semidirect
26. C2×C42×C149C22semidirect
30. #14558736D4semidirect
34. C2×Dic298D4semidirect
35. C2×D596D4semidirect
47. #14558720C23semidirect
60. C2×D4×C149C23semidirect
64. C42×C149C23semidirect
69. Dic298C2×D4semidirect
71. D596C2×D4semidirect
123. C2×C149#453semidirect
126. C149C2×#453semidirect
130. C2×#127D149semidirect
143. C22×D4C2×D149semidirect
150. #127C2×D149semidirect
151. C2×C42C2×D149semidirect
180. C2×D4C22×D149semidirect
191. C42C22×D149semidirect
251. C2#23749792direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180119562
C2×#180119372
#237497922
C2×#180118392
C2×#180118282
C2×#127×C1492
C2×#453149