Finite Group Databasebeta

← C2×#23749802 #34054020

Subgroups — C2×#23749802 #34054020

Order 19072.

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

normal subgroups only

This group has 760 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
2C2×#18011942C212yesmaximal, complemented
3#23749802C218yesmaximal, direct product factor
4C2×#18011839C212yesmaximal, complemented
5C2×#18011828C211yesmaximal, characteristic, complemented
6C2×#124×C149C211yesmaximal, characteristic, complemented
7#18011956—22no—
8#18011956—24no—
9#18011956C2214yes—
10C2×#14558736C2212yes—
11C2×#14558735—22no—
12C22×C22⋊D149—22no—
13C2×D4×D149—22no—
14#18011942—24no—
15#18011942C2218yescomplemented
16C2×#14558726—22no—
17C2×#14558723—22no—
18C2×#14558720C2212yescomplemented
19#18011839C2218yescomplemented
20#18011828C2214yescomplemented
21C22×Q8×C149C2211yescharacteristic, complemented
22C22×D4×C149C2211yescharacteristic
23#124×C149—22no—
24#124×C149C2214yescomplemented
25C2×C22⋊C4×C149—22no—
26C2×C42×C149C2211yescharacteristic, complemented
27C23×D149—22no—
28#14558736—22no—
29#14558736—22no—
30#14558736D414yes—
31#14558736C2314yes—
32#14558735—28no—
33#14558735—28no—
34C2×Dic298D412yes—
35C2×D596D412yes—
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#14558726—28no—
45#14558723—28no—
46#14558720—22no—
47#14558720C2314yescomplemented
48C2×#11924746—22no—
49C24×C149D412yes—
50C2×Q8×C149—21no—
51C2×Q8×C149—22no—
52C2×Q8×C149—22no—
53C2×Q8×C149C2312yescomplemented
54C2×D4×C149—22no—
55C2×D4×C149—22no—
56C2×D4×C149D412yes—
57C2×D4×C149C2312yes—
58C22×C4×C149—21no—
59C22×C4×C149—21no—
60C22×C4×C149C2311yescharacteristic
61C22⋊C4×C149—28no—
62C42×C149—21no—
63C42×C149C2312yescomplemented
64C22×D149—22no—
65C22×D149—28no—
66C22×D149—84no—
67Dic298—22no—
68Dic298C2×D414yes—
69D596—22no—
70D596C2×D414yes—
71C22⋊D149—216no—
72C22⋊D149—24no—
73C22⋊D149—24no—
74C2×Dic149—28no—
75C2×Dic149—22no—
76C4×D149—24no—
77C4×D149—24no—
78#11924746—24no—
79C23×C149—22no—
80C23×C149—22no—
81C23×C149—44no—
82C23×C149C2×D411yescharacteristic
83C23×C149C2×D414yes—
84Q8×C149—24no—
85Q8×C149—42no—
86D4×C149—24no—
87D4×C149—24no—
88C2×C4×C149—22no—
89C2×C4×C149—22no—
90C2×C4×C149—42no—
91C2×C4×C149—41no—
92C2×C4×C149—41no—
93C2×C4×C149C2×D412yes—
94C2×C4×C149C2×D412yes—
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2411yescharacteristic
97C22×C149—22no—
98C22×C149—24no—
99C22×C149—44no—
100C22×C149—44no—
101C22×C149—82no—
102C22×C149#12011yescharacteristic
103C22×C149#12011yescharacteristic
104C22×C149C22×D411yescharacteristic
105C2×D149—24no—
106C2×D149—44no—
107C2×D149—88no—
108C4×C149—42no—
109C4×C149—42no—
110C4×C149#12012yes—
111C4×C149C22×D412yes—
112Dic149—24no—
113C2×C149—21no—
114C2×C149—21no—
115C2×C149—44no—
116C2×C149#45512yescomplemented
117C2×C149C2×#12011yescharacteristic
118D149—44no—
119C149C2×#45511yescharacteristic, complemented, Sylow
120C2×#455—1491nomaximal, Sylow
121C2×H(5,𝔽2)—1491no—
122C2×#137—1492no—
123C2×#124D14911yescharacteristic, complemented
124#455—1498no—
125C2×#104—1492no—
126C2×#100—1491no—
127H(5,𝔽2)—2984no—
128H(5,𝔽2)—2982no—
129H(5,𝔽2)—1494no—
130C2×#41—2982no—
131C2×#41—1492no—
132C22×Q8C2×D14911yescharacteristic, complemented
133C22×D4—2982no—
134C22×D4—2982no—
135C22×D4C2×D14911yescharacteristic
136#137—2984no—
137#137—1498no—
138C2×Q16—2982no—
139C2×SD16—2982no—
140C2×M16—1492no—
141#124—22no—
142#124C2×D14914yescomplemented
143C2×C22⋊C4—22no—
144C2×C42C2×D14911yescharacteristic, complemented
145#104—1498no—
146#100—1494no—
147C24—2982no—
148C24C22⋊D14912yes—
149#41—2988no—
150#41—2988no—
151#41—2982no—
152#41—2982no—
153#41—1494no—
154#41—1494no—
155C2×Q8—21no—
156C2×Q8—22no—
157C2×Q8—22no—
158C2×Q8—1492no—
159C2×Q8C22×D14912yescomplemented
160C2×D4—22no—
161C2×D4—22no—
162C2×D4—2988no—
163C2×D4—2988no—
164C2×D4—2984no—
165C2×D4—2988no—
166C2×D4—2982no—
167C2×D4—2988no—
168C2×D4—1492no—
169C2×D4C22⋊D14912yes—
170C2×D4C22×D14912yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—2982no—
174C22×C4—2982no—
175C22×C4C22×D14911yescharacteristic
176Q16—2988no—
177SD16—2988no—
178M16—2982no—
179M16—1494no—
180C2×C8—2982no—
181C22⋊C4—28no—
182C42—21no—
183C42C22×D14912yescomplemented
184C23—22no—
185C23—22no—
186C23—44no—
187C23—2988no—
188C23—2982no—
189C23—11924no—
190C23C2×C22⋊D14911yescharacteristic
191C23C2×C22⋊D14914yes—
192Q8—24no—
193Q8—42no—
194Q8—2982no—
195Q8—1494no—
196D4—24no—
197D4—24no—
198D4—29816no—
199D4—2984no—
200D4—2984no—
201D4—2982no—
202D4—1494no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—2988no—
209C2×C4—2982no—
210C2×C4—2984no—
211C2×C4—2984no—
212C2×C4D4×D14912yes—
213C2×C4D4×D14912yes—
214C2×C4C2×C22⋊D14911yescharacteristic
215C2×C4C23×D14911yescharacteristic
216C8—2984no—
217C22—22no—
218C22—24no—
219C22—44no—
220C22—44no—
221C22—82no—
222C22—2984no—
223C22—5964no—
224C22—11928no—
225C22#1801187911yescharacteristic
226C22#1801187911yescharacteristic
227C22C22×C22⋊D14911yescharacteristic
228C4—42no—
229C4—42no—
230C4—2984no—
231C4#1801187912yes—
232C4C2×D4×D14912yes—
233C2—21no—
234C2—21no—
235C2—44no—
236C2—5964no—
237C2#2374980212yesdirect product factor
238C2C2×#1801187911yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#124×C149C2
socleC22×C149#120
prime radicalC2×#18011956C2
hypercenterC2×#124D149
hypocenterC149C2×#455
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#18011942C2semidirect
3. #23749802C2direct (N × H)
4. C2×#18011839C2semidirect
5. C2×#18011828C2semidirect
6. C2×#124×C149C2semidirect
15. #18011942C22semidirect
18. C2×#14558720C22semidirect
19. #18011839C22semidirect
20. #18011828C22semidirect
21. C22×Q8×C149C22semidirect
24. #124×C149C22semidirect
26. C2×C42×C149C22semidirect
47. #14558720C23semidirect
53. C2×Q8×C149C23semidirect
63. C42×C149C23semidirect
116. C2×C149#455semidirect
119. C149C2×#455semidirect
123. C2×#124D149semidirect
132. C22×Q8C2×D149semidirect
142. #124C2×D149semidirect
144. C2×C42C2×D149semidirect
159. C2×Q8C22×D149semidirect
183. C42C22×D149semidirect
237. C2#23749802direct (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×#180119422
#237498022
C2×#180118392
C2×#180118282
C2×#124×C1492
C2×#455149