Finite Group Databasebeta

← C2×#23750654 #34061396

Subgroups — C2×#23750654 #34061396

Order 19072.

564 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 194 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×#14558746C211yesmaximal, characteristic, complemented
2C23×#11924753C211yesmaximal, characteristic, complemented
3#23750654C218yesmaximal, direct product factor
4C2×C4⋊#11924753C211yesmaximal, characteristic, complemented
5C2×#18011968C211yesmaximal, characteristic, complemented
6C2×C22⋊#11924753C211yesmaximal, characteristic, complemented
7C2×#18011966C211yesmaximal, characteristic, complemented
8C2×#18011871C211yesmaximal, characteristic
9C2×#14558746—24no—
10C2×#14558746C2214yescomplemented
11C22×#11924753—24no—
12C22×#11924753C2211yescharacteristic
13C22×#11924753C2211yescharacteristic
14C22×#11924753C2211yescharacteristic
15C22×#11924753C2211yescharacteristic
16C22×#11924753C2214yescomplemented
17C4⋊#11924753C2214yescomplemented
18#18011968C2214yescomplemented
19C22⋊#11924753C2214yescomplemented
20#18011966C2214yescomplemented
21C22×C22⋊D149C411yescharacteristic
22C23×Dic149C2211yescharacteristic
23C22×C4×D149C2211yescharacteristic
24#18011871C414yes—
25#18011871C2214yes—
26C2×#14558715C411yescharacteristic
27C2×#14558713C411yescharacteristic
28C2×C4×Dic149C2211yescharacteristic
29C2×C22⋊C4×C149C411yescharacteristic
30#14558746—28no—
31C2×#11924753—28no—
32C2×#11924753—22no—
33C2×#11924753—22no—
34C2×#11924753—22no—
35C2×#11924753D414yescomplemented
36C2×#11924753C2312yes—
37C2×#11924753C2312yes—
38C2×#11924753C2312yes—
39C2×#11924753C2312yes—
40C23×D149C2×C411yescharacteristic
41C2×C22⋊D149—24no—
42C2×C22⋊D149C2×C414yes—
43C22×Dic149—22no—
44C22×Dic149—22no—
45C22×Dic149C2×C411yescharacteristic
46C22×Dic149C2×C412yes—
47C22×Dic149C2×C411yescharacteristic
48C22×Dic149C2312yes—
49C22×Dic149C2311yescharacteristic
50C2×C4×D149—22no—
51C2×C4×D149—22no—
52C2×C4×D149C2×C412yes—
53C2×C4×D149C2312yes—
54#14558715C2×C414yes—
55#14558713C2×C414yes—
56C4×Dic149C2×C412yes—
57C4×Dic149C2312yes—
58C24×C149C2×C411yescharacteristic
59C22×C4×C149C2×C411yescharacteristic
60C22×C4×C149C2×C411yescharacteristic
61C22⋊C4×C149C2×C414yes—
62#11924753—22no—
63#11924753—22no—
64#11924753—22no—
65#11924753C2×D414yescomplemented
66C22×D149—22no—
67C22×D149—22no—
68C22×D149—22no—
69C22×D149C22×C412yes—
70C22⋊D149—28no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149—24no—
74C2×Dic149—22no—
75C2×Dic149—22no—
76C2×Dic149C22×C412yes—
77C2×Dic149C22×C412yes—
78C2×Dic149C22×C411yescharacteristic
79C2×Dic149C2×D412yes—
80C2×Dic149#4112yes—
81C2×Dic149C2411yescharacteristic
82C4×D149—24no—
83C4×D149—22no—
84C4×D149—22no—
85C23×C149—22no—
86C23×C149—22no—
87C23×C149M1614yescomplemented
88C23×C149C22×C412yes—
89C23×C149C22×C411yescharacteristic
90C2×C4×C149—22no—
91C2×C4×C149—22no—
92C2×C4×C149C22×C412yes—
93C2×C4×C149C22×C412yes—
94C22×C149—22no—
95C22×C149—22no—
96C22×C149—28no—
97C22×C149C4×D412yes—
98C22×C149C2×M1612yes—
99C22×C149C2×M1614yescomplemented
100C22×C149#13112yes—
101C22×C149C23×C411yescharacteristic
102C2×D149—22no—
103C2×D149—22no—
104C2×D149—22no—
105C2×D149—44no—
106C4×C149—22no—
107C4×C149—22no—
108Dic149—22no—
109Dic149—22no—
110Dic149C4×D412yes—
111Dic149C22×D411yescharacteristic
112Dic149C2×#4111yescharacteristic
113C2×C149—24no—
114C2×C149#43514yescomplemented
115C2×C149C2×C4×D411yescharacteristic
116C2×C149C22×M1611yescharacteristic
117C2×C149C2×#13111yescharacteristic
118D149—42no—
119C149C2×#43511yescharacteristic, complemented, Sylow
120C2×#435—1491nomaximal, Sylow
121C22×M16—1491no—
122C23×C8—1491no—
123C2×C4×D4—1491no—
124#435—1498no—
125C2×C4⋊C8—1491no—
126C2×C22⋊C8—1491no—
127C2×C22⋊C8—1491no—
128C2×#97—1491no—
129C22×D4—1491no—
130C23×C4—1491no—
131C23×C4—1491no—
132C2×M16—2984no—
133C2×M16—1494no—
134C22×C8—2984no—
135C22×C8—1491no—
136C22×C8—1494no—
137C22×C8—1491no—
138C22×C8—1491no—
139C22×C8—1491no—
140C4×D4—1494no—
141C4×D4—1494no—
142C2×C4⋊C4—1491no—
143C2×C22⋊C4—1491no—
144C2×C22⋊C4#1059701011yescharacteristic
145C2×C42—1491no—
146C4⋊C8—1494no—
147C22⋊C8—1494no—
148C22⋊C8—1494no—
149#97—1494no—
150C24—1491no—
151C24C2×#1059701011yescharacteristic
152C2×D4—2984no—
153C2×D4—1494no—
154C22×C4—2982no—
155C22×C4—2982no—
156C22×C4—2982no—
157C22×C4—2982no—
158C22×C4—1492no—
159C22×C4—1492no—
160C22×C4—1491no—
161C22×C4—1491no—
162C22×C4—1492no—
163C22×C4—1492no—
164C22×C4—1491no—
165C22×C4C2×#1059701011yescharacteristic
166C22×C4C2×#1059701011yescharacteristic
167M16—2988no—
168C2×C8—2982no—
169C2×C8—2982no—
170C2×C8—2982no—
171C2×C8—2988no—
172C2×C8—1492no—
173C2×C8—1492no—
174C2×C8—1492no—
175C2×C8—1494no—
176C2×C8—1492no—
177C4⋊C4—1494no—
178C22⋊C4—1494no—
179C22⋊C4C2×#1059701014yes—
180C42—1492no—
181C42—1492no—
182C23—22no—
183C23—22no—
184C23—2982no—
185C23—2982no—
186C23—2982no—
187C23—1492no—
188C23#1455874614yescomplemented
189C23C22×#1059701012yes—
190C23C22×#1059701011yescharacteristic
191D4—2988no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2984no—
197C2×C4—2982no—
198C2×C4—2982no—
199C2×C4—2982no—
200C2×C4—2982no—
201C2×C4—2984no—
202C2×C4—1492no—
203C2×C4—1492no—
204C2×C4—1492no—
205C2×C4—1492no—
206C2×C4—1491no—
207C2×C4—1491no—
208C2×C4C22×#1059701012yes—
209C2×C4C22×#1059701012yes—
210C8—2982no—
211C8—2982no—
212C8—2982no—
213C8—1494no—
214C22—22no—
215C22—22no—
216C22—28no—
217C22—2982no—
218C22—2982no—
219C22—2982no—
220C22—5964no—
221C22D4×#1059701012yes—
222C22C2×#1455874612yes—
223C22C2×#1455874614yescomplemented
224C22#1801199812yes—
225C22C23×#1059701011yescharacteristic
226C4—22no—
227C4—22no—
228C4—2982no—
229C4—2982no—
230C4—1491no—
231C4—1491no—
232C4—1492no—
233C2—24no—
234C2—5962no—
235C2#2375065414yesdirect product factor
236C2C2×D4×#1059701011yescharacteristic
237C2C22×#1455874611yescharacteristic
238C2C2×#1801199811yescharacteristic
subgroupG/H
centerC23C22×#10597010
commutatorC22×C149C23×C4
FrattiniC22C23×#10597010
FittingC2×C22⋊C4×C149C4
socleC23×C149C22×C4
prime radicalC22×C22⋊D149C4
cosocleC2×Dic149C24
hypercenterC2×C22⋊C4#10597010
hypocenterC149C2×#435
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14558746C2semidirect
2. C23×#11924753C2semidirect
3. #23750654C2direct (N × H)
4. C2×C4⋊#11924753C2semidirect
5. C2×#18011968C2semidirect
6. C2×C22⋊#11924753C2semidirect
7. C2×#18011966C2semidirect
10. C2×#14558746C22semidirect
16. C22×#11924753C22semidirect
17. C4⋊#11924753C22semidirect
18. #18011968C22semidirect
19. C22⋊#11924753C22semidirect
20. #18011966C22semidirect
35. C2×#11924753D4semidirect
65. #11924753C2×D4semidirect
87. C23×C149M16semidirect
99. C22×C149C2×M16semidirect
114. C2×C149#435semidirect
119. C149C2×#435semidirect
188. C23#14558746semidirect
223. C22C2×#14558746semidirect
235. C2#23750654direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587462
C23×#119247532
#237506542
C2×C4⋊#119247532
C2×#180119682
C2×C22⋊#119247532
C2×#180119662
C2×#180118712
C2×#435149