Finite Group Databasebeta

← C2×#23750656 #34061398

Subgroups — C2×#23750656 #34061398

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×#14558745C211yesmaximal, characteristic, complemented
2C23×#11924753C211yesmaximal, characteristic, complemented
3#23750656C218yesmaximal, direct product factor
4C2×#18011978C211yesmaximal, characteristic, complemented
5C2×C22⋊#11924753C211yesmaximal, characteristic, complemented
6C2×C22⋊#11924753C211yesmaximal, characteristic, complemented
7C2×#18011966C211yesmaximal, characteristic, complemented
8C2×D4×Dic149C211yesmaximal, characteristic
9C2×#14558745—24no—
10C2×#14558745C2214yescomplemented
11C22×#11924753—24no—
12C22×#11924753C2211yescharacteristic
13C22×#11924753C2211yescharacteristic
14C22×#11924753C2211yescharacteristic
15C22×#11924753C2211yescharacteristic
16C22×#11924753C2214yescomplemented
17#18011978C2214yescomplemented
18C22⋊#11924753C2214yescomplemented
19C22⋊#11924753C2214yescomplemented
20#18011966C2214yescomplemented
21C23×Dic149C2211yescharacteristic
22C23×Dic149C2211yescharacteristic
23D4×Dic149C414yes—
24D4×Dic149C2214yes—
25C2×C4⋊Dic149C411yescharacteristic
26C2×C22⋊Dic149C411yescharacteristic
27C2×C22⋊Dic149C411yescharacteristic
28C2×C4×Dic149C2211yescharacteristic
29C22×D4×C149C411yescharacteristic
30#14558745—28no—
31C2×#11924753—28no—
32C2×#11924753—22no—
33C2×#11924753—22no—
34C2×#11924753—22no—
35C2×#11924753D414yescomplemented
36C2×#11924753C2312yes—
37C2×#11924753C2312yes—
38C2×#11924753C2312yes—
39C2×#11924753C2312yes—
40C22×Dic149—22no—
41C22×Dic149—22no—
42C22×Dic149—22no—
43C22×Dic149—22no—
44C22×Dic149C2×C411yescharacteristic
45C22×Dic149C2×C411yescharacteristic
46C22×Dic149C2×C412yes—
47C22×Dic149C2×C412yes—
48C22×Dic149C2×C411yescharacteristic
49C22×Dic149C2312yes—
50C22×Dic149C2312yes—
51C22×Dic149C2311yescharacteristic
52C4⋊Dic149C2×C414yes—
53C22⋊Dic149C2×C414yes—
54C22⋊Dic149C2×C414yes—
55C4×Dic149C2×C412yes—
56C4×Dic149C2312yes—
57C24×C149C2×C411yescharacteristic
58C24×C149C2×C411yescharacteristic
59C2×D4×C149—24no—
60C2×D4×C149C2×C414yes—
61C22×C4×C149C2×C411yescharacteristic
62#11924753—22no—
63#11924753—22no—
64#11924753—22no—
65#11924753C2×D414yescomplemented
66C2×Dic149—22no—
67C2×Dic149—22no—
68C2×Dic149—22no—
69C2×Dic149—24no—
70C2×Dic149—24no—
71C2×Dic149—22no—
72C2×Dic149—22no—
73C2×Dic149—22no—
74C2×Dic149—22no—
75C2×Dic149C22×C412yes—
76C2×Dic149C22×C412yes—
77C2×Dic149C22×C412yes—
78C2×Dic149C22×C411yescharacteristic
79C2×Dic149C2×D412yes—
80C2×Dic149#4112yes—
81C2×Dic149C2411yescharacteristic
82C23×C149—22no—
83C23×C149—22no—
84C23×C149—22no—
85C23×C149—22no—
86C23×C149—22no—
87C23×C149M1614yescomplemented
88C23×C149C22×C412yes—
89C23×C149C22×C412yes—
90C23×C149C22×C411yescharacteristic
91D4×C149—28no—
92C2×C4×C149—22no—
93C2×C4×C149C22×C412yes—
94C22×C149—22no—
95C22×C149—22no—
96C22×C149—28no—
97C22×C149—22no—
98C22×C149—22no—
99C22×C149—22no—
100C22×C149—44no—
101C22×C149C4×D412yes—
102C22×C149C2×M1612yes—
103C22×C149C2×M1614yescomplemented
104C22×C149#13112yes—
105C22×C149C23×C411yescharacteristic
106C4×C149—22no—
107Dic149—22no—
108Dic149—22no—
109Dic149—22no—
110Dic149C4×D412yes—
111Dic149C22×D411yescharacteristic
112Dic149C2×#4111yescharacteristic
113C2×C149—24no—
114C2×C149—42no—
115C2×C149#43514yescomplemented
116C2×C149C2×C4×D411yescharacteristic
117C2×C149C22×M1611yescharacteristic
118C2×C149C2×#13111yescharacteristic
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#1059701011yescharacteristic
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—1491no—
145C2×C42—1491no—
146C4⋊C8—1494no—
147C22⋊C8—1494no—
148C22⋊C8—1494no—
149#97—1494no—
150C24C2×#1059701011yescharacteristic
151C24C2×#1059701011yescharacteristic
152C2×D4—24no—
153C2×D4C2×#1059701014yes—
154C22×C4—2982no—
155C22×C4—2982no—
156C22×C4—2982no—
157C22×C4—2982no—
158C22×C4—1492no—
159C22×C4—1492no—
160C22×C4—1492no—
161C22×C4—1492no—
162C22×C4—1491no—
163C22×C4—1491no—
164C22×C4—1491no—
165C22×C4—1491no—
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⋊C4—1494no—
180C42—1492no—
181C42—1492no—
182C23—22no—
183C23—22no—
184C23—22no—
185C23—22no—
186C23—22no—
187C23#1455874514yescomplemented
188C23C22×#1059701012yes—
189C23C22×#1059701012yes—
190C23C22×#1059701011yescharacteristic
191D4—28no—
192C2×C4—22no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—2982no—
198C2×C4—2982no—
199C2×C4—2982no—
200C2×C4—2984no—
201C2×C4—2984no—
202C2×C4—1492no—
203C2×C4—1492no—
204C2×C4—1492no—
205C2×C4—1492no—
206C2×C4—1492no—
207C2×C4—1491no—
208C2×C4—1491no—
209C2×C4C22×#1059701012yes—
210C8—2982no—
211C8—2982no—
212C8—2982no—
213C8—1494no—
214C22—28no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—22no—
219C22—22no—
220C22—44no—
221C22D4×#1059701012yes—
222C22C2×#1455874512yes—
223C22C2×#1455874514yescomplemented
224C22#1801199812yes—
225C22C23×#1059701011yescharacteristic
226C4—22no—
227C4—2982no—
228C4—2982no—
229C4—2982no—
230C4—1491no—
231C4—1491no—
232C4—1492no—
233C2—24no—
234C2—42no—
235C2#2375065614yesdirect product factor
236C2C2×D4×#1059701011yescharacteristic
237C2C22×#1455874511yescharacteristic
238C2C2×#1801199811yescharacteristic
subgroupG/H
centerC23C22×#10597010
commutatorC22×C149C23×C4
FrattiniC22C23×#10597010
Fitting, prime radicalC22×D4×C149C4
socleC23×C149C22×C4
cosocleC2×Dic149C24
hypercenterC22×D4#10597010
hypocenterC149C2×#435
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14558745C2semidirect
2. C23×#11924753C2semidirect
3. #23750656C2direct (N × H)
4. C2×#18011978C2semidirect
5. C2×C22⋊#11924753C2semidirect
6. C2×C22⋊#11924753C2semidirect
7. C2×#18011966C2semidirect
10. C2×#14558745C22semidirect
16. C22×#11924753C22semidirect
17. #18011978C22semidirect
18. C22⋊#11924753C22semidirect
19. C22⋊#11924753C22semidirect
20. #18011966C22semidirect
35. C2×#11924753D4semidirect
65. #11924753C2×D4semidirect
87. C23×C149M16semidirect
103. C22×C149C2×M16semidirect
115. C2×C149#435semidirect
119. C149C2×#435semidirect
187. C23#14558745semidirect
223. C22C2×#14558745semidirect
235. C2#23750656direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587452
C23×#119247532
#237506562
C2×#180119782
C2×C22⋊#119247532
C2×#180119662
C2×D4×Dic1492
C2×#435149