Finite Group Databasebeta

← C2×#23750526 #34060938

Subgroups — C2×#23750526 #34060938

Order 19072.

438 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 58 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×#18011971C211yesmaximal, characteristic, complemented
2C2×#18011969C211yesmaximal, characteristic, complemented
3#23750526C214yesmaximal, direct product factor
4C2×#18011881C211yesmaximal, characteristic
5C2×#14558745—21no—
6C2×C22⋊#10597010—21no—
7#18011971—21no—
8#18011971C2212yescomplemented
9#18011969—21no—
10#18011969C2212yescomplemented
11C24×D149C411yescharacteristic, complemented
12C22×D596—21no—
13C22×C22⋊D149C2211yescharacteristic
14#18011881—21no—
15#18011881—21no—
16#18011881C412yescomplemented
17#18011881C2212yes—
18C2×#14558713—21no—
19C2×C22⋊C4×C149C411yescharacteristic, complemented
20C22×#10597010—41no—
21#14558745—22no—
22#14558745—41no—
23C2×#11924753—41no—
24C22⋊#10597010—22no—
25C22⋊#10597010—41no—
26C23×D149—21no—
27C23×D149—21no—
28C23×D149—41no—
29C23×D149—41no—
30C23×D149—44no—
31C23×D149C2×C412yescomplemented
32C23×D149D411yescharacteristic
33C2×D596—22no—
34C2×D596—22no—
35C2×D596—44no—
36C2×C22⋊D149—41no—
37C2×C22⋊D149—41no—
38C2×C22⋊D149C2×C411yescharacteristic
39C2×C22⋊D149D411yescharacteristic
40C2×C22⋊D149D411yescharacteristic
41C2×C22⋊D149C2311yescharacteristic
42C22×Dic149D411yescharacteristic
43#14558713—22no—
44#14558713—22no—
45C24×C149C2×C411yescharacteristic
46C22×C4×C149—21no—
47C22⋊C4×C149—21no—
48C22⋊C4×C149C2×C412yescomplemented
49C2×#10597010—42no—
50C2×#10597010—82no—
51#11924753—42no—
52C22×D149—24no—
53C22×D149—21no—
54C22×D149—22no—
55C22×D149—21no—
56C22×D149—44no—
57C22×D149—44no—
58C22×D149—42no—
59C22×D149—42no—
60C22×D149—48no—
61C22×D149—44no—
62C22×D149—41no—
63C22×D149—41no—
64C22×D149—42no—
65C22×D149—44no—
66C22×D149—42no—
67C22×D149C22⋊C411yescharacteristic
68C22×D149C2×D411yescharacteristic
69D596—44no—
70D596—44no—
71C22⋊D149—41no—
72C22⋊D149—41no—
73C22⋊D149—41no—
74C22⋊D149—41no—
75C2×Dic149—21no—
76C2×Dic149—21no—
77C2×Dic149C22⋊C411yescharacteristic
78C2×Dic149C2×D411yescharacteristic
79C23×C149—21no—
80C23×C149—21no—
81C23×C149—42no—
82C23×C149C22⋊C411yescharacteristic
83C23×C149C22⋊C411yescharacteristic
84C23×C149C22×C411yescharacteristic
85C2×C4×C149—22no—
86C2×C4×C149—42no—
87C22×C149—22no—
88C22×C149—21no—
89C22×C149—21no—
90C22×C149—41no—
91C22×C149—41no—
92C22×C149—42no—
93C22×C149—42no—
94C22×C149#9911yescharacteristic
95C22×C149#9911yescharacteristic
96C22×C149C2×C22⋊C411yescharacteristic
97C2×D149—24no—
98C2×D149—21no—
99C2×D149—21no—
100C2×D149—42no—
101C2×D149—44no—
102C2×D149—48no—
103C2×D149—44no—
104C2×D149—44no—
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—41no—
108C2×D149—41no—
109C2×D149—44no—
110C2×D149—81no—
111#10597010—82no—
112C4×C149—42no—
113Dic149—21no—
114Dic149—21no—
115C2×C149—21no—
116C2×C149—21no—
117C2×C149—41no—
118C2×C149—41no—
119C2×C149AΣL(1,𝔽16)12yescomplemented
120C2×C149C2×#9911yescharacteristic
121D149—41no—
122D149—44no—
123D149—41no—
124C149C2×AΣL(1,𝔽16)11yescharacteristic, complemented, Sylow
125C2×AΣL(1,𝔽16)—1491nomaximal, Sylow
126C2×#120—1491no—
127C2×#100—1491no—
128C2×#99—1491no—
129AΣL(1,𝔽16)—1494no—
130C25—1491no—
131C22×D4—2981no—
132C22×D4—1491no—
133C2×M16—2981no—
134#120—2981no—
135#120—2981no—
136#120—1492no—
137#120—1492no—
138C2×C22⋊C4—2981no—
139C2×C22⋊C4—2981no—
140C2×C22⋊C4#1059701011yescharacteristic, complemented
141#100—2981no—
142#100—1492no—
143#99—2981no—
144#99—1492no—
145C24—2981no—
146C24—2981no—
147C24—5961no—
148C24—5961no—
149C24—5964no—
150C24—1491no—
151C24—1492no—
152C24C2×#1059701011yescharacteristic
153C2×D4—2982no—
154C2×D4—2982no—
155C2×D4—5964no—
156C2×D4—5961no—
157C2×D4—5961no—
158C2×D4—1491no—
159C2×D4—1491no—
160C2×D4—1491no—
161C2×D4—1491no—
162C22×C4—21no—
163C22×C4—5961no—
164C22×C4—1491no—
165M16—2982no—
166M16—5961no—
167C2×C8—5961no—
168C22⋊C4—21no—
169C22⋊C4—2982no—
170C22⋊C4—2982no—
171C22⋊C4—2982no—
172C22⋊C4—5961no—
173C22⋊C4C2×#1059701012yescomplemented
174C23—21no—
175C23—21no—
176C23—42no—
177C23—2984no—
178C23—2981no—
179C23—2982no—
180C23—2981no—
181C23—5962no—
182C23—5962no—
183C23—5962no—
184C23—5962no—
185C23—5964no—
186C23—5964no—
187C23—5964no—
188C23—5968no—
189C23—5964no—
190C23—5961no—
191C23—5961no—
192C23—1491no—
193C23—1491no—
194C23C22⋊#1059701011yescharacteristic
195C23C22⋊#1059701011yescharacteristic
196C23C22×#1059701011yescharacteristic
197D4—5964no—
198D4—5964no—
199D4—5961no—
200D4—5961no—
201D4—5961no—
202D4—5961no—
203C2×C4—22no—
204C2×C4—42no—
205C2×C4—2981no—
206C2×C4—2981no—
207C2×C4—5962no—
208C2×C4—1491no—
209C2×C4—1491no—
210C2×C4—11922no—
211C8—5962no—
212C22—22no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—42no—
218C22—42no—
219C22—2984no—
220C22—2981no—
221C22—2981no—
222C22—5961no—
223C22—5961no—
224C22—5962no—
225C22—5964no—
226C22—5964no—
227C22—5964no—
228C22—5968no—
229C22—5962no—
230C22—5964no—
231C22—5962no—
232C22—11921no—
233C22#1801197011yescharacteristic
234C22#1801197011yescharacteristic
235C22C2×C22⋊#1059701011yescharacteristic
236C4—42no—
237C4—2981no—
238C4—2981no—
239C4—11922no—
240C2—21no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2—5961no—
245C2—5964no—
246C2—5961no—
247C2#2375052612yesdirect product factor
248C2C2×#1801197011yescharacteristic
subgroupG/H
centerC22#18011970
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149#99
prime radicalC2×#18011881C2
cosocleC2×C22⋊D149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149C2×AΣL(1,𝔽16)
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#18011971C2semidirect
2. C2×#18011969C2semidirect
3. #23750526C2direct (N × H)
8. #18011971C22semidirect
10. #18011969C22semidirect
11. C24×D149C4semidirect
16. #18011881C4semidirect
19. C2×C22⋊C4×C149C4semidirect
31. C23×D149C2×C4semidirect
48. C22⋊C4×C149C2×C4semidirect
119. C2×C149AΣL(1,𝔽16)semidirect
124. C149C2×AΣL(1,𝔽16)semidirect
140. C2×C22⋊C4#10597010semidirect
173. C22⋊C4C2×#10597010semidirect
247. C2#23750526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180119712
C2×#180119692
#237505262
C2×#180118812
C2×AΣL(1,𝔽16)149