Finite Group Databasebeta

← C2×#23752464 #34078705

Subgroups — C2×#23752464 #34078705

Order 19328.

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

normal subgroups only

This group has 596 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
1C22×#14558989C211yesmaximal, characteristic, complemented
2C22×#14558987C211yesmaximal, characteristic, complemented
3C2×#18012714C211yesmaximal, characteristic, complemented
4C2×#18012710C211yesmaximal, characteristic, complemented
5#23752464C218yesmaximal, direct product factor
6C2×#18012670C211yesmaximal, characteristic, complemented
7C2×#18012661C211yesmaximal, characteristic, complemented
8C2×#102×C151C211yesmaximal, characteristic, complemented
9C22×D604—21no—
10C22×D604C2211yescharacteristic
11C22×C22⋊D151—21no—
12C22×C4×D151C2211yescharacteristic
13C2×#14558989—24no—
14C2×#14558989C2214yescomplemented
15C2×#14558987—24no—
16C2×#14558987C2214yescomplemented
17C22×C151⋊C8C2211yescharacteristic
18#18012714—22no—
19#18012714C2214yescomplemented
20#18012710—22no—
21#18012710C2214yescomplemented
22C2×C4⋊Dic151C2211yescharacteristic
23C2×C22⋊Dic151—21no—
24C2×(C2×D151)⋊C4—21no—
25#18012670C2214yescomplemented
26#18012661C2214yescomplemented
27C22×D4×C151C2211yescharacteristic
28C22×C8×C151C2211yescharacteristic
29C2×C4⋊C4×C151C2211yescharacteristic
30#102×C151C2214yescomplemented
31C23×D151—21no—
32C23×D151D411yescharacteristic
33C2×D604—24no—
34C2×D604—22no—
35C2×D604—21no—
36C2×D604—22no—
37C2×D604—44no—
38C2×D604C2312yes—
39C2×C22⋊D151—24no—
40C2×C22⋊D151—44no—
41C22×Dic151—21no—
42C22×Dic151D411yescharacteristic
43C2×C4×D151—22no—
44C2×C4×D151—22no—
45C2×C4×D151D412yes—
46C2×C4×D151C2312yes—
47#14558989—28no—
48#14558987—28no—
49C2×C151⋊C8D414yescomplemented
50C2×C151⋊C8C2312yes—
51C4⋊Dic151—21no—
52C4⋊Dic151C2312yes—
53C22⋊Dic151—24no—
54(C2×D151)⋊C4—24no—
55C24×C151—21no—
56C2×D4×C151—22no—
57C2×D4×C151—21no—
58C2×D4×C151—22no—
59C2×D4×C151C2312yes—
60C22×C4×C151—21no—
61C22×C4×C151C2311yescharacteristic
62C2×C8×C151—22no—
63C2×C8×C151C2312yes—
64C4⋊C4×C151—21no—
65C4⋊C4×C151C2312yes—
66C22×D151—22no—
67C22×D151—22no—
68C22×D151—22no—
69C22×D151—22no—
70C22×D151—42no—
71C22×D151—42no—
72C22×D151—42no—
73C22×D151C2×D412yes—
74D604—22no—
75D604—22no—
76D604—48no—
77D604—42no—
78C22⋊D151—48no—
79C2×Dic151—22no—
80C2×Dic151—22no—
81C2×Dic151—42no—
82C2×Dic151C2×D412yes—
83C4×D151—24no—
84C4×D151—22no—
85C4×D151—22no—
86C151⋊C8C2×D414yescomplemented
87C23×C151—22no—
88C23×C151—42no—
89C23×C151—42no—
90C23×C151—42no—
91C23×C151C2×D411yescharacteristic
92D4×C151—22no—
93D4×C151—22no—
94D4×C151—42no—
95C2×C4×C151—22no—
96C2×C4×C151—42no—
97C2×C4×C151C2×D411yescharacteristic
98C2×C4×C151C2×D412yes—
99C2×C4×C151#4112yes—
100C2×C4×C151C2411yescharacteristic
101C8×C151—22no—
102C22×C151—42no—
103C22×C151—42no—
104C22×C151—42no—
105C22×C151—84no—
106C22×C151#12112yes—
107C22×C151AGL(1,ℤ/8)12yes—
108C22×C151AGL(1,ℤ/8)12yes—
109C22×C151C22×D411yescharacteristic
110C2×D151—22no—
111C2×D151—22no—
112C2×D151—22no—
113C2×D151—44no—
114C2×D151—42no—
115C2×D151—42no—
116C2×D151—42no—
117C2×D151—84no—
118C4×C151—42no—
119C4×C151#12112yes—
120C4×C151C22×D411yescharacteristic
121C4×C151C2×#4111yescharacteristic
122Dic151—22no—
123Dic151—42no—
124C2×C151—82no—
125C2×C151#46914yescomplemented
126C2×C151C2×#12111yescharacteristic
127C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
128C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
129D151—42no—
130D151—82no—
131C151C2×#46911yescharacteristic, complemented, Sylow
132C2×#469—1511nomaximal, Sylow
133C22×D8—1511no—
134C22×M16—1511no—
135C2×#121—1511no—
136C2×#121—1511no—
137#469—1518no—
138C2×#106—1511no—
139C2×#102—1511no—
140C2×#102D15111yescharacteristic, complemented
141C22×D4—3021no—
142C22×D4—3021no—
143C22×D4—1511no—
144C22×D4C2×D15111yescharacteristic
145C23×C4—1511no—
146C2×D8—3024no—
147C2×D8—1514no—
148C2×M16—3024no—
149C2×M16—1514no—
150C22×C8—1511no—
151C22×C8C2×D15111yescharacteristic
152#121—3022no—
153#121—3022no—
154#121—1514no—
155#121—1514no—
156C2×C4⋊C4—1511no—
157C2×C4⋊C4C2×D15111yescharacteristic
158C2×C22⋊C4—3021no—
159C2×C22⋊C4—3021no—
160#106—1514no—
161#102—1514no—
162#102C2×D15114yescomplemented
163C24—21no—
164C24—3021no—
165C24—1511no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—3024no—
170C2×D4—3024no—
171C2×D4—3022no—
172C2×D4—3021no—
173C2×D4—3022no—
174C2×D4—6044no—
175C2×D4—6044no—
176C2×D4—1512no—
177C2×D4C22×D15112yes—
178C22×C4—21no—
179C22×C4—3022no—
180C22×C4—3022no—
181C22×C4—3021no—
182C22×C4—1511no—
183C22×C4—1512no—
184C22×C4—1512no—
185C22×C4C22×D15111yescharacteristic
186D8—3028no—
187M16—3028no—
188C2×C8—22no—
189C2×C8—1514no—
190C2×C8—1512no—
191C2×C8C22×D15112yes—
192C4⋊C4—21no—
193C4⋊C4—3021no—
194C4⋊C4—1512no—
195C4⋊C4C22×D15112yes—
196C22⋊C4—3024no—
197C22⋊C4—3024no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23—42no—
202C23—3022no—
203C23—3022no—
204C23—3022no—
205C23—3022no—
206C23—6042no—
207C23—6042no—
208C23—6042no—
209C23—1512no—
210C23D4×D15111yescharacteristic
211D4—22no—
212D4—22no—
213D4—42no—
214D4—3022no—
215D4—3022no—
216D4—6048no—
217D4—6048no—
218D4—6042no—
219C2×C4—22no—
220C2×C4—42no—
221C2×C4—3022no—
222C2×C4—3024no—
223C2×C4—3022no—
224C2×C4—3022no—
225C2×C4—3022no—
226C2×C4—6042no—
227C2×C4—1512no—
228C2×C4D4×D15111yescharacteristic
229C2×C4D4×D15112yes—
230C2×C4#1455900412yes—
231C2×C4C23×D15111yescharacteristic
232C8—22no—
233C8—1514no—
234C22—42no—
235C22—42no—
236C22—42no—
237C22—84no—
238C22—3022no—
239C22—3022no—
240C22—3022no—
241C22—6044no—
242C22—6042no—
243C22—6042no—
244C22—6042no—
245C22—12084no—
246C22#1801271212yes—
247C22#1801276312yes—
248C22#1801276612yes—
249C22C2×D4×D15111yescharacteristic
250C4—42no—
251C4—3022no—
252C4—6042no—
253C4#1801271212yes—
254C4C2×D4×D15111yescharacteristic
255C4C2×#1455900411yescharacteristic
256C2—82no—
257C2—6042no—
258C2—12082no—
259C2#2375246414yesdirect product factor
260C2C2×#1801271211yescharacteristic
261C2C2×#1801276311yescharacteristic
262C2C2×#1801276611yescharacteristic
subgroupG/H
centerC23D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#102×C151C2
socleC23×C151C2×D4
hypercenterC2×#102D151
hypocenterC151C2×#469
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#14558989C2semidirect
2. C22×#14558987C2semidirect
3. C2×#18012714C2semidirect
4. C2×#18012710C2semidirect
5. #23752464C2direct (N × H)
6. C2×#18012670C2semidirect
7. C2×#18012661C2semidirect
8. C2×#102×C151C2semidirect
14. C2×#14558989C22semidirect
16. C2×#14558987C22semidirect
19. #18012714C22semidirect
21. #18012710C22semidirect
25. #18012670C22semidirect
26. #18012661C22semidirect
30. #102×C151C22semidirect
49. C2×C151⋊C8D4semidirect
86. C151⋊C8C2×D4semidirect
125. C2×C151#469semidirect
131. C151C2×#469semidirect
140. C2×#102D151semidirect
162. #102C2×D151semidirect
259. C2#23752464direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145589892
C22×#145589872
C2×#180127142
C2×#180127102
#237524642
C2×#180126702
C2×#180126612
C2×#102×C1512
C2×#469151