Finite Group Databasebeta

← C2×#23752379 #34078433

Subgroups — C2×#23752379 #34078433

Order 19328.

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

normal subgroups only

This group has 844 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×#18012784C211yesmaximal, characteristic, complemented
2C2×#18012765C212yesmaximal, complemented
3#23752379C218yesmaximal, direct product factor
4C2×#18012667C212yesmaximal, complemented
5C2×#18012656C211yesmaximal, characteristic, complemented
6C2×#127×C151C211yesmaximal, characteristic, complemented
7#18012784—22no—
8#18012784—24no—
9#18012784C2214yescomplemented
10C2×#14559004C2212yes—
11C2×#14559003—22no—
12C22×C22⋊D151—22no—
13C2×D4×D151—22no—
14#18012765—24no—
15#18012765C2218yescomplemented
16C2×#14558992—22no—
17C2×#14558989—22no—
18C2×#14558988C2212yescomplemented
19#18012667C2218yescomplemented
20#18012656C2214yescomplemented
21C22×D4×C151—22no—
22C22×D4×C151C2211yescharacteristic
23C22×D4×C151C2211yescharacteristic, complemented
24#127×C151—22no—
25#127×C151C2214yescomplemented
26C2×C42×C151C2211yescharacteristic, complemented
27C23×D151—22no—
28#14559004—22no—
29#14559004—22no—
30#14559004D414yescomplemented
31#14559004C2314yes—
32#14559003—28no—
33#14559003—28no—
34C2×Dic302D412yescomplemented
35C2×D604D412yescomplemented
36C2×C22⋊D151—24no—
37C2×C22⋊D151—28no—
38C2×C22⋊D151—22no—
39C2×C22⋊D151—28no—
40D4×D151—28no—
41D4×D151—28no—
42C22×Dic151—22no—
43C2×C4×D151—22no—
44#14558992—28no—
45#14558989—28no—
46#14558988—22no—
47#14558988C2314yescomplemented
48C2×C151⋊C8—22no—
49C24×C151—21no—
50C24×C151D412yes—
51C2×D4×C151—28no—
52C2×D4×C151—22no—
53C2×D4×C151—22no—
54C2×D4×C151—22no—
55C2×D4×C151—22no—
56C2×D4×C151—21no—
57C2×D4×C151—48no—
58C2×D4×C151D412yes—
59C2×D4×C151C2312yes—
60C2×D4×C151C2312yescomplemented
61C22×C4×C151—21no—
62C22×C4×C151C2311yescharacteristic
63C42×C151—21no—
64C42×C151C2312yescomplemented
65C22×D151—22no—
66C22×D151—28no—
67C22×D151—84no—
68Dic302—22no—
69Dic302C2×D414yescomplemented
70D604—22no—
71D604C2×D414yescomplemented
72C22⋊D151—216no—
73C22⋊D151—24no—
74C22⋊D151—24no—
75C2×Dic151—28no—
76C2×Dic151—22no—
77C4×D151—24no—
78C4×D151—24no—
79C151⋊C8—24no—
80C23×C151—22no—
81C23×C151—22no—
82C23×C151—22no—
83C23×C151—44no—
84C23×C151—44no—
85C23×C151—41no—
86C23×C151—41no—
87C23×C151C2×D411yescharacteristic
88C23×C151C2×D414yes—
89D4×C151—24no—
90D4×C151—24no—
91D4×C151—24no—
92D4×C151—416no—
93D4×C151—42no—
94C2×C4×C151—24no—
95C2×C4×C151—22no—
96C2×C4×C151C2×D412yes—
97C2×C4×C151C2×D412yes—
98C2×C4×C151C2×D411yescharacteristic
99C2×C4×C151C2411yescharacteristic
100C22×C151—22no—
101C22×C151—24no—
102C22×C151—44no—
103C22×C151—44no—
104C22×C151—44no—
105C22×C151—42no—
106C22×C151—82no—
107C22×C151—82no—
108C22×C151—82no—
109C22×C151#12011yescharacteristic
110C22×C151#12011yescharacteristic
111C22×C151C22×D411yescharacteristic
112C2×D151—24no—
113C2×D151—44no—
114C2×D151—88no—
115C4×C151—24no—
116C4×C151#12012yes—
117C4×C151C22×D412yes—
118Dic151—24no—
119C2×C151—21no—
120C2×C151—21no—
121C2×C151—44no—
122C2×C151—82no—
123C2×C151#45312yescomplemented
124C2×C151C2×#12011yescharacteristic
125D151—44no—
126C151C2×#45311yescharacteristic, complemented, Sylow
127C2×#453—1511nomaximal, Sylow
128C2×H(5,𝔽2)—1511no—
129C2×AGL(1,ℤ/8)—1512no—
130C2×#127D15111yescharacteristic, complemented
131#453—1518no—
132C2×#104—1512no—
133C2×#100—1511no—
134H(5,𝔽2)—3024no—
135H(5,𝔽2)—3022no—
136H(5,𝔽2)—1514no—
137C2×#41—3022no—
138C2×#41—1512no—
139C22×D4—22no—
140C22×D4—3022no—
141C22×D4—3022no—
142C22×D4C2×D15111yescharacteristic
143C22×D4C2×D15111yescharacteristic, complemented
144AGL(1,ℤ/8)—3024no—
145AGL(1,ℤ/8)—1518no—
146C2×SD16—3022no—
147C2×D8—3022no—
148C2×M16—1512no—
149#127—22no—
150#127C2×D15114yescomplemented
151C2×C42C2×D15111yescharacteristic, complemented
152#104—1518no—
153#100—1514no—
154C24—21no—
155C24—3022no—
156C24C22⋊D15112yes—
157#41—3028no—
158#41—3028no—
159#41—3022no—
160#41—3022no—
161#41—1514no—
162#41—1514no—
163C2×Q8—1512no—
164C2×D4—28no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—21no—
170C2×D4—48no—
171C2×D4—3028no—
172C2×D4—3028no—
173C2×D4—3024no—
174C2×D4—3028no—
175C2×D4—3022no—
176C2×D4—3028no—
177C2×D4—1512no—
178C2×D4C22⋊D15112yes—
179C2×D4C22×D15112yes—
180C2×D4C22×D15112yescomplemented
181C22×C4—21no—
182C22×C4—3022no—
183C22×C4—3022no—
184C22×C4C22×D15111yescharacteristic
185SD16—3028no—
186D8—3028no—
187M16—3022no—
188M16—1514no—
189C2×C8—3022no—
190C42—21no—
191C42C22×D15112yescomplemented
192C23—22no—
193C23—22no—
194C23—22no—
195C23—44no—
196C23—44no—
197C23—41no—
198C23—41no—
199C23—3028no—
200C23—3022no—
201C23—12084no—
202C23C2×C22⋊D15111yescharacteristic
203C23C2×C22⋊D15114yes—
204Q8—3022no—
205Q8—1514no—
206D4—24no—
207D4—24no—
208D4—24no—
209D4—416no—
210D4—42no—
211D4—30216no—
212D4—3024no—
213D4—3024no—
214D4—3022no—
215D4—1514no—
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—3028no—
219C2×C4—3022no—
220C2×C4—3024no—
221C2×C4—3024no—
222C2×C4D4×D15112yes—
223C2×C4D4×D15112yes—
224C2×C4C2×C22⋊D15111yescharacteristic
225C2×C4C23×D15111yescharacteristic
226C8—3024no—
227C22—22no—
228C22—24no—
229C22—44no—
230C22—44no—
231C22—44no—
232C22—42no—
233C22—82no—
234C22—82no—
235C22—82no—
236C22—3024no—
237C22—6044no—
238C22—12088no—
239C22#1801270711yescharacteristic
240C22#1801270711yescharacteristic
241C22C22×C22⋊D15111yescharacteristic
242C4—24no—
243C4—3024no—
244C4#1801270712yes—
245C4C2×D4×D15112yes—
246C2—21no—
247C2—21no—
248C2—44no—
249C2—82no—
250C2—6044no—
251C2#2375237912yesdirect product factor
252C2C2×#1801270711yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×#127×C151C2
socleC22×C151#120
hypercenterC2×#127D151
hypocenterC151C2×#453
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#18012784C2semidirect
2. C2×#18012765C2semidirect
3. #23752379C2direct (N × H)
4. C2×#18012667C2semidirect
5. C2×#18012656C2semidirect
6. C2×#127×C151C2semidirect
9. #18012784C22semidirect
15. #18012765C22semidirect
18. C2×#14558988C22semidirect
19. #18012667C22semidirect
20. #18012656C22semidirect
23. C22×D4×C151C22semidirect
25. #127×C151C22semidirect
26. C2×C42×C151C22semidirect
30. #14559004D4semidirect
34. C2×Dic302D4semidirect
35. C2×D604D4semidirect
47. #14558988C23semidirect
60. C2×D4×C151C23semidirect
64. C42×C151C23semidirect
69. Dic302C2×D4semidirect
71. D604C2×D4semidirect
123. C2×C151#453semidirect
126. C151C2×#453semidirect
130. C2×#127D151semidirect
143. C22×D4C2×D151semidirect
150. #127C2×D151semidirect
151. C2×C42C2×D151semidirect
180. C2×D4C22×D151semidirect
191. C42C22×D151semidirect
251. C2#23752379direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#180127842
C2×#180127652
#237523792
C2×#180126672
C2×#180126562
C2×#127×C1512
C2×#453151