Finite Group Databasebeta

← C2×#23750666 #34061444

Subgroups — C2×#23750666 #34061444

Order 19072.

608 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 608 conjugacy classes of subgroups — too many to draw. Only its 170 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×D4×#10597010C212yesmaximal, complemented
2#23750666C218yesmaximal, direct product factor
3C2×#18011979C211yesmaximal, characteristic, complemented
4C2×#18011973C212yesmaximal, complemented
5C2×#18011965C211yesmaximal, characteristic, complemented
6C2×D8×D149C211yesmaximal, characteristic
7C23×#10597010—22no—
8C2×D149⋊C8C2211yescharacteristic
9D4×#10597010—24no—
10D4×#10597010C2218yescomplemented
11C2×C4⋊#10597010C2212yes—
12C2×C22⋊#10597010—22no—
13C2×C4×#10597010C2211yescharacteristic
14#18011979C2214yescomplemented
15#18011973C2218yescomplemented
16#18011965C2214yescomplemented
17C2×D4×D149C2212yes—
18C2×D1192C411yescharacteristic, complemented
19C2×#14558721C412yescomplemented
20D8×D149C414yescomplemented
21D8×D149C2214yes—
22C2×C8×D149C2211yescharacteristic
23C2×D8×C149C411yescharacteristic, complemented
24C22×#10597010—28no—
25C22×#10597010—22no—
26C22×#10597010—48no—
27C22×#10597010D412yes—
28D149⋊C8—21no—
29D149⋊C8C2312yes—
30C2×#11924753—21no—
31C4⋊#10597010—22no—
32C4⋊#10597010C2314yes—
33C22⋊#10597010—28no—
34C4×#10597010D412yes—
35C4×#10597010C2312yes—
36C23×D149—22no—
37C2×D596C2×C412yescomplemented
38C2×C22⋊D149—22no—
39D4×D149—22no—
40D4×D149—22no—
41D4×D149C2×C414yescomplemented
42D4×D149C2314yes—
43C2×C4×D149C2311yescharacteristic
44D1192C2×C414yescomplemented
45#14558721C2×C418yescomplemented
46C2×#11924746C2×C411yescharacteristic, complemented
47C8×D149C2×C412yescomplemented
48C8×D149C2312yes—
49C2×D4×C149C2×C412yescomplemented
50D8×C149C2×C414yescomplemented
51C2×C8×C149C2×C411yescharacteristic, complemented
52C2×#10597010—24no—
53C2×#10597010—24no—
54C2×#10597010—416no—
55C2×#10597010—44no—
56C2×#10597010C2×D414yes—
57#11924753—22no—
58C22×D149—22no—
59C22×D149—24no—
60C22×D149—24no—
61C22×D149—44no—
62C22×D149—44no—
63C22×D149C2×D411yescharacteristic
64D596—22no—
65D596C22×C414yescomplemented
66C22⋊D149—24no—
67C22⋊D149—24no—
68C2×Dic149#4111yescharacteristic
69C4×D149C22×C411yescharacteristic
70C4×D149C2×D411yescharacteristic
71C4×D149#4111yescharacteristic
72C4×D149C2411yescharacteristic
73#11924746C22×C412yescomplemented
74C23×C149—22no—
75D4×C149—22no—
76D4×C149C22×C414yescomplemented
77C2×C4×C149C22×C411yescharacteristic
78C8×C149C22×C412yescomplemented
79C22×C149—24no—
80C22×C149—44no—
81C22×C149C4×D411yescharacteristic
82C2×D149—24no—
83C2×D149—44no—
84C2×D149—44no—
85C2×D149—44no—
86C2×D149—48no—
87C2×D149C4×D411yescharacteristic
88C2×D149AGL(1,ℤ/8)14yes—
89C2×D149C22×D411yescharacteristic
90#10597010—24no—
91#10597010—44no—
92C4×C149C4×D411yescharacteristic
93C4×C149C23×C411yescharacteristic
94Dic149C4×D411yescharacteristic
95Dic149C2×#4111yescharacteristic
96C2×C149—44no—
97C2×C149#44212yescomplemented
98C2×C149C2×C4×D411yescharacteristic
99D149—44no—
100D149#44212yescomplemented
101D149C2×AGL(1,ℤ/8)12yes—
102C149C2×#44211yescharacteristic, complemented, Sylow
103C2×#442—1491nomaximal, Sylow
104C22×D8—1491no—
105C2×C4×D4—1492no—
106#442—1498no—
107C2×#106—1491no—
108C2×#102—1492no—
109C2×#97—1491no—
110C22×D4—1492no—
111C23×C4—2982no—
112C2×D8—1492no—
113C2×D8—1494no—
114C2×D8—1494no—
115C2×D8—1491no—
116C2×D8#1059701011yescharacteristic, complemented
117C22×C8—1491no—
118C22×C8—1491no—
119C4×D4—2984no—
120C4×D4—1498no—
121C2×C4⋊C4—1492no—
122C2×C22⋊C4—2982no—
123C2×C42—1491no—
124#106—1494no—
125#102—1498no—
126#97—1494no—
127C24—2982no—
128C2×D4—2982no—
129C2×D4—2982no—
130C2×D4—2982no—
131C2×D4—1494no—
132C2×D4—1494no—
133C2×D4—1492no—
134C2×D4C2×#1059701012yescomplemented
135C22×C4—2982no—
136C22×C4—2988no—
137C22×C4—5968no—
138C22×C4—1492no—
139C22×C4—1491no—
140D8—1498no—
141D8—1494no—
142D8C2×#1059701014yescomplemented
143C2×C8—2981no—
144C2×C8—2981no—
145C2×C8—1492no—
146C2×C8—1491no—
147C2×C8—1492no—
148C2×C8—1492no—
149C2×C8C2×#1059701011yescharacteristic, complemented
150C4⋊C4—2982no—
151C4⋊C4—1494no—
152C22⋊C4—2988no—
153C42—1492no—
154C42—1492no—
155C23—22no—
156C23—2984no—
157C23—2984no—
158C23—2982no—
159C23—5964no—
160C23—5964no—
161C23—1491no—
162D4—22no—
163D4—2984no—
164D4—2984no—
165D4—2982no—
166D4—1494no—
167D4C22×#1059701014yescomplemented
168C2×C4—2984no—
169C2×C4—2984no—
170C2×C4—59616no—
171C2×C4—5964no—
172C2×C4—1494no—
173C2×C4—1491no—
174C2×C4—1491no—
175C2×C4—1491no—
176C2×C4—1491no—
177C2×C4—1491no—
178C2×C4C22×#1059701011yescharacteristic
179C8—2982no—
180C8—1492no—
181C8C22×#1059701012yescomplemented
182C22—24no—
183C22—44no—
184C22—2984no—
185C22—5964no—
186C22—5964no—
187C22—5968no—
188C22—5964no—
189C22—1494no—
190C22—1491no—
191C22—1491no—
192C22D4×#1059701011yescharacteristic
193C4—2984no—
194C4—5964no—
195C4—1491no—
196C4—1491no—
197C4D4×#1059701011yescharacteristic
198C4C23×#1059701011yescharacteristic
199C2—44no—
200C2—5964no—
201C2—1492no—
202C2—1492no—
203C2#2375066612yesdirect product factor
204C2C2×D4×#1059701011yescharacteristic
subgroupG/H
centerC22D4×#10597010
commutatorC4×C149C23×C4
FrattiniC4C23×#10597010
FittingC2×D8×C149C4
socleC22×C149C4×D4
prime radicalC2×D8×D149C2
cosocleC4×D149C24
hypercenterC2×D8#10597010
hypocenterC149C2×#442
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#10597010C2semidirect
2. #23750666C2direct (N × H)
3. C2×#18011979C2semidirect
4. C2×#18011973C2semidirect
5. C2×#18011965C2semidirect
10. D4×#10597010C22semidirect
14. #18011979C22semidirect
15. #18011973C22semidirect
16. #18011965C22semidirect
18. C2×D1192C4semidirect
19. C2×#14558721C4semidirect
20. D8×D149C4semidirect
23. C2×D8×C149C4semidirect
37. C2×D596C2×C4semidirect
41. D4×D149C2×C4semidirect
44. D1192C2×C4semidirect
45. #14558721C2×C4semidirect
46. C2×#11924746C2×C4semidirect
47. C8×D149C2×C4semidirect
49. C2×D4×C149C2×C4semidirect
50. D8×C149C2×C4semidirect
51. C2×C8×C149C2×C4semidirect
65. D596C22×C4semidirect
73. #11924746C22×C4semidirect
76. D4×C149C22×C4semidirect
78. C8×C149C22×C4semidirect
97. C2×C149#442semidirect
100. D149#442semidirect
102. C149C2×#442semidirect
116. C2×D8#10597010semidirect
134. C2×D4C2×#10597010semidirect
142. D8C2×#10597010semidirect
149. C2×C8C2×#10597010semidirect
167. D4C22×#10597010semidirect
181. C8C22×#10597010semidirect
203. C2#23750666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#105970102
#237506662
C2×#180119792
C2×#180119732
C2×#180119652
C2×D8×D1492
C2×#442149