Finite Group Databasebeta

← C2×#20296067 #28379785

Subgroups — C2×#20296067 #28379785

Order 13952.

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×#89137C212yesmaximal, complemented
2#20296067C218yesmaximal, direct product factor
3C2×#16812767C211yesmaximal, characteristic, complemented
4C2×#16812761C212yesmaximal, complemented
5C2×#16812753C211yesmaximal, characteristic, complemented
6C2×D8×D109C211yesmaximal, characteristic
7C23×#89137—22no—
8C2×D109⋊C8C2211yescharacteristic
9D4×#89137—24no—
10D4×#89137C2218yescomplemented
11C2×C4⋊#89137C2212yes—
12C2×C22⋊#89137—22no—
13C2×C4×#89137C2211yescharacteristic
14#16812767C2214yescomplemented
15#16812761C2218yescomplemented
16#16812753C2214yescomplemented
17C2×D4×D109C2212yes—
18C2×D872C411yescharacteristic, complemented
19C2×#13182014C412yescomplemented
20D8×D109C414yescomplemented
21D8×D109C2214yes—
22C2×C8×D109C2211yescharacteristic
23C2×D8×C109C411yescharacteristic, complemented
24C22×#89137—22no—
25C22×#89137—28no—
26C22×#89137—48no—
27C22×#89137D412yes—
28D109⋊C8—21no—
29D109⋊C8C2312yes—
30C2×#11724786—21no—
31C4⋊#89137—22no—
32C4⋊#89137C2314yes—
33C22⋊#89137—28no—
34C4×#89137D412yes—
35C4×#89137C2312yes—
36C23×D109—22no—
37C2×D436C2×C412yescomplemented
38C2×C22⋊D109—22no—
39D4×D109—22no—
40D4×D109—22no—
41D4×D109C2×C414yescomplemented
42D4×D109C2314yes—
43C2×C4×D109C2311yescharacteristic
44D872C2×C414yescomplemented
45#13182014C2×C418yescomplemented
46C2×#11724784C2×C411yescharacteristic, complemented
47C8×D109C2×C412yescomplemented
48C8×D109C2312yes—
49C2×D4×C109C2×C412yescomplemented
50D8×C109C2×C414yescomplemented
51C2×C8×C109C2×C411yescharacteristic, complemented
52C23×C109—22no—
53C22×D109—22no—
54C22×D109—24no—
55C22×D109—24no—
56C22×D109—44no—
57C22×D109—44no—
58C22×D109C2×D411yescharacteristic
59C2×#89137—24no—
60C2×#89137—24no—
61C2×#89137—416no—
62C2×#89137—44no—
63C2×#89137C2×D414yes—
64D4×C109—22no—
65D4×C109C22×C414yescomplemented
66C2×C4×C109C22×C411yescharacteristic
67C22⋊D109—24no—
68C22⋊D109—24no—
69C2×Dic109#4111yescharacteristic
70D436—22no—
71D436C22×C414yescomplemented
72C4×D109C22×C411yescharacteristic
73C4×D109C2×D411yescharacteristic
74C4×D109#4111yescharacteristic
75C4×D109C2411yescharacteristic
76#11724786—22no—
77C8×C109C22×C412yescomplemented
78#11724784C22×C412yescomplemented
79C22×C109—24no—
80C22×C109—44no—
81C22×C109C4×D411yescharacteristic
82C2×D109—24no—
83C2×D109—44no—
84C2×D109—44no—
85C2×D109—44no—
86C2×D109—48no—
87C2×D109C4×D411yescharacteristic
88C2×D109AGL(1,ℤ/8)14yes—
89C2×D109C22×D411yescharacteristic
90#89137—24no—
91#89137—44no—
92C4×C109C4×D411yescharacteristic
93C4×C109C23×C411yescharacteristic
94Dic109C4×D411yescharacteristic
95Dic109C2×#4111yescharacteristic
96C2×C109—44no—
97C2×C109#44212yescomplemented
98C2×C109C2×C4×D411yescharacteristic
99D109—44no—
100D109#44212yescomplemented
101D109C2×AGL(1,ℤ/8)12yes—
102C2×#442—1091nomaximal, Sylow
103C109C2×#44211yescharacteristic, complemented, Sylow
104C22×D8—1091no—
105C2×C4×D4—1092no—
106#442—1098no—
107C2×#106—1091no—
108C2×#102—1092no—
109C2×#97—1091no—
110C22×D4—1092no—
111C23×C4—2182no—
112C2×D8—1092no—
113C2×D8—1094no—
114C2×D8—1094no—
115C2×D8—1091no—
116C2×D8#8913711yescharacteristic, complemented
117C22×C8—1091no—
118C22×C8—1091no—
119C4×D4—1098no—
120C4×D4—2184no—
121C2×C4⋊C4—1092no—
122C2×C22⋊C4—2182no—
123C2×C42—1091no—
124#106—1094no—
125#102—1098no—
126#97—1094no—
127C24—2182no—
128C2×D4—1094no—
129C2×D4—1094no—
130C2×D4—1092no—
131C2×D4—2182no—
132C2×D4—2182no—
133C2×D4—2182no—
134C2×D4C2×#8913712yescomplemented
135C22×C4—1091no—
136C22×C4—1092no—
137C22×C4—4368no—
138C22×C4—2188no—
139C22×C4—2182no—
140D8—1098no—
141D8—1094no—
142D8C2×#8913714yescomplemented
143C2×C8—1091no—
144C2×C8—1092no—
145C2×C8—1092no—
146C2×C8—1092no—
147C2×C8—2181no—
148C2×C8—2181no—
149C2×C8C2×#8913711yescharacteristic, complemented
150C4⋊C4—1094no—
151C4⋊C4—2182no—
152C22⋊C4—2188no—
153C42—1092no—
154C42—1092no—
155C23—22no—
156C23—1091no—
157C23—4364no—
158C23—4364no—
159C23—2184no—
160C23—2184no—
161C23—2182no—
162D4—22no—
163D4—1094no—
164D4—2184no—
165D4—2184no—
166D4—2182no—
167D4C22×#8913714yescomplemented
168C2×C4—1091no—
169C2×C4—1091no—
170C2×C4—1091no—
171C2×C4—1091no—
172C2×C4—1091no—
173C2×C4—1094no—
174C2×C4—4364no—
175C2×C4—43616no—
176C2×C4—2184no—
177C2×C4—2184no—
178C2×C4C22×#8913711yescharacteristic
179C8—1092no—
180C8—2182no—
181C8C22×#8913712yescomplemented
182C22—24no—
183C22—44no—
184C22—1094no—
185C22—1091no—
186C22—1091no—
187C22—4364no—
188C22—4364no—
189C22—4368no—
190C22—4364no—
191C22—2184no—
192C22D4×#8913711yescharacteristic
193C4—1091no—
194C4—1091no—
195C4—4364no—
196C4—2184no—
197C4D4×#8913711yescharacteristic
198C4C23×#8913711yescharacteristic
199C2—44no—
200C2—1092no—
201C2—1092no—
202C2—4364no—
203C2#2029606712yesdirect product factor
204C2C2×D4×#8913711yescharacteristic
subgroupG/H
centerC22D4×#89137
commutatorC4×C109C23×C4
FrattiniC4C23×#89137
FittingC2×D8×C109C4
socleC22×C109C4×D4
prime radicalC2×D8×D109C2
cosocleC4×D109C24
hypercenterC2×D8#89137
hypocenterC109C2×#442
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×D4×#89137C2semidirect
2. #20296067C2direct (N × H)
3. C2×#16812767C2semidirect
4. C2×#16812761C2semidirect
5. C2×#16812753C2semidirect
10. D4×#89137C22semidirect
14. #16812767C22semidirect
15. #16812761C22semidirect
16. #16812753C22semidirect
18. C2×D872C4semidirect
19. C2×#13182014C4semidirect
20. D8×D109C4semidirect
23. C2×D8×C109C4semidirect
37. C2×D436C2×C4semidirect
41. D4×D109C2×C4semidirect
44. D872C2×C4semidirect
45. #13182014C2×C4semidirect
46. C2×#11724784C2×C4semidirect
47. C8×D109C2×C4semidirect
49. C2×D4×C109C2×C4semidirect
50. D8×C109C2×C4semidirect
51. C2×C8×C109C2×C4semidirect
65. D4×C109C22×C4semidirect
71. D436C22×C4semidirect
77. C8×C109C22×C4semidirect
78. #11724784C22×C4semidirect
97. C2×C109#442semidirect
100. D109#442semidirect
103. C109C2×#442semidirect
116. C2×D8#89137semidirect
134. C2×D4C2×#89137semidirect
142. D8C2×#89137semidirect
149. C2×C8C2×#89137semidirect
167. D4C22×#89137semidirect
181. C8C22×#89137semidirect
203. C2#20296067direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×#891372
#202960672
C2×#168127672
C2×#168127612
C2×#168127532
C2×D8×D1092
C2×#442109