Finite Group Databasebeta

← C2×#16840614 #21461186

Subgroups — C2×#16840614 #21461186

Order 7808.

388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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×#14519834C211yesmaximal, characteristic, complemented
2C2×(C2×#6923)⋊C4C211yesmaximal, characteristic, complemented
3#16840614C214yesmaximal, direct product factor
4C2×#14519752C211yesmaximal, characteristic
5C23×#6923—21no—
6C22×#92420—21no—
7#14519834—21no—
8#14519834C2212yescomplemented
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4C2212yescomplemented
11C22×D244—21no—
12C22×D244C411yescharacteristic, complemented
13C22×C4×D61C2211yescharacteristic
14#14519752—21no—
15#14519752—21no—
16#14519752C412yescomplemented
17#14519752C2212yes—
18C2×#11758198—21no—
19C2×C4⋊C4×C61C411yescharacteristic, complemented
20C23×D61—21no—
21C23×D61D411yescharacteristic
22C22×#6923—24no—
23C22×#6923—22no—
24C22×#6923—42no—
25C22×#6923—42no—
26C22×C4×C61—21no—
27C22×C4×C61C2×C411yescharacteristic
28C22×Dic61D411yescharacteristic
29C2×D244—22no—
30C2×D244—22no—
31C2×D244—21no—
32C2×D244—42no—
33C2×D244—42no—
34C2×D244—42no—
35C2×D244C2×C412yescomplemented
36C2×C4×D61—42no—
37C2×C4×D61C2×C411yescharacteristic
38C2×C4×D61D411yescharacteristic
39C2×C4×D61D411yescharacteristic
40C2×C4×D61C2311yescharacteristic
41C2×#92420—22no—
42C2×#92420—42no—
43C4⋊C4×C61—21no—
44C4⋊C4×C61C2×C412yescomplemented
45#11758198—22no—
46#11758198—22no—
47C23×C61C22⋊C411yescharacteristic
48C22×D61—22no—
49C22×D61—22no—
50C22×D61—22no—
51C22×D61—42no—
52C22×D61—42no—
53C22×D61—42no—
54C22×D61C22⋊C411yescharacteristic
55C22×D61D812yes—
56C22×D61SD1612yes—
57C22×D61C2×D411yescharacteristic
58C2×#6923—24no—
59C2×#6923—48no—
60C2×#6923—42no—
61C2×#6923—42no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—42no—
65C2×C4×C61C22⋊C411yescharacteristic
66C2×C4×C61C22×C411yescharacteristic
67C2×Dic61—22no—
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C2×D411yescharacteristic
70D244—42no—
71D244—42no—
72D244—44no—
73D244—42no—
74D244—42no—
75C4×D61—41no—
76C4×D61—41no—
77C4×D61—41no—
78C4×D61—41no—
79#92420—42no—
80C22×C61#9912yes—
81C22×C61#10212yes—
82C22×C61#10412yes—
83C22×C61C2×C22⋊C411yescharacteristic
84C2×D61—24no—
85C2×D61—24no—
86C2×D61—21no—
87C2×D61—21no—
88C2×D61—21no—
89C2×D61—21no—
90C2×D61—42no—
91C2×D61—42no—
92C2×D61—42no—
93C2×D61—84no—
94C2×D61#10212yes—
95C2×D61C2×D811yescharacteristic
96C2×D61C2×SD1611yescharacteristic
97#6923—44no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—42no—
101Dic61—21no—
102Dic61—21no—
103C2×#327—611nomaximal, Sylow
104C2×C61#32714yescomplemented
105C2×C61C2×#9911yescharacteristic
106C2×C61C2×#10211yescharacteristic
107C2×C61C2×#10411yescharacteristic
108D61—21no—
109D61—22no—
110D61—21no—
111D61—82no—
112C2×#121—611no—
113C2×C22⋊C8—611no—
114C2×#95—611no—
115#327—614no—
116C61C2×#32711yescharacteristic, complemented, Sylow
117C22×D4—611no—
118C22×D4—1221no—
119C23×C4—611no—
120C23×C4—1221no—
121C22×C8—1221no—
122#121—612no—
123#121—612no—
124#121—1221no—
125#121—1221no—
126C2×C4⋊C4#692311yescharacteristic, complemented
127C2×C22⋊C4—1221no—
128C22⋊C8—612no—
129C22⋊C8—1221no—
130#95—612no—
131#95—1221no—
132C24—611no—
133C24—1221no—
134C2×D4—612no—
135C2×D4—1222no—
136C2×D4—1222no—
137C2×D4—1221no—
138C2×D4—2442no—
139C2×D4—2442no—
140C2×D4—2442no—
141C22×C4—21no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—1222no—
148C22×C4—1224no—
149C22×C4—2442no—
150C22×C4—2442no—
151C22×C4—2442no—
152C22×C4C2×#692311yescharacteristic
153C2×C8—1222no—
154C2×C8—2442no—
155C4⋊C4—21no—
156C4⋊C4C2×#692312yescomplemented
157C22⋊C4—1222no—
158C22⋊C4—1222no—
159C23—612no—
160C23—612no—
161C23—611no—
162C23—611no—
163C23—1222no—
164C23—1222no—
165C23—1222no—
166C23—2442no—
167C23—2442no—
168C23—2442no—
169C23C22⋊#692311yescharacteristic
170D4—2442no—
171D4—2442no—
172D4—2442no—
173D4—2444no—
174D4—2442no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—611no—
179C2×C4—611no—
180C2×C4—1222no—
181C2×C4—1224no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4—2441no—
186C2×C4—2442no—
187C2×C4—2442no—
188C2×C4—2448no—
189C2×C4C22⋊#692311yescharacteristic
190C2×C4C22×#692311yescharacteristic
191C8—2442no—
192C22—611no—
193C22—612no—
194C22—611no—
195C22—1221no—
196C22—1221no—
197C22—1221no—
198C22—1221no—
199C22—1224no—
200C22—1224no—
201C22—4884no—
202C22—2442no—
203C22—2442no—
204C22—2442no—
205C22#1451983612yes—
206C22#1451983912yes—
207C22#1451984212yes—
208C22C2×C22⋊#692311yescharacteristic
209C4—21no—
210C4—21no—
211C4—42no—
212C4—1221no—
213C4—1221no—
214C4—2444no—
215C2—1221no—
216C2—1222no—
217C2—1221no—
218C2—4882no—
219C2#1684061414yesdirect product factor
220C2C2×#1451983611yescharacteristic
221C2C2×#1451983911yescharacteristic
222C2C2×#1451984211yescharacteristic
subgroupG/H
centerC23C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C4⋊C4×C61C4
socleC23×C61C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61C2×#327
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519834C2semidirect
2. C2×(C2×#6923)⋊C4C2semidirect
3. #16840614C2direct (N × H)
8. #14519834C22semidirect
10. (C2×#6923)⋊C4C22semidirect
12. C22×D244C4semidirect
16. #14519752C4semidirect
19. C2×C4⋊C4×C61C4semidirect
35. C2×D244C2×C4semidirect
44. C4⋊C4×C61C2×C4semidirect
104. C2×C61#327semidirect
116. C61C2×#327semidirect
126. C2×C4⋊C4#6923semidirect
156. C4⋊C4C2×#6923semidirect
219. C2#16840614direct (N × H)