Finite Group Databasebeta

← #21461865

Subgroups — #21461865

Order 7808.

362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 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
1#16840829C211yesmaximal, characteristic, complemented
2#16840760C212yesmaximal, complemented
3D61⋊#100C211yesmaximal, characteristic, complemented
4#16840629C212yesmaximal, complemented
5#16840325C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7D4×#6923—24no—
8#14519856C2212yes—
9C2×C22⋊#6923—22no—
10#14519841—24no—
11#14519837—22no—
12C2×#11758224C2211yescharacteristic
13C2×D4×D61C2211yescharacteristic
14#14519773C411yescharacteristic, complemented
15#14519765C411yescharacteristic, complemented
16#14519764C411yescharacteristic, complemented
17#14519749—22no—
18#14519745—22no—
19#14519734C2211yescharacteristic
20#127×C61C411yescharacteristic, complemented
21C23×D61D412yes—
22C22×#6923—24no—
23C2×D4×C61—22no—
24C2×D4×C61C2×C411yescharacteristic
25C2×D4×C61C2×C411yescharacteristic, complemented
26C2×C22⋊D61—21no—
27C2×C22⋊D61—22no—
28C2×C22⋊D61D412yes—
29C22×Dic61—21no—
30#11758224—22no—
31#11758224—22no—
32D4×D61—22no—
33D4×D61—22no—
34C2×D244C2×C411yescharacteristic
35C2×C4×D61C2311yescharacteristic
36C2×Dic122C2×C411yescharacteristic, complemented
37C22⋊#6923—24no—
38C22⋊#6923—22no—
39#11758217—22no—
40C4⋊#6923—22no—
41C4×#6923D414yescomplemented
42#11758213—22no—
43D61⋊C8—22no—
44C42×C61C2×C411yescharacteristic, complemented
45C22⋊Dic61—22no—
46#11758198—22no—
47#11758198—21no—
48#11758196—21no—
49C4×Dic61C2×C411yescharacteristic, complemented
50C23×C61—21no—
51C23×C61C22⋊C412yes—
52C22×D61—22no—
53C22×D61—22no—
54C22×D61—82no—
55C22×D61C22⋊C412yes—
56C22×D61C2×D411yescharacteristic
57C2×#6923—24no—
58C2×#6923—84no—
59D4×C61—22no—
60D4×C61—22no—
61D4×C61—82no—
62C2×C4×C61—21no—
63C2×C4×C61C22×C411yescharacteristic
64C22⋊D61—24no—
65C22⋊D61—41no—
66C22⋊D61—41no—
67C22⋊D61—82no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—42no—
71C2×Dic61C2×D411yescharacteristic
72D244—22no—
73C4×D61C2×D412yes—
74C4×D61#4112yes—
75Dic122—22no—
76#92420—42no—
77C22×C61—22no—
78C22×C61—42no—
79C22×C61—42no—
80C22×C61—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—22no—
83C2×D61—41no—
84C2×D61—44no—
85C2×D61—42no—
86C2×D61—82no—
87C2×D61#12011yescharacteristic
88C2×D61#12311yescharacteristic
89#6923—44no—
90C4×C61—41no—
91C4×C61C4×D412yes—
92Dic61—41no—
93Dic61—41no—
94Dic61#12112yes—
95#1911—611nomaximal, Sylow
96C2×C61—21no—
97C2×C61—42no—
98C2×C61—81no—
99C2×C61#38611yescharacteristic
100D61—21no—
101D61—21no—
102D61—42no—
103#535—611no—
104#518—611no—
105#421—612no—
106C2×#100—611no—
107H(3,ℤ/4)—612no—
108C61#191111yescharacteristic, complemented, Sylow
109C2×#41—611no—
110C22×D4—611no—
111C2×M16—612no—
112#127—611no—
113#127#692311yescharacteristic, complemented
114#124—611no—
115#124—611no—
116#121—1222no—
117#120—1222no—
118C4×D4—1224no—
119#117—612no—
120#117—611no—
121C2×C22⋊C4—1222no—
122#104—1224no—
123#100—1222no—
124C24—612no—
125#41—1222no—
126#41—1222no—
127C2×Q8—611no—
128C2×D4—22no—
129C2×D4—612no—
130C2×D4—611no—
131C2×D4—1222no—
132C2×D4—1222no—
133C2×D4—1222no—
134C2×D4—1221no—
135C2×D4C2×#692311yescharacteristic
136C2×D4C2×#692311yescharacteristic, complemented
137C22×C4—611no—
138C22×C4—1221no—
139C22×C4—1224no—
140M16—1222no—
141M16—1222no—
142C2×C8—1222no—
143C4⋊C4—1221no—
144C4⋊C4—1222no—
145C22⋊C4—1221no—
146C22⋊C4—1222no—
147C22⋊C4—1222no—
148C22⋊C4—1224no—
149C22⋊C4—1222no—
150C42—614no—
151C42—611no—
152C42C2×#692311yescharacteristic, complemented
153C23—21no—
154C23—611no—
155C23—612no—
156C23—1222no—
157C23—1222no—
158C23—4882no—
159C23C22⋊#692312yes—
160Q8—1222no—
161D4—22no—
162D4—22no—
163D4—82no—
164D4—1224no—
165D4—1222no—
166D4—4882no—
167D4—2441no—
168D4—2441no—
169C2×C4—21no—
170C2×C4—611no—
171C2×C4—612no—
172C2×C4—612no—
173C2×C4—1224no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4—4884no—
177C2×C4—2442no—
178C2×C4C22×#692311yescharacteristic
179C8—2442no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—611no—
185C22—611no—
186C22—1222no—
187C22—4882no—
188C22—2441no—
189C22—2442no—
190C22—2444no—
191C22C2×C22⋊#692311yescharacteristic
192C4—41no—
193C4—612no—
194C4—2441no—
195C4—2444no—
196C4—2441no—
197C4D4×#692312yes—
198C2—21no—
199C2—42no—
200C2—81no—
201C2—1221no—
202C2—1221no—
203C2—2442no—
204C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#127×C61C4
socleC2×C61#386
hypercenter#127#6923
hypocenterC61#1911
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #16840829C2semidirect
2. #16840760C2semidirect
3. D61⋊#100C2semidirect
4. #16840629C2semidirect
14. #14519773C4semidirect
15. #14519765C4semidirect
16. #14519764C4semidirect
20. #127×C61C4semidirect
25. C2×D4×C61C2×C4semidirect
36. C2×Dic122C2×C4semidirect
41. C4×#6923D4semidirect
44. C42×C61C2×C4semidirect
49. C4×Dic61C2×C4semidirect
108. C61#1911semidirect
113. #127#6923semidirect
136. C2×D4C2×#6923semidirect
152. C42C2×#6923semidirect