Finite Group Databasebeta

← #21446769

Subgroups — #21446769

Order 7808.

292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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×#14519776C211yesmaximal, characteristic
2C2×#14519706C211yesmaximal, characteristic
3C4⋊C4×Dic61C211yesmaximal, characteristic
4#16839525C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×Dic122—21no—
9C22×#92418C2211yescharacteristic
10#14519776—22no—
11#14519776C414yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—21no—
15C2×C4×Dic61—21no—
16C2×C4×Dic61C2211yescharacteristic
17#14519706—22no—
18#14519684—21no—
19C22×C8×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61—21no—
27C22×Dic61D411yescharacteristic
28C22×Dic61D411yescharacteristic
29C2×Dic122—24no—
30C2×Dic122—42no—
31C2×Dic122—42no—
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61C2×C412yes—
38C4⋊C4×C61Q812yescomplemented
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C412yes—
42C4⋊Dic61Q812yescomplemented
43#11758196—24no—
44C4×Dic61—42no—
45C4×Dic61C2×C412yes—
46C4×Dic61D412yes—
47C2×#92418—21no—
48C2×#92418—21no—
49C2×#92418—21no—
50C23×C61C2×D411yescharacteristic
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C22×C411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×Q811yescharacteristic
60C2×C4×C61C2×Q811yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—22no—
66C2×Dic61—22no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61C22⋊C412yes—
72C2×Dic61C22⋊C412yes—
73C2×Dic61D812yes—
74C2×Dic61SD1612yes—
75Dic122—48no—
76C8×C61—41no—
77#92418—41no—
78C22×C61C2×C22⋊C411yescharacteristic
79C22×C61C22⋊Q811yescharacteristic
80C22×C61C22⋊Q811yescharacteristic
81C22×C61C2×D811yescharacteristic
82C22×C61C2×SD1611yescharacteristic
83C22×C61#13711yescharacteristic
84C22×C61#13711yescharacteristic
85C4×C61—42no—
86C4×C61—42no—
87C4×C61C4×Q811yescharacteristic
88C4×C61C4×Q811yescharacteristic
89C4×C61#12411yescharacteristic
90C4×C61C4⋊Q811yescharacteristic
91Dic61—22no—
92Dic61—42no—
93Dic61—42no—
94Dic61#10214yes—
95#1988—611nomaximal, Sylow
96C2×C61#39111yescharacteristic
97C2×C61C2×#10211yescharacteristic
98C2×C61#41911yescharacteristic
99C2×C61#47411yescharacteristic
100C2×C61#47411yescharacteristic
101C2×C61#47511yescharacteristic
102C2×C61#47511yescharacteristic
103C2×C4⋊Q8—611no—
104C2×C4⋊C8—611no—
105C4×C4⋊C4—611no—
106#340—611no—
107#340—611no—
108#340—611no—
109#340D6111yescharacteristic
110C61#198811yescharacteristic, complemented, Sylow
111C22×Q8—1221no—
112C22×C8—611no—
113C22×C8C2×D6111yescharacteristic
114C4⋊Q8—614no—
115C4⋊Q8—1222no—
116C2×C4⋊C4—611no—
117C2×C4⋊C4—611no—
118C2×C4⋊C4—1221no—
119C2×C4⋊C4C2×D6111yescharacteristic
120C2×C4⋊C4C2×D6111yescharacteristic
121C2×C42—611no—
122C2×C42—1221no—
123C4⋊C8—1222no—
124#95—1221no—
125C2×Q8—1224no—
126C2×Q8—2442no—
127C2×Q8—2442no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4C22×D6111yescharacteristic
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—1221no—
139C2×C8—1221no—
140C2×C8—1221no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—612no—
144C4⋊C4—612no—
145C4⋊C4—1224no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4Dic12212yescomplemented
149C4⋊C4C4×D6112yes—
150C42—612no—
151C42—612no—
152C42—2442no—
153C23D4×D6111yescharacteristic
154Q8—2448no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—612no—
162C2×C4—612no—
163C2×C4—612no—
164C2×C4—612no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—1222no—
168C2×C4—1222no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4—2441no—
173C2×C4C2×Dic12211yescharacteristic
174C2×C4C2×C4×D6111yescharacteristic
175C2×C4#1175822211yescharacteristic
176C2×C4D4×D6111yescharacteristic
177C2×C4#1175822411yescharacteristic
178C2×C4Q8×D6111yescharacteristic
179C8—41no—
180C8—2441no—
181C22C22⋊C4×D6111yescharacteristic
182C22#1451975411yescharacteristic
183C22#1451975511yescharacteristic
184C22D8×D6111yescharacteristic
185C22SD16×D6111yescharacteristic
186C22#1451980611yescharacteristic
187C22#1451980911yescharacteristic
188C4—42no—
189C4—42no—
190C4—614no—
191C4—1222no—
192C4—2442no—
193C4—2442no—
194C4#1451974211yescharacteristic
195C4C4×Dic12211yescharacteristic
196C4#1451976311yescharacteristic
197C4#1451977611yescharacteristic
198C2#1683966611yescharacteristic
199C2#102×D6111yescharacteristic
200C2#1683976911yescharacteristic
201C2#1684004011yescharacteristic
202C2#1684004111yescharacteristic
203C2#1684004511yescharacteristic
204C2#1684004611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1988
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #14519776C4semidirect
38. C4⋊C4×C61Q8semidirect
42. C4⋊Dic61Q8semidirect
110. C61#1988semidirect
148. C4⋊C4Dic122semidirect