Finite Group Databasebeta

← #21446775

Subgroups — #21446775

Order 7808.

260 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 99 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×#14519768C211yesmaximal, characteristic
2C2×#14519706C211yesmaximal, characteristic
3C4⋊C4×Dic61C211yesmaximal, characteristic
4#16839525C211yesmaximal, characteristic
5#16839524C211yesmaximal, characteristic
6#16839524C211yesmaximal, characteristic
7C61×#340C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9#14519768—22no—
10#14519768C414yescomplemented
11C2×C4⋊Dic61—21no—
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×C8×C61—21no—
30C2×C8×C61—21no—
31C2×C8×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C412yes—
35C4⋊C4×C61Q812yes—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61—24no—
39C4⋊Dic61C2×C412yes—
40C4⋊Dic61Q812yes—
41#11758196—24no—
42C4×Dic61—42no—
43C4×Dic61C2×C412yes—
44C4×Dic61D412yes—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C23×C61C2×D411yescharacteristic
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×Q811yescharacteristic
58C2×C4×C61C2×Q811yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×Dic61—21no—
62C2×Dic61—21no—
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—
73C8×C61—41no—
74#92418—41no—
75C22×C61C2×C22⋊C411yescharacteristic
76C22×C61C22⋊Q811yescharacteristic
77C22×C61C22⋊Q811yescharacteristic
78C22×C61#13511yescharacteristic
79C22×C61#13511yescharacteristic
80C22×C61AGL(1,ℤ/8)11yescharacteristic
81C22×C61#13711yescharacteristic
82C4×C61—42no—
83C4×C61—42no—
84C4×C61C4×Q811yescharacteristic
85C4×C61C4×Q811yescharacteristic
86C4×C61#12411yescharacteristic
87C4×C61C4⋊Q811yescharacteristic
88Dic61—22no—
89Dic61—22no—
90Dic61—42no—
91Dic61—42no—
92#1989—611nomaximal, Sylow
93C2×C61#39111yescharacteristic
94C2×C61#41611yescharacteristic
95C2×C61#41711yescharacteristic
96C2×C61#47811yescharacteristic
97C2×C61#47811yescharacteristic
98C2×C61#47911yescharacteristic
99C2×C61#47911yescharacteristic
100C2×#125—611no—
101C2×C4⋊C8—611no—
102C4×C4⋊C4—611no—
103#340—611no—
104#340—611no—
105#340—611no—
106#340D6111yescharacteristic
107C61#198911yescharacteristic, complemented, Sylow
108C22×C8—611no—
109C22×C8C2×D6111yescharacteristic
110#125—614no—
111#125—1222no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—611no—
114C2×C4⋊C4—1221no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4C2×D6111yescharacteristic
117C2×C4⋊C4C2×D6111yescharacteristic
118C2×C42—611no—
119C2×C42—1221no—
120C4⋊C8—1222no—
121#95—1221no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—611no—
125C22×C4—611no—
126C22×C4—1221no—
127C22×C4—1221no—
128C22×C4C22×D6111yescharacteristic
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—1221no—
133C2×C8—1221no—
134C2×C8—1221no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—612no—
138C4⋊C4—612no—
139C4⋊C4—1224no—
140C4⋊C4—1224no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4Dic12212yes—
144C4⋊C4C4×D6112yes—
145C42—612no—
146C42—612no—
147C42—2442no—
148C23D4×D6111yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—612no—
156C2×C4—612no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—2441no—
164C2×C4—2441no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4C2×Dic12211yescharacteristic
168C2×C4C2×C4×D6111yescharacteristic
169C2×C4#1175822211yescharacteristic
170C2×C4D4×D6111yescharacteristic
171C2×C4#1175822411yescharacteristic
172C2×C4Q8×D6111yescharacteristic
173C8—41no—
174C8—2441no—
175C22C22⋊C4×D6111yescharacteristic
176C22#1451975411yescharacteristic
177C22#1451975511yescharacteristic
178C22#1451979611yescharacteristic
179C22#1451979811yescharacteristic
180C22#1451980411yescharacteristic
181C22#1451980911yescharacteristic
182C4—42no—
183C4—42no—
184C4—1222no—
185C4—1222no—
186C4—2442no—
187C4—2442no—
188C4#1451974211yescharacteristic
189C4C4×Dic12211yescharacteristic
190C4#1451976311yescharacteristic
191C4#1451977611yescharacteristic
192C2#1683966611yescharacteristic
193C2#1683975511yescharacteristic
194C2#1683976211yescharacteristic
195C2#1684006011yescharacteristic
196C2#1684006111yescharacteristic
197C2#1684006711yescharacteristic
198C2#1684006811yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1989
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
10. #14519768C4semidirect
107. C61#1989semidirect