Finite Group Databasebeta

← #21446782

Subgroups — #21446782

Order 7808.

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

normal subgroups only

This group has 252 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×C8×Dic61C211yesmaximal, characteristic
3#16839627C211yesmaximal, 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×Dic61C2211yescharacteristic
16C8×Dic61—22no—
17#14519684—21no—
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×C61Q812yes—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61C2×C412yes—
36C4⋊Dic61—21no—
37C4⋊Dic61—24no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41#11758196—24no—
42C4×Dic61C2×C412yes—
43C4×Dic61D412yes—
44C2×#92418—21no—
45C2×#92418—21no—
46C2×#92418Q812yes—
47C23×C61C2×D411yescharacteristic
48C2×C4×C61—22no—
49C2×C4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61—41no—
54C2×C4×C61C22×C411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×Q811yescharacteristic
57C2×C4×C61C2×Q811yescharacteristic
58C2×C4×C61#4111yescharacteristic
59C2×C4×C61#4111yescharacteristic
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—22no—
65C2×Dic61—41no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61C22⋊C412yes—
71C2×Dic61C22⋊C412yes—
72C8×C61—22no—
73#92418—22no—
74C22×C61C2×C22⋊C411yescharacteristic
75C22×C61#12411yescharacteristic
76C22×C61C4⋊Q811yescharacteristic
77C22×C61#13511yescharacteristic
78C22×C61#13511yescharacteristic
79C22×C61#13511yescharacteristic
80C22×C61#13511yescharacteristic
81C4×C61—42no—
82C4×C61—81no—
83C4×C61C4×Q811yescharacteristic
84C4×C61C4×Q811yescharacteristic
85C4×C61C22⋊Q811yescharacteristic
86C4×C61C22⋊Q811yescharacteristic
87Dic61—22no—
88Dic61—22no—
89Dic61—42no—
90Dic61—81no—
91#1991—611nomaximal, Sylow
92C2×C61#39111yescharacteristic
93C2×C61#41611yescharacteristic
94C2×C61#41611yescharacteristic
95C2×C61#48811yescharacteristic
96C2×C61#48811yescharacteristic
97C2×C61#49911yescharacteristic
98C2×C61#49911yescharacteristic
99C2×#125—611no—
100C2×C4×C8—611no—
101#382—611no—
102#340—611no—
103#340—611no—
104#340—611no—
105#340D6111yescharacteristic
106C61#199111yescharacteristic, complemented, Sylow
107C22×C8—611no—
108C22×C8C2×D6111yescharacteristic
109#125—614no—
110#125—1222no—
111C2×C4⋊C4—611no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—1221no—
114C2×C4⋊C4—1221no—
115C2×C4⋊C4C2×D6111yescharacteristic
116C2×C4⋊C4C2×D6111yescharacteristic
117C2×C42—611no—
118C4×C8—1222no—
119#95—1221no—
120#95—1221no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—611no—
124C22×C4—611no—
125C22×C4—1221no—
126C22×C4—1221no—
127C22×C4C22×D6111yescharacteristic
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—612no—
131C2×C8—1221no—
132C2×C8—1221no—
133C2×C8Dic12212yes—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—612no—
138C4⋊C4—1224no—
139C4⋊C4—1224no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4C4×D6112yes—
144C42—612no—
145C42—612no—
146C23D4×D6111yescharacteristic
147C2×C4—22no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—612no—
154C2×C4—612no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—1222no—
160C2×C4—2441no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4—2441no—
164C2×C4—2441no—
165C2×C4C2×Dic12211yescharacteristic
166C2×C4C2×C4×D6111yescharacteristic
167C2×C4#1175822211yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C2×C4#1175822411yescharacteristic
170C2×C4Q8×D6111yescharacteristic
171C8—22no—
172C8—1222no—
173C22C22⋊C4×D6111yescharacteristic
174C22#1451976311yescharacteristic
175C22#1451977611yescharacteristic
176C22#1451979611yescharacteristic
177C22#1451979811yescharacteristic
178C22#1451979811yescharacteristic
179C22#1451980011yescharacteristic
180C4—42no—
181C4—81no—
182C4—1222no—
183C4—1222no—
184C4—4881no—
185C4—2442no—
186C4#1451974211yescharacteristic
187C4C4×Dic12211yescharacteristic
188C4#1451975411yescharacteristic
189C4#1451975511yescharacteristic
190C2#1683966611yescharacteristic
191C2#1683975511yescharacteristic
192C2#1683975711yescharacteristic
193C2#1684011511yescharacteristic
194C2#1684011811yescharacteristic
195C2#1684016211yescharacteristic
196C2#1684016311yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1991
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
106. C61#1991semidirect