Finite Group Databasebeta

← #21446790

Subgroups — #21446790

Order 7808.

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

normal subgroups only

This group has 276 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×#14519776C211yesmaximal, characteristic
2C2×#14519687C211yesmaximal, characteristic
3#16839627C211yesmaximal, 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×Dic61C2211yescharacteristic
16#14519687—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×Dic122—24no—
30C2×Dic122—42no—
31C2×Dic122—42no—
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C2×C8×C61Q812yescomplemented
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61C2×C412yes—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61C2×C412yes—
43#11758196—24no—
44C4×Dic61C2×C412yes—
45C4×Dic61D412yes—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418Q812yescomplemented
49C23×C61C2×D411yescharacteristic
50C2×C4×C61—22no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61C22×C411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×Q811yescharacteristic
59C2×C4×C61C2×Q811yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—22no—
67C2×Dic61—41no—
68C2×Dic61—41no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61C22⋊C412yes—
73C2×Dic61C22⋊C412yes—
74Dic122—48no—
75C8×C61—22no—
76#92418—22no—
77C22×C61C2×C22⋊C411yescharacteristic
78C22×C61#12411yescharacteristic
79C22×C61C4⋊Q811yescharacteristic
80C22×C61AGL(1,ℤ/8)11yescharacteristic
81C22×C61AGL(1,ℤ/8)11yescharacteristic
82C22×C61#13711yescharacteristic
83C22×C61#13711yescharacteristic
84C4×C61—42no—
85C4×C61—81no—
86C4×C61C4×Q811yescharacteristic
87C4×C61C4×Q811yescharacteristic
88C4×C61C22⋊Q811yescharacteristic
89C4×C61C22⋊Q811yescharacteristic
90Dic61—22no—
91Dic61—22no—
92Dic61—42no—
93Dic61—81no—
94#1993—611nomaximal, Sylow
95C2×C61#39111yescharacteristic
96C2×C61#41811yescharacteristic
97C2×C61#41911yescharacteristic
98C2×C61#48911yescharacteristic
99C2×C61#48911yescharacteristic
100C2×C61#50111yescharacteristic
101C2×C61#50111yescharacteristic
102C2×C4⋊Q8—611no—
103C2×#97—611no—
104#382—611no—
105#340—611no—
106#340—611no—
107#340—611no—
108#340D6111yescharacteristic
109C61#199311yescharacteristic, complemented, Sylow
110C22×Q8—1221no—
111C22×C8—611no—
112C22×C8C2×D6111yescharacteristic
113C4⋊Q8—614no—
114C4⋊Q8—1222no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4—611no—
117C2×C4⋊C4—1221no—
118C2×C4⋊C4C2×D6111yescharacteristic
119C2×C4⋊C4C2×D6111yescharacteristic
120C2×C42—611no—
121#97—1222no—
122#95—1221no—
123#95—1221no—
124C2×Q8—1224no—
125C2×Q8—2442no—
126C2×Q8—2442no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—611no—
130C22×C4—611no—
131C22×C4—1221no—
132C22×C4—1221no—
133C22×C4C22×D6111yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—612no—
137C2×C8—1221no—
138C2×C8—1221no—
139C2×C8Dic12212yescomplemented
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—612no—
144C4⋊C4—1224no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4C4×D6112yes—
149C42—612no—
150C42—612no—
151C23D4×D6111yescharacteristic
152Q8—2448no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—612no—
160C2×C4—612no—
161C2×C4—1221no—
162C2×C4—1221no—
163C2×C4—1221no—
164C2×C4—1221no—
165C2×C4—1222no—
166C2×C4—2441no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4C2×Dic12211yescharacteristic
172C2×C4C2×C4×D6111yescharacteristic
173C2×C4#1175822211yescharacteristic
174C2×C4D4×D6111yescharacteristic
175C2×C4#1175822411yescharacteristic
176C2×C4Q8×D6111yescharacteristic
177C8—22no—
178C8—1222no—
179C22C22⋊C4×D6111yescharacteristic
180C22#1451976311yescharacteristic
181C22#1451977611yescharacteristic
182C22#1451980111yescharacteristic
183C22#1451980411yescharacteristic
184C22#1451980611yescharacteristic
185C22#1451980911yescharacteristic
186C4—42no—
187C4—81no—
188C4—1222no—
189C4—1222no—
190C4—4881no—
191C4—2442no—
192C4#1451974211yescharacteristic
193C4C4×Dic12211yescharacteristic
194C4#1451975411yescharacteristic
195C4#1451975511yescharacteristic
196C2#1683966611yescharacteristic
197C2#1683976511yescharacteristic
198C2#1683976911yescharacteristic
199C2#1684012011yescharacteristic
200C2#1684012311yescharacteristic
201C2#1684016911yescharacteristic
202C2#1684017011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1993
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
34. C2×C8×C61Q8semidirect
48. C2×#92418Q8semidirect
109. C61#1993semidirect
139. C2×C8Dic122semidirect