Finite Group Databasebeta

← #21447342

Subgroups — #21447342

Order 7808.

274 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14519710C211yesmaximal, characteristic, complemented
2C2×#14519709C211yesmaximal, characteristic, complemented
3C2×#14519698C211yesmaximal, characteristic
4#16839665C211yesmaximal, characteristic
5#16839627C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C22⋊Dic61—22no—
12C2×C4×Dic61C2211yescharacteristic
13#14519710—22no—
14#14519709—22no—
15#14519698—22no—
16#14519684—22no—
17C22×D4×C61C2211yescharacteristic
18C22×C8×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20#102×C61—22no—
21C24×C61—21no—
22C2×D4×C61—21no—
23C2×D4×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61Q812yes—
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C22×Dic61—21no—
31C22×Dic61—21no—
32C22×Dic61D412yes—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C2×C8×C61D412yes—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C22⋊Dic61—44no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4×Dic61—21no—
44C4×Dic61—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418D412yes—
48C23×C61—22no—
49C23×C61—41no—
50C23×C61—41no—
51C23×C61—42no—
52C23×C61—42no—
53C23×C61C2×D411yescharacteristic
54D4×C61—22no—
55D4×C61—22no—
56D4×C61—41no—
57D4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—42no—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×Q811yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—42no—
72C2×Dic61—42no—
73C8×C61—22no—
74#92418—22no—
75C22×C61—42no—
76C22×C61—44no—
77C22×C61—82no—
78C22×C61—81no—
79C22×C61—81no—
80C22×C61C22⋊Q811yescharacteristic
81C22×C61#12311yescharacteristic
82C22×C61#12711yescharacteristic
83C22×C61#13512yes—
84C22×C61AGL(1,ℤ/8)12yes—
85C4×C61—81no—
86C4×C61C22⋊Q811yescharacteristic
87C4×C61C22⋊Q811yescharacteristic
88C4×C61#12311yescharacteristic
89C4×C61#12311yescharacteristic
90Dic61—42no—
91Dic61—81no—
92Dic61—81no—
93#2092—611nomaximal, Sylow
94C2×C61—82no—
95C2×C61#39911yescharacteristic
96C2×C61#47812yes—
97C2×C61#48212yes—
98C2×C61#49511yescharacteristic
99C2×C61#49611yescharacteristic
100C2×#107—611no—
101C2×#106—611no—
102C2×#102—611no—
103C2×#102D6111yescharacteristic
104#390—611no—
105#382—611no—
106#336—611no—
107C61#209211yescharacteristic, complemented, Sylow
108C22×D4C2×D6111yescharacteristic
109C22×C8—611no—
110C22×C8C2×D6111yescharacteristic
111C2×C4⋊C4—611no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4C2×D6111yescharacteristic
114C2×C22⋊C4—1222no—
115C2×C42—611no—
116#107—1222no—
117#106—1222no—
118#102—22no—
119#102—1222no—
120#95—1222no—
121C24—21no—
122C2×D4—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4Dic12212yes—
128C22×C4—21no—
129C22×C4—612no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4C22×D6111yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—612no—
136C2×C8—1221no—
137C2×C8—1221no—
138C2×C8C22⋊D6112yes—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C22⋊C4—2444no—
146C42—1221no—
147C42—1221no—
148C23—22no—
149C23—41no—
150C23—41no—
151C23—42no—
152C23—42no—
153C23D4×D6111yescharacteristic
154D4—22no—
155D4—22no—
156D4—41no—
157D4—41no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—1222no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—2441no—
164C2×C4—2441no—
165C2×C4—2442no—
166C2×C4—2442no—
167C2×C4C2×Dic12211yescharacteristic
168C2×C4#1175822211yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C2×C4#1175822411yescharacteristic
171C2×C4#1175822411yescharacteristic
172C2×C4C2×C22⋊D6111yescharacteristic
173C8—22no—
174C8—1222no—
175C22—42no—
176C22—44no—
177C22—82no—
178C22—81no—
179C22—81no—
180C22#1451975411yescharacteristic
181C22#1451975911yescharacteristic
182C22#1451977311yescharacteristic
183C22#1451979812yes—
184C22#1451980112yes—
185C4—81no—
186C4—4881no—
187C4—4881no—
188C4—2442no—
189C4#1451975411yescharacteristic
190C4#1451975611yescharacteristic
191C4#1451975811yescharacteristic
192C4#1451975911yescharacteristic
193C2—82no—
194C2#1683969811yescharacteristic
195C2#1684006412yes—
196C2#1684008512yes—
197C2#1684014311yescharacteristic
198C2#1684015011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#2092
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#14519710C2semidirect
2. C2×#14519709C2semidirect
5. #16839627C2semidirect
6. #16839516C2semidirect
107. C61#2092semidirect