Finite Group Databasebeta

← #21447350

Subgroups — #21447350

Order 7808.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14519709C211yesmaximal, characteristic, complemented
2C2×#14519708C211yesmaximal, characteristic, complemented
3C2×#14519698C211yesmaximal, characteristic
4#16839665C211yesmaximal, characteristic
5#16839631C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic
8C22×#92418C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758196—22no—
12C2×C22⋊Dic61—22no—
13C2×C4×Dic61C2211yescharacteristic
14#14519709—22no—
15#14519708—22no—
16#14519698—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—
43#11758196—44no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C2×#92418D412yes—
49C23×C61—22no—
50C23×C61—41no—
51C23×C61—41no—
52C23×C61—42no—
53C23×C61—42no—
54C23×C61C2×D411yescharacteristic
55D4×C61—22no—
56D4×C61—22no—
57D4×C61—41no—
58D4×C61—41no—
59C2×C4×C61—41no—
60C2×C4×C61—42no—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×Q811yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—42no—
72C2×Dic61—42no—
73C2×Dic61SD1614yes—
74C8×C61—22no—
75#92418—22no—
76C22×C61—42no—
77C22×C61—44no—
78C22×C61—82no—
79C22×C61—81no—
80C22×C61—81no—
81C22×C61C22⋊Q811yescharacteristic
82C22×C61#12311yescharacteristic
83C22×C61#12711yescharacteristic
84C22×C61C2×SD1612yes—
85C22×C61AGL(1,ℤ/8)12yes—
86C4×C61—81no—
87C4×C61C22⋊Q811yescharacteristic
88C4×C61C22⋊Q811yescharacteristic
89C4×C61#12311yescharacteristic
90C4×C61#12311yescharacteristic
91Dic61—24no—
92Dic61—81no—
93Dic61—81no—
94#2094—611nomaximal, Sylow
95C2×C61—82no—
96C2×C61#39911yescharacteristic
97C2×C61#47612yes—
98C2×C61#48112yes—
99C2×C61#49211yescharacteristic
100C2×C61#49611yescharacteristic
101C2×#106—611no—
102C2×#106—611no—
103C2×#102—611no—
104C2×#102D6111yescharacteristic
105#390—611no—
106#384—611no—
107#336—611no—
108C61#209411yescharacteristic, complemented, Sylow
109C22×D4C2×D6111yescharacteristic
110C22×C8—611no—
111C22×C8C2×D6111yescharacteristic
112C2×C4⋊C4—611no—
113C2×C4⋊C4—611no—
114C2×C4⋊C4—1222no—
115C2×C4⋊C4C2×D6111yescharacteristic
116C2×C22⋊C4—1222no—
117C2×C42—611no—
118#106—1222no—
119#106—1222no—
120#102—22no—
121#102—1222no—
122C24—21no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4Dic12212yes—
129C22×C4—21no—
130C22×C4—612no—
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×C8C22⋊D6112yes—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—2444no—
147C22⋊C4—2444no—
148C42—1221no—
149C42—1221no—
150C23—22no—
151C23—41no—
152C23—41no—
153C23—42no—
154C23—42no—
155C23D4×D6111yescharacteristic
156D4—22no—
157D4—22no—
158D4—41no—
159D4—41no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—614no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—2441no—
166C2×C4—2441no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4C2×Dic12211yescharacteristic
170C2×C4#1175822211yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C2×C4#1175822411yescharacteristic
173C2×C4#1175822411yescharacteristic
174C2×C4C2×C22⋊D6111yescharacteristic
175C8—22no—
176C8—1222no—
177C22—42no—
178C22—44no—
179C22—82no—
180C22—81no—
181C22—81no—
182C22#1451975411yescharacteristic
183C22#1451975911yescharacteristic
184C22#1451977311yescharacteristic
185C22SD16×D6112yes—
186C22#1451980112yes—
187C4—81no—
188C4—1224no—
189C4—4881no—
190C4—4881no—
191C4#1451975411yescharacteristic
192C4#1451975611yescharacteristic
193C4#1451975811yescharacteristic
194C4#1451975911yescharacteristic
195C2—82no—
196C2#1683969811yescharacteristic
197C2#1684005012yes—
198C2#1684007912yes—
199C2#1684013311yescharacteristic
200C2#1684015011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#2094
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×#14519709C2semidirect
2. C2×#14519708C2semidirect
5. #16839631C2semidirect
6. #16839516C2semidirect
108. C61#2094semidirect