Finite Group Databasebeta

← #21447339

Subgroups — #21447339

Order 7808.

274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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×#14519711C211yesmaximal, characteristic, complemented
2C2×#14519709C211yesmaximal, characteristic, complemented
3C2×#14519699C211yesmaximal, characteristic
4C2×#14519699C211yesmaximal, characteristic
5#16839664C211yesmaximal, characteristic
6#16839628C211yesmaximal, characteristic, complemented
7C61×#336C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×C4⋊Dic61C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758198—22no—
13#14519711—22no—
14#14519709—22no—
15#14519699—22no—
16#14519699—22no—
17#14519684—22no—
18C22×C8×C61C2211yescharacteristic
19C22×C8×C61C2211yescharacteristic
20C2×C42×C61C2211yescharacteristic
21C23×D61—21no—
22C22×C4×C61D412yes—
23C22×C4×C61C2311yescharacteristic
24C22×Dic61—21no—
25C22×Dic61—21no—
26C22×Dic61—21no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244Q812yes—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61D412yes—
38C2×C8×C61D412yes—
39C42×C61—21no—
40C42×C61—21no—
41#11758198—44no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61—21no—
48C23×C61C2×D411yescharacteristic
49C22×D61—22no—
50C22×D61—41no—
51C22×D61—41no—
52C22×D61—42no—
53C22×D61—42no—
54C2×C4×C61—22no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×Q811yescharacteristic
60C2×C4×C61#4111yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×Dic61—41no—
64C2×Dic61—41no—
65C2×Dic61—41no—
66C2×Dic61—42no—
67C2×Dic61—42no—
68C2×Dic61—42no—
69D244—22no—
70D244—22no—
71D244—41no—
72D244—41no—
73C8×C61—22no—
74C8×C61—22no—
75C22×C61C22⋊Q811yescharacteristic
76C22×C61#12311yescharacteristic
77C22×C61#12711yescharacteristic
78C22×C61#13512yes—
79C22×C61AGL(1,ℤ/8)12yes—
80C2×D61—42no—
81C2×D61—44no—
82C2×D61—82no—
83C2×D61—81no—
84C2×D61—81no—
85C4×C61—42no—
86C4×C61C22⋊Q811yescharacteristic
87C4×C61C22⋊Q811yescharacteristic
88C4×C61#12311yescharacteristic
89C4×C61#12311yescharacteristic
90Dic61—81no—
91Dic61—81no—
92Dic61—81no—
93#2092—611nomaximal, Sylow
94C2×C61#39911yescharacteristic
95C2×C61#47812yes—
96C2×C61#48212yes—
97C2×C61#49511yescharacteristic
98C2×C61#49611yescharacteristic
99D61—82no—
100C2×#107—611no—
101C2×#106—611no—
102C2×#102—611no—
103C2×#102—611no—
104#390—611no—
105#382—611no—
106#336D6111yescharacteristic, complemented
107C61#209211yescharacteristic, complemented, Sylow
108C22×D4—611no—
109C22×C8C2×D6111yescharacteristic
110C22×C8C2×D6111yescharacteristic
111C2×C4⋊C4—611no—
112C2×C4⋊C4—611no—
113C2×C4⋊C4—611no—
114C2×C22⋊C4—1222no—
115C2×C42C2×D6111yescharacteristic
116#107—1222no—
117#106—1222no—
118#102—1222no—
119#102—1222no—
120#95—1222no—
121C24—1221no—
122C2×D4—612no—
123C2×D4—1221no—
124C2×D4—1221no—
125C2×D4—1221no—
126C2×D4—1221no—
127C2×D4—1221no—
128C22×C4—1221no—
129C22×C4—1221no—
130C22×C4—1221no—
131C22×C4D24412yes—
132C22×C4C22×D6111yescharacteristic
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8D24412yes—
138C2×C8D24412yes—
139C4⋊C4—1221no—
140C4⋊C4—1221no—
141C4⋊C4—1221no—
142C4⋊C4—1221no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C22⋊C4—2444no—
146C42—21no—
147C42—21no—
148C23—1222no—
149C23—2441no—
150C23—2441no—
151C23—2442no—
152C23—2442no—
153C23C2×D24411yescharacteristic
154D4—1222no—
155D4—1222no—
156D4—2441no—
157D4—2441no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—2441no—
162C2×C4—2441no—
163C2×C4—2441no—
164C2×C4—2442no—
165C2×C4—2442no—
166C2×C4—2442no—
167C2×C4C2×D24411yescharacteristic
168C2×C4C2×D24411yescharacteristic
169C2×C4#1175822411yescharacteristic
170C2×C4#1175822411yescharacteristic
171C2×C4#1175822411yescharacteristic
172C2×C4Q8×D6111yescharacteristic
173C8—22no—
174C8—22no—
175C22—4882no—
176C22—4881no—
177C22—4881no—
178C22—2442no—
179C22—2444no—
180C22#1451975711yescharacteristic
181C22#1451976111yescharacteristic
182C22#1451977411yescharacteristic
183C22#1451979912yes—
184C22#1451980512yes—
185C4—42no—
186C4—4881no—
187C4—4881no—
188C4—4881no—
189C4#1451975711yescharacteristic
190C4#1451975711yescharacteristic
191C4#1451976111yescharacteristic
192C4#1451976111yescharacteristic
193C2—4882no—
194C2#1683969911yescharacteristic
195C2#1684006312yes—
196C2#1684008712yes—
197C2#1684014611yescharacteristic
198C2#1684015111yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#336C2
socleC23×C61C2×D4
hypercenter#336D61
hypocenterC61#2092
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
1. C2×#14519711C2semidirect
2. C2×#14519709C2semidirect
6. #16839628C2semidirect
7. C61×#336C2semidirect
106. #336D61semidirect
107. C61#2092semidirect