Finite Group Databasebeta

← #21447337

Subgroups — #21447337

Order 7808.

274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14519708C211yesmaximal, characteristic, complemented
2C2×#14519699C211yesmaximal, characteristic
3C2×#14519697C211yesmaximal, characteristic
4#16839663C211yesmaximal, characteristic
5#16839627C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C2×#107×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×#11758198—22no—
12C2×C4×Dic61C2211yescharacteristic
13#14519708—22no—
14#14519699—22no—
15#14519697—22no—
16#14519684—22no—
17C22×C8×C61C2211yescharacteristic
18C2×C4⋊C4×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20#107×C61—22no—
21C23×D61—21no—
22C22×C4×C61—21no—
23C22×C4×C61—21no—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—21no—
26C22×Dic61D412yes—
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×C61D412yes—
36C4⋊C4×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40#11758198—44no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4×Dic61—21no—
44C4×Dic61—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C2×#92418D412yes—
48C23×C61C2×D411yescharacteristic
49C22×D61—22no—
50C22×D61—41no—
51C22×D61—41no—
52C22×D61—42no—
53C22×D61—42no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—42no—
57C2×C4×C61—42no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×Q811yescharacteristic
61C2×C4×C61#4111yescharacteristic
62C2×C4×C61#4111yescharacteristic
63C2×C4×C61#4111yescharacteristic
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—22no—
67C2×Dic61—41no—
68C2×Dic61—42no—
69D244—22no—
70D244—22no—
71D244—41no—
72D244—41no—
73C8×C61—22no—
74#92418—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—81no—
86C4×C61—81no—
87C4×C61C22⋊Q811yescharacteristic
88C4×C61C22⋊Q811yescharacteristic
89C4×C61#12311yescharacteristic
90C4×C61#12311yescharacteristic
91Dic61—42no—
92Dic61—81no—
93#2092—611nomaximal, Sylow
94C2×C61#39911yescharacteristic
95C2×C61#47812yes—
96C2×C61#48212yes—
97C2×C61#49511yescharacteristic
98C2×C61#49611yescharacteristic
99D61—82no—
100C2×#107D6111yescharacteristic, complemented
101C2×#106—611no—
102C2×#102—611no—
103C2×#102—611no—
104#390—611no—
105#382—611no—
106#336—611no—
107C61#209211yescharacteristic, complemented, Sylow
108C22×D4—611no—
109C22×C8—611no—
110C22×C8C2×D6111yescharacteristic
111C2×C4⋊C4—611no—
112C2×C4⋊C4C2×D6111yescharacteristic
113C2×C4⋊C4C2×D6111yescharacteristic
114C2×C22⋊C4—1222no—
115C2×C42—611no—
116#107—22no—
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—21no—
129C22×C4—21no—
130C22×C4—612no—
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—21no—
142C4⋊C4—21no—
143C4⋊C4—1221no—
144C4⋊C4—1221no—
145C22⋊C4—2444no—
146C42—1221no—
147C42—1221no—
148C23—1222no—
149C23—2441no—
150C23—2441no—
151C23—2442no—
152C23—2442no—
153C23D4×D6111yescharacteristic
154D4—1222no—
155D4—1222no—
156D4—2441no—
157D4—2441no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—2441no—
166C2×C4—2442no—
167C2×C4#1175822211yescharacteristic
168C2×C4#1175822211yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C2×C4Q8×D6111yescharacteristic
171C2×C4#1175822611yescharacteristic
172C2×C4C2×C22⋊D6111yescharacteristic
173C8—22no—
174C8—1222no—
175C22—4882no—
176C22—4881no—
177C22—4881no—
178C22—2442no—
179C22—2444no—
180C22#1451975511yescharacteristic
181C22#1451976211yescharacteristic
182C22#1451977311yescharacteristic
183C22#1451980012yes—
184C22#1451980112yes—
185C4—81no—
186C4—81no—
187C4—4881no—
188C4—2442no—
189C4#1451975311yescharacteristic
190C4#1451975511yescharacteristic
191C4#1451976011yescharacteristic
192C4#1451976211yescharacteristic
193C2—4882no—
194C2#1683969711yescharacteristic
195C2#1684006512yes—
196C2#1684008912yes—
197C2#1684014711yescharacteristic
198C2#1684015011yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#107×C61C2
socleC23×C61C2×D4
hypercenterC2×#107D61
hypocenterC61#2092
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×#14519708C2semidirect
5. #16839627C2semidirect
6. #16839516C2semidirect
7. C2×#107×C61C2semidirect
100. C2×#107D61semidirect
107. C61#2092semidirect