Finite Group Databasebeta

← #21447050

Subgroups — #21447050

Order 7808.

402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 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×#14519698C212yesmaximal, complemented
2C2×#14519698C212yesmaximal, complemented
3#16839660C211yesmaximal, characteristic, complemented
4#16839517C211yesmaximal, characteristic, complemented
5C2×#127×C61C211yesmaximal, characteristic
6C22×#92418C2212yes—
7C2×C4⋊Dic61C2211yescharacteristic
8C2×C4⋊Dic61C2211yescharacteristic
9C2×#11758196—21no—
10#14519698—24no—
11#14519698—24no—
12#14519684—21no—
13C22×D4×C61—21no—
14C22×D4×C61—21no—
15C22×D4×C61C2212yes—
16#127×C61—24no—
17C2×C42×C61C2211yescharacteristic
18C24×C61—22no—
19C2×D4×C61—24no—
20C2×D4×C61—24no—
21C2×D4×C61—22no—
22C2×D4×C61—22no—
23C2×D4×C61—22no—
24C2×D4×C61—22no—
25C2×D4×C61—22no—
26C2×D4×C61—42no—
27C2×D4×C61—42no—
28C2×D4×C61—42no—
29C2×D4×C61—42no—
30C2×D4×C61D414yes—
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C22×Dic61—21no—
36C42×C61—22no—
37C4⋊Dic61—21no—
38C4⋊Dic61—22no—
39C4⋊Dic61D412yescomplemented
40#11758196—42no—
41C2×#92418—22no—
42C2×#92418—22no—
43C2×#92418—22no—
44C23×C61—24no—
45C23×C61—42no—
46C23×C61—42no—
47C23×C61—42no—
48C23×C61—42no—
49C23×C61—42no—
50C23×C61—42no—
51C23×C61C2×D411yescharacteristic
52D4×C61—24no—
53D4×C61—24no—
54D4×C61—48no—
55D4×C61—48no—
56D4×C61—42no—
57D4×C61—42no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—21no—
62C2×C4×C61D812yes—
63C2×C4×C61SD1612yes—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D412yes—
66C2×C4×C61#4112yes—
67C2×C4×C61#4111yescharacteristic
68C2×Dic61—22no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74#92418—42no—
75C22×C61—44no—
76C22×C61—44no—
77C22×C61—44no—
78C22×C61—82no—
79C22×C61—82no—
80C22×C61—82no—
81C22×C61—82no—
82C22×C61#12011yescharacteristic
83C22×C61#12111yescharacteristic
84C22×C61#12411yescharacteristic
85C22×C61C2×D811yescharacteristic
86C22×C61C2×SD1611yescharacteristic
87C22×C61AGL(1,ℤ/8)11yescharacteristic
88C22×C61AGL(1,ℤ/8)11yescharacteristic
89C4×C61—22no—
90C4×C61—22no—
91C4×C61#12112yes—
92C4×C61#12312yes—
93Dic61—42no—
94Dic61—81no—
95#2041—611nomaximal, Sylow
96C2×C61—84no—
97C2×C61#39411yescharacteristic
98C2×C61#44711yescharacteristic
99C2×C61#45011yescharacteristic
100C2×C61#45911yescharacteristic
101C2×C61#46011yescharacteristic
102C2×C61#48611yescharacteristic
103C2×C61#49011yescharacteristic
104C2×#127D6111yescharacteristic
105C2×#102—612no—
106C2×#102—612no—
107#389—611no—
108#336—611no—
109C61#204111yescharacteristic, complemented, Sylow
110C22×D4—21no—
111C22×D4—21no—
112C22×D4C2×D6112yes—
113C22×C8—612no—
114#127—24no—
115C2×C4⋊C4—611no—
116C2×C4⋊C4—611no—
117C2×C4⋊C4—1221no—
118C2×C42C2×D6111yescharacteristic
119#102—1224no—
120#102—1224no—
121#95—1221no—
122C24—22no—
123C2×D4—24no—
124C2×D4—24no—
125C2×D4—22no—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—42no—
131C2×D4—42no—
132C2×D4—42no—
133C2×D4—42no—
134C2×D4C22⋊D6114yes—
135C22×C4—1221no—
136C22×C4—1221no—
137C22×C4C22⋊D6111yescharacteristic
138C22×C4C22⋊D6111yescharacteristic
139C22×C4C22×D6111yescharacteristic
140C2×C8—1222no—
141C2×C8—1222no—
142C2×C8—1222no—
143C4⋊C4—612no—
144C4⋊C4—1221no—
145C4⋊C4—1222no—
146C4⋊C4—2442no—
147C42—22no—
148C23—24no—
149C23—42no—
150C23—42no—
151C23—42no—
152C23—42no—
153C23—42no—
154C23—42no—
155C23C2×C22⋊D6111yescharacteristic
156D4—24no—
157D4—24no—
158D4—48no—
159D4—48no—
160D4—42no—
161D4—42no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1222no—
167C2×C4—2441no—
168C2×C4—2441no—
169C2×C4—2441no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4#1175819912yes—
173C2×C4#1175820012yes—
174C2×C4D4×D6111yescharacteristic
175C2×C4#1175822412yes—
176C2×C4#1175822411yescharacteristic
177C2×C4C2×C22⋊D6112yes—
178C8—2442no—
179C22—44no—
180C22—44no—
181C22—44no—
182C22—82no—
183C22—82no—
184C22—82no—
185C22—82no—
186C22#1451974611yescharacteristic
187C22#1451974811yescharacteristic
188C22#1451976411yescharacteristic
189C22C2×#1175819911yescharacteristic
190C22C2×#1175820011yescharacteristic
191C22#1451980311yescharacteristic
192C22#1451980311yescharacteristic
193C4—22no—
194C4—22no—
195C4—4881no—
196C4—2442no—
197C4#1451974912yes—
198C4#1451975812yes—
199C2—84no—
200C2#1683967611yescharacteristic
201C2#1683989611yescharacteristic
202C2#1683991311yescharacteristic
203C2#1683995411yescharacteristic
204C2#1683995911yescharacteristic
205C2#1684010811yescharacteristic
206C2#1684012611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D61
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#127×C61C2
socleC23×C61C2×D4
hypercenterC2×#127D61
hypocenterC61#2041
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#14519698C2semidirect
2. C2×#14519698C2semidirect
3. #16839660C2semidirect
4. #16839517C2semidirect
39. C4⋊Dic61D4semidirect
109. C61#2041semidirect