Finite Group Databasebeta

← #21447045

Subgroups — #21447045

Order 7808.

290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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×#14519704C212yesmaximal, complemented
2#16839763C212yesmaximal, complemented
3#16839627C211yesmaximal, characteristic, complemented
4#16839531C211yesmaximal, characteristic, complemented
5C61×#537C211yesmaximal, characteristic
6C2×#11758194C2212yes—
7C2×C4⋊Dic61C2211yescharacteristic
8C2×C4×Dic61C2211yescharacteristic
9#14519704—24no—
10#14519701—22no—
11#14519698—22no—
12#14519684—22no—
13C2×#41×C61C2212yes—
14C22⋊Q8×C61—22no—
15#121×C61—22no—
16#121×C61—22no—
17C2×C4⋊C4×C61C2211yescharacteristic
18#41×C61—22no—
19#41×C61—22no—
20#41×C61—22no—
21#41×C61—22no—
22C2×Q8×C61D412yes—
23C2×D4×C61—22no—
24C2×D4×C61—22no—
25C2×D4×C61D412yes—
26C22×C4×C61—22no—
27C22×C4×C61D412yes—
28C22×C4×C61C2311yescharacteristic
29C22×Dic61—21no—
30C22×Dic61—21no—
31C4⋊C4×C61—22no—
32C4⋊C4×C61—22no—
33C22⋊C4×C61—24no—
34C4⋊Dic61—22no—
35C4×Dic61—21no—
36C4×Dic61D412yescomplemented
37#11758194—22no—
38#11758194—22no—
39C2×#92418—22no—
40C23×C61—22no—
41C23×C61C2×D411yescharacteristic
42Q8×C61—22no—
43Q8×C61—22no—
44D4×C61—22no—
45D4×C61—22no—
46D4×C61—42no—
47D4×C61—42no—
48D4×C61—82no—
49C2×C4×C61—22no—
50C2×C4×C61—22no—
51C2×C4×C61—42no—
52C2×C4×C61—42no—
53C2×C4×C61—42no—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D412yes—
56C2×C4×C61#4112yes—
57C2×C4×C61#4111yescharacteristic
58C2×Dic61—22no—
59C2×Dic61—41no—
60C2×Dic61—41no—
61C2×Dic61—42no—
62C2×Dic61—41no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61—42no—
67C22×C61—42no—
68C22×C61—42no—
69C22×C61#12011yescharacteristic
70C22×C61#12111yescharacteristic
71C22×C61#12411yescharacteristic
72C4×C61—42no—
73C4×C61—42no—
74C4×C61#12112yes—
75C4×C61#12312yes—
76Dic61—42no—
77Dic61—81no—
78#2040—611nomaximal, Sylow
79C2×C61—21no—
80C2×C61—21no—
81C2×C61—82no—
82C2×C61#39411yescharacteristic
83C2×C61#45411yescharacteristic
84C2×C61#45511yescharacteristic
85#537D6111yescharacteristic
86C2×#104—612no—
87#417—612no—
88#382—611no—
89#343—611no—
90C61#204011yescharacteristic, complemented, Sylow
91C2×#41C2×D6112yes—
92C2×M16—612no—
93C22⋊Q8—22no—
94#121—22no—
95#121—22no—
96C2×C4⋊C4—611no—
97C2×C4⋊C4C2×D6111yescharacteristic
98C2×C42—611no—
99#104—1224no—
100#103—1222no—
101#102—1222no—
102#95—1222no—
103#41—22no—
104#41—22no—
105#41—22no—
106#41—22no—
107C2×Q8C22⋊D6112yes—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4C22⋊D6112yes—
111C22×C4—22no—
112C22×C4—1221no—
113C22×C4—1221no—
114C22×C4C22⋊D6112yes—
115C22×C4C22×D6111yescharacteristic
116M16—1222no—
117M16—1222no—
118C2×C8—1222no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—1222no—
122C22⋊C4—24no—
123C42—612no—
124C42—1221no—
125C23—22no—
126C23C2×C22⋊D6111yescharacteristic
127Q8—22no—
128Q8—22no—
129D4—22no—
130D4—22no—
131D4—42no—
132D4—42no—
133D4—82no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—42no—
139C2×C4—1222no—
140C2×C4—2442no—
141C2×C4—2441no—
142C2×C4—2441no—
143C2×C4—2441no—
144C2×C4D4×D6111yescharacteristic
145C2×C4#1175822412yes—
146C2×C4#1175822411yescharacteristic
147C2×C4C2×C22⋊D6112yes—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—42no—
152C22—42no—
153C22—42no—
154C22#1451974611yescharacteristic
155C22#1451974811yescharacteristic
156C22#1451976411yescharacteristic
157C4—42no—
158C4—42no—
159C4—4881no—
160C4—2442no—
161C4#1451974912yes—
162C4#1451975812yes—
163C2—21no—
164C2—21no—
165C2—82no—
166C2#1683967611yescharacteristic
167C2#1683993511yescharacteristic
168C2#1683994011yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#537C2
socleC22×C61#120
hypercenter#537D61
hypocenterC61#2040
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#14519704C2semidirect
2. #16839763C2semidirect
3. #16839627C2semidirect
4. #16839531C2semidirect
36. C4×Dic61D4semidirect
90. C61#2040semidirect