Finite Group Databasebeta

← #21461698

Subgroups — #21461698

Order 7808.

292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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×#14519847C212yesmaximal, complemented
2#16840733C212yesmaximal
3#16840638C212yesmaximal, complemented
4C22×C8×D61C211yesmaximal, characteristic
5C2×#11758213C2214yes—
6#14519847—24no—
7#14519834—22no—
8C22⋊#92420—22no—
9C22×C4×D61C2211yescharacteristic
10C22×#92418C411yescharacteristic
11C2×C8×D61—24no—
12C2×C8×D61C411yescharacteristic
13C2×C8×D61C411yescharacteristic
14C2×C8×D61C2211yescharacteristic
15C2×C8×D61C2211yescharacteristic
16C22×C8×C61C411yescharacteristic
17C23×D61Q811yescharacteristic
18C22×C4×C61C2×C411yescharacteristic
19C22×Dic61D411yescharacteristic
20C2×C4×D61—22no—
21C2×C4×D61—22no—
22C2×C4×D61C2×C411yescharacteristic
23C2×C4×D61D411yescharacteristic
24C2×C4×D61Q811yescharacteristic
25C2×C4×D61C2311yescharacteristic
26C2×#92420—24no—
27#11758213—24no—
28#11758213—24no—
29C2×C8×C61—22no—
30C2×C8×C61C2×C411yescharacteristic
31C2×C8×C61C2×C411yescharacteristic
32C2×#92418—22no—
33C2×#92418C2×C411yescharacteristic
34C2×#92418C2×C411yescharacteristic
35C8×D61—22no—
36C8×D61—22no—
37C8×D61—22no—
38C8×D61D414yes—
39C23×C61C4⋊C411yescharacteristic
40C22×D61—22no—
41C22×D61—22no—
42C22×D61—22no—
43C22×D61C4⋊C411yescharacteristic
44C22×D61C2×Q811yescharacteristic
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61C4⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C2×Dic61—22no—
50C2×Dic61C4⋊C411yescharacteristic
51C2×Dic61C2×D411yescharacteristic
52C4×D61—22no—
53C4×D61—21no—
54C4×D61—21no—
55C4×D61—22no—
56C4×D61C2×D412yes—
57C4×D61#4112yes—
58#92420—44no—
59C8×C61—21no—
60C8×C61C22⋊C412yes—
61#92418—21no—
62#92418C22⋊C412yes—
63C22×C61—21no—
64C22×C61—21no—
65C22×C61#10812yescomplemented
66C22×C61C2×C4⋊C411yescharacteristic
67C2×D61—28no—
68C2×D61—21no—
69C2×D61—21no—
70C2×D61—21no—
71C2×D61—21no—
72C2×D61#10812yescomplemented
73C2×D61C22⋊Q812yes—
74C4×C61—21no—
75C4×C61C2×C22⋊C411yescharacteristic
76C4×C61#11711yescharacteristic
77Dic61—21no—
78Dic61#12112yes—
79#1810—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61#38011yescharacteristic
82C2×C61C2×#10811yescharacteristic
83C2×C61C2×#10811yescharacteristic
84D61—22no—
85D61—22no—
86C23×C8—611no—
87C2×#108—612no—
88#407—612no—
89#341—612no—
90C61#181011yescharacteristic, complemented, Sylow
91C23×C4—611no—
92C2×M16—614no—
93C22×C8—611no—
94C22×C8—611no—
95C22×C8—611no—
96C22×C8—611no—
97C22×C8—611no—
98C22×C8—1224no—
99C22×C8#692311yescharacteristic
100#108—1224no—
101C22⋊C8—1222no—
102C22⋊C8—1222no—
103C24—611no—
104C22×C4—611no—
105C22×C4—611no—
106C22×C4—611no—
107C22×C4—611no—
108C22×C4—611no—
109C22×C4—1222no—
110C22×C4—1222no—
111C22×C4C2×#692311yescharacteristic
112M16—1224no—
113M16—1224no—
114C2×C8—22no—
115C2×C8—611no—
116C2×C8—614no—
117C2×C8—611no—
118C2×C8—1222no—
119C2×C8—1222no—
120C2×C8—1222no—
121C2×C8—1222no—
122C2×C8—1224no—
123C2×C8C2×#692311yescharacteristic
124C2×C8C2×#692311yescharacteristic
125C23—611no—
126C23—611no—
127C23—1222no—
128C23—1222no—
129C23—1222no—
130C23C4⋊#692311yescharacteristic
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—611no—
134C2×C4—612no—
135C2×C4—612no—
136C2×C4—611no—
137C2×C4—1222no—
138C2×C4—1222no—
139C2×C4—1222no—
140C2×C4—1221no—
141C2×C4—1221no—
142C2×C4C4⋊#692311yescharacteristic
143C2×C4C22×#692311yescharacteristic
144C8—21no—
145C8—612no—
146C8—1221no—
147C8—2444no—
148C8C22⋊#692312yes—
149C22—21no—
150C22—21no—
151C22—612no—
152C22—612no—
153C22—1228no—
154C22—1221no—
155C22—1221no—
156C22—1221no—
157C22—1221no—
158C22#1451984712yescomplemented
159C22C2×C4⋊#692311yescharacteristic
160C4—21no—
161C4—612no—
162C4—1221no—
163C4C2×C22⋊#692311yescharacteristic
164C4#1451985611yescharacteristic
165C2—22no—
166C2—1222no—
167C2—1222no—
168C2#1684070411yescharacteristic
169C2C2×#1451984711yescharacteristic
170C2D61⋊#10811yescharacteristic
subgroupG/H
centerC22C2×C4⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC22×C8#6923
hypocenterC61#1810
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#14519847C2semidirect
3. #16840638C2semidirect
65. C22×C61#108semidirect
72. C2×D61#108semidirect
90. C61#1810semidirect
158. C22#14519847semidirect