Finite Group Databasebeta

← #21461703

Subgroups — #21461703

Order 7808.

252 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 72 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
1D61⋊#108C212yesmaximal, complemented
2#16840748C212yesmaximal
3#16840631C212yesmaximal, complemented
4C2×#14519783C211yesmaximal, characteristic
5D61⋊M16C2214yes—
6#14519848—22no—
7#14519847—22no—
8#14519838—22no—
9#14519837—22no—
10C2×#11758222C2211yescharacteristic
11#14519783—22no—
12#14519783—22no—
13C2×#11758194C411yescharacteristic
14C2×#11758189C411yescharacteristic
15C2×#11758189C2211yescharacteristic
16C2×C8×D61C411yescharacteristic
17C2×C8×D61C2211yescharacteristic
18C22×C8×C61C411yescharacteristic
19C22×C4×C61C2×C411yescharacteristic
20C2×C22⋊D61D411yescharacteristic
21C2×C22⋊D61Q811yescharacteristic
22#11758222—22no—
23#11758222—22no—
24C2×D244Q811yescharacteristic
25C2×C4×D61C2×C411yescharacteristic
26C2×C4×D61C2311yescharacteristic
27C2×Dic122D411yescharacteristic
28#11758217—24no—
29#11758213—24no—
30D61⋊C8—24no—
31C2×C8×C61—21no—
32C2×C8×C61—21no—
33C2×C8×C61C2×C411yescharacteristic
34C2×C8×C61C2×C411yescharacteristic
35#11758194—22no—
36C2×#92418C2×C411yescharacteristic
37C2×#92418C2×C411yescharacteristic
38#11758189—22no—
39#11758189—22no—
40C8×D61—21no—
41C8×D61—21no—
42C8×D61D412yes—
43C8×D61D412yes—
44C23×C61C4⋊C411yescharacteristic
45C22×D61C4⋊C411yescharacteristic
46C22×D61C2×Q811yescharacteristic
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61C4⋊C411yescharacteristic
50C2×C4×C61C22×C411yescharacteristic
51C22⋊D61—22no—
52C22⋊D61—22no—
53C2×Dic61C4⋊C411yescharacteristic
54C2×Dic61C2×D411yescharacteristic
55D244—22no—
56C4×D61—21no—
57C4×D61—21no—
58C4×D61C2×D412yes—
59C4×D61#4112yes—
60Dic122—22no—
61#92420—44no—
62C8×C61—21no—
63C8×C61C22⋊C411yescharacteristic
64C8×C61C22⋊C411yescharacteristic
65#92418—21no—
66#92418C22⋊C412yes—
67C22×C61—21no—
68C22×C61—41no—
69C22×C61C2×C4⋊C411yescharacteristic
70C2×D61—21no—
71C2×D61—41no—
72C2×D61—41no—
73C2×D61C22⋊Q812yes—
74C4×C61—21no—
75C4×C61C2×C22⋊C411yescharacteristic
76C4×C61#11711yescharacteristic
77Dic61—21no—
78Dic61#12112yes—
79#1813—611nomaximal, Sylow
80C2×C61—21no—
81C2×C61—41no—
82C2×C61#38011yescharacteristic
83D61—22no—
84D61—41no—
85C2×#131—611no—
86C2×#108—612no—
87#413—612no—
88#338—612no—
89C61#181311yescharacteristic, complemented, Sylow
90C2×#41—611no—
91#131—1222no—
92#131—1222no—
93C2×M16—611no—
94C2×M16—611no—
95C2×M16—611no—
96C2×M16—614no—
97C22×C8—611no—
98C22×C8—611no—
99C22×C8#692311yescharacteristic
100#108—1222no—
101#108—1222no—
102#101—1222no—
103#100—1222no—
104#41—1222no—
105#41—1222no—
106C2×Q8—611no—
107C2×D4—611no—
108C2×D4—611no—
109C2×D4—611no—
110C22×C4—611no—
111C22×C4—611no—
112C22×C4C2×#692311yescharacteristic
113M16—1222no—
114M16—1222no—
115M16—1222no—
116M16—1224no—
117M16—1224no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—611no—
121C2×C8—612no—
122C2×C8—612no—
123C2×C8—611no—
124C2×C8—1221no—
125C2×C8—1221no—
126C2×C8—1224no—
127C2×C8C2×#692311yescharacteristic
128C2×C8C2×#692311yescharacteristic
129C23—611no—
130C23—611no—
131C23C4⋊#692311yescharacteristic
132Q8—1222no—
133D4—1222no—
134D4—1222no—
135D4—1222no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—611no—
139C2×C4—612no—
140C2×C4—612no—
141C2×C4—611no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4C4⋊#692311yescharacteristic
145C2×C4C22×#692311yescharacteristic
146C8—21no—
147C8—612no—
148C8—1221no—
149C8—2444no—
150C8C22⋊#692311yescharacteristic
151C8C22⋊#692311yescharacteristic
152C22—21no—
153C22—41no—
154C22—612no—
155C22—1221no—
156C22—2441no—
157C22—2441no—
158C22C2×C4⋊#692311yescharacteristic
159C4—21no—
160C4—612no—
161C4—1221no—
162C4C2×C22⋊#692311yescharacteristic
163C4#1451985611yescharacteristic
164C2—21no—
165C2—41no—
166C2—1222no—
167C2—2441no—
168C2#1684070411yescharacteristic
subgroupG/H
centerC4#14519856
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22×C8×C61C4
socleC2×C61#380
hypercenterC22×C8#6923
hypocenterC61#1813
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. D61⋊#108C2semidirect
3. #16840631C2semidirect
89. C61#1813semidirect