Finite Group Databasebeta

← #21444855

Subgroups — #21444855

Order 7808.

246 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#16840343C211yesmaximal, characteristic
2#16840080C212yesmaximal, complemented
3#16839495C212yesmaximal, complemented
4#16839488C211yesmaximal, characteristic, complemented
5C61×#400C211yesmaximal, characteristic, complemented
6C2×#11758222—21no—
7#14519757—22no—
8#14519752—22no—
9#14519751—21no—
10#14519751C2212yes—
11#14519708—22no—
12#14519697—22no—
13C22⋊#92418C2212yes—
14C2×C4⋊C4×C61C2211yescharacteristic
15C2×C4⋊C4×C61C2211yescharacteristic
16#95×C61—21no—
17#95×C61—21no—
18#95×C61C2211yescharacteristic
19C22×C4×C61—21no—
20C22×C4×C61—21no—
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C2×C22⋊D61—22no—
25#11758222—42no—
26#11758222—42no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244D412yes—
30C2×C4×D61—22no—
31C2×Dic122—21no—
32C4⋊C4×C61—22no—
33C4⋊C4×C61—22no—
34#11758198—22no—
35#11758198—22no—
36C4⋊Dic61—21no—
37C4⋊Dic61D412yes—
38C2×#92418—22no—
39C23×C61C2×D411yescharacteristic
40C22×D61—22no—
41C2×C4×C61—21no—
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61—42no—
49C2×C4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61SD1612yes—
52C2×C4×C61C2×D412yes—
53C22⋊D61—42no—
54C22⋊D61—42no—
55C2×Dic61—22no—
56D244—42no—
57D244—42no—
58D244—81no—
59C4×D61—44no—
60Dic122—42no—
61#92418—42no—
62C22×C61—21no—
63C22×C61—21no—
64C22×C61#12011yescharacteristic
65C22×C61C2×SD1611yescharacteristic
66C22×C61AGL(1,ℤ/8)11yescharacteristic
67C2×D61—42no—
68C2×D61—42no—
69C2×D61—42no—
70C4×C61—22no—
71C4×C61—22no—
72C4×C61—41no—
73C4×C61—81no—
74C4×C61—81no—
75Dic61—42no—
76#1616—611nomaximal, Sylow
77C2×C61—21no—
78C2×C61—21no—
79C2×C61#45011yescharacteristic
80C2×C61#45411yescharacteristic
81C2×C61#45811yescharacteristic
82D61—82no—
83#537—611no—
84#481—612no—
85#400D6111yescharacteristic, complemented
86#327—612no—
87#324—611no—
88C61#161611yescharacteristic, complemented, Sylow
89C2×#41—1221no—
90C22⋊Q8—1222no—
91#121—612no—
92#121—1222no—
93#121—1221no—
94C2×C4⋊C4C2×D6111yescharacteristic
95C2×C4⋊C4C2×D6111yescharacteristic
96#106—1222no—
97#102—1222no—
98C22⋊C8—612no—
99#95—21no—
100#95—21no—
101#95C2×D6111yescharacteristic
102#41—2442no—
103#41—2442no—
104C2×Q8—1221no—
105C2×D4—612no—
106C2×D4—1221no—
107C2×D4—1221no—
108C2×D4—1222no—
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—1222no—
112C22×C4C22⋊D6111yescharacteristic
113C22×C4C22⋊D6111yescharacteristic
114C22×C4C22×D6111yescharacteristic
115C2×C8—1222no—
116C4⋊C4—22no—
117C4⋊C4—22no—
118C4⋊C4—612no—
119C4⋊C4—1221no—
120C22⋊C4—1222no—
121C22⋊C4—1222no—
122C23—1222no—
123C23C2×C22⋊D6111yescharacteristic
124Q8—2442no—
125D4—4881no—
126D4—2442no—
127D4—2442no—
128D4—2442no—
129D4—2442no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—1222no—
141C2×C4—2444no—
142C2×C4#1175820112yes—
143C2×C4D4×D6112yes—
144C8—2442no—
145C22—21no—
146C22—21no—
147C22—2442no—
148C22—2442no—
149C22—2442no—
150C22#1451974511yescharacteristic
151C22C2×#1175820111yescharacteristic
152C22#1451980211yescharacteristic
153C4—22no—
154C4—22no—
155C4—41no—
156C4—81no—
157C4—81no—
158C4—2442no—
159C2—21no—
160C2—21no—
161C2—4882no—
162C2#1683991211yescharacteristic
163C2#1683993411yescharacteristic
164C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#400C2
socleC22×C61#120
hypercenter#400D61
hypocenterC61#1616
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #16840080C2semidirect
3. #16839495C2semidirect
4. #16839488C2semidirect
5. C61×#400C2semidirect
85. #400D61semidirect
88. C61#1616semidirect