Finite Group Databasebeta

← #21445072

Subgroups — #21445072

Order 7808.

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

normal subgroups only

This group has 200 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#16840486C211yesmaximal, characteristic
2#16840044C211yesmaximal, characteristic, complemented
3#16839964C211yesmaximal, characteristic
4#16839508C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic
7C61×#500C211yesmaximal, characteristic, complemented
8C2×#11758201—21no—
9#14519772—22no—
10#14519766—21no—
11#14519757—21no—
12Q8×Dic61—21no—
13C4×Dic122C2211yescharacteristic
14C4×D244C2211yescharacteristic
15#14519735—21no—
16#14519708—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519701—21no—
20#14519700—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23#107×C61—22no—
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×D244D411yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122D411yescharacteristic
30C2×C8×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61D412yes—
35C42×C61C2311yescharacteristic
36#11758201—42no—
37#11758198—22no—
38#11758198—22no—
39#11758198—21no—
40C4⋊Dic61—22no—
41C4⋊Dic61D411yescharacteristic
42C4⋊Dic61D411yescharacteristic
43#11758196—21no—
44C4×Dic61—22no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C22×D61—21no—
49Q8×C61—41no—
50Q8×C61—41no—
51Q8×C61—41no—
52Q8×C61—41no—
53C2×C4×C61—22no—
54C2×C4×C61—41no—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—21no—
61D244—21no—
62D244—21no—
63C4×D61—41no—
64C4×D61—41no—
65Dic122—21no—
66Dic122—21no—
67C8×C61—22no—
68#92418—41no—
69#92418—41no—
70C22×C61#12011yescharacteristic
71C2×D61—41no—
72C2×D61—41no—
73C2×D61—41no—
74C4×C61—21no—
75C4×C61—42no—
76C4×C61—81no—
77C4×C61#13511yescharacteristic
78C4×C61#13511yescharacteristic
79C4×C61AGL(1,ℤ/8)11yescharacteristic
80C4×C61#13711yescharacteristic
81Dic61—41no—
82Dic61—41no—
83Dic61—41no—
84#1650—611nomaximal, Sylow
85C2×C61#44911yescharacteristic
86C2×C61#45211yescharacteristic
87C2×C61#45611yescharacteristic
88D61—81no—
89#556—611no—
90#500D6111yescharacteristic, complemented
91#475—611no—
92#461—611no—
93#332—611no—
94Q8⋊C8—611no—
95D4⋊C8—611no—
96C61#165011yescharacteristic, complemented, Sylow
97C2×SD16—1221no—
98C4⋊Q8C2×D6111yescharacteristic
99C4⋊Q8C2×D6111yescharacteristic
100#126—1222no—
101#124—1221no—
102C22⋊Q8—1221no—
103C4×Q8—611no—
104C4×Q8—1221no—
105C4×D4—611no—
106#117—1221no—
107#107—22no—
108#106—1221no—
109C4⋊C8—611no—
110C4⋊C8—611no—
111#103—1221no—
112#103—1221no—
113C4×C8C2×D6111yescharacteristic
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—611no—
117C2×D4—611no—
118C22×C4—1221no—
119SD16—2442no—
120C2×C8—21no—
121C2×C8—1221no—
122C2×C8—1221no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—611no—
127C4⋊C4—611no—
128C4⋊C4—1222no—
129C4⋊C4—1221no—
130C4⋊C4C22⋊D6112yes—
131C22⋊C4—1222no—
132C22⋊C4—1222no—
133C22⋊C4—1221no—
134C42—1222no—
135C42—1221no—
136C42C22×D6111yescharacteristic
137C23—1221no—
138Q8—41no—
139Q8—41no—
140Q8—41no—
141Q8—41no—
142Q8—1221no—
143Q8—1221no—
144D4—1221no—
145D4—1221no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—1221no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4D4×D6111yescharacteristic
154C2×C4D4×D6111yescharacteristic
155C2×C4C2×C22⋊D6111yescharacteristic
156C8—22no—
157C8—2441no—
158C8—2441no—
159C22—2441no—
160C22—2441no—
161C22—2441no—
162C22#1451974511yescharacteristic
163C4—21no—
164C4—42no—
165C4—81no—
166C4—2441no—
167C4—2441no—
168C4—2441no—
169C4#1451979611yescharacteristic
170C4#1451980011yescharacteristic
171C4#1451980111yescharacteristic
172C4#1451980911yescharacteristic
173C2—4881no—
174C2#1683990411yescharacteristic
175C2#1683992311yescharacteristic
176C2#1683994411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#500C2
socleC22×C61#120
hypercenter#500D61
hypocenterC61#1650
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. #16840044C2semidirect
4. #16839508C2semidirect
5. #16839494C2semidirect
7. C61×#500C2semidirect
90. #500D61semidirect
96. C61#1650semidirect