Finite Group Databasebeta

← #21445073

Subgroups — #21445073

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#16840482C211yesmaximal, characteristic
2#16840165C211yesmaximal, characteristic, complemented
3#16840044C211yesmaximal, characteristic, complemented
4#16839509C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic
7C61×#461C211yesmaximal, characteristic
8#14519777C2211yescharacteristic
9#14519770—22no—
10#14519764—21no—
11#14519756—21no—
12C4×Dic122C2211yescharacteristic
13#14519742—21no—
14#14519736—21no—
15#14519710—22no—
16#14519708—21no—
17C4⋊#92418C2211yescharacteristic
18#14519700—21no—
19C4×#92418C2211yescharacteristic
20C2×SD16×C61—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24#103×C61—21no—
25C2×Q8×C61—21no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C2×Dic122—21no—
29C2×Dic122D411yescharacteristic
30SD16×C61—42no—
31C2×C8×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61D411yescharacteristic
35C22⋊C4×C61—21no—
36C42×C61C2311yescharacteristic
37C22⋊Dic61—22no—
38C22⋊Dic61—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61D411yescharacteristic
41C4⋊Dic61D412yes—
42#11758196—22no—
43#11758196—21no—
44C4×Dic61—22no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C23×C61—21no—
49Q8×C61—41no—
50Q8×C61—41no—
51D4×C61—21no—
52D4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—22no—
63Dic122—21no—
64Dic122—21no—
65Dic122—41no—
66Dic122—41no—
67C8×C61—41no—
68#92418—22no—
69#92418—41no—
70C22×C61—41no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61#12011yescharacteristic
74C4×C61—21no—
75C4×C61—41no—
76C4×C61—81no—
77C4×C61#13511yescharacteristic
78C4×C61#13511yescharacteristic
79C4×C61AGL(1,ℤ/8)11yescharacteristic
80C4×C61#13711yescharacteristic
81Dic61—42no—
82Dic61—41no—
83Dic61—41no—
84#1650—611nomaximal, Sylow
85C2×C61—81no—
86C2×C61#44911yescharacteristic
87C2×C61#45211yescharacteristic
88C2×C61#45611yescharacteristic
89#556—611no—
90#500—611no—
91#475—611no—
92#461D6111yescharacteristic
93#332—611no—
94Q8⋊C8—611no—
95D4⋊C8—611no—
96C61#165011yescharacteristic, complemented, Sylow
97C2×SD16—21no—
98C4⋊Q8—611no—
99C4⋊Q8C2×D6111yescharacteristic
100#126—1222no—
101#124—1221no—
102C22⋊Q8—1221no—
103C4×Q8—611no—
104C4×Q8—1221no—
105C4×D4C2×D6111yescharacteristic
106#117—1221no—
107#107—1222no—
108#106—1221no—
109C4⋊C8—611no—
110C4⋊C8C2×D6111yescharacteristic
111#103—21no—
112#103—1221no—
113C4×C8—611no—
114C2×Q8—21no—
115C2×Q8—611no—
116C2×Q8—1221no—
117C2×D4C22⋊D6111yescharacteristic
118C22×C4—21no—
119SD16—42no—
120C2×C8—21no—
121C2×C8—1221no—
122C2×C8—1221no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—611no—
126C4⋊C4—612no—
127C4⋊C4—1222no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4C22⋊D6111yescharacteristic
131C22⋊C4—21no—
132C22⋊C4—1222no—
133C22⋊C4—1222no—
134C42—1222no—
135C42—1221no—
136C42C22×D6111yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—1221no—
141Q8—1221no—
142Q8—2441no—
143Q8—2441no—
144D4—21no—
145D4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—1221no—
151C2×C4—1222no—
152C2×C4—1221no—
153C2×C4D4×D6111yescharacteristic
154C2×C4D4×D6111yescharacteristic
155C2×C4C2×C22⋊D6111yescharacteristic
156C8—41no—
157C8—1222no—
158C8—2441no—
159C22—41no—
160C22—41no—
161C22—41no—
162C22#1451974511yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—2441no—
167C4—2442no—
168C4—2441no—
169C4#1451979711yescharacteristic
170C4#1451979811yescharacteristic
171C4#1451980311yescharacteristic
172C4#1451980611yescharacteristic
173C2—81no—
174C2#1683990511yescharacteristic
175C2#1683992111yescharacteristic
176C2#1683994311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#461C2
socleC22×C61#120
hypercenter#461D61
hypocenterC61#1650
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #16840165C2semidirect
3. #16840044C2semidirect
4. #16839509C2semidirect
5. #16839492C2semidirect
96. C61#1650semidirect