Finite Group Databasebeta

← #21444988

Subgroups — #21444988

Order 7808.

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

normal subgroups only

This group has 194 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#16840054C211yesmaximal, characteristic, complemented
3#16840049C211yesmaximal, characteristic
4#16839508C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic
7C61×#487C211yesmaximal, characteristic, complemented
8#14519772—22no—
9#14519766—21no—
10#14519757—21no—
11Q8×Dic61—21no—
12C4×Dic122C2211yescharacteristic
13C4×D244C2211yescharacteristic
14#14519735—21no—
15#14519710—21no—
16#14519708—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519700—21no—
20#14519697—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23#103×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#11758198—22no—
37#11758198—22no—
38#11758198—21no—
39C4⋊Dic61—22no—
40C4⋊Dic61D411yescharacteristic
41C4⋊Dic61D411yescharacteristic
42#11758196—21no—
43C4×Dic61—22no—
44C4×Dic61—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C22×D61—21no—
48Q8×C61—42no—
49Q8×C61—41no—
50Q8×C61—41no—
51C2×C4×C61—22no—
52C2×C4×C61—41no—
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×Dic61—21no—
57C2×Dic61—21no—
58C2×Dic61—21no—
59D244—21no—
60D244—21no—
61C4×D61—41no—
62C4×D61—41no—
63Dic122—21no—
64Dic122—21no—
65C8×C61—41no—
66#92418—41no—
67#92418—41no—
68C22×C61#12011yescharacteristic
69C2×D61—41no—
70C2×D61—41no—
71C2×D61—41no—
72C4×C61—21no—
73C4×C61—42no—
74C4×C61—81no—
75C4×C61#13511yescharacteristic
76C4×C61#13511yescharacteristic
77C4×C61#13711yescharacteristic
78C4×C61#13711yescharacteristic
79Dic61—41no—
80Dic61—41no—
81Dic61—41no—
82#1638—611nomaximal, Sylow
83C2×C61#45211yescharacteristic
84C2×C61#45211yescharacteristic
85C2×C61#45411yescharacteristic
86D61—81no—
87#556—611no—
88#487D6111yescharacteristic, complemented
89#477—611no—
90#476—611no—
91#332—611no—
92Q8⋊C8—611no—
93D4⋊C8—611no—
94C61#163811yescharacteristic, complemented, Sylow
95C4⋊Q8C2×D6111yescharacteristic
96C4⋊Q8C2×D6111yescharacteristic
97#126—1222no—
98#124—1221no—
99C22⋊Q8—1221no—
100C4×Q8—611no—
101C4×Q8—1221no—
102C4×D4—611no—
103#117—1221no—
104#107—1221no—
105#106—1221no—
106C4⋊C8—611no—
107C4⋊C8—611no—
108#103—22no—
109#103—1221no—
110#102—1221no—
111C4×C8C2×D6111yescharacteristic
112C2×Q8—21no—
113C2×Q8—21no—
114C2×Q8—611no—
115C2×D4—611no—
116C22×C4—1221no—
117C2×C8—21no—
118C2×C8—1221no—
119C2×C8—1221no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—611no—
124C4⋊C4—611no—
125C4⋊C4—1222no—
126C4⋊C4—1221no—
127C4⋊C4C22⋊D6112yes—
128C22⋊C4—1222no—
129C22⋊C4—1222no—
130C22⋊C4—1221no—
131C42—1222no—
132C42—1221no—
133C42C22×D6111yescharacteristic
134C23—1221no—
135Q8—42no—
136Q8—41no—
137Q8—41no—
138Q8—1221no—
139Q8—1221no—
140D4—1221no—
141D4—1221no—
142C2×C4—22no—
143C2×C4—41no—
144C2×C4—1221no—
145C2×C4—1221no—
146C2×C4—1221no—
147C2×C4—2441no—
148C2×C4—2441no—
149C2×C4D4×D6111yescharacteristic
150C2×C4D4×D6111yescharacteristic
151C2×C4C2×C22⋊D6111yescharacteristic
152C8—41no—
153C8—2441no—
154C8—2441no—
155C22—2441no—
156C22—2441no—
157C22—2441no—
158C22#1451974511yescharacteristic
159C4—21no—
160C4—42no—
161C4—81no—
162C4—2441no—
163C4—2441no—
164C4—2441no—
165C4#1451979811yescharacteristic
166C4#1451980011yescharacteristic
167C4#1451980611yescharacteristic
168C4#1451980911yescharacteristic
169C2—4881no—
170C2#1683992111yescharacteristic
171C2#1683992311yescharacteristic
172C2#1683993411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#487C2
socleC22×C61#120
hypercenter#487D61
hypocenterC61#1638
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #16840054C2semidirect
4. #16839508C2semidirect
5. #16839494C2semidirect
7. C61×#487C2semidirect
88. #487D61semidirect
94. C61#1638semidirect