Finite Group Databasebeta

← #21444989

Subgroups — #21444989

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#16840482C211yesmaximal, characteristic
2#16840112C211yesmaximal, characteristic, complemented
3#16840054C211yesmaximal, characteristic, complemented
4#16839509C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic
7C61×#476C211yesmaximal, characteristic
8#14519777C2211yescharacteristic
9#14519770—22no—
10#14519764—21no—
11#14519756—21no—
12C4×Dic122C2211yescharacteristic
13#14519742—21no—
14#14519736—21no—
15#14519710—21no—
16C4⋊#92418C2211yescharacteristic
17#14519701—22no—
18#14519700—21no—
19C4×#92418C2211yescharacteristic
20C4⋊Q8×C61C2211yescharacteristic
21C4×D4×C61C2211yescharacteristic
22#106×C61—21no—
23C4⋊C8×C61C2211yescharacteristic
24#102×C61—21no—
25C2×Q8×C61—21no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C2×Dic122—21no—
29C2×Dic122D411yescharacteristic
30C2×C8×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C22⋊C4×C61—21no—
35C42×C61C2311yescharacteristic
36C22⋊Dic61—22no—
37C22⋊Dic61—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61D412yes—
40C4⋊Dic61D411yescharacteristic
41#11758196—22no—
42#11758196—21no—
43C4×Dic61—22no—
44C4×Dic61—21no—
45C2×#92418—21no—
46C2×#92418—21no—
47C23×C61—21no—
48Q8×C61—42no—
49D4×C61—21no—
50D4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—41no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—22no—
61Dic122—21no—
62Dic122—21no—
63Dic122—41no—
64Dic122—41no—
65C8×C61—41no—
66#92418—41no—
67#92418—41no—
68C22×C61—41no—
69C22×C61—41no—
70C22×C61—41no—
71C22×C61#12011yescharacteristic
72C4×C61—21no—
73C4×C61—41no—
74C4×C61—81no—
75C4×C61#13511yescharacteristic
76C4×C61#13511yescharacteristic
77C4×C61#13711yescharacteristic
78C4×C61#13711yescharacteristic
79Dic61—41no—
80Dic61—42no—
81Dic61—41no—
82#1638—611nomaximal, Sylow
83C2×C61—81no—
84C2×C61#45211yescharacteristic
85C2×C61#45211yescharacteristic
86C2×C61#45411yescharacteristic
87#556—611no—
88#487—611no—
89#477—611no—
90#476D6111yescharacteristic
91#332—611no—
92Q8⋊C8—611no—
93D4⋊C8—611no—
94C61#163811yescharacteristic, complemented, Sylow
95C4⋊Q8—611no—
96C4⋊Q8C2×D6111yescharacteristic
97#126—1222no—
98#124—1221no—
99C22⋊Q8—1221no—
100C4×Q8—611no—
101C4×Q8—1221no—
102C4×D4C2×D6111yescharacteristic
103#117—1221no—
104#107—1221no—
105#106—21no—
106C4⋊C8—611no—
107C4⋊C8C2×D6111yescharacteristic
108#103—1221no—
109#103—1222no—
110#102—21no—
111C4×C8—611no—
112C2×Q8—21no—
113C2×Q8—611no—
114C2×Q8—1221no—
115C2×D4C22⋊D6111yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—1221no—
119C2×C8—1221no—
120C4⋊C4—21no—
121C4⋊C4—21no—
122C4⋊C4—612no—
123C4⋊C4—611no—
124C4⋊C4—1222no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4C22⋊D6111yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—1222no—
130C22⋊C4—1222no—
131C42—1222no—
132C42—1221no—
133C42C22×D6111yescharacteristic
134C23—21no—
135Q8—42no—
136Q8—1221no—
137Q8—1221no—
138Q8—2441no—
139Q8—2441no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—1221no—
147C2×C4—1222no—
148C2×C4—1221no—
149C2×C4D4×D6111yescharacteristic
150C2×C4D4×D6111yescharacteristic
151C2×C4C2×C22⋊D6111yescharacteristic
152C8—41no—
153C8—2441no—
154C8—2441no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1451974511yescharacteristic
159C4—21no—
160C4—41no—
161C4—81no—
162C4—2441no—
163C4—2442no—
164C4—2441no—
165C4#1451979711yescharacteristic
166C4#1451979811yescharacteristic
167C4#1451980611yescharacteristic
168C4#1451980811yescharacteristic
169C2—81no—
170C2#1683992111yescharacteristic
171C2#1683992211yescharacteristic
172C2#1683993311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#476C2
socleC22×C61#120
hypercenter#476D61
hypocenterC61#1638
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #16840112C2semidirect
3. #16840054C2semidirect
4. #16839509C2semidirect
5. #16839492C2semidirect
94. C61#1638semidirect