Finite Group Databasebeta

← #21445032

Subgroups — #21445032

Order 7808.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840469C211yesmaximal, characteristic
2#16840114C211yesmaximal, characteristic, complemented
3#16839969C211yesmaximal, characteristic, complemented
4#16839510C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6D4⋊#92418C211yesmaximal, characteristic
7C61×#474C211yesmaximal, characteristic
8C2×#11758202—21no—
9#14519777C2211yescharacteristic
10#14519768—21no—
11#14519756—21no—
12#14519754—22no—
13C4×Dic122C2211yescharacteristic
14D4×Dic61—21no—
15C2×C4⋊Dic61—21no—
16C4⋊#92418C2211yescharacteristic
17#14519701—21no—
18#14519700—22no—
19C4×#92418C2211yescharacteristic
20C4⋊Q8×C61C2211yescharacteristic
21C4×D4×C61C2211yescharacteristic
22#107×C61—21no—
23C4⋊C8×C61C2211yescharacteristic
24#102×C61—21no—
25C2×Q8×C61—21no—
26C2×D4×C61D411yescharacteristic
27C22×C4×C61—21no—
28C22×Dic61—22no—
29C2×Dic122D411yescharacteristic
30C2×Dic122D412yes—
31C2×C8×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61D411yescharacteristic
35C22⋊C4×C61—21no—
36C42×C61C2311yescharacteristic
37C22⋊Dic61—22no—
38#11758202—42no—
39C4⋊Dic61—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61D411yescharacteristic
43#11758196—22no—
44#11758196—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C23×C61—21no—
49Q8×C61—41no—
50Q8×C61—41no—
51D4×C61—21no—
52D4×C61Q1612yescomplemented
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—
63C2×Dic61—82no—
64Dic122—21no—
65Dic122—21no—
66Dic122—42no—
67C8×C61—41no—
68#92418—41no—
69#92418—41no—
70C22×C61—22no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61#12011yescharacteristic
74C4×C61—21no—
75C4×C61—41no—
76C4×C61—81no—
77C4×C61C2×Q1611yescharacteristic
78C4×C61#13511yescharacteristic
79C4×C61AGL(1,ℤ/8)11yescharacteristic
80C4×C61#13711yescharacteristic
81Dic61—41no—
82Dic61—42no—
83Dic61—41no—
84#1644—611nomaximal, Sylow
85C2×C61—42no—
86C2×C61#44911yescharacteristic
87C2×C61#45111yescharacteristic
88C2×C61#45511yescharacteristic
89#554—611no—
90#487—611no—
91#474D6111yescharacteristic
92#462—611no—
93#333—611no—
94Q8⋊C8—611no—
95D4⋊C8—611no—
96C61#164411yescharacteristic, complemented, Sylow
97C2×Q16—1221no—
98C4⋊Q8—611no—
99C4⋊Q8C2×D6111yescharacteristic
100#125—1221no—
101C22⋊Q8—1222no—
102C22⋊Q8—1221no—
103C4×Q8—611no—
104C4×D4—1221no—
105C4×D4C2×D6111yescharacteristic
106C2×C4⋊C4—1221no—
107#107—21no—
108C4⋊C8—611no—
109C4⋊C8C2×D6111yescharacteristic
110#103—1222no—
111#103—1221no—
112#102—21no—
113C4×C8—611no—
114C2×Q8—21no—
115C2×Q8—611no—
116C2×Q8—612no—
117C2×D4C22⋊D6111yescharacteristic
118C22×C4—21no—
119C22×C4—1222no—
120Q16—2442no—
121C2×C8—21no—
122C2×C8—1221no—
123C2×C8—1221no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—611no—
127C4⋊C4—1222no—
128C4⋊C4—1222no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4C22⋊D6111yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—1222no—
135C42—1221no—
136C42C22×D6111yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—1221no—
141Q8—1221no—
142Q8—2442no—
143D4—21no—
144D4#1175820212yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—1222no—
152C2×C4—4882no—
153C2×C4D4×D6111yescharacteristic
154C2×C4D4×D6111yescharacteristic
155C2×C4C2×C22⋊D6111yescharacteristic
156C8—41no—
157C8—2441no—
158C8—2441no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1451974511yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—2441no—
167C4—2442no—
168C4—2441no—
169C4C2×#1175820211yescharacteristic
170C4#1451979611yescharacteristic
171C4#1451980111yescharacteristic
172C4#1451980711yescharacteristic
173C2—42no—
174C2#1683990411yescharacteristic
175C2#1683991711yescharacteristic
176C2#1683993811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#474C2
socleC22×C61#120
hypercenter#474D61
hypocenterC61#1644
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #16840114C2semidirect
3. #16839969C2semidirect
4. #16839510C2semidirect
5. #16839492C2semidirect
52. D4×C61Q16semidirect
96. C61#1644semidirect
144. D4#11758202semidirect