Finite Group Databasebeta

← #21445036

Subgroups — #21445036

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#16840113C211yesmaximal, characteristic, complemented
3#16840042C211yesmaximal, characteristic
4#16839973C211yesmaximal, characteristic, complemented
5#16839510C211yesmaximal, characteristic, complemented
6#16839494C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic
8C2×Dic244—21no—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519768—21no—
12#14519756—21no—
13#14519754—22no—
14C4×Dic122C2211yescharacteristic
15D4×Dic61—21no—
16C2×C4⋊Dic61—21no—
17#14519710—21no—
18C4⋊#92418C2211yescharacteristic
19#14519702—22no—
20#14519702—21no—
21#14519698—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C22×Dic61—22no—
28C2×Dic122—21no—
29C2×Dic122D411yescharacteristic
30C2×Dic122D412yes—
31C2×C8×C61—21no—
32C2×C8×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C22⋊C4×C61—21no—
35C42×C61C2311yescharacteristic
36C22⋊Dic61—22no—
37C4⋊Dic61—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61D411yescharacteristic
43#11758196—22no—
44#11758196—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47Dic244—42no—
48C23×C61—21no—
49D4×C61—21no—
50D4×C61Q1612yescomplemented
51C2×C4×C61—21no—
52C2×C4×C61—41no—
53C2×C4×C61—41no—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—22no—
60C2×Dic61—41no—
61C2×Dic61—82no—
62Dic122—21no—
63Dic122—21no—
64Dic122—42no—
65Dic122—41no—
66Dic122—41no—
67C8×C61—41no—
68C8×C61—41no—
69#92418—41no—
70C22×C61—22no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61#12011yescharacteristic
74C4×C61—21no—
75C4×C61—41no—
76C4×C61C2×Q1611yescharacteristic
77C4×C61#13511yescharacteristic
78C4×C61AGL(1,ℤ/8)11yescharacteristic
79C4×C61#13711yescharacteristic
80Dic61—41no—
81Dic61—42no—
82Dic61—41no—
83Dic61—81no—
84#1644—611nomaximal, Sylow
85C2×C61—42no—
86C2×C61#44911yescharacteristic
87C2×C61#45111yescharacteristic
88C2×C61#45511yescharacteristic
89#554—611no—
90#487—611no—
91#474—611no—
92#462—611no—
93#333—611no—
94Q8⋊C8—611no—
95D4⋊C8D6111yescharacteristic
96C61#164411yescharacteristic, complemented, Sylow
97C2×Q16—1221no—
98C4⋊Q8—611no—
99C4⋊Q8—611no—
100#125—1221no—
101C22⋊Q8—1222no—
102C22⋊Q8—1221no—
103C4×Q8—611no—
104C4×D4—1221no—
105C4×D4C2×D6111yescharacteristic
106C2×C4⋊C4—1221no—
107#107—1221no—
108C4⋊C8—611no—
109C4⋊C8C2×D6111yescharacteristic
110#103—1221no—
111#103—1222no—
112#102—1221no—
113C4×C8C2×D6111yescharacteristic
114C2×Q8—611no—
115C2×Q8—612no—
116C2×Q8—1221no—
117C2×D4D24411yescharacteristic
118C22×C4—21no—
119C22×C4—1222no—
120Q16—2442no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—1221no—
124C4⋊C4—611no—
125C4⋊C4—1222no—
126C4⋊C4—1222no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4D24411yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—1222no—
135C42—1221no—
136C42C22×D6111yescharacteristic
137C23—21no—
138Q8—1221no—
139Q8—1221no—
140Q8—2442no—
141Q8—2441no—
142Q8—2441no—
143D4—21no—
144D4Dic24412yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—1221no—
149C2×C4—1221no—
150C2×C4—1222no—
151C2×C4—4882no—
152C2×C4—2441no—
153C2×C4C2×D24411yescharacteristic
154C2×C4D4×D6111yescharacteristic
155C2×C4D4×D6111yescharacteristic
156C8—41no—
157C8—41no—
158C8—2441no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1451974711yescharacteristic
163C4—21no—
164C4—41no—
165C4—4881no—
166C4—2441no—
167C4—2442no—
168C4—2441no—
169C4C2×Dic24411yescharacteristic
170C4#1451979811yescharacteristic
171C4#1451980111yescharacteristic
172C4#1451981011yescharacteristic
173C2—42no—
174C2#1683990811yescharacteristic
175C2#1683992011yescharacteristic
176C2#1683994111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1644
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16840113C2semidirect
4. #16839973C2semidirect
5. #16839510C2semidirect
6. #16839494C2semidirect
50. D4×C61Q16semidirect
96. C61#1644semidirect
144. D4Dic244semidirect