Finite Group Databasebeta

← #21445049

Subgroups — #21445049

Order 7808.

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

normal subgroups only

This group has 212 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#16840477C211yesmaximal, characteristic
2#16840113C211yesmaximal, characteristic, complemented
3#16840043C211yesmaximal, characteristic, complemented
4#16839967C211yesmaximal, characteristic, complemented
5#16839510C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758200—21no—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519763—22no—
12#14519751—21no—
13#14519748—21no—
14C4×D244C2211yescharacteristic
15#14519736—21no—
16#14519735—21no—
17#14519711—21no—
18C4⋊#92418C2211yescharacteristic
19#14519702—22no—
20#14519700—21no—
21#14519699—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C2×C22⋊D61—22no—
28C2×D244D411yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122—21no—
31C2×Dic122D412yes—
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C4⋊C4×C61D411yescharacteristic
35C22⋊C4×C61—21no—
36C42×C61C2311yescharacteristic
37C22⋊Dic61—22no—
38#11758200—42no—
39#11758198—22no—
40#11758198—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61D411yescharacteristic
46C4×Dic61—22no—
47C2×#92418—21no—
48C23×C61—21no—
49C22×D61—21no—
50D4×C61—21no—
51D4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61—41no—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C22⋊D61—82no—
59C2×Dic61—21no—
60C2×Dic61—22no—
61C2×Dic61—41no—
62D244—21no—
63D244—21no—
64C4×D61—41no—
65C4×D61—41no—
66Dic122—42no—
67Dic122—41no—
68Dic122—41no—
69C8×C61—41no—
70C8×C61—41no—
71#92418—41no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61#12011yescharacteristic
76C2×D61—41no—
77C2×D61—41no—
78C2×D61—41no—
79C4×C61—21no—
80C4×C61—41no—
81C4×C61#13511yescharacteristic
82C4×C61#13511yescharacteristic
83C4×C61AGL(1,ℤ/8)11yescharacteristic
84C4×C61#13711yescharacteristic
85Dic61—41no—
86Dic61—42no—
87Dic61—81no—
88#1646—611nomaximal, Sylow
89C2×C61—81no—
90C2×C61#44911yescharacteristic
91C2×C61#45211yescharacteristic
92C2×C61#45511yescharacteristic
93D61—81no—
94#555—611no—
95#487—611no—
96#474—611no—
97#461—611no—
98#333—611no—
99D4⋊C8—611no—
100D4⋊C8D6111yescharacteristic, complemented
101C61#164611yescharacteristic, complemented, Sylow
102C2×SD16—1221no—
103C4⋊Q8—611no—
104C4⋊Q8—611no—
105#124—1222no—
106#121—1221no—
107#121—1221no—
108C4×D4—611no—
109C4×D4C2×D6111yescharacteristic
110#117—1221no—
111#117—1221no—
112#107—1221no—
113C4⋊C8—611no—
114C4⋊C8C2×D6111yescharacteristic
115#103—1222no—
116#103—1221no—
117#102—1221no—
118C4×C8C2×D6111yescharacteristic
119C2×Q8—612no—
120C2×Q8—1221no—
121C2×D4—611no—
122C2×D4—1222no—
123C2×D4D24411yescharacteristic
124C22×C4—21no—
125C22×C4—1221no—
126SD16—2442no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1221no—
130C4⋊C4—611no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4D24411yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—1222no—
138C22⋊C4—1222no—
139C22⋊C4—1221no—
140C42—1222no—
141C42C22×D6111yescharacteristic
142C23—21no—
143C23—1221no—
144Q8—2442no—
145Q8—2441no—
146Q8—2441no—
147D4—21no—
148D4—21no—
149D4—1221no—
150D4—1221no—
151D4—4882no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—1221no—
156C2×C4—1222no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4C2×D24411yescharacteristic
161C2×C4D4×D6111yescharacteristic
162C2×C4D4×D6111yescharacteristic
163C8—41no—
164C8—41no—
165C8—2441no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—2441no—
170C22—2441no—
171C22—2441no—
172C22#1451974711yescharacteristic
173C4—21no—
174C4—41no—
175C4—4881no—
176C4—2442no—
177C4—2441no—
178C4#1451979611yescharacteristic
179C4#1451979911yescharacteristic
180C4#1451980511yescharacteristic
181C4#1451980611yescharacteristic
182C2—81no—
183C2—4881no—
184C2#1683990911yescharacteristic
185C2#1683992511yescharacteristic
186C2#1683994111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1646
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
3. #16840043C2semidirect
4. #16839967C2semidirect
5. #16839510C2semidirect
6. #16839491C2semidirect
7. C61×D4⋊C8C2semidirect
100. D4⋊C8D61semidirect
101. C61#1646semidirect