Finite Group Databasebeta

← #21445048

Subgroups — #21445048

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#16840478C211yesmaximal, characteristic
2#16840112C211yesmaximal, characteristic, complemented
3#16840043C211yesmaximal, characteristic, complemented
4#16839968C211yesmaximal, characteristic, complemented
5#16839489C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#333C211yesmaximal, characteristic, complemented
8C2×#11758190—21no—
9#14519777C2211yescharacteristic
10#14519766—22no—
11#14519752—21no—
12#14519752—21no—
13C4×D244C2211yescharacteristic
14C4×D244C2211yescharacteristic
15#14519735—21no—
16#14519735—21no—
17#14519711—21no—
18#14519702—21no—
19#14519701—22no—
20#14519699—21no—
21C4×#92418C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×Q8×C61D412yes—
26C2×D244—22no—
27C2×D244D411yescharacteristic
28C2×D244D411yescharacteristic
29C2×C4×D61—21no—
30C2×C4×D61—21no—
31C2×Dic122—21no—
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C42×C61C2311yescharacteristic
37#11758198—22no—
38#11758198—22no—
39#11758198—21no—
40#11758198—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61D411yescharacteristic
44C4⋊Dic61D411yescharacteristic
45C4×Dic61—22no—
46C2×#92418—21no—
47#11758190—42no—
48C22×D61—21no—
49C22×D61—21no—
50Q8×C61—42no—
51C2×C4×C61—22no—
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×Dic61—21no—
56C2×Dic61—21no—
57C2×Dic61—41no—
58D244—21no—
59D244—21no—
60D244—21no—
61D244—21no—
62D244—82no—
63C4×D61—41no—
64C4×D61—41no—
65C4×D61—41no—
66C4×D61—41no—
67Dic122—41no—
68Dic122—41no—
69C8×C61—41no—
70C8×C61—41no—
71#92418—41no—
72C22×C61#12011yescharacteristic
73C2×D61—41no—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61—41no—
77C2×D61—41no—
78C2×D61—41no—
79C4×C61—21no—
80C4×C61—42no—
81C4×C61#13511yescharacteristic
82C4×C61#13511yescharacteristic
83C4×C61AGL(1,ℤ/8)11yescharacteristic
84C4×C61#13711yescharacteristic
85Dic61—41no—
86Dic61—41no—
87Dic61—81no—
88#1646—611nomaximal, Sylow
89C2×C61#44911yescharacteristic
90C2×C61#45211yescharacteristic
91C2×C61#45511yescharacteristic
92D61—81no—
93D61—81no—
94#555—611no—
95#487—611no—
96#474—611no—
97#461—611no—
98#333D6111yescharacteristic, complemented
99D4⋊C8—611no—
100D4⋊C8—611no—
101C61#164611yescharacteristic, complemented, Sylow
102C2×SD16—1221no—
103C4⋊Q8—611no—
104C4⋊Q8C2×D6111yescharacteristic
105#124—1222no—
106#121—1221no—
107#121—1221no—
108C4×D4—611no—
109C4×D4—611no—
110#117—1221no—
111#117—1221no—
112#107—1221no—
113C4⋊C8C2×D6111yescharacteristic
114C4⋊C8C2×D6111yescharacteristic
115#103—1221no—
116#103—1222no—
117#102—1221no—
118C4×C8—611no—
119C2×Q8—1221no—
120C2×Q8D24412yes—
121C2×D4—611no—
122C2×D4—611no—
123C2×D4—1222no—
124C22×C4—1221no—
125C22×C4—1221no—
126SD16—2442no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1221no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—611no—
133C4⋊C4—611no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C22⋊C4—1222no—
137C22⋊C4—1222no—
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C42—1222no—
141C42C22×D6111yescharacteristic
142C23—1221no—
143C23—1221no—
144Q8—42no—
145Q8—2441no—
146Q8—2441no—
147D4—1221no—
148D4—1221no—
149D4—1221no—
150D4—1221no—
151D4—4882no—
152C2×C4—22no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—2441no—
156C2×C4—2441no—
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—2441no—
167C22—2441no—
168C22—2441no—
169C22—2441no—
170C22—2441no—
171C22—2441no—
172C22#1451974711yescharacteristic
173C4—21no—
174C4—42no—
175C4—4881no—
176C4—2441no—
177C4—2441no—
178C4#1451979811yescharacteristic
179C4#1451980011yescharacteristic
180C4#1451980411yescharacteristic
181C4#1451980911yescharacteristic
182C2—4881no—
183C2—4881no—
184C2#1683991011yescharacteristic
185C2#1683992711yescharacteristic
186C2#1683994211yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#333C2
socleC22×C61#120
hypercenter#333D61
hypocenterC61#1646
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #16840112C2semidirect
3. #16840043C2semidirect
4. #16839968C2semidirect
5. #16839489C2semidirect
6. #16839489C2semidirect
7. C61×#333C2semidirect
98. #333D61semidirect
101. C61#1646semidirect