Finite Group Databasebeta

← #21444813

Subgroups — #21444813

Order 7808.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840357C211yesmaximal, characteristic
2#16840092C211yesmaximal, characteristic, complemented
3#16839693C211yesmaximal, characteristic, complemented
4#16839500C211yesmaximal, characteristic, complemented
5#16839496C211yesmaximal, characteristic
6#16839487C211yesmaximal, characteristic, complemented
7C61×#480C211yesmaximal, characteristic
8#14519770—21no—
9#14519767—21no—
10#14519758—21no—
11#14519758—21no—
12#14519756C2211yescharacteristic
13#14519754—21no—
14D4×Dic61—21no—
15C2×#11758196—21no—
16C2×#11758196C2211yescharacteristic
17#14519708—21no—
18#14519700—21no—
19C22⋊#92418C2211yescharacteristic
20#14519684—21no—
21#14519684C2211yescharacteristic
22#121×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24#107×C61—21no—
25#102×C61—21no—
26C22⋊C8×C61C2211yescharacteristic
27C2×D4×C61—21no—
28C2×D4×C61D411yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C22×Dic61—21no—
32C22×Dic61—21no—
33C22×Dic61D411yescharacteristic
34C22×Dic61D411yescharacteristic
35C2×Dic122D411yescharacteristic
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61D411yescharacteristic
40C22⋊C4×C61—21no—
41C22⋊Dic61—21no—
42C22⋊Dic61—21no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61D411yescharacteristic
47#11758196—21no—
48#11758196—21no—
49#11758196—21no—
50#11758196—21no—
51#11758196—21no—
52#11758196—42no—
53C4×Dic61—21no—
54C2×#92418—21no—
55C23×C61—21no—
56C23×C61C2×D411yescharacteristic
57D4×C61—41no—
58D4×C61—41no—
59D4×C61—41no—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×Dic61—22no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—81no—
78Dic122—41no—
79C8×C61—41no—
80#92418—41no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61#12011yescharacteristic
87C22×C61#13511yescharacteristic
88C22×C61AGL(1,ℤ/8)11yescharacteristic
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—41no—
92C4×C61—81no—
93Dic61—42no—
94Dic61—41no—
95Dic61—41no—
96Dic61—41no—
97Dic61—41no—
98#1609—611nomaximal, Sylow
99C2×C61—21no—
100C2×C61—21no—
101C2×C61—81no—
102C2×C61#44911yescharacteristic
103C2×C61#45611yescharacteristic
104C2×C61#45811yescharacteristic
105#539—611no—
106#483—611no—
107#480D6111yescharacteristic
108#398—611no—
109#328—611no—
110#327—611no—
111#324—611no—
112C61#160911yescharacteristic, complemented, Sylow
113#126—1221no—
114#125—1221no—
115#123—1221no—
116#123—1221no—
117C22⋊Q8—611no—
118C22⋊Q8—1221no—
119#121C2×D6111yescharacteristic
120C4×D4—1221no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—1221no—
123C2×C4⋊C4C2×D6111yescharacteristic
124#107—21no—
125#106—1221no—
126#103—1221no—
127#102—21no—
128C22⋊C8—611no—
129C22⋊C8C2×D6111yescharacteristic
130#95—611no—
131#95—1221no—
132C2×Q8—611no—
133C2×D4—21no—
134C2×D4C22⋊D6111yescharacteristic
135C22×C4—21no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—1221no—
139C22×C4—1221no—
140C22×C4C22×D6111yescharacteristic
141C2×C8—21no—
142C2×C8—1221no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—611no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—2442no—
153C4⋊C4C22⋊D6111yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—1221no—
156C22⋊C4—1221no—
157C22⋊C4—1221no—
158C22⋊C4—1221no—
159C42—1221no—
160C23—21no—
161C23D4×D6111yescharacteristic
162Q8—2441no—
163D4—41no—
164D4—41no—
165D4—41no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4—1221no—
177C2×C4—1221no—
178C2×C4—4881no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4D4×D6111yescharacteristic
183C2×C4C2×C22⋊D6111yescharacteristic
184C8—41no—
185C8—2441no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22#1451974511yescharacteristic
192C22#1451979611yescharacteristic
193C22#1451980111yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—81no—
198C4—2442no—
199C4—2441no—
200C4—2441no—
201C4—2441no—
202C4—2441no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2#1683990411yescharacteristic
207C2#1683994311yescharacteristic
208C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#480C2
socleC22×C61#120
hypercenter#480D61
hypocenterC61#1609
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #16840092C2semidirect
3. #16839693C2semidirect
4. #16839500C2semidirect
6. #16839487C2semidirect
112. C61#1609semidirect