Finite Group Databasebeta

← #21444906

Subgroups — #21444906

Order 7808.

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

normal subgroups only

This group has 256 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#16840416C211yesmaximal, characteristic, complemented
2#16840108C211yesmaximal, characteristic, complemented
3#16839954C211yesmaximal, characteristic, complemented
4#16839509C211yesmaximal, characteristic, complemented
5D4⋊#92418C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#459C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9C2×#11758199—21no—
10#14519777C2211yescharacteristic
11#14519761—22no—
12#14519757—21no—
13#14519751—21no—
14C4×D244C2211yescharacteristic
15C2×C4⋊Dic61—21no—
16C4⋊#92418C2211yescharacteristic
17#14519698—21no—
18#14519698—22no—
19C4×#92418C2211yescharacteristic
20C2×D8×C61—21no—
21#127×C61C2211yescharacteristic
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24#102×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61D411yescharacteristic
29C22×C4×C61—21no—
30C2×C22⋊D61—22no—
31C22×Dic61—22no—
32#11758224—42no—
33#11758224—42no—
34C2×D244D411yescharacteristic
35C2×C4×D61—21no—
36C2×Dic122—21no—
37D8×C61—42no—
38C2×C8×C61—21no—
39C4⋊C4×C61D411yescharacteristic
40C22⋊C4×C61—21no—
41C42×C61C2311yescharacteristic
42#11758199—42no—
43#11758198—22no—
44#11758198—21no—
45C4⋊Dic61—22no—
46C4⋊Dic61—21no—
47C4⋊Dic61D411yescharacteristic
48C4⋊Dic61D412yes—
49C2×#92418—21no—
50C2×#92418—21no—
51C23×C61—21no—
52C23×C61—41no—
53C22×D61—21no—
54D4×C61—21no—
55D4×C61—42no—
56D4×C61—41no—
57D4×C61—41no—
58D4×C61—41no—
59D4×C61—41no—
60D4×C61D812yescomplemented
61C2×C4×C61—21no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C22⋊D61—44no—
68C2×Dic61—22no—
69C2×Dic61—21no—
70C2×Dic61—44no—
71D244—21no—
72D244—21no—
73C4×D61—41no—
74C4×D61—41no—
75Dic122—41no—
76Dic122—41no—
77C8×C61—41no—
78#92418—41no—
79#92418—41no—
80C22×C61—22no—
81C22×C61—41no—
82C22×C61—41no—
83C22×C61—81no—
84C22×C61—81no—
85C22×C61—81no—
86C22×C61#12011yescharacteristic
87C2×D61—41no—
88C2×D61—41no—
89C2×D61—41no—
90C4×C61—21no—
91C4×C61—41no—
92C4×C61C2×D811yescharacteristic
93C4×C61#13511yescharacteristic
94C4×C61AGL(1,ℤ/8)11yescharacteristic
95C4×C61AGL(1,ℤ/8)11yescharacteristic
96Dic61—42no—
97Dic61—41no—
98#1625—611nomaximal, Sylow
99C2×C61—42no—
100C2×C61—161no—
101C2×C61#44711yescharacteristic
102C2×C61#44911yescharacteristic
103C2×C61#45411yescharacteristic
104D61—81no—
105#547—611no—
106#486—611no—
107#459—611no—
108#459D6111yescharacteristic, complemented
109#332—611no—
110D4⋊C8—611no—
111D4⋊C8—611no—
112C61#162511yescharacteristic, complemented, Sylow
113C2×#41—1221no—
114C2×D8—21no—
115C2×D8—1221no—
116C4⋊Q8—611no—
117#127C2×D6111yescharacteristic
118#123—1222no—
119C22⋊Q8—1221no—
120#121—1221no—
121C4×D4—611no—
122C4×D4C2×D6111yescharacteristic
123C2×C4⋊C4—1221no—
124C4⋊C8—611no—
125C4⋊C8C2×D6111yescharacteristic
126#102—21no—
127#102—1221no—
128#102—1222no—
129C4×C8—611no—
130#41—2442no—
131#41—2442no—
132C2×Q8—1221no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—611no—
137C2×D4—1222no—
138C2×D4C22⋊D6111yescharacteristic
139C22×C4—21no—
140C22×C4—1222no—
141C22×C4—1221no—
142D8—42no—
143D8—2442no—
144C2×C8—21no—
145C2×C8—1221no—
146C2×C8—1221no—
147C4⋊C4—611no—
148C4⋊C4—612no—
149C4⋊C4—1222no—
150C4⋊C4—1221no—
151C4⋊C4C22⋊D6111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1222no—
154C22⋊C4—1221no—
155C42C22×D6111yescharacteristic
156C23—21no—
157C23—41no—
158C23—1221no—
159Q8—2441no—
160Q8—2441no—
161D4—21no—
162D4—42no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—1221no—
168D4—1221no—
169D4—2444no—
170D4#1175819912yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—1221no—
175C2×C4—1222no—
176C2×C4—2444no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4D4×D6111yescharacteristic
180C2×C4D4×D6111yescharacteristic
181C2×C4C2×C22⋊D6111yescharacteristic
182C8—41no—
183C8—2441no—
184C8—2441no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—2441no—
192C22—2441no—
193C22—2441no—
194C22#1451974511yescharacteristic
195C4—21no—
196C4—41no—
197C4—2441no—
198C4—2442no—
199C4C2×#1175819911yescharacteristic
200C4#1451979611yescharacteristic
201C4#1451980111yescharacteristic
202C4#1451980211yescharacteristic
203C2—42no—
204C2—161no—
205C2—4881no—
206C2#1683989511yescharacteristic
207C2#1683990411yescharacteristic
208C2#1683993311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#459C2
socleC22×C61#120
hypercenter#459D61
hypocenterC61#1625
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840416C2semidirect
2. #16840108C2semidirect
3. #16839954C2semidirect
4. #16839509C2semidirect
5. D4⋊#92418C2semidirect
6. #16839489C2semidirect
7. C61×#459C2semidirect
60. D4×C61D8semidirect
108. #459D61semidirect
112. C61#1625semidirect
170. D4#11758199semidirect