Finite Group Databasebeta

← #21444905

Subgroups — #21444905

Order 7808.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840415C211yesmaximal, characteristic, complemented
2#16839954C211yesmaximal, characteristic, complemented
3#16839954C211yesmaximal, characteristic, complemented
4#16839508C211yesmaximal, characteristic, complemented
5#16839491C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×#486C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9C2×#11758199—21no—
10C2×#11758199—21no—
11#14519762—22no—
12#14519753—21no—
13#14519752—21no—
14C4×D244C2211yescharacteristic
15C4×D244C2211yescharacteristic
16C4⋊C4×D61—21no—
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519698—21no—
20#14519698—21no—
21C4⋊Q8×C61C2211yescharacteristic
22#127×C61C2211yescharacteristic
23#102×C61—22no—
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29#11758226—42no—
30#11758226—42no—
31C2×D244—22no—
32C2×D244D411yescharacteristic
33C2×D244D411yescharacteristic
34C2×C4×D61—22no—
35C2×C4×D61—21no—
36C2×C4×D61—21no—
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61D412yes—
40C42×C61C2311yescharacteristic
41#11758199—42no—
42#11758199—42no—
43#11758198—22no—
44#11758198—21no—
45#11758198—21no—
46C4⋊Dic61D411yescharacteristic
47C4⋊Dic61D411yescharacteristic
48#11758196—22no—
49C2×#92418—21no—
50C2×#92418—21no—
51C23×C61—41no—
52C22×D61—21no—
53C22×D61—21no—
54Q8×C61—41no—
55Q8×C61—41no—
56D4×C61—42no—
57D4×C61—41no—
58D4×C61—41no—
59D4×C61—41no—
60D4×C61—41no—
61C2×C4×C61—22no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×Dic61—21no—
66C2×Dic61—21no—
67D244—21no—
68D244—21no—
69D244—21no—
70D244—44no—
71D244D812yescomplemented
72C4×D61—44no—
73C4×D61—41no—
74C4×D61—41no—
75C4×D61—41no—
76C4×D61—41no—
77C8×C61—41no—
78#92418—41no—
79#92418—41no—
80C22×C61—81no—
81C22×C61—81no—
82C22×C61—81no—
83C22×C61#12011yescharacteristic
84C2×D61—22no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—41no—
88C2×D61—41no—
89C2×D61—41no—
90C4×C61—21no—
91C4×C61—42no—
92C4×C61C2×D811yescharacteristic
93C4×C61#13511yescharacteristic
94C4×C61AGL(1,ℤ/8)11yescharacteristic
95C4×C61AGL(1,ℤ/8)11yescharacteristic
96Dic61—41no—
97Dic61—41no—
98#1625—611nomaximal, Sylow
99C2×C61—161no—
100C2×C61#44711yescharacteristic
101C2×C61#44911yescharacteristic
102C2×C61#45411yescharacteristic
103D61—42no—
104D61—81no—
105#547—611no—
106#486D6111yescharacteristic, complemented
107#459—611no—
108#459—611no—
109#332—611no—
110D4⋊C8—611no—
111D4⋊C8—611no—
112C61#162511yescharacteristic, complemented, Sylow
113C2×#41—1221no—
114C2×D8—1221no—
115C2×D8—1221no—
116C4⋊Q8C2×D6111yescharacteristic
117#127C2×D6111yescharacteristic
118#123—1222no—
119C22⋊Q8—1221no—
120#121—1221no—
121C4×D4—611no—
122C4×D4—611no—
123C2×C4⋊C4—1221no—
124C4⋊C8—611no—
125C4⋊C8—611no—
126#102—22no—
127#102—1221no—
128#102—1221no—
129C4×C8C2×D6111yescharacteristic
130#41—2442no—
131#41—2442no—
132C2×Q8—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—611no—
137C2×D4—611no—
138C2×D4—1222no—
139C22×C4—1222no—
140C22×C4—1221no—
141C22×C4—1221no—
142D8—2442no—
143D8—2442no—
144C2×C8—21no—
145C2×C8—1221no—
146C2×C8—1221no—
147C4⋊C4—21no—
148C4⋊C4—611no—
149C4⋊C4—611no—
150C4⋊C4—1222no—
151C4⋊C4C22⋊D6112yes—
152C22⋊C4—1222no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C42C22×D6111yescharacteristic
156C23—41no—
157C23—1221no—
158C23—1221no—
159Q8—41no—
160Q8—41no—
161D4—42no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—612no—
167D4—1221no—
168D4—1221no—
169D4—1221no—
170D4—2444no—
171C2×C4—22no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—2444no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4D4×D6111yescharacteristic
180C2×C4D4×D6111yescharacteristic
181C2×C4C2×C22⋊D6111yescharacteristic
182C8—41no—
183C8—2441no—
184C8—2441no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—1222no—
189C22—2441no—
190C22—2441no—
191C22—2441no—
192C22—2441no—
193C22—2441no—
194C22#1451974511yescharacteristic
195C4—21no—
196C4—42no—
197C4—2441no—
198C4—2441no—
199C4D8×D6111yescharacteristic
200C4#1451979811yescharacteristic
201C4#1451980111yescharacteristic
202C4#1451980411yescharacteristic
203C2—161no—
204C2—4881no—
205C2—2442no—
206C2#1683989411yescharacteristic
207C2#1683990611yescharacteristic
208C2#1683993411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#486C2
socleC22×C61#120
hypercenter#486D61
hypocenterC61#1625
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #16840415C2semidirect
2. #16839954C2semidirect
3. #16839954C2semidirect
4. #16839508C2semidirect
5. #16839491C2semidirect
6. #16839491C2semidirect
7. C61×#486C2semidirect
71. D244D8semidirect
106. #486D61semidirect
112. C61#1625semidirect