Finite Group Databasebeta

← #21444909

Subgroups — #21444909

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#16840110C211yesmaximal, characteristic, complemented
3#16839958C211yesmaximal, characteristic, complemented
4#16839958C211yesmaximal, characteristic, complemented
5#16839489C211yesmaximal, characteristic, complemented
6#16839489C211yesmaximal, characteristic, complemented
7C61×#332C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9C2×D488—21no—
10C2×D488—21no—
11#14519774C2211yescharacteristic
12#14519762—22no—
13#14519753—21no—
14#14519752—21no—
15C4×D244C2211yescharacteristic
16C4×D244C2211yescharacteristic
17C4⋊C4×D61—21no—
18#14519699—21no—
19#14519699—21no—
20#14519697—22no—
21C4×#92418C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26#11758226—42no—
27#11758226—42no—
28C2×D244—22no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244D411yescharacteristic
33C2×D244D411yescharacteristic
34C2×C4×D61—22no—
35C2×C4×D61—21no—
36C2×C4×D61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61D412yes—
41C42×C61C2311yescharacteristic
42#11758198—22no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61D411yescharacteristic
46C4⋊Dic61D411yescharacteristic
47#11758196—22no—
48C2×#92418—21no—
49D488—42no—
50D488—42no—
51C22×D61—21no—
52C22×D61—21no—
53C22×D61—41no—
54Q8×C61—41no—
55Q8×C61—41no—
56C2×C4×C61—22no—
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61—21no—
62D244—21no—
63D244—21no—
64D244—21no—
65D244—42no—
66D244—44no—
67D244—41no—
68D244—41no—
69D244—41no—
70D244—41no—
71D244D812yescomplemented
72C4×D61—44no—
73C4×D61—41no—
74C4×D61—41no—
75C4×D61—41no—
76C4×D61—41no—
77C8×C61—41no—
78C8×C61—41no—
79#92418—41no—
80C22×C61#12011yescharacteristic
81C2×D61—22no—
82C2×D61—41no—
83C2×D61—41no—
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—81no—
88C2×D61—81no—
89C2×D61—81no—
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#44711yescharacteristic
100C2×C61#44911yescharacteristic
101C2×C61#45411yescharacteristic
102D61—42no—
103D61—81no—
104D61—161no—
105#547—611no—
106#486—611no—
107#459—611no—
108#459—611no—
109#332D6111yescharacteristic, complemented
110D4⋊C8—611no—
111D4⋊C8—611no—
112C61#162511yescharacteristic, complemented, Sylow
113C2×#41—1221no—
114C2×D8—1221no—
115C2×D8—1221no—
116C4⋊Q8C2×D6111yescharacteristic
117#127—611no—
118#123—1222no—
119C22⋊Q8—1221no—
120#121—1221no—
121C4×D4—611no—
122C4×D4—611no—
123C2×C4⋊C4—1221no—
124C4⋊C8C2×D6111yescharacteristic
125C4⋊C8C2×D6111yescharacteristic
126#102—1221no—
127#102—1221no—
128#102—1222no—
129C4×C8—611no—
130#41—2442no—
131#41—2442no—
132C2×Q8—21no—
133C2×D4—611no—
134C2×D4—611no—
135C2×D4—1222no—
136C2×D4—1221no—
137C2×D4—1221no—
138C2×D4—1221no—
139C22×C4—1222no—
140C22×C4—1221no—
141C22×C4—1221no—
142D8—2442no—
143D8—2442no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—1221no—
147C4⋊C4—21no—
148C4⋊C4—611no—
149C4⋊C4—611no—
150C4⋊C4—1222no—
151C4⋊C4D24412yes—
152C22⋊C4—1222no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C42C22×D6111yescharacteristic
156C23—1221no—
157C23—1221no—
158C23—2441no—
159Q8—41no—
160Q8—41no—
161D4—612no—
162D4—1221no—
163D4—1221no—
164D4—1221no—
165D4—2442no—
166D4—2444no—
167D4—2441no—
168D4—2441no—
169D4—2441no—
170D4—2441no—
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×C4C2×D24411yescharacteristic
180C2×C4D4×D6111yescharacteristic
181C2×C4D4×D6111yescharacteristic
182C8—41no—
183C8—41no—
184C8—2441no—
185C22—1222no—
186C22—4881no—
187C22—4881no—
188C22—4881no—
189C22—2441no—
190C22—2441no—
191C22—2441no—
192C22—2441no—
193C22—2441no—
194C22#1451974711yescharacteristic
195C4—21no—
196C4—42no—
197C4—2441no—
198C4—2441no—
199C4D8×D6111yescharacteristic
200C4#1451980011yescharacteristic
201C4#1451980411yescharacteristic
202C4#1451980411yescharacteristic
203C2—9761no—
204C2—4881no—
205C2—2442no—
206C2#1683989711yescharacteristic
207C2#1683991011yescharacteristic
208C2#1683993711yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#332C2
socleC22×C61#120
hypercenter#332D61
hypocenterC61#1625
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #16840415C2semidirect
2. #16840110C2semidirect
3. #16839958C2semidirect
4. #16839958C2semidirect
5. #16839489C2semidirect
6. #16839489C2semidirect
7. C61×#332C2semidirect
71. D244D8semidirect
109. #332D61semidirect
112. C61#1625semidirect