Finite Group Databasebeta

← #21444911

Subgroups — #21444911

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#16840417C211yesmaximal, characteristic, complemented
2#16840109C211yesmaximal, characteristic, complemented
3#16839958C211yesmaximal, characteristic, complemented
4#16839957C211yesmaximal, characteristic, complemented
5#16839509C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758222—21no—
9C2×D488—21no—
10C2×#11758199—21no—
11#14519777C2211yescharacteristic
12#14519774C2211yescharacteristic
13#14519759—22no—
14#14519756—21no—
15#14519748—21no—
16C4×D244C2211yescharacteristic
17C4⋊C4×D61—21no—
18C4⋊#92418C2211yescharacteristic
19#14519699—21no—
20#14519699—22no—
21#14519697—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C2×C22⋊D61—22no—
28#11758222—42no—
29#11758222—42no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244D411yescharacteristic
34C2×C4×D61—22no—
35C2×C4×D61—21no—
36C2×Dic122—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C4⋊C4×C61D411yescharacteristic
40C22⋊C4×C61—21no—
41C42×C61C2311yescharacteristic
42C22⋊Dic61—22no—
43#11758199—42no—
44#11758198—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61D411yescharacteristic
47C4⋊Dic61D412yes—
48#11758196—22no—
49C2×#92418—21no—
50D488—42no—
51C23×C61—21no—
52C22×D61—21no—
53C22×D61—41no—
54D4×C61—21no—
55D4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C22⋊D61—44no—
63C2×Dic61—21no—
64C2×Dic61—22no—
65D244—21no—
66D244—42no—
67D244—41no—
68D244—41no—
69D244—41no—
70D244—41no—
71D244D812yescomplemented
72C4×D61—44no—
73C4×D61—41no—
74C4×D61—41no—
75Dic122—41no—
76Dic122—41no—
77C8×C61—41no—
78C8×C61—41no—
79#92418—41no—
80C22×C61—41no—
81C22×C61—41no—
82C22×C61—41no—
83C22×C61#12011yescharacteristic
84C2×D61—22no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—81no—
88C2×D61—81no—
89C2×D61—81no—
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—81no—
100C2×C61#44711yescharacteristic
101C2×C61#44911yescharacteristic
102C2×C61#45411yescharacteristic
103D61—42no—
104D61—161no—
105#547—611no—
106#486—611no—
107#459—611no—
108#459—611no—
109#332—611no—
110D4⋊C8—611no—
111D4⋊C8D6111yescharacteristic, complemented
112C61#162511yescharacteristic, complemented, Sylow
113C2×#41—1221no—
114C2×D8—1221no—
115C2×D8—1221no—
116C4⋊Q8—611no—
117#127—611no—
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—1221no—
127#102—1222no—
128#102—1221no—
129C4×C8C2×D6111yescharacteristic
130#41—2442no—
131#41—2442no—
132C2×Q8—1221no—
133C2×D4—611no—
134C2×D4—1222no—
135C2×D4—1221no—
136C2×D4—1221no—
137C2×D4—1221no—
138C2×D4D24411yescharacteristic
139C22×C4—21no—
140C22×C4—1222no—
141C22×C4—1221no—
142D8—2442no—
143D8—2442no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—1221no—
147C4⋊C4—611no—
148C4⋊C4—612no—
149C4⋊C4—1222no—
150C4⋊C4—1221no—
151C4⋊C4D24411yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1222no—
154C22⋊C4—1221no—
155C42C22×D6111yescharacteristic
156C23—21no—
157C23—1221no—
158C23—2441no—
159Q8—2441no—
160Q8—2441no—
161D4—21no—
162D4—21no—
163D4—612no—
164D4—1221no—
165D4—2442no—
166D4—2444no—
167D4—2441no—
168D4—2441no—
169D4—2441no—
170D4—2441no—
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×C4C2×D24411yescharacteristic
180C2×C4D4×D6111yescharacteristic
181C2×C4D4×D6111yescharacteristic
182C8—41no—
183C8—41no—
184C8—2441no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—1222no—
189C22—4881no—
190C22—4881no—
191C22—4881no—
192C22—2441no—
193C22—2441no—
194C22#1451974711yescharacteristic
195C4—21no—
196C4—41no—
197C4—2442no—
198C4—2441no—
199C4D8×D6111yescharacteristic
200C4#1451979911yescharacteristic
201C4#1451980411yescharacteristic
202C4#1451980511yescharacteristic
203C2—81no—
204C2—9761no—
205C2—2442no—
206C2#1683989711yescharacteristic
207C2#1683990911yescharacteristic
208C2#1683993611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1625
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #16840417C2semidirect
2. #16840109C2semidirect
3. #16839958C2semidirect
4. #16839957C2semidirect
5. #16839509C2semidirect
6. #16839491C2semidirect
7. C61×D4⋊C8C2semidirect
71. D244D8semidirect
111. D4⋊C8D61semidirect
112. C61#1625semidirect