Finite Group Databasebeta

← #21444919

Subgroups — #21444919

Order 7808.

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

normal subgroups only

This group has 250 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#16840427C211yesmaximal, characteristic, complemented
2#16839959C211yesmaximal, characteristic, complemented
3#16839954C211yesmaximal, characteristic
4#16839508C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic, complemented
7C61×#486C211yesmaximal, characteristic, complemented
8C2×Q8×D61—21no—
9C2×#11758200—21no—
10C2×#11758199—21no—
11#14519776—21no—
12#14519755—22no—
13#14519753—21no—
14C4×Dic122C2211yescharacteristic
15C4×D244C2211yescharacteristic
16#14519739—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—
29Q8×D61—42no—
30Q8×D61—42no—
31C2×D244D411yescharacteristic
32C2×C4×D61—22no—
33C2×C4×D61—21no—
34C2×Dic122—22no—
35C2×Dic122D411yescharacteristic
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61D412yes—
39C42×C61C2311yescharacteristic
40#11758200—42no—
41#11758199—42no—
42#11758198—22no—
43#11758198—21no—
44C4⋊Dic61D411yescharacteristic
45C4⋊Dic61D411yescharacteristic
46#11758196—22no—
47#11758196—21no—
48C4×Dic61—21no—
49C2×#92418—21no—
50C2×#92418—21no—
51C23×C61—41no—
52C22×D61—21no—
53Q8×C61—41no—
54Q8×C61—41no—
55D4×C61—42no—
56D4×C61—41no—
57D4×C61—41no—
58D4×C61—41no—
59D4×C61—41no—
60C2×C4×C61—22no—
61C2×C4×C61C2×D411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×Dic61—21no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67D244—21no—
68D244SD1612yescomplemented
69C4×D61—44no—
70C4×D61—41no—
71C4×D61—41no—
72Dic122—21no—
73Dic122—44no—
74Dic122D812yescomplemented
75C8×C61—41no—
76#92418—41no—
77#92418—41no—
78C22×C61—81no—
79C22×C61—81no—
80C22×C61—81no—
81C22×C61#12011yescharacteristic
82C2×D61—22no—
83C2×D61—41no—
84C2×D61—41no—
85C4×C61—21no—
86C4×C61—42no—
87C4×C61C2×D811yescharacteristic
88C4×C61C2×SD1611yescharacteristic
89C4×C61AGL(1,ℤ/8)11yescharacteristic
90C4×C61#13711yescharacteristic
91Dic61—22no—
92Dic61—41no—
93Dic61—41no—
94#1627—611nomaximal, Sylow
95C2×C61—161no—
96C2×C61#44711yescharacteristic
97C2×C61#44811yescharacteristic
98C2×C61#45411yescharacteristic
99D61—42no—
100D4×Q8—611no—
101#486D6111yescharacteristic, complemented
102#460—611no—
103#459—611no—
104#332—611no—
105Q8⋊C8—611no—
106D4⋊C8—611no—
107C61#162711yescharacteristic, complemented, Sylow
108C22×Q8—1221no—
109C2×SD16—1221no—
110C2×D8—1221no—
111C4⋊Q8—1221no—
112C4⋊Q8C2×D6111yescharacteristic
113#127C2×D6111yescharacteristic
114C22⋊Q8—1221no—
115C22⋊Q8—1222no—
116C4×Q8—611no—
117C4×D4—611no—
118C4×D4—1221no—
119C4⋊C8—611no—
120C4⋊C8—611no—
121#102—22no—
122#102—1221no—
123#102—1221no—
124C4×C8C2×D6111yescharacteristic
125C2×Q8—21no—
126C2×Q8—611no—
127C2×Q8—1222no—
128C2×Q8—2442no—
129C2×Q8—2442no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—611no—
134C22×C4—1222no—
135C22×C4—1221no—
136SD16—2442no—
137D8—2442no—
138C2×C8—21no—
139C2×C8—1221no—
140C2×C8—1221no—
141C4⋊C4—21no—
142C4⋊C4—611no—
143C4⋊C4—611no—
144C4⋊C4—1222no—
145C4⋊C4—1221no—
146C4⋊C4C22⋊D6112yes—
147C22⋊C4—1222no—
148C22⋊C4—1221no—
149C42—1221no—
150C42C22×D6111yescharacteristic
151C23—41no—
152C23—1221no—
153Q8—41no—
154Q8—41no—
155Q8—612no—
156Q8—1221no—
157Q8—2444no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—612no—
164D4—1221no—
165C2×C4—22no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—2444no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4D4×D6111yescharacteristic
173C2×C4D4×D6111yescharacteristic
174C2×C4C2×C22⋊D6111yescharacteristic
175C8—41no—
176C8—2441no—
177C8—2441no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—1222no—
182C22—2441no—
183C22—2441no—
184C22#1451974511yescharacteristic
185C4—21no—
186C4—42no—
187C4—1222no—
188C4—2441no—
189C4—2441no—
190C4D8×D6111yescharacteristic
191C4SD16×D6111yescharacteristic
192C4#1451980111yescharacteristic
193C4#1451980611yescharacteristic
194C2—161no—
195C2—2442no—
196C2#1683989411yescharacteristic
197C2#1683989911yescharacteristic
198C2#1683993411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#486C2
socleC22×C61#120
hypercenter#486D61
hypocenterC61#1627
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. #16840427C2semidirect
2. #16839959C2semidirect
4. #16839508C2semidirect
5. #16839494C2semidirect
6. #16839491C2semidirect
7. C61×#486C2semidirect
68. D244SD16semidirect
74. Dic122D8semidirect
101. #486D61semidirect
107. C61#1627semidirect