Finite Group Databasebeta

← #21444467

Subgroups — #21444467

Order 7808.

256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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#16840313C211yesmaximal, characteristic
2#16839814C211yesmaximal, characteristic, complemented
3C4⋊C8×D61C211yesmaximal, characteristic, complemented
4#16839508C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic, complemented
6#16839505C211yesmaximal, characteristic, complemented
7C61×#332C211yesmaximal, characteristic, complemented
8C2×#11758226—21no—
9C2×C8×D61—21no—
10#14519774C2211yescharacteristic
11#14519766—21no—
12#14519752—21no—
13#14519752C412yes—
14#14519739—21no—
15#14519739C412yes—
16C42×D61C2211yescharacteristic
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21C8×Dic61—21no—
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×D244C2×C412yes—
32C2×C4×D61—22no—
33C2×C4×D61C2×C411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61C2×C412yes—
40C42×C61C2311yescharacteristic
41#11758198—22no—
42#11758198—22no—
43C4×Dic61C2×C411yescharacteristic
44C4×Dic61D411yescharacteristic
45C4×Dic61D411yescharacteristic
46C2×#92418—21no—
47C2×#92418—21no—
48C8×D61—42no—
49C22×D61—22no—
50C22×D61C22⋊C411yescharacteristic
51Q8×C61—41no—
52Q8×C61—41no—
53C2×C4×C61—22no—
54C2×C4×C61C22×C411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C22⋊C411yescharacteristic
59C2×Dic61C22⋊C411yescharacteristic
60D244—42no—
61D244—44no—
62D244—41no—
63D244—41no—
64D244—41no—
65D244—41no—
66C4×D61—21no—
67C4×D61—21no—
68C4×D61—41no—
69C4×D61—44no—
70C4×D61D812yes—
71C4×D61SD1612yes—
72C8×C61—41no—
73C8×C61—41no—
74#92418—41no—
75#92418—41no—
76C22×C61C2×C22⋊C411yescharacteristic
77C2×D61—21no—
78C2×D61—21no—
79C2×D61—42no—
80C2×D61—42no—
81C2×D61—42no—
82C2×D61#10212yes—
83C4×C61—21no—
84C4×C61—42no—
85C4×C61C2×D811yescharacteristic
86C4×C61C2×SD1611yescharacteristic
87C4×C61#13511yescharacteristic
88C4×C61#13511yescharacteristic
89Dic61—21no—
90Dic61—21no—
91Dic61#10212yes—
92#1540—611nomaximal, Sylow
93C2×C61#41311yescharacteristic
94C2×C61C2×#10211yescharacteristic
95C2×C61#41611yescharacteristic
96D61—22no—
97D61—82no—
98#532—611no—
99#431—611no—
100C2×C4⋊C8—611no—
101#332—611no—
102#332D6111yescharacteristic, complemented
103#331—611no—
104#331—611no—
105C61#154011yescharacteristic, complemented, Sylow
106C2×#41—1221no—
107C22×C8—1221no—
108C4⋊Q8C2×D6111yescharacteristic
109#127—611no—
110#124—1221no—
111#121—612no—
112#121—1221no—
113C4×D4—612no—
114C4×D4—1221no—
115C2×C42—611no—
116C4⋊C8—611no—
117C4⋊C8—611no—
118C4⋊C8—1221no—
119C4⋊C8C2×D6111yescharacteristic
120C4⋊C8C2×D6111yescharacteristic
121C22⋊C8—1221no—
122C4×C8—1221no—
123#41—2442no—
124#41—2442no—
125C2×Q8—21no—
126C2×D4—612no—
127C2×D4—1222no—
128C2×D4—1221no—
129C2×D4—1221no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—1222no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1221no—
137C2×C8—1221no—
138C2×C8—2442no—
139C4⋊C4—21no—
140C4⋊C4C4×D6112yes—
141C22⋊C4—1222no—
142C22⋊C4—1222no—
143C42—611no—
144C42—611no—
145C42—611no—
146C42C22×D6111yescharacteristic
147C23—611no—
148C23—1222no—
149Q8—41no—
150Q8—41no—
151D4—2442no—
152D4—2444no—
153D4—2441no—
154D4—2441no—
155D4—2441no—
156D4—2441no—
157C2×C4—22no—
158C2×C4—611no—
159C2×C4—612no—
160C2×C4—612no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—1221no—
164C2×C4—1221no—
165C2×C4—2441no—
166C2×C4—2444no—
167C2×C4C2×C4×D6111yescharacteristic
168C2×C4D4×D6111yescharacteristic
169C2×C4D4×D6111yescharacteristic
170C8—41no—
171C8—41no—
172C8—2441no—
173C8—2441no—
174C22—612no—
175C22—1221no—
176C22—1221no—
177C22—2442no—
178C22—2442no—
179C22—2442no—
180C22C22⋊C4×D6111yescharacteristic
181C4—21no—
182C4—42no—
183C4—612no—
184C4—1221no—
185C4—1221no—
186C4D8×D6111yescharacteristic
187C4SD16×D6111yescharacteristic
188C4#1451979811yescharacteristic
189C4#1451980011yescharacteristic
190C2—1222no—
191C2—4882no—
192C2#1683974511yescharacteristic
193C2#102×D6111yescharacteristic
194C2#1683975711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#332C2
socleC22×C61C2×C22⋊C4
hypercenter#332D61
hypocenterC61#1540
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #16839814C2semidirect
3. C4⋊C8×D61C2semidirect
4. #16839508C2semidirect
5. #16839505C2semidirect
6. #16839505C2semidirect
7. C61×#332C2semidirect
102. #332D61semidirect
105. C61#1540semidirect