Finite Group Databasebeta

← #21444495

Subgroups — #21444495

Order 7808.

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

normal subgroups only

This group has 260 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#16839784C211yesmaximal, 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×#11758189—21no—
10C2×C8×D61—21no—
11#14519774C2211yescharacteristic
12#14519766—21no—
13#14519752—21no—
14#14519752C412yes—
15#14519739—21no—
16#14519739C412yes—
17C42×D61C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19C4⋊#92418C2211yescharacteristic
20#14519706—21no—
21#14519706—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—
48#11758189—42no—
49C8×D61—42no—
50C22×D61—22no—
51C22×D61C22⋊C411yescharacteristic
52Q8×C61—41no—
53Q8×C61—41no—
54C2×C4×C61—22no—
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×Dic61C22⋊C411yescharacteristic
59C2×Dic61C22⋊C411yescharacteristic
60C2×Dic61C22⋊C411yescharacteristic
61D244—42no—
62D244—44no—
63D244—41no—
64D244—41no—
65D244—41no—
66D244—41no—
67C4×D61—21no—
68C4×D61—21no—
69C4×D61—41no—
70C4×D61—44no—
71C4×D61D812yes—
72C4×D61SD1612yes—
73C8×C61—41no—
74C8×C61—41no—
75#92418—41no—
76#92418—41no—
77C22×C61C2×C22⋊C411yescharacteristic
78C2×D61—21no—
79C2×D61—21no—
80C2×D61—42no—
81C2×D61—42no—
82C2×D61—42no—
83C2×D61#10212yes—
84C4×C61—21no—
85C4×C61—42no—
86C4×C61C2×D811yescharacteristic
87C4×C61C2×SD1611yescharacteristic
88C4×C61AGL(1,ℤ/8)11yescharacteristic
89C4×C61#13711yescharacteristic
90Dic61—21no—
91Dic61—21no—
92Dic61#10212yes—
93#1547—611nomaximal, Sylow
94C2×C61#41311yescharacteristic
95C2×C61C2×#10211yescharacteristic
96C2×C61#41711yescharacteristic
97D61—22no—
98D61—82no—
99#532—611no—
100#423—611no—
101C2×C4⋊C8—611no—
102#332—611no—
103#332D6111yescharacteristic, complemented
104#331—611no—
105#331—611no—
106C61#154711yescharacteristic, complemented, Sylow
107C2×#41—1221no—
108C2×M16—1221no—
109C22×C8—1221no—
110C4⋊Q8C2×D6111yescharacteristic
111#127—611no—
112#124—1221no—
113#121—612no—
114#121—1221no—
115C4×D4—612no—
116C4×D4—1221no—
117C2×C42—611no—
118C4⋊C8—611no—
119C4⋊C8—611no—
120C4⋊C8—1221no—
121C4⋊C8—1221no—
122C4⋊C8C2×D6111yescharacteristic
123C4⋊C8C2×D6111yescharacteristic
124#41—2442no—
125#41—2442no—
126C2×Q8—21no—
127C2×D4—612no—
128C2×D4—1222no—
129C2×D4—1221no—
130C2×D4—1221no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—1222no—
135M16—2442no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—1221no—
139C2×C8—1221no—
140C2×C8—2442no—
141C4⋊C4—21no—
142C4⋊C4C4×D6112yes—
143C22⋊C4—1222no—
144C22⋊C4—1222no—
145C42—611no—
146C42—611no—
147C42—611no—
148C42C22×D6111yescharacteristic
149C23—611no—
150C23—1222no—
151Q8—41no—
152Q8—41no—
153D4—2442no—
154D4—2444no—
155D4—2441no—
156D4—2441no—
157D4—2441no—
158D4—2441no—
159C2×C4—22no—
160C2×C4—611no—
161C2×C4—612no—
162C2×C4—612no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—2441no—
168C2×C4—2444no—
169C2×C4C2×C4×D6111yescharacteristic
170C2×C4D4×D6111yescharacteristic
171C2×C4D4×D6111yescharacteristic
172C8—41no—
173C8—41no—
174C8—2441no—
175C8—2441no—
176C22—612no—
177C22—1221no—
178C22—1221no—
179C22—2442no—
180C22—2442no—
181C22—2442no—
182C22C22⋊C4×D6111yescharacteristic
183C4—21no—
184C4—42no—
185C4—612no—
186C4—1221no—
187C4—1221no—
188C4D8×D6111yescharacteristic
189C4SD16×D6111yescharacteristic
190C4#1451980411yescharacteristic
191C4#1451980911yescharacteristic
192C2—1222no—
193C2—4882no—
194C2#1683974511yescharacteristic
195C2#102×D6111yescharacteristic
196C2#1683976211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#332C2
socleC22×C61C2×C22⋊C4
hypercenter#332D61
hypocenterC61#1547
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. #16839784C2semidirect
3. C4⋊C8×D61C2semidirect
4. #16839508C2semidirect
5. #16839505C2semidirect
6. #16839505C2semidirect
7. C61×#332C2semidirect
103. #332D61semidirect
106. C61#1547semidirect