Finite Group Databasebeta

← #21444513

Subgroups — #21444513

Order 7808.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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#16839818C211yesmaximal, characteristic, complemented
3C4⋊C8×D61C211yesmaximal, characteristic, complemented
4#16839511C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic, complemented
6#16839505C211yesmaximal, characteristic, complemented
7C61×#333C211yesmaximal, characteristic, complemented
8C2×#11758226C412yes—
9C2×C8×D61—21no—
10#14519774C2211yescharacteristic
11#14519766C412yes—
12#14519752—21no—
13#14519752—21no—
14#14519739—21no—
15#14519739—21no—
16C42×D61C2211yescharacteristic
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519687—21no—
22C4⋊Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×Q8×C61C2×C412yes—
26#11758226—44no—
27C2×D244—22no—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244C2×C412yes—
31C2×C4×D61—22no—
32C2×C4×D61C2×C411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C4⋊C4×C61—21no—
38C4⋊C4×C61—21no—
39C42×C61C2311yescharacteristic
40#11758198—22no—
41#11758198—22no—
42C4×Dic61C2×C411yescharacteristic
43C4×Dic61D411yescharacteristic
44C4×Dic61D411yescharacteristic
45C2×#92418—21no—
46C2×#92418—21no—
47C8×D61—42no—
48C22×D61—22no—
49C22×D61C22⋊C411yescharacteristic
50Q8×C61—42no—
51C2×C4×C61—22no—
52C2×C4×C61C22×C411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×Dic61C22⋊C411yescharacteristic
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C22⋊C411yescharacteristic
58D244—42no—
59D244—44no—
60D244—41no—
61D244—41no—
62D244—41no—
63D244—41no—
64C4×D61—22no—
65C4×D61—21no—
66C4×D61—21no—
67C4×D61—21no—
68C4×D61—21no—
69C4×D61—44no—
70C8×C61—41no—
71C8×C61—41no—
72#92418—41no—
73#92418—41no—
74C22×C61C2×C22⋊C411yescharacteristic
75C2×D61—21no—
76C2×D61—21no—
77C2×D61—42no—
78C2×D61—42no—
79C2×D61—42no—
80C2×D61#10012yes—
81C4×C61—21no—
82C4×C61—42no—
83C4×C61#13511yescharacteristic
84C4×C61#13511yescharacteristic
85C4×C61AGL(1,ℤ/8)11yescharacteristic
86C4×C61#13711yescharacteristic
87Dic61—21no—
88Dic61—21no—
89Dic61—21no—
90#1551—611nomaximal, Sylow
91C2×C61C2×#10011yescharacteristic
92C2×C61#41611yescharacteristic
93C2×C61#41711yescharacteristic
94D61—22no—
95D61—82no—
96#532—611no—
97#432—611no—
98C2×C4⋊C8—611no—
99#333—611no—
100#333D6111yescharacteristic, complemented
101#331—611no—
102#331—611no—
103C61#155111yescharacteristic, complemented, Sylow
104C2×#41—612no—
105C22×C8—1221no—
106C4⋊Q8C2×D6111yescharacteristic
107#127—611no—
108#124—612no—
109#121—1221no—
110#121—1221no—
111C4×D4—1221no—
112C4×D4—1221no—
113C2×C42—611no—
114C4⋊C8—611no—
115C4⋊C8—611no—
116C4⋊C8—1221no—
117C4⋊C8C2×D6111yescharacteristic
118C4⋊C8C2×D6111yescharacteristic
119C22⋊C8—1221no—
120#97—1221no—
121#41—2444no—
122C2×Q8C4×D6112yes—
123C2×D4—612no—
124C2×D4—1222no—
125C2×D4—1221no—
126C2×D4—1221no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—1222no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—1221no—
134C2×C8—1221no—
135C2×C8—2442no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C22⋊C4—1222no—
139C22⋊C4—1222no—
140C42—611no—
141C42—611no—
142C42—611no—
143C42C22×D6111yescharacteristic
144C23—611no—
145C23—1222no—
146Q8—42no—
147D4—2442no—
148D4—2444no—
149D4—2441no—
150D4—2441no—
151D4—2441no—
152D4—2441no—
153C2×C4—22no—
154C2×C4—611no—
155C2×C4—611no—
156C2×C4—611no—
157C2×C4—1222no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—2444no—
163C2×C4C2×C4×D6111yescharacteristic
164C2×C4D4×D6111yescharacteristic
165C2×C4D4×D6111yescharacteristic
166C8—41no—
167C8—41no—
168C8—2441no—
169C8—2441no—
170C22—612no—
171C22—1221no—
172C22—1221no—
173C22—2442no—
174C22—2442no—
175C22—2442no—
176C22C22⋊C4×D6111yescharacteristic
177C4—21no—
178C4—42no—
179C4—1221no—
180C4—1221no—
181C4—1221no—
182C4#1451979811yescharacteristic
183C4#1451980011yescharacteristic
184C4#1451980411yescharacteristic
185C4#1451980911yescharacteristic
186C2—1222no—
187C2—4882no—
188C2#100×D6111yescharacteristic
189C2#1683975711yescharacteristic
190C2#1683976211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#333C2
socleC22×C61C2×C22⋊C4
hypercenter#333D61
hypocenterC61#1551
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #16839818C2semidirect
3. C4⋊C8×D61C2semidirect
4. #16839511C2semidirect
5. #16839505C2semidirect
6. #16839505C2semidirect
7. C61×#333C2semidirect
100. #333D61semidirect
103. C61#1551semidirect