Finite Group Databasebeta

← #21444552

Subgroups — #21444552

Order 7808.

254 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 77 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#16840312C211yesmaximal, characteristic
2#16839786C211yesmaximal, characteristic, complemented
3#16839510C212yesmaximal, complemented
4#16839505C212yesmaximal, complemented
5C61×#423C211yesmaximal, characteristic, complemented
6C2×#11758222C412yes—
7C2×#11758194—21no—
8#14519777C2211yescharacteristic
9#14519774C2211yescharacteristic
10#14519765C412yes—
11#14519751—21no—
12#14519751—21no—
13C4×D244—21no—
14C4×D244—21no—
15C4⋊#92418—21no—
16C4⋊#92418C2212yes—
17C2×M16×C61—21no—
18C2×C42×C61C2211yescharacteristic
19C4⋊C8×C61—21no—
20C4⋊C8×C61C2212yes—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C2×C22⋊D61—22no—
25#11758222—44no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244C2×C412yes—
29C2×C4×D61—22no—
30C2×Dic122C2×C412yes—
31M16×C61—42no—
32C2×C8×C61—22no—
33C42×C61C2×C411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61C2311yescharacteristic
37#11758198—22no—
38#11758198—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41#11758194—42no—
42C2×#92418—22no—
43C23×C61C22⋊C411yescharacteristic
44C22×D61—22no—
45C2×C4×C61—22no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61—21no—
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22×C411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C22⋊D61—44no—
57C2×Dic61—22no—
58D244—42no—
59D244—41no—
60D244—41no—
61D244—41no—
62D244—41no—
63C4×D61—44no—
64Dic122—42no—
65C8×C61—42no—
66#92418—42no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—42no—
72C2×D61—42no—
73C2×D61—42no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61#10012yes—
78C4×C61AGL(1,ℤ/8)11yescharacteristic
79C4×C61AGL(1,ℤ/8)11yescharacteristic
80C4×C61#13711yescharacteristic
81C4×C61#13711yescharacteristic
82Dic61—42no—
83#1560—611nomaximal, Sylow
84C2×C61—41no—
85C2×C61C2×#10011yescharacteristic
86C2×C61#41711yescharacteristic
87C2×C61#41711yescharacteristic
88D61—82no—
89#532—611no—
90#423—611no—
91#423D6111yescharacteristic, complemented
92#333—612no—
93#331—612no—
94C61#156011yescharacteristic, complemented, Sylow
95C2×#41—612no—
96C2×M16—21no—
97C2×M16—1221no—
98C4⋊Q8—611no—
99#127—611no—
100#124—612no—
101#121—1221no—
102#121—1221no—
103C4×D4—1221no—
104C4×D4—1221no—
105C2×C42C2×D6111yescharacteristic
106C4⋊C8—21no—
107C4⋊C8—612no—
108C4⋊C8—1221no—
109C4⋊C8C2×D6112yes—
110#41—2444no—
111C2×Q8—612no—
112C2×D4—612no—
113C2×D4—1222no—
114C2×D4—1221no—
115C2×D4—1221no—
116C22×C4—1222no—
117C22×C4C4×D6111yescharacteristic
118C22×C4D24411yescharacteristic
119C22×C4C22⋊D6111yescharacteristic
120M16—42no—
121M16—2442no—
122C2×C8—22no—
123C2×C8—1222no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C22⋊C4—1222no—
127C22⋊C4—1222no—
128C42C4×D6111yescharacteristic
129C42D24411yescharacteristic
130C42C22⋊D6111yescharacteristic
131C42C22×D6111yescharacteristic
132C23—1222no—
133C23#1175819811yescharacteristic
134Q8—2442no—
135D4—2442no—
136D4—2444no—
137D4—2441no—
138D4—2441no—
139D4—2441no—
140D4—2441no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—1222no—
147C2×C4—2444no—
148C2×C4#1175819811yescharacteristic
149C2×C4#1175819811yescharacteristic
150C2×C4#1175819811yescharacteristic
151C2×C4C2×C4×D6111yescharacteristic
152C2×C4C2×D24411yescharacteristic
153C2×C4C2×C22⋊D6111yescharacteristic
154C8—42no—
155C8—2442no—
156C22—21no—
157C22—21no—
158C22—21no—
159C22—2442no—
160C22—2442no—
161C22—2442no—
162C22C2×#1175819811yescharacteristic
163C4—21no—
164C4—21no—
165C4—21no—
166C4—2442no—
167C4#1451969312yes—
168C4#1451980311yescharacteristic
169C4#1451980511yescharacteristic
170C4#1451980811yescharacteristic
171C4#1451981011yescharacteristic
172C2—41no—
173C2—4882no—
174C2C2×#1451969311yescharacteristic
175C2#1683976111yescharacteristic
176C2#1683976411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#423C2
socleC22×C61C2×C22⋊C4
hypercenter#423D61
hypocenterC61#1560
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #16839786C2semidirect
3. #16839510C2semidirect
4. #16839505C2semidirect
5. C61×#423C2semidirect
91. #423D61semidirect
94. C61#1560semidirect