Finite Group Databasebeta

← #21444515

Subgroups — #21444515

Order 7808.

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

normal subgroups only

This group has 252 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
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3#16839510C212yesmaximal, complemented
4#16839505C212yesmaximal, complemented
5C61×#432C211yesmaximal, characteristic, complemented
6C2×#11758222C412yes—
7C22×#92418—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×C42×C61C2211yescharacteristic
18C4⋊C8×C61C2212yes—
19C22⋊C8×C61—21no—
20#97×C61—21no—
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—
31C2×C8×C61—22no—
32C42×C61C2×C411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61C2311yescharacteristic
36#11758198—22no—
37#11758198—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C2×#92418—22no—
41C2×#92418—42no—
42C23×C61C22⋊C411yescharacteristic
43C22×D61—22no—
44C2×C4×C61—22no—
45C2×C4×C61—22no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C22⋊D61—44no—
55C2×Dic61—22no—
56D244—42no—
57D244—42no—
58D244—41no—
59D244—41no—
60C4×D61—44no—
61Dic122—42no—
62C8×C61—42no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#10012yes—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—42no—
69C2×D61—42no—
70C2×D61—42no—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61—21no—
75C4×C61#13512yes—
76C4×C61AGL(1,ℤ/8)11yescharacteristic
77C4×C61#13711yescharacteristic
78Dic61—42no—
79#1551—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61C2×#10011yescharacteristic
82C2×C61#41611yescharacteristic
83C2×C61#41711yescharacteristic
84D61—82no—
85#532—611no—
86#432D6111yescharacteristic, complemented
87C2×C4⋊C8—611no—
88#333—612no—
89#331—612no—
90C61#155111yescharacteristic, complemented, Sylow
91C2×#41—612no—
92C22×C8—1221no—
93C4⋊Q8—611no—
94#127—611no—
95#124—612no—
96#121—1221no—
97#121—1221no—
98C4×D4—1221no—
99C4×D4—1221no—
100C2×C42C2×D6111yescharacteristic
101C4⋊C8—612no—
102C4⋊C8—1221no—
103C4⋊C8C2×D6112yes—
104C22⋊C8—21no—
105#97—21no—
106#41—2444no—
107C2×Q8—612no—
108C2×D4—612no—
109C2×D4—1222no—
110C2×D4—1221no—
111C2×D4—1221no—
112C22×C4—1222no—
113C22×C4C4×D6111yescharacteristic
114C22×C4D24411yescharacteristic
115C22×C4C22⋊D6111yescharacteristic
116C2×C8—22no—
117C2×C8—1222no—
118C2×C8—2442no—
119C4⋊C4—1221no—
120C4⋊C4—1221no—
121C22⋊C4—1222no—
122C22⋊C4—1222no—
123C42C4×D6111yescharacteristic
124C42D24411yescharacteristic
125C42C22⋊D6111yescharacteristic
126C42C22×D6111yescharacteristic
127C23—1222no—
128C23#1175819811yescharacteristic
129Q8—2442no—
130D4—2442no—
131D4—2444no—
132D4—2441no—
133D4—2442no—
134D4—2441no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—1222no—
140C2×C4—2444no—
141C2×C4#1175819811yescharacteristic
142C2×C4#1175819811yescharacteristic
143C2×C4#1175819811yescharacteristic
144C2×C4C2×C4×D6111yescharacteristic
145C2×C4C2×D24411yescharacteristic
146C2×C4C2×C22⋊D6111yescharacteristic
147C8—42no—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—2442no—
152C22—2442no—
153C22—2442no—
154C22#1451969312yes—
155C22C2×#1175819811yescharacteristic
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—2442no—
161C4#1451979712yes—
162C4#1451980511yescharacteristic
163C4#1451981011yescharacteristic
164C2—22no—
165C2—4882no—
166C2C2×#1451969311yescharacteristic
167C2#1683975611yescharacteristic
168C2#1683976411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1551
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#92418C2semidirect
3. #16839510C2semidirect
4. #16839505C2semidirect
5. C61×#432C2semidirect
86. #432D61semidirect
90. C61#1551semidirect