Finite Group Databasebeta

← #21444539

Subgroups — #21444539

Order 7808.

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

normal subgroups only

This group has 246 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#16840312C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic, complemented
3#16839507C212yesmaximal, complemented
4#16839505C212yesmaximal, complemented
5C61×#423C211yesmaximal, characteristic, complemented
6C2×#11758222—21no—
7#14519777C2211yescharacteristic
8#14519774C2211yescharacteristic
9#14519765—21no—
10#14519751—21no—
11#14519751C412yes—
12C4×D244—21no—
13C4×D244C412yes—
14C4⋊#92418C2212yes—
15C22⋊#92418—21no—
16#14519688—21no—
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×Dic122—21no—
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⋊Dic61C2×C412yes—
41C2×#92418—22no—
42C23×C61C22⋊C411yescharacteristic
43C22×D61—22no—
44C2×C4×C61—21no—
45C2×C4×C61—22no—
46C2×C4×C61—21no—
47C2×C4×C61—41no—
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—41no—
58D244—42no—
59D244—41no—
60C4×D61—44no—
61Dic122—42no—
62C8×C61—42no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61—21no—
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×C61AGL(1,ℤ/8)11yescharacteristic
76C4×C61AGL(1,ℤ/8)12yes—
77C4×C61#13711yescharacteristic
78Dic61—42no—
79#1557—611nomaximal, Sylow
80C2×C61—41no—
81C2×C61#41311yescharacteristic
82C2×C61#41711yescharacteristic
83C2×C61#41811yescharacteristic
84D61—82no—
85#532—611no—
86#432—611no—
87#423D6111yescharacteristic, complemented
88#332—612no—
89#331—612no—
90C61#155711yescharacteristic, complemented, Sylow
91C2×#41—1221no—
92C2×M16—21no—
93C4⋊Q8—611no—
94#127—611no—
95#124—1221no—
96#121—612no—
97#121—1221no—
98C4×D4—612no—
99C4×D4—1221no—
100C2×C42C2×D6111yescharacteristic
101C4⋊C8—21no—
102C4⋊C8—612no—
103C4⋊C8C2×D6112yes—
104C22⋊C8—1221no—
105#97—1221no—
106#41—2444no—
107C2×Q8—1221no—
108C2×D4—612no—
109C2×D4—1222no—
110C2×D4—1221no—
111C2×D4—1221no—
112C22×C4—1222no—
113C22×C4C4×D6111yescharacteristic
114C22×C4D24411yescharacteristic
115C22×C4C22⋊D6111yescharacteristic
116M16—42no—
117C2×C8—22no—
118C2×C8—1222no—
119C4⋊C4—612no—
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—2441no—
134D4—2442no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—41no—
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—21no—
152C22—2442no—
153C22—2442no—
154C22—2442no—
155C22C2×#1175819811yescharacteristic
156C4—21no—
157C4—21no—
158C4—21no—
159C4—21no—
160C4—2442no—
161C4#1451980311yescharacteristic
162C4#1451980512yes—
163C4#1451980811yescharacteristic
164C2—41no—
165C2—4882no—
166C2#1683974411yescharacteristic
167C2#1683976111yescharacteristic
168C2#1683976811yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#423C2
socleC22×C61C2×C22⋊C4
hypercenter#423D61
hypocenterC61#1557
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. #16839819C2semidirect
3. #16839507C2semidirect
4. #16839505C2semidirect
5. C61×#423C2semidirect
87. #423D61semidirect
90. C61#1557semidirect