Finite Group Databasebeta

← #21453728

Subgroups — #21453728

Order 7808.

420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C61⋊#401C211yesmaximal, characteristic, complemented
2#16839699C211yesmaximal, characteristic, complemented
3#16839678C213yesmaximal
4#16839661C213yesmaximal, complemented
5#16839655C213yesmaximal, complemented
6#16839652C213yesmaximal, complemented
7C61×#396C211yesmaximal, characteristic, complemented
8C22×C22⋊D61C2211yescharacteristic
9C2×C4⋊Dic61C2213yes—
10C2×C4⋊Dic61C2213yes—
11C2×C22⋊Dic61C2213yes—
12C2×#11758198C2213yes—
13C2×#11758198C2213yes—
14C2×C4×Dic61C2213yes—
15#14519684C2213yes—
16#14519684C2213yes—
17#14519684C2213yes—
18C2×C4⋊C4×C61C2213yes—
19C2×C22⋊C4×C61C2213yes—
20#95×C61C2211yescharacteristic
21C24×C61C2311yescharacteristic
22C23×D61C2311yescharacteristic
23C22×C4×C61C2313yes—
24C22×C4×C61C2313yes—
25C2×C22⋊D61—43no—
26C22×Dic61C2311yescharacteristic
27C22×Dic61C2313yes—
28C22×Dic61C2313yes—
29C4⋊C4×C61—26no—
30C22⋊C4×C61—26no—
31C22⋊Dic61—43no—
32#11758198—26no—
33#11758198—43no—
34C4⋊Dic61—43no—
35C4⋊Dic61—43no—
36C4×Dic61—43no—
37C23×C61—23no—
38C23×C61—23no—
39C23×C61—21no—
40C23×C61C2411yescharacteristic
41C22×D61—23no—
42C22×D61—23no—
43C22×D61—21no—
44C2×C4×C61—23no—
45C2×C4×C61—23no—
46C2×C4×C61—23no—
47C2×C4×C61—23no—
48C2×C4×C61—23no—
49C2×C4×C61#4116yes—
50C22⋊D61—44no—
51C2×Dic61—23no—
52C2×Dic61—23no—
53C2×Dic61—23no—
54C2×Dic61—23no—
55C2×Dic61—23no—
56C2×Dic61—23no—
57C2×Dic61—23no—
58C22×C61—43no—
59C22×C61—43no—
60C22×C61—41no—
61C22×C61C2×#4113yes—
62C22×C61H(5,𝔽2)13yes—
63C22×C612−1+411yescharacteristic
64C2×D61—43no—
65C2×D61—43no—
66C2×D61—41no—
67C4×C61—26no—
68C4×C61—43no—
69Dic61—43no—
70Dic61—43no—
71Dic61—41no—
72#2801—611nomaximal, Sylow
73C2×C61—81no—
74C2×C61#54213yes—
75C2×C61#55313yes—
76C2×C61#56011yescharacteristic
77D61—81no—
78#401—611no—
79#399—611no—
80#396D6111yescharacteristic, complemented
81#394—613no—
82#389—613no—
83#388—613no—
84#388—613no—
85C61#280111yescharacteristic, complemented, Sylow
86C22×D4—611no—
87C2×C4⋊C4—613no—
88C2×C4⋊C4—613no—
89C2×C4⋊C4C2×D6113yes—
90C2×C22⋊C4—613no—
91C2×C22⋊C4—613no—
92C2×C22⋊C4—613no—
93C2×C22⋊C4C2×D6113yes—
94C2×C42—613no—
95#95—613no—
96#95—613no—
97#95—613no—
98#95C2×D6111yescharacteristic
99C24—611no—
100C24C22×D6111yescharacteristic
101C2×D4—2443no—
102C22×C4—613no—
103C22×C4—611no—
104C22×C4—613no—
105C22×C4C22×D6113yes—
106C22×C4C22×D6113yes—
107C4⋊C4—26no—
108C4⋊C4—2443no—
109C4⋊C4—2443no—
110C22⋊C4—26no—
111C22⋊C4—1226no—
112C22⋊C4—2443no—
113C22⋊C4—2443no—
114C42—2443no—
115C23—23no—
116C23—23no—
117C23—21no—
118C23—1223no—
119C23—1223no—
120C23—1221no—
121C23C23×D6111yescharacteristic
122D4—2444no—
123C2×C4—23no—
124C2×C4—23no—
125C2×C4—23no—
126C2×C4—23no—
127C2×C4—23no—
128C2×C4—1223no—
129C2×C4—1223no—
130C2×C4—1223no—
131C2×C4—1223no—
132C2×C4—1223no—
133C2×C4—1223no—
134C2×C4—1223no—
135C2×C4#1175822416yes—
136C22—43no—
137C22—41no—
138C22—43no—
139C22—2443no—
140C22—2441no—
141C22—2443no—
142C22C2×#1175822413yes—
143C22#1451982313yes—
144C22#1451982511yescharacteristic
145C4—26no—
146C4—43no—
147C4—2443no—
148C4—2441no—
149C4—2443no—
150C2—81no—
151C2—4881no—
152C2#1684038513yes—
153C2#1684046413yes—
154C2#1684050311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#396C2
hypercenter#396D61
hypocenterC61#2801
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C61⋊#401C2semidirect
2. #16839699C2semidirect
4. #16839661C2semidirect
5. #16839655C2semidirect
6. #16839652C2semidirect
7. C61×#396C2semidirect
80. #396D61semidirect
85. C61#2801semidirect