Finite Group Databasebeta

← #21444277

Subgroups — #21444277

Order 7808.

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

normal subgroups only

This group has 230 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#16840296C211yesmaximal, characteristic
2C2×C4×#92418C211yesmaximal, characteristic, complemented
3#16839492C212yesmaximal, complemented
4#16839489C212yesmaximal, complemented
5C61×#432C211yesmaximal, characteristic, complemented
6C22×#92418—21no—
7#14519771—21no—
8#14519769C411yescharacteristic
9#14519765C411yescharacteristic
10#14519760—21no—
11#14519756C411yescharacteristic
12#14519751C411yescharacteristic
13C4×Dic122C2211yescharacteristic
14C4×D244C2211yescharacteristic
15C4×C22⋊D61—21no—
16#14519734—21no—
17C4×#92418—21no—
18C4×#92418C2212yes—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61C2212yes—
21C22⋊C8×C61—21no—
22#97×C61—21no—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C2×C22⋊D61—21no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122C2×C411yescharacteristic
30C2×C8×C61—22no—
31C42×C61C2×C411yescharacteristic
32C42×C61D411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61C2311yescharacteristic
35C22⋊Dic61—21no—
36#11758198—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40C4⋊Dic61C2×C411yescharacteristic
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C2×#92418—24no—
48C2×#92418—22no—
49C23×C61C22⋊C411yescharacteristic
50C22×D61—21no—
51C2×C4×C61—22no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C22⋊D61—42no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64D244—22no—
65C4×D61—42no—
66Dic122—22no—
67C8×C61—42no—
68#92418—24no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61#10412yes—
72C22×C61C2×C22⋊C411yescharacteristic
73C2×D61—41no—
74C2×D61—41no—
75C2×D61—41no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61#13112yes—
81C4×C61#13512yes—
82Dic61—41no—
83Dic61—41no—
84Dic61—41no—
85#1494—611nomaximal, Sylow
86C2×C61—22no—
87C2×C61#40811yescharacteristic
88C2×C61#41611yescharacteristic
89C2×C61C2×#10411yescharacteristic
90D61—81no—
91#529—611no—
92#432D6111yescharacteristic, complemented
93C2×C4×C8—611no—
94Q8⋊C8—612no—
95D4⋊C8—612no—
96C61#149411yescharacteristic, complemented, Sylow
97C22×C8—1221no—
98#126—1221no—
99#125—611no—
100#124—611no—
101#123—1221no—
102C22⋊Q8—611no—
103#121—611no—
104C4×Q8—611no—
105C4×D4—611no—
106C4×D4—1221no—
107#117—1221no—
108C2×C42C2×D6111yescharacteristic
109C4⋊C8C2×D6112yes—
110C22⋊C8—21no—
111#97—21no—
112C4×C8—612no—
113C4×C8—1221no—
114C2×Q8—611no—
115C2×D4—611no—
116C2×D4—1221no—
117C22×C4—1221no—
118C22×C4C4×D6111yescharacteristic
119C22×C4D24411yescharacteristic
120C22×C4C22⋊D6111yescharacteristic
121C2×C8—22no—
122C2×C8—1224no—
123C2×C8—1222no—
124C4⋊C4—611no—
125C4⋊C4—611no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C22⋊C4—1221no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C42—1221no—
136C42C4×D6111yescharacteristic
137C42D24411yescharacteristic
138C42C22⋊D6111yescharacteristic
139C42C22×D6111yescharacteristic
140C23—1221no—
141C23#1175819811yescharacteristic
142Q8—1222no—
143D4—1222no—
144D4—2442no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—1221no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—2442no—
152C2×C4#1175819811yescharacteristic
153C2×C4#1175819811yescharacteristic
154C2×C4#1175819811yescharacteristic
155C2×C4C2×C4×D6111yescharacteristic
156C2×C4C2×D24411yescharacteristic
157C2×C4C2×C22⋊D6111yescharacteristic
158C8—42no—
159C8—1224no—
160C22—21no—
161C22—21no—
162C22—2441no—
163C22—2441no—
164C22—2441no—
165C22#1451970312yes—
166C22C2×#1175819811yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—2441no—
172C4—2441no—
173C4—2441no—
174C4#1451978512yes—
175C4#1451979712yes—
176C2—22no—
177C2—4881no—
178C2#1683973011yescharacteristic
179C2#1683975611yescharacteristic
180C2C2×#1451970311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1494
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×#92418C2semidirect
3. #16839492C2semidirect
4. #16839489C2semidirect
5. C61×#432C2semidirect
92. #432D61semidirect
96. C61#1494semidirect