Finite Group Databasebeta

← #21444852

Subgroups — #21444852

Order 7808.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840359C211yesmaximal, characteristic
2#16840098C211yesmaximal, characteristic, complemented
3#16840081C211yesmaximal, characteristic
4#16839701C211yesmaximal, characteristic, complemented
5#16839500C211yesmaximal, characteristic, complemented
6#16839497C211yesmaximal, characteristic
7C61×#324C211yesmaximal, characteristic, complemented
8#14519772—21no—
9#14519767—21no—
10#14519762—21no—
11#14519760—21no—
12#14519756C2211yescharacteristic
13#14519755—21no—
14#14519751C2211yescharacteristic
15C4×C22⋊D61—21no—
16C2×C4⋊Dic61C2211yescharacteristic
17#14519711—21no—
18#14519709—21no—
19#14519702—21no—
20#14519699—21no—
21#14519684—21no—
22#14519684—21no—
23#14519684C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26C22⋊C8×C61C2211yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32C22×Dic61—21no—
33C2×D244D411yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122D411yescharacteristic
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C22⋊Dic61—21no—
41#11758198—21no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61D411yescharacteristic
48C4⋊Dic61D411yescharacteristic
49#11758196—21no—
50#11758196—21no—
51#11758196—21no—
52#11758196—21no—
53C4×Dic61—21no—
54C23×C61C2×D411yescharacteristic
55C22×D61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—21no—
60C2×C4×C61—41no—
61C2×C4×C61—41no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C22⋊D61—41no—
65C22⋊D61—41no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61—41no—
70C2×Dic61—41no—
71C2×Dic61—42no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74D244—41no—
75C4×D61—81no—
76Dic122—41no—
77C8×C61—41no—
78C8×C61—41no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61#12011yescharacteristic
82C22×C61#13511yescharacteristic
83C22×C61#13711yescharacteristic
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—41no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—41no—
90C4×C61—41no—
91Dic61—41no—
92Dic61—41no—
93Dic61—41no—
94Dic61—81no—
95Dic61—81no—
96#1615—611nomaximal, Sylow
97C2×C61—21no—
98C2×C61—21no—
99C2×C61#45211yescharacteristic
100C2×C61#45411yescharacteristic
101C2×C61#45811yescharacteristic
102D61—81no—
103#539—611no—
104#484—611no—
105#481—611no—
106#400—611no—
107#328—611no—
108#327—611no—
109#324D6111yescharacteristic, complemented
110C61#161511yescharacteristic, complemented, Sylow
111#126—1221no—
112#125—1221no—
113#123—1221no—
114#123—1221no—
115C22⋊Q8—611no—
116C22⋊Q8—1221no—
117#121—611no—
118C4×D4—1221no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4C2×D6111yescharacteristic
121#107—1221no—
122#106—1221no—
123#103—1221no—
124#102—1221no—
125C22⋊C8C2×D6111yescharacteristic
126C22⋊C8C2×D6111yescharacteristic
127#95—611no—
128#95—1221no—
129#95—1221no—
130C2×Q8—611no—
131C2×D4—611no—
132C2×D4—1221no—
133C22×C4—1221no—
134C22×C4—1221no—
135C22×C4—1221no—
136C22×C4D24411yescharacteristic
137C22×C4D24411yescharacteristic
138C22×C4C22×D6111yescharacteristic
139C2×C8—21no—
140C2×C8—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—611no—
144C4⋊C4—611no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C22⋊C4—1221no—
152C22⋊C4—1221no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C42—1221no—
157C23—1221no—
158C23C2×D24411yescharacteristic
159Q8—2441no—
160D4—2441no—
161D4—2441no—
162D4—2441no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—1221no—
172C2×C4—4881no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4—2442no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4D4×D6111yescharacteristic
179C2×C4D4×D6111yescharacteristic
180C8—41no—
181C8—41no—
182C22—21no—
183C22—21no—
184C22—2441no—
185C22—2441no—
186C22—2441no—
187C22#1451974711yescharacteristic
188C22#1451979911yescharacteristic
189C22#1451981011yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—4881no—
195C4—4881no—
196C4—2441no—
197C4—2441no—
198C4—2441no—
199C2—21no—
200C2—21no—
201C2—4881no—
202C2#1683992611yescharacteristic
203C2#1683993711yescharacteristic
204C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#324C2
socleC22×C61#120
hypercenter#324D61
hypocenterC61#1615
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #16840098C2semidirect
4. #16839701C2semidirect
5. #16839500C2semidirect
7. C61×#324C2semidirect
109. #324D61semidirect
110. C61#1615semidirect