Finite Group Databasebeta

← #21444835

Subgroups — #21444835

Order 7808.

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

normal subgroups only

This group has 232 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#16840350C211yesmaximal, characteristic
2#16840093C211yesmaximal, characteristic, complemented
3#16840076C211yesmaximal, characteristic, complemented
4#16839687C211yesmaximal, characteristic, complemented
5#16839500C211yesmaximal, characteristic, complemented
6#16839497C211yesmaximal, characteristic, complemented
7C61×#323C211yesmaximal, characteristic, complemented
8#14519770—21no—
9#14519763—21no—
10#14519759—21no—
11#14519756C2211yescharacteristic
12#14519751C2211yescharacteristic
13#14519750—21no—
14#14519746—21no—
15C4×C22⋊D61—21no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C22⋊Dic61—21no—
18#14519711—21no—
19#14519709—21no—
20#14519702—21no—
21#14519699—21no—
22#14519684—21no—
23#14519684C2211yescharacteristic
24C2×C22⋊C4×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26C22⋊C8×C61C2211yescharacteristic
27C24×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C22×Dic61—21no—
34C22×Dic61—21no—
35C2×D244D411yescharacteristic
36C2×C4×D61—21no—
37C2×Dic122D411yescharacteristic
38C2×C8×C61—21no—
39C2×C8×C61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61—21no—
42C22⋊Dic61—21no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—42no—
46#11758198—21no—
47#11758198—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61D411yescharacteristic
51C4⋊Dic61D411yescharacteristic
52#11758196—21no—
53#11758196—21no—
54C4×Dic61—21no—
55C23×C61—21no—
56C23×C61—21no—
57C23×C61—21no—
58C23×C61—41no—
59C23×C61—41no—
60C23×C61C2×D411yescharacteristic
61C22×D61—21no—
62C2×C4×C61—21no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C22⋊D61—41no—
68C22⋊D61—41no—
69C22⋊D61—81no—
70C22⋊D61—81no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80D244—41no—
81C4×D61—81no—
82Dic122—41no—
83C8×C61—41no—
84C8×C61—41no—
85C22×C61—21no—
86C22×C61—21no—
87C22×C61—42no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61—81no—
92C22×C61#12011yescharacteristic
93C22×C61#13511yescharacteristic
94C22×C61AGL(1,ℤ/8)11yescharacteristic
95C2×D61—41no—
96C2×D61—41no—
97C2×D61—41no—
98C4×C61—21no—
99C4×C61—21no—
100C4×C61—41no—
101Dic61—41no—
102Dic61—41no—
103Dic61—41no—
104Dic61—81no—
105Dic61—81no—
106#1612—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—21no—
109C2×C61—81no—
110C2×C61#44911yescharacteristic
111C2×C61#45511yescharacteristic
112C2×C61#45811yescharacteristic
113D61—81no—
114#538—611no—
115#483—611no—
116#480—611no—
117#397—611no—
118#328—611no—
119#327—611no—
120#323D6111yescharacteristic, complemented
121C61#161211yescharacteristic, complemented, Sylow
122#126—1221no—
123#124—1221no—
124#123—1221no—
125C22⋊Q8—611no—
126#121—611no—
127#121—1221no—
128#120—1221no—
129C4×D4—1221no—
130C2×C4⋊C4—611no—
131C2×C22⋊C4—1221no—
132C2×C22⋊C4C2×D6111yescharacteristic
133#107—1221no—
134#106—1221no—
135#103—1221no—
136#102—1221no—
137C22⋊C8C2×D6111yescharacteristic
138C22⋊C8C2×D6111yescharacteristic
139#95—611no—
140#95—1221no—
141C24D24411yescharacteristic
142C2×Q8—611no—
143C2×D4—611no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4D24411yescharacteristic
151C22×C4C22×D6111yescharacteristic
152C2×C8—21no—
153C2×C8—21no—
154C4⋊C4—611no—
155C4⋊C4—611no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C4⋊C4—1221no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C22⋊C4—1221no—
167C22⋊C4—2442no—
168C42—1221no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—1221no—
175C23C2×D24411yescharacteristic
176Q8—2441no—
177D4—4881no—
178D4—4881no—
179D4—2441no—
180D4—2441no—
181D4—2441no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—1221no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—4881no—
189C2×C4—2441no—
190C2×C4—2441no—
191C2×C4—2441no—
192C2×C4—2441no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4D4×D6111yescharacteristic
196C2×C4D4×D6111yescharacteristic
197C8—41no—
198C8—41no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—2441no—
207C22—2441no—
208C22—2441no—
209C22#1451974711yescharacteristic
210C22#1451979911yescharacteristic
211C22#1451980511yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—4881no—
216C4—4881no—
217C4—2441no—
218C4—2441no—
219C4—2441no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—4881no—
224C2#1683990911yescharacteristic
225C2#1683994211yescharacteristic
226C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#323C2
socleC22×C61#120
hypercenter#323D61
hypocenterC61#1612
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #16840093C2semidirect
3. #16840076C2semidirect
4. #16839687C2semidirect
5. #16839500C2semidirect
6. #16839497C2semidirect
7. C61×#323C2semidirect
120. #323D61semidirect
121. C61#1612semidirect