Finite Group Databasebeta

← #21444767

Subgroups — #21444767

Order 7808.

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

normal subgroups only

This group has 320 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, complemented
2#16839915C211yesmaximal, characteristic, complemented
3#16839898C211yesmaximal, characteristic, complemented
4#16839671C211yesmaximal, characteristic, complemented
5#16839500C211yesmaximal, characteristic, complemented
6#16839497C211yesmaximal, characteristic, complemented
7C61×#323C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×C22⋊D61—21no—
10C2×#11758190—21no—
11C2×D488—21no—
12#14519770—21no—
13#14519763—21no—
14#14519759—21no—
15#14519756C2211yescharacteristic
16#14519751C2211yescharacteristic
17#14519750—21no—
18#14519746—21no—
19C4×C22⋊D61—21no—
20C2×#11758198—21no—
21#14519699—21no—
22#14519699—21no—
23#14519684C2211yescharacteristic
24C2×C22⋊C4×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26C22⋊C8×C61C2211yescharacteristic
27C24×C61D411yescharacteristic
28C23×D61—21no—
29C22×C4×C61D411yescharacteristic
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—42no—
35C2×C22⋊D61—42no—
36C2×C22⋊D61—42no—
37C22×Dic61—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—42no—
41C2×D244D411yescharacteristic, complemented
42C2×C4×D61—21no—
43C2×Dic122D411yescharacteristic, complemented
44C2×C8×C61—21no—
45C2×C8×C61—21no—
46C22⋊C4×C61—21no—
47C22⋊C4×C61—21no—
48C22⋊Dic61—21no—
49C22⋊Dic61—21no—
50C22⋊Dic61—21no—
51#11758198—21no—
52#11758198—21no—
53#11758198—42no—
54C4⋊Dic61D411yescharacteristic, complemented
55C4⋊Dic61D411yescharacteristic, complemented
56#11758196—21no—
57#11758196—21no—
58C4×Dic61—21no—
59D488—42no—
60#11758190—42no—
61C23×C61—21no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61—41no—
65C23×C61—41no—
66C23×C61C2×D411yescharacteristic
67C22×D61—22no—
68C22×D61—21no—
69C22×D61—41no—
70C22×D61—41no—
71C22×D61—41no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—41no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C22⋊D61—48no—
81C22⋊D61—41no—
82C22⋊D61—41no—
83C22⋊D61—81no—
84C22⋊D61—81no—
85C2×Dic61—22no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—41no—
90C2×Dic61—41no—
91D244—22no—
92D244—22no—
93D244—41no—
94D244—41no—
95D244—41no—
96C4×D61—81no—
97Dic122—41no—
98C8×C61—41no—
99C8×C61—41no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61—42no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—81no—
107C22×C61#12011yescharacteristic
108C22×C61#13511yescharacteristic
109C22×C61AGL(1,ℤ/8)11yescharacteristic
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—42no—
115C2×D61—41no—
116C2×D61—81no—
117C2×D61—81no—
118C2×D61—81no—
119C2×D61—81no—
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—41no—
123Dic61—42no—
124Dic61—41no—
125Dic61—41no—
126Dic61—41no—
127#1600—611nomaximal, Sylow
128C2×C61—21no—
129C2×C61—21no—
130C2×C61—81no—
131C2×C61#44911yescharacteristic
132C2×C61#45311yescharacteristic
133C2×C61B(4,𝔽2)11yescharacteristic
134D61—81no—
135D61—82no—
136#538—611no—
137#450—611no—
138#447—611no—
139#392—611no—
140#328—611no—
141#327—611no—
142#323D6111yescharacteristic, complemented
143C61#160011yescharacteristic, complemented, Sylow
144C22×D4—611no—
145C22×D4—1221no—
146C2×SD16—1221no—
147C2×D8—1221no—
148#126—1221no—
149#124—1221no—
150#123—1221no—
151C22⋊Q8—611no—
152#121—611no—
153#121—1221no—
154#120—1221no—
155C4×D4—1221no—
156C2×C22⋊C4—1221no—
157C2×C22⋊C4C2×D6111yescharacteristic
158#102—1221no—
159#102—1221no—
160C22⋊C8C2×D6111yescharacteristic
161C22⋊C8C2×D6111yescharacteristic
162#95—611no—
163C24—1221no—
164C24D24411yescharacteristic
165C2×Q8—611no—
166C2×D4—611no—
167C2×D4—1221no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—2442no—
173C2×D4—2442no—
174C2×D4—2442no—
175C2×D4—2442no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4D24411yescharacteristic
179C22×C4C22×D6111yescharacteristic
180SD16—2442no—
181D8—2442no—
182C2×C8—21no—
183C2×C8—21no—
184C4⋊C4—611no—
185C4⋊C4—611no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—1221no—
191C22⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C22⋊C4—1221no—
195C22⋊C4—2442no—
196C42—1221no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—41no—
201C23—41no—
202C23—1222no—
203C23—1221no—
204C23—2441no—
205C23—2441no—
206C23—2441no—
207C23—2441no—
208C23—2441no—
209C23—2441no—
210C23C2×D24411yescharacteristic
211Q8—2441no—
212D4—1222no—
213D4—1222no—
214D4—4881no—
215D4—4881no—
216D4—2441no—
217D4—2441no—
218D4—2441no—
219D4—2448no—
220D4—2441no—
221D4—2441no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—1222no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—4881no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4D4×D6111yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C8—41no—
235C8—41no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—81no—
243C22—4881no—
244C22—4881no—
245C22—4881no—
246C22—4881no—
247C22—2442no—
248C22—2442no—
249C22—2442no—
250C22—2441no—
251C22—2441no—
252C22—2441no—
253C22#1451974711yescharacteristic
254C22#1451979911yescharacteristic
255C22#1451980511yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—2442no—
260C4—2441no—
261C4—2441no—
262C4—2441no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—4882no—
267C2—4881no—
268C2#1683990911yescharacteristic
269C2#1683993211yescharacteristic
270C2#1683995011yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#323C2
socleC22×C61#120
hypercenter#323D61
hypocenterC61#1600
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
1. #16840350C2semidirect
2. #16839915C2semidirect
3. #16839898C2semidirect
4. #16839671C2semidirect
5. #16839500C2semidirect
6. #16839497C2semidirect
7. C61×#323C2semidirect
41. C2×D244D4semidirect
43. C2×Dic122D4semidirect
54. C4⋊Dic61D4semidirect
55. C4⋊Dic61D4semidirect
142. #323D61semidirect
143. C61#1600semidirect