Finite Group Databasebeta

← #21444768

Subgroups — #21444768

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#16840352C211yesmaximal, characteristic, complemented
2#16839912C211yesmaximal, characteristic, complemented
3#16839898C211yesmaximal, characteristic, complemented
4#16839672C211yesmaximal, characteristic, complemented
5#16839495C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic, complemented
7C61×#328C211yesmaximal, characteristic, complemented
8C22×D244—21no—
9C22×D244C2211yescharacteristic
10C2×#11758201—21no—
11C2×D488—21no—
12#14519772—21no—
13#14519766—21no—
14#14519762—21no—
15#14519752—21no—
16#14519751C2211yescharacteristic
17#14519747—21no—
18#14519737—21no—
19C2×#11758198—21no—
20C2×#11758198C2211yescharacteristic
21#14519699—21no—
22#14519697—21no—
23C22⋊#92418C2211yescharacteristic
24C22⋊Q8×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C23×D61—21no—
28C23×D61D411yescharacteristic
29C2×Q8×C61D411yescharacteristic, complemented
30C22×C4×C61—21no—
31C22×C4×C61C2311yescharacteristic
32C2×C22⋊D61—21no—
33C22×Dic61D411yescharacteristic
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—21no—
38C2×D244—42no—
39C2×D244—42no—
40C2×D244—42no—
41C2×D244—42no—
42C2×D244D411yescharacteristic, complemented
43C2×C4×D61—21no—
44C2×C8×C61—21no—
45C4⋊C4×C61—21no—
46C4⋊C4×C61D411yescharacteristic, complemented
47C22⋊C4×C61—21no—
48#11758201—42no—
49#11758198—21no—
50#11758198—21no—
51#11758198—21no—
52#11758198—21no—
53#11758198—21no—
54#11758198—21no—
55#11758198—42no—
56C4⋊Dic61D411yescharacteristic, complemented
57#11758196—21no—
58C4×Dic61—21no—
59C2×#92418—21no—
60D488—42no—
61C23×C61C2×D411yescharacteristic
62C22×D61—22no—
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—41no—
68C22×D61—41no—
69C22×D61—41no—
70C22×D61—41no—
71C22×D61—41no—
72C22×D61—41no—
73C22×D61—41no—
74C22×D61—41no—
75Q8×C61—41no—
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C22⋊D61—41no—
85C22⋊D61—41no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—41no—
89D244—22no—
90D244—22no—
91D244—41no—
92D244—41no—
93D244—41no—
94D244—48no—
95D244—81no—
96D244—81no—
97C4×D61—81no—
98C8×C61—41no—
99#92418—41no—
100C22×C61—21no—
101C22×C61—21no—
102C22×C61#12011yescharacteristic
103C22×C61#13511yescharacteristic
104C22×C61AGL(1,ℤ/8)11yescharacteristic
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—42no—
113C2×D61—41no—
114C2×D61—41no—
115C2×D61—81no—
116C2×D61—81no—
117C2×D61—81no—
118C2×D61—81no—
119C2×D61—81no—
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—42no—
123C4×C61—41no—
124C4×C61—41no—
125Dic61—41no—
126Dic61—41no—
127#1600—611nomaximal, Sylow
128C2×C61—21no—
129C2×C61—21no—
130C2×C61#44911yescharacteristic
131C2×C61#45311yescharacteristic
132C2×C61B(4,𝔽2)11yescharacteristic
133D61—81no—
134D61—81no—
135D61—82no—
136#538—611no—
137#450—611no—
138#447—611no—
139#392—611no—
140#328D6111yescharacteristic, complemented
141#327—611no—
142#323—611no—
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⋊Q8C2×D6111yescharacteristic
152#121—611no—
153#121—1221no—
154#120—1221no—
155C4×D4—1221no—
156C2×C22⋊C4—611no—
157C2×C22⋊C4—1221no—
158#102—1221no—
159#102—1221no—
160C22⋊C8—611no—
161C22⋊C8C2×D6111yescharacteristic
162#95C2×D6111yescharacteristic
163C24—611no—
164C24—1221no—
165C2×Q8D24411yescharacteristic, complemented
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—21no—
177C22×C4—611no—
178C22×C4—1221no—
179C22×C4C22×D6111yescharacteristic
180SD16—2442no—
181D8—2442no—
182C2×C8—21no—
183C2×C8—1221no—
184C4⋊C4—21no—
185C4⋊C4—611no—
186C4⋊C4—1221no—
187C4⋊C4D24411yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—1221no—
190C22⋊C4—1221no—
191C22⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C22⋊C4—1221no—
195C22⋊C4—2442no—
196C42—1221no—
197C23—1222no—
198C23—1221no—
199C23—1221no—
200C23—1221no—
201C23—1221no—
202C23—2441no—
203C23—2441no—
204C23—2441no—
205C23—2441no—
206C23—2441no—
207C23—2441no—
208C23—2441no—
209C23—2441no—
210C23D4×D6111yescharacteristic
211Q8—41no—
212D4—1222no—
213D4—1222no—
214D4—4881no—
215D4—4881no—
216D4—2441no—
217D4—2441no—
218D4—2441no—
219D4—2448no—
220D4—2441no—
221D4—2441no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—4881no—
231C2×C4—2441no—
232C2×C4C2×D24411yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C8—41no—
235C8—2441no—
236C22—21no—
237C22—21no—
238C22—4881no—
239C22—4881no—
240C22—4881no—
241C22—4881no—
242C22—4881no—
243C22—2442no—
244C22—2442no—
245C22—2442no—
246C22—2442no—
247C22—2441no—
248C22—2441no—
249C22—2441no—
250C22—2441no—
251C22—2441no—
252C22—2441no—
253C22#1451974711yescharacteristic
254C22#1451980011yescharacteristic
255C22#1451980411yescharacteristic
256C4—21no—
257C4—21no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—2441no—
262C4—2441no—
263C2—21no—
264C2—21no—
265C2—4882no—
266C2—4881no—
267C2—4881no—
268C2#1683991011yescharacteristic
269C2#1683993111yescharacteristic
270C2#1683995011yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61#120
hypercenter#328D61
hypocenterC61#1600
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
1. #16840352C2semidirect
2. #16839912C2semidirect
3. #16839898C2semidirect
4. #16839672C2semidirect
5. #16839495C2semidirect
6. #16839485C2semidirect
7. C61×#328C2semidirect
29. C2×Q8×C61D4semidirect
42. C2×D244D4semidirect
46. C4⋊C4×C61D4semidirect
56. C4⋊Dic61D4semidirect
140. #328D61semidirect
143. C61#1600semidirect
165. C2×Q8D244semidirect
187. C4⋊C4D244semidirect