Finite Group Databasebeta

← #21447464

Subgroups — #21447464

Order 7808.

280 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840323C211yesmaximal, characteristic
2#100×D61C211yesmaximal, characteristic, complemented
3#99×D61C211yesmaximal, characteristic, complemented
4#16839552C211yesmaximal, characteristic, complemented
5#16839550C211yesmaximal, characteristic, complemented
6#16839548C211yesmaximal, characteristic, complemented
7C61×#352C211yesmaximal, characteristic, complemented
8C22×D244C411yescharacteristic, complemented
9C2×D4×D61C2211yescharacteristic
10M16×D61—21no—
11#14519762—21no—
12#14519760C411yescharacteristic, complemented
13#14519752—21no—
14#14519750—21no—
15#14519747—21no—
16#14519747C411yescharacteristic, complemented
17#14519745C2211yescharacteristic
18C22⋊C4×D61—21no—
19C22⋊C4×D61C411yescharacteristic, complemented
20#14519694C2211yescharacteristic
21#14519693—21no—
22#14519692C2211yescharacteristic
23#14519691—21no—
24#123×C61C2211yescharacteristic
25#100×C61C2211yescharacteristic
26#99×C61C2211yescharacteristic
27C23×D61C2×C411yescharacteristic
28C23×D61C2×C411yescharacteristic, complemented
29C23×D61D411yescharacteristic
30C2×D4×C61C2311yescharacteristic
31C22×C4×C61C2×C411yescharacteristic, complemented
32C2×C22⋊D61—21no—
33C2×C22⋊D61C2×C411yescharacteristic
34C2×C22⋊D61D411yescharacteristic
35D4×D61—41no—
36D4×D61—41no—
37C2×D244—21no—
38C2×D244—21no—
39C2×D244—21no—
40C2×D244—41no—
41C2×D244—41no—
42C2×D244D411yescharacteristic
43C2×C4×D61—21no—
44C2×C4×D61—41no—
45C2×C4×D61D411yescharacteristic
46M16×C61—21no—
47C4⋊C4×C61—21no—
48C22⋊C4×C61—21no—
49C22⋊C4×C61—21no—
50C22⋊C4×C61C2×C411yescharacteristic, complemented
51C22⋊Dic61—21no—
52C22⋊Dic61C2×C411yescharacteristic, complemented
53#11758198—21no—
54#11758198—21no—
55#11758198—21no—
56#11758198—21no—
57#11758198—41no—
58#11758196—21no—
59#11758194—21no—
60#11758189—41no—
61C8×D61—41no—
62C23×C61C22×C411yescharacteristic
63C23×C61C2×D411yescharacteristic
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—21no—
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—41no—
70C22×D61—81no—
71C22×D61—81no—
72C22×D61—81no—
73C22×D61C22⋊C411yescharacteristic
74C22×D61C22⋊C411yescharacteristic
75C22×D61C22⋊C411yescharacteristic
76D4×C61—41no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61C2×D411yescharacteristic
82C22⋊D61—41no—
83C22⋊D61—41no—
84C22⋊D61—81no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87C2×Dic61C22⋊C411yescharacteristic
88D244—41no—
89D244—42no—
90D244—41no—
91D244—41no—
92D244—81no—
93C4×D61—21no—
94C4×D61—21no—
95C4×D61—81no—
96C4×D61—82no—
97C8×C61—41no—
98#92418—41no—
99C22×C61—21no—
100C22×C61—21no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61C2×C22⋊C411yescharacteristic
104C2×D61—21no—
105C2×D61—21no—
106C2×D61—41no—
107C2×D61—42no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—41no—
113C2×D61—81no—
114C2×D61—81no—
115C2×D61—81no—
116C2×D61—82no—
117C2×D61#9911yescharacteristic
118C2×D61#9911yescharacteristic
119C4×C61—21no—
120C4×C61—41no—
121C4×C61—41no—
122C4×C61—81no—
123Dic61—21no—
124Dic61—41no—
125Dic61—81no—
126#2121—611nomaximal, Sylow
127C2×C61—21no—
128C2×C61—41no—
129C2×C61—41no—
130C2×C61C2×#9911yescharacteristic
131D61—21no—
132D61—21no—
133D61—41no—
134D61—41no—
135D61—81no—
136#534—611no—
137C2×#100—611no—
138C2×#99—611no—
139#352—611no—
140#352D6111yescharacteristic, complemented
141AΣL(1,𝔽16)—611no—
142AΣL(1,𝔽16)—611no—
143C61#212111yescharacteristic, complemented, Sylow
144C22×D4—611no—
145C22×D4—611no—
146C2×M16—1221no—
147#123—611no—
148#123—1221no—
149#123C2×D6111yescharacteristic
150#121—1221no—
151#121—1221no—
152#120—611no—
153#120—611no—
154#120—1221no—
155C2×C22⋊C4—611no—
156C2×C22⋊C4—1221no—
157#100—611no—
158#100—1221no—
159#100C2×D6111yescharacteristic
160#99—611no—
161#99—1221no—
162#99C2×D6111yescharacteristic
163C24—611no—
164C24—611no—
165C24—611no—
166C2×D4—611no—
167C2×D4—611no—
168C2×D4—611no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4—1221no—
172C2×D4—1221no—
173C2×D4—2441no—
174C2×D4—2441no—
175C2×D4—2441no—
176C2×D4—2441no—
177C2×D4C22×D6111yescharacteristic
178C22×C4—611no—
179C22×C4—1221no—
180C22×C4—2441no—
181C22×C4C4×D6111yescharacteristic, complemented
182M16—21no—
183M16—1221no—
184M16—2441no—
185C2×C8—2441no—
186C4⋊C4—21no—
187C4⋊C4—1221no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—611no—
191C22⋊C4—1221no—
192C22⋊C4—1221no—
193C22⋊C4—1221no—
194C22⋊C4—1221no—
195C22⋊C4—1221no—
196C22⋊C4—2441no—
197C22⋊C4C4×D6111yescharacteristic, complemented
198C23—611no—
199C23—611no—
200C23—611no—
201C23—1221no—
202C23—1221no—
203C23—1221no—
204C23—1221no—
205C23—1221no—
206C23—4881no—
207C23—4881no—
208C23—4881no—
209C23—2441no—
210C23C2×C4×D6111yescharacteristic
211C23D4×D6111yescharacteristic
212D4—41no—
213D4—4881no—
214D4—4881no—
215D4—2441no—
216D4—2441no—
217D4—2441no—
218D4—2442no—
219D4—2441no—
220D4—2441no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—611no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—4881no—
230C2×C4—4882no—
231C2×C4—2441no—
232C2×C4D4×D6111yescharacteristic
233C8—41no—
234C8—2441no—
235C22—21no—
236C22—21no—
237C22—41no—
238C22—41no—
239C22—611no—
240C22—611no—
241C22—1221no—
242C22—1221no—
243C22—4881no—
244C22—4881no—
245C22—4881no—
246C22—4882no—
247C22—2441no—
248C22—2441no—
249C22—2441no—
250C22—2441no—
251C22—2441no—
252C22—2442no—
253C22—2441no—
254C22C22⋊C4×D6111yescharacteristic
255C4—21no—
256C4—41no—
257C4—41no—
258C4—81no—
259C4—1221no—
260C4—4881no—
261C4—2441no—
262C2—21no—
263C2—41no—
264C2—41no—
265C2—1221no—
266C2—1221no—
267C2—4881no—
268C2—2441no—
269C2—2441no—
270C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC23×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#352C2
socleC2×C61C2×#99
hypercenter#352D61
hypocenterC61#2121
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
2. #100×D61C2semidirect
3. #99×D61C2semidirect
4. #16839552C2semidirect
5. #16839550C2semidirect
6. #16839548C2semidirect
7. C61×#352C2semidirect
8. C22×D244C4semidirect
12. #14519760C4semidirect
16. #14519747C4semidirect
19. C22⋊C4×D61C4semidirect
28. C23×D61C2×C4semidirect
31. C22×C4×C61C2×C4semidirect
50. C22⋊C4×C61C2×C4semidirect
52. C22⋊Dic61C2×C4semidirect
140. #352D61semidirect
143. C61#2121semidirect
181. C22×C4C4×D61semidirect
197. C22⋊C4C4×D61semidirect