Finite Group Databasebeta

← #21447467

Subgroups — #21447467

Order 7808.

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

normal subgroups only

This group has 266 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#16840327C211yesmaximal, characteristic
2#16839743C211yesmaximal, characteristic, complemented
3#16839734C211yesmaximal, characteristic, complemented
4#16839550C211yesmaximal, characteristic, complemented
5#16839549C211yesmaximal, characteristic, complemented
6#16839548C211yesmaximal, characteristic, complemented
7C61×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C2×#11758224C2211yescharacteristic
9C22×C22⋊D61C411yescharacteristic, complemented
10M16×D61—21no—
11#14519773—21no—
12#14519763—21no—
13#14519750—21no—
14#14519749—21no—
15#14519747C411yescharacteristic, complemented
16#14519746C411yescharacteristic, complemented
17#14519745C2211yescharacteristic
18#14519733—21no—
19#14519733C411yescharacteristic, complemented
20#14519695—21no—
21#14519694C2211yescharacteristic
22#14519692C2211yescharacteristic
23#14519691—21no—
24#120×C61C2211yescharacteristic
25#100×C61C2211yescharacteristic
26#99×C61C2211yescharacteristic
27C24×C61C2×C411yescharacteristic
28C23×D61C2×C411yescharacteristic
29C2×D4×C61—21no—
30C2×D4×C61C2311yescharacteristic
31C2×C22⋊D61—21no—
32C2×C22⋊D61—21no—
33C2×C22⋊D61—21no—
34C2×C22⋊D61—21no—
35C2×C22⋊D61—41no—
36C2×C22⋊D61—41no—
37C2×C22⋊D61C2×C411yescharacteristic
38C2×C22⋊D61D411yescharacteristic
39C22×Dic61C2×C411yescharacteristic
40C22×Dic61D411yescharacteristic
41#11758224—41no—
42#11758224—41no—
43C2×D244—21no—
44C2×C4×D61D411yescharacteristic
45C2×Dic122D411yescharacteristic
46M16×C61—21no—
47C22⋊C4×C61—21no—
48C22⋊C4×C61—21no—
49C22⋊C4×C61C2×C411yescharacteristic
50C22⋊Dic61—21no—
51C22⋊Dic61—21no—
52C22⋊Dic61C2×C411yescharacteristic
53#11758198—21no—
54#11758198—21no—
55#11758196—21no—
56#11758196—41no—
57C4×Dic61—21no—
58C4×Dic61—41no—
59#11758194—21no—
60#11758189—41no—
61C8×D61—41no—
62C23×C61—21no—
63C23×C61—41no—
64C23×C61—81no—
65C23×C61C22×C411yescharacteristic
66C23×C61C2×D411yescharacteristic
67C22×D61—21no—
68C22×D61—41no—
69C22×D61—81no—
70C22×D61C22⋊C411yescharacteristic
71D4×C61—41no—
72D4×C61—81no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61C2×D411yescharacteristic
76C22⋊D61—41no—
77C22⋊D61—41no—
78C22⋊D61—42no—
79C22⋊D61—41no—
80C22⋊D61—41no—
81C22⋊D61—81no—
82C22⋊D61—81no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—41no—
89C2×Dic61C22⋊C411yescharacteristic
90C2×Dic61C22⋊C411yescharacteristic
91C2×Dic61C22⋊C411yescharacteristic
92D244—81no—
93C4×D61—21no—
94C4×D61—21no—
95Dic122—41no—
96C8×C61—41no—
97#92418—41no—
98C22×C61—21no—
99C22×C61—21no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—82no—
106C22×C61C2×C22⋊C411yescharacteristic
107C2×D61—21no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61—82no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61—81no—
116Dic61—21no—
117Dic61—21no—
118Dic61—41no—
119Dic61—81no—
120Dic61#9911yescharacteristic
121Dic61#9911yescharacteristic
122#2122—611nomaximal, Sylow
123C2×C61—21no—
124C2×C61—41no—
125C2×C61—41no—
126C2×C61—81no—
127C2×C61C2×#9911yescharacteristic
128D61—41no—
129D61—81no—
130#535—611no—
131#413—611no—
132#410—611no—
133AΣL(1,𝔽16)—611no—
134AΣL(1,𝔽16)—611no—
135AΣL(1,𝔽16)—611no—
136AΣL(1,𝔽16)D6111yescharacteristic, complemented
137C61#212211yescharacteristic, complemented, Sylow
138C2×#41—611no—
139C22×D4—611no—
140C2×M16—1221no—
141#127—1221no—
142#124—1221no—
143#121—1221no—
144#121—1221no—
145#120—611no—
146#120—611no—
147#120—611no—
148#120C2×D6111yescharacteristic
149#117—611no—
150#117—1221no—
151#101—1221no—
152#100—611no—
153#100C2×D6111yescharacteristic
154#99—611no—
155#99—1221no—
156#99C2×D6111yescharacteristic
157C24—611no—
158C24C4×D6111yescharacteristic
159#41—2441no—
160#41—2441no—
161C2×Q8—611no—
162C2×D4—21no—
163C2×D4—611no—
164C2×D4—611no—
165C2×D4—1221no—
166C2×D4—1221no—
167C2×D4—1221no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—2441no—
171C2×D4—2441no—
172C2×D4C22×D6111yescharacteristic
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—611no—
176M16—21no—
177M16—1221no—
178M16—2441no—
179C2×C8—2441no—
180C4⋊C4—1221no—
181C4⋊C4—2441no—
182C22⋊C4—21no—
183C22⋊C4—21no—
184C22⋊C4—611no—
185C22⋊C4—1221no—
186C22⋊C4—1221no—
187C22⋊C4—1221no—
188C22⋊C4—1221no—
189C22⋊C4C4×D6111yescharacteristic
190C42—1221no—
191C42—2441no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—611no—
196C23—1221no—
197C23—4881no—
198C23—2441no—
199C23C2×C4×D6111yescharacteristic
200C23D4×D6111yescharacteristic
201Q8—2441no—
202D4—41no—
203D4—81no—
204D4—4881no—
205D4—4881no—
206D4—4881no—
207D4—2441no—
208D4—2441no—
209D4—2441no—
210D4—2441no—
211D4—2442no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—2441no—
225C2×C4D4×D6111yescharacteristic
226C8—41no—
227C8—2441no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22—82no—
236C22—1221no—
237C22—4882no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22—2441no—
242C22C22⋊C4×D6111yescharacteristic
243C4—21no—
244C4—41no—
245C4—81no—
246C4—611no—
247C4—611no—
248C4—1221no—
249C4—1221no—
250C4—4881no—
251C4—2441no—
252C2—21no—
253C2—41no—
254C2—41no—
255C2—81no—
256C2—4881no—
257C2—2441no—
258C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC23×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×AΣL(1,𝔽16)C2
socleC2×C61C2×#99
hypercenterAΣL(1,𝔽16)D61
hypocenterC61#2122
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #16839743C2semidirect
3. #16839734C2semidirect
4. #16839550C2semidirect
5. #16839549C2semidirect
6. #16839548C2semidirect
7. C61×AΣL(1,𝔽16)C2semidirect
9. C22×C22⋊D61C4semidirect
15. #14519747C4semidirect
16. #14519746C4semidirect
19. #14519733C4semidirect
136. AΣL(1,𝔽16)D61semidirect
137. C61#2122semidirect