Finite Group Databasebeta

← #21462075

Subgroups — #21462075

Order 7808.

280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 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
1D61⋊#100C211yesmaximal, characteristic, complemented
2D61⋊#99C211yesmaximal, characteristic, complemented
3#16840665C212yesmaximal, complemented
4#16840662C212yesmaximal, complemented
5#16840322C211yesmaximal, characteristic
6D61⋊M16—21no—
7C2×C22⋊#6923—21no—
8#14519837—21no—
9#14519837C2212yes—
10#14519836—21no—
11#14519835C2212yes—
12C22×C22⋊D61C411yescharacteristic, complemented
13C2×D4×D61C2211yescharacteristic
14#14519761C2211yescharacteristic
15#14519759—21no—
16#14519758C411yescharacteristic, complemented
17#14519750—21no—
18#14519748—21no—
19#14519746C2211yescharacteristic
20#14519745—21no—
21C22⋊C4×D61C411yescharacteristic, complemented
22#120×C61C411yescharacteristic, complemented
23C24×C61C2×C411yescharacteristic, complemented
24C23×D61C2×C411yescharacteristic
25C23×D61D411yescharacteristic
26C22×#6923—41no—
27C2×D4×C61—21no—
28C2×D4×C61C2×C411yescharacteristic
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C2×C22⋊D61—41no—
33C2×C22⋊D61—41no—
34C2×C22⋊D61D411yescharacteristic
35C2×C22⋊D61C2311yescharacteristic
36C22×Dic61C2×C411yescharacteristic, complemented
37D4×D61—41no—
38D4×D61—41no—
39C2×D244D411yescharacteristic
40C2×C4×D61—21no—
41C2×C4×D61D411yescharacteristic
42C22⋊#6923—22no—
43C22⋊#6923—41no—
44#11758217—22no—
45#11758213—41no—
46D61⋊C8—41no—
47C22⋊C4×C61—21no—
48C22⋊C4×C61C2×C411yescharacteristic, complemented
49C22⋊Dic61—21no—
50C22⋊Dic61—21no—
51C22⋊Dic61C2×C411yescharacteristic, complemented
52#11758198—21no—
53#11758198—21no—
54C4⋊Dic61—21no—
55#11758196—21no—
56C23×C61—21no—
57C23×C61—41no—
58C23×C61—81no—
59C23×C61C22⋊C411yescharacteristic
60C23×C61C22×C411yescharacteristic
61C22×D61—21no—
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—21no—
65C22×D61—81no—
66C22×D61—81no—
67C22×D61C22⋊C411yescharacteristic
68C22×D61C22⋊C411yescharacteristic
69C22×D61C2×D411yescharacteristic
70C2×#6923—42no—
71C2×#6923—82no—
72D4×C61—41no—
73D4×C61—81no—
74C2×C4×C61—21no—
75C2×C4×C61C22⋊C411yescharacteristic
76C22⋊D61—41no—
77C22⋊D61—41no—
78C22⋊D61—42no—
79C22⋊D61—41no—
80C22⋊D61—41no—
81C22⋊D61—81no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—41no—
85C2×Dic61C2×D411yescharacteristic
86D244—41no—
87C4×D61—21no—
88C4×D61—21no—
89C4×D61—81no—
90#92420—42no—
91C22×C61—21no—
92C22×C61—21no—
93C22×C61—41no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—82no—
99C22×C61C2×C22⋊C411yescharacteristic
100C2×D61—21no—
101C2×D61—21no—
102C2×D61—41no—
103C2×D61—42no—
104C2×D61—41no—
105C2×D61—41no—
106C2×D61—81no—
107C2×D61—81no—
108C2×D61—81no—
109C2×D61#9911yescharacteristic
110C2×D61#9911yescharacteristic
111#6923—82no—
112C4×C61—21no—
113C4×C61—41no—
114Dic61—21no—
115Dic61—41no—
116Dic61—41no—
117#2121—611nomaximal, Sylow
118C2×C61—21no—
119C2×C61—41no—
120C2×C61—41no—
121C2×C61—81no—
122C2×C61C2×#9911yescharacteristic
123D61—21no—
124D61—21no—
125D61—41no—
126D61—41no—
127#534—611no—
128C2×#100—611no—
129C2×#99—611no—
130#352—612no—
131AΣL(1,𝔽16)—612no—
132C61#212111yescharacteristic, complemented, Sylow
133C22×D4—611no—
134C22×D4—611no—
135C2×M16—1221no—
136#123—611no—
137#123—611no—
138#123—1221no—
139#121—1221no—
140#121—1221no—
141#120—611no—
142#120—1221no—
143#120#692311yescharacteristic, complemented
144C2×C22⋊C4—611no—
145C2×C22⋊C4—1221no—
146#100—612no—
147#100—1221no—
148#99—612no—
149#99—1221no—
150C24—611no—
151C24—611no—
152C24C2×#692311yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—611no—
155C2×D4—611no—
156C2×D4—611no—
157C2×D4—1221no—
158C2×D4—1221no—
159C2×D4—1221no—
160C2×D4—2441no—
161C2×D4—2441no—
162C2×D4—2441no—
163C2×D4—2441no—
164C2×D4C2×#692311yescharacteristic
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—1221no—
168C22×C4—2441no—
169M16—1222no—
170M16—2441no—
171C2×C8—2441no—
172C4⋊C4—1221no—
173C4⋊C4—1221no—
174C22⋊C4—21no—
175C22⋊C4—611no—
176C22⋊C4—1221no—
177C22⋊C4—1221no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C22⋊C4—1222no—
181C22⋊C4—2441no—
182C22⋊C4C2×#692311yescharacteristic, complemented
183C23—21no—
184C23—41no—
185C23—81no—
186C23—611no—
187C23—611no—
188C23—611no—
189C23—1221no—
190C23—1221no—
191C23—1221no—
192C23—1221no—
193C23—4881no—
194C23—4881no—
195C23C22⋊#692311yescharacteristic
196C23C22×#692311yescharacteristic
197D4—41no—
198D4—81no—
199D4—4881no—
200D4—2441no—
201D4—2441no—
202D4—2441no—
203D4—2441no—
204D4—2441no—
205D4—2442no—
206C2×C4—21no—
207C2×C4—611no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—4881no—
213C2×C4—4882no—
214C2×C4—2442no—
215C2×C4—2441no—
216C2×C4C22⋊#692311yescharacteristic
217C8—2442no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—82no—
226C22—611no—
227C22—611no—
228C22—1221no—
229C22—1221no—
230C22—4881no—
231C22—4881no—
232C22—4881no—
233C22—2441no—
234C22—2441no—
235C22—2441no—
236C22—2442no—
237C22C2×C22⋊#692311yescharacteristic
238C4—21no—
239C4—41no—
240C4—1221no—
241C4—4882no—
242C4—2441no—
243C4—2441no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2—81no—
248C2—1221no—
249C2—1221no—
250C2—2441no—
251C2—2441no—
252C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#120×C61C4
socleC2×C61C2×#99
hypercenter#120#6923
hypocenterC61#2121
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #120

Complements

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

NH ≅ G/Ntype
1. D61⋊#100C2semidirect
2. D61⋊#99C2semidirect
3. #16840665C2semidirect
4. #16840662C2semidirect
12. C22×C22⋊D61C4semidirect
16. #14519758C4semidirect
21. C22⋊C4×D61C4semidirect
22. #120×C61C4semidirect
23. C24×C61C2×C4semidirect
36. C22×Dic61C2×C4semidirect
48. C22⋊C4×C61C2×C4semidirect
51. C22⋊Dic61C2×C4semidirect
132. C61#2121semidirect
143. #120#6923semidirect
152. C24C2×#6923semidirect
182. C22⋊C4C2×#6923semidirect