Finite Group Databasebeta

← #21462077

Subgroups — #21462077

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#16840664C212yesmaximal, complemented
4#16840663C212yesmaximal, complemented
5#16840323C211yesmaximal, characteristic
6D61⋊M16—21no—
7C2×C22⋊#6923—21no—
8#14519837—21no—
9#14519837C2212yes—
10#14519836—21no—
11#14519835C2212yes—
12C22×D244C411yescharacteristic, complemented
13C2×D4×D61C2211yescharacteristic
14#14519762—21no—
15#14519760C2211yescharacteristic
16#14519752—21no—
17#14519750—21no—
18#14519747—21no—
19#14519747C2211yescharacteristic
20#14519745C411yescharacteristic, complemented
21C22⋊C4×D61C411yescharacteristic, complemented
22#123×C61C411yescharacteristic, complemented
23C23×D61C2×C411yescharacteristic
24C23×D61C2×C411yescharacteristic, complemented
25C23×D61D411yescharacteristic
26C22×#6923—41no—
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61C2×C411yescharacteristic, complemented
29C2×C22⋊D61—21no—
30C2×C22⋊D61D411yescharacteristic
31C2×C22⋊D61C2311yescharacteristic
32D4×D61—41no—
33D4×D61—41no—
34C2×D244—21no—
35C2×D244—21no—
36C2×D244—21no—
37C2×D244—41no—
38C2×D244—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—
47C4⋊C4×C61—21no—
48C22⋊C4×C61—21no—
49C22⋊C4×C61C2×C411yescharacteristic, complemented
50C22⋊Dic61C2×C411yescharacteristic, complemented
51#11758198—21no—
52#11758198—21no—
53#11758198—21no—
54#11758198—21no—
55#11758196—21no—
56C23×C61C22⋊C411yescharacteristic
57C23×C61C22×C411yescharacteristic
58C22×D61—21no—
59C22×D61—21no—
60C22×D61—21no—
61C22×D61—21no—
62C22×D61—21no—
63C22×D61—41no—
64C22×D61—81no—
65C22×D61—81no—
66C22×D61—81no—
67C22×D61C22⋊C411yescharacteristic
68C22×D61C22⋊C411yescharacteristic
69C22×D61C2×D411yescharacteristic
70C2×#6923—42no—
71C2×#6923—82no—
72D4×C61—41no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61C22⋊C411yescharacteristic
77C22⋊D61—41no—
78C22⋊D61—41no—
79C22⋊D61—81no—
80C2×Dic61—21no—
81C2×Dic61C2×D411yescharacteristic
82D244—41no—
83D244—42no—
84D244—41no—
85D244—41no—
86D244—81no—
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×C61C2×C22⋊C411yescharacteristic
96C2×D61—21no—
97C2×D61—21no—
98C2×D61—41no—
99C2×D61—42no—
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—81no—
106C2×D61—81no—
107C2×D61—81no—
108C2×D61—82no—
109C2×D61#9911yescharacteristic
110C2×D61#9911yescharacteristic
111#6923—82no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—41no—
115Dic61—21no—
116Dic61—41no—
117#2121—611nomaximal, Sylow
118C2×C61—21no—
119C2×C61—41no—
120C2×C61—41no—
121C2×C61C2×#9911yescharacteristic
122D61—21no—
123D61—21no—
124D61—41no—
125D61—41no—
126D61—81no—
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—1221no—
138#123#692311yescharacteristic, complemented
139#121—1221no—
140#121—1221no—
141#120—611no—
142#120—611no—
143#120—1221no—
144C2×C22⋊C4—611no—
145C2×C22⋊C4—1221no—
146#100—612no—
147#100—1221no—
148#99—612no—
149#99—1221no—
150C24—611no—
151C24—611no—
152C24—611no—
153C2×D4—611no—
154C2×D4—611no—
155C2×D4—611no—
156C2×D4—1221no—
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—1221no—
167C22×C4—2441no—
168C22×C4C2×#692311yescharacteristic, complemented
169M16—1222no—
170M16—2441no—
171C2×C8—2441no—
172C4⋊C4—21no—
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—611no—
184C23—611no—
185C23—611no—
186C23—1221no—
187C23—1221no—
188C23—1221no—
189C23—1221no—
190C23—1221no—
191C23—4881no—
192C23—4881no—
193C23—4881no—
194C23—2441no—
195C23C22⋊#692311yescharacteristic
196C23C22×#692311yescharacteristic
197D4—41no—
198D4—4881no—
199D4—4881no—
200D4—2441no—
201D4—2441no—
202D4—2441no—
203D4—2442no—
204D4—2441no—
205D4—2441no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—611no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—4881no—
214C2×C4—4882no—
215C2×C4—2442no—
216C2×C4C22⋊#692311yescharacteristic
217C8—2442no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—611no—
223C22—611no—
224C22—1221no—
225C22—1221no—
226C22—4881no—
227C22—4881no—
228C22—4881no—
229C22—4882no—
230C22—2441no—
231C22—2441no—
232C22—2441no—
233C22—2441no—
234C22—2441no—
235C22—2442no—
236C22—2441no—
237C22C2×C22⋊#692311yescharacteristic
238C4—21no—
239C4—41no—
240C4—41no—
241C4—1221no—
242C4—4882no—
243C4—2441no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2—1221no—
248C2—1221no—
249C2—4881no—
250C2—2441no—
251C2—2441no—
252C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#123×C61C4
socleC2×C61C2×#99
hypercenter#123#6923
hypocenterC61#2121
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
1. D61⋊#100C2semidirect
2. D61⋊#99C2semidirect
3. #16840664C2semidirect
4. #16840663C2semidirect
12. C22×D244C4semidirect
20. #14519745C4semidirect
21. C22⋊C4×D61C4semidirect
22. #123×C61C4semidirect
24. C23×D61C2×C4semidirect
28. C22×C4×C61C2×C4semidirect
49. C22⋊C4×C61C2×C4semidirect
50. C22⋊Dic61C2×C4semidirect
132. C61#2121semidirect
138. #123#6923semidirect
168. C22×C4C2×#6923semidirect
182. C22⋊C4C2×#6923semidirect