Finite Group Databasebeta

← #21462079

Subgroups — #21462079

Order 7808.

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

normal subgroups only

This group has 266 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
1#16840749C211yesmaximal, characteristic, complemented
2#16840742C211yesmaximal, characteristic, complemented
3#16840663C212yesmaximal, complemented
4#16840662C212yesmaximal, complemented
5#16840327C211yesmaximal, characteristic
6C2×#11758217—21no—
7#14519856—21no—
8#14519838—21no—
9#14519837C2212yes—
10#14519835—21no—
11#14519835C2212yes—
12C2×#11758224C2211yescharacteristic
13C22×C22⋊D61C411yescharacteristic, complemented
14#14519773—21no—
15#14519763—21no—
16#14519750—21no—
17#14519749—21no—
18#14519747C2211yescharacteristic
19#14519746C2211yescharacteristic
20#14519745C411yescharacteristic, complemented
21#14519733C411yescharacteristic, complemented
22#120×C61C411yescharacteristic, complemented
23C24×C61C2×C411yescharacteristic
24C23×D61C2×C411yescharacteristic
25C2×D4×C61—21no—
26C2×D4×C61C2×C411yescharacteristic
27C2×C22⋊D61—21no—
28C2×C22⋊D61—21no—
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C2×C22⋊D61—41no—
32C2×C22⋊D61—41no—
33C2×C22⋊D61D411yescharacteristic
34C2×C22⋊D61C2311yescharacteristic
35C22×Dic61C2×C411yescharacteristic
36C22×Dic61D411yescharacteristic
37#11758224—41no—
38#11758224—41no—
39C2×D244—21no—
40C2×C4×D61D411yescharacteristic
41C2×Dic122D411yescharacteristic
42C22⋊#6923—22no—
43#11758217—22no—
44#11758217—41no—
45C2×#92420—41no—
46C4⋊#6923—41no—
47C4×#6923—41no—
48C22⋊C4×C61—21no—
49C22⋊C4×C61C2×C411yescharacteristic
50C22⋊Dic61—21no—
51C22⋊Dic61C2×C411yescharacteristic
52#11758198—21no—
53#11758198—21no—
54#11758196—21no—
55C4×Dic61—21no—
56C23×C61—21no—
57C23×C61—41no—
58C23×C61—81no—
59C23×C61C22⋊C411yescharacteristic
60C23×C61C22×C411yescharacteristic
61C22×D61—21no—
62C22×D61—41no—
63C22×D61—81no—
64C22×D61C2×D411yescharacteristic
65C2×#6923—42no—
66D4×C61—41no—
67D4×C61—81no—
68C2×C4×C61—21no—
69C2×C4×C61C22⋊C411yescharacteristic
70C22⋊D61—41no—
71C22⋊D61—41no—
72C22⋊D61—42no—
73C22⋊D61—41no—
74C22⋊D61—41no—
75C22⋊D61—81no—
76C22⋊D61—81no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61C22⋊C411yescharacteristic
83C2×Dic61C22⋊C411yescharacteristic
84C2×Dic61C2×D411yescharacteristic
85D244—81no—
86C4×D61—21no—
87C4×D61—21no—
88Dic122—41no—
89#92420—42no—
90C22×C61—21no—
91C22×C61—21no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—82no—
98C22×C61C2×C22⋊C411yescharacteristic
99C2×D61—21no—
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—82no—
105#6923—82no—
106C4×C61—21no—
107C4×C61—41no—
108Dic61—21no—
109Dic61—21no—
110Dic61—41no—
111Dic61#9911yescharacteristic
112Dic61#9911yescharacteristic
113#2122—611nomaximal, Sylow
114C2×C61—21no—
115C2×C61—41no—
116C2×C61—41no—
117C2×C61—81no—
118C2×C61C2×#9911yescharacteristic
119D61—41no—
120D61—81no—
121#535—611no—
122#413—611no—
123#410—611no—
124AΣL(1,𝔽16)—612no—
125AΣL(1,𝔽16)—612no—
126C61#212211yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×D4—611no—
129C2×M16—1221no—
130#127—1221no—
131#124—1221no—
132#121—1221no—
133#121—1221no—
134#120—611no—
135#120—611no—
136#120—611no—
137#120#692311yescharacteristic, complemented
138#117—611no—
139#117—1221no—
140#101—1221no—
141#100—612no—
142#99—612no—
143#99—1221no—
144C24—611no—
145C24C2×#692311yescharacteristic
146#41—2441no—
147#41—2441no—
148C2×Q8—611no—
149C2×D4—21no—
150C2×D4—611no—
151C2×D4—611no—
152C2×D4—1221no—
153C2×D4—1221no—
154C2×D4—1221no—
155C2×D4—1221no—
156C2×D4—1221no—
157C2×D4—2441no—
158C2×D4—2441no—
159C2×D4C2×#692311yescharacteristic
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163M16—1222no—
164M16—2441no—
165C2×C8—2441no—
166C4⋊C4—1221no—
167C4⋊C4—2441no—
168C22⋊C4—21no—
169C22⋊C4—611no—
170C22⋊C4—1221no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1222no—
174C22⋊C4C2×#692311yescharacteristic
175C42—1221no—
176C42—2441no—
177C23—21no—
178C23—41no—
179C23—81no—
180C23—611no—
181C23—1221no—
182C23—4881no—
183C23—2441no—
184C23C22⋊#692311yescharacteristic
185C23C22×#692311yescharacteristic
186Q8—2441no—
187D4—41no—
188D4—81no—
189D4—4881no—
190D4—4881no—
191D4—4881no—
192D4—2441no—
193D4—2441no—
194D4—2441no—
195D4—2441no—
196D4—2442no—
197C2×C4—21no—
198C2×C4—611no—
199C2×C4—611no—
200C2×C4—611no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—2442no—
209C2×C4C22⋊#692311yescharacteristic
210C8—2442no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—82no—
219C22—1221no—
220C22—4882no—
221C22—2441no—
222C22—2441no—
223C22—2441no—
224C22—2441no—
225C22C2×C22⋊#692311yescharacteristic
226C4—21no—
227C4—41no—
228C4—611no—
229C4—611no—
230C4—1221no—
231C4—1221no—
232C4—4882no—
233C4—2441no—
234C2—21no—
235C2—41no—
236C2—41no—
237C2—81no—
238C2—4881no—
239C2—2441no—
240C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
Fitting#120×C61C4
socleC2×C61C2×#99
hypercenter#120#6923
hypocenterC61#2122
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. #16840749C2semidirect
2. #16840742C2semidirect
3. #16840663C2semidirect
4. #16840662C2semidirect
13. C22×C22⋊D61C4semidirect
20. #14519745C4semidirect
21. #14519733C4semidirect
22. #120×C61C4semidirect
126. C61#2122semidirect
137. #120#6923semidirect