Finite Group Databasebeta

← #21452779

Subgroups — #21452779

Order 7808.

476 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#14519772C212yesmaximal, complemented
2#16839697C212yesmaximal, complemented
3#16839684C212yesmaximal, complemented
4#16839680C212yesmaximal
5#16839664C211yesmaximal, characteristic
6#16839660C211yesmaximal, characteristic, complemented
7#16839659C212yesmaximal, complemented
8#16839652C212yesmaximal, complemented
9C61×#389C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11#14519772—28no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C2×C4⋊C4×C61C2212yes—
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30C2×C42×C61C2211yescharacteristic
31#95×C61C2212yes—
32C23×D61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2311yescharacteristic
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C2×D244—22no—
42C2×D244—41no—
43C2×D244—41no—
44C4⋊C4×C61—24no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61—41no—
47C42×C61—41no—
48#11758198—24no—
49#11758198—24no—
50#11758198—24no—
51#11758198—24no—
52#11758198—42no—
53#11758198—42no—
54C4⋊Dic61—41no—
55C4⋊Dic61—41no—
56C4⋊Dic61D414yescomplemented
57#11758196—24no—
58#11758196—24no—
59#11758196—42no—
60C4×Dic61—24no—
61C23×C61C2411yescharacteristic
62C22×D61—22no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61#4112yes—
83C2×C4×C61#4112yes—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61C2×D414yes—
93D244—44no—
94C22×C61C22×D411yescharacteristic
95C22×C61C2×#4111yescharacteristic
96C22×C61C2×#4111yescharacteristic
97C22×C61H(5,𝔽2)11yescharacteristic
98C22×C61H(5,𝔽2)11yescharacteristic
99C22×C612−1+411yescharacteristic
100C22×C612−1+411yescharacteristic
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C4×C61—22no—
109C4×C61—22no—
110C4×C61—22no—
111C4×C61—42no—
112C4×C61—42no—
113Dic61—24no—
114Dic61—42no—
115Dic61—42no—
116#2727—611nomaximal, Sylow
117C2×C61#53711yescharacteristic
118C2×C61#53811yescharacteristic
119C2×C61#53911yescharacteristic
120C2×C61#54711yescharacteristic
121C2×C61#55011yescharacteristic
122C2×C61#55611yescharacteristic
123C2×C61#56311yescharacteristic
124D61—82no—
125C2×#126—612no—
126#399—612no—
127#396—612no—
128#394—612no—
129#390—611no—
130#389—611no—
131#389—612no—
132#389D6111yescharacteristic, complemented
133#388—612no—
134C61#272711yescharacteristic, complemented, Sylow
135C22×D4—611no—
136#126—1228no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4—611no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4C2×D6112yes—
144C2×C4⋊C4C2×D6111yescharacteristic
145C2×C4⋊C4C2×D6111yescharacteristic
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4—612no—
152C2×C42—612no—
153C2×C42C2×D6111yescharacteristic
154#95—612no—
155#95—612no—
156#95C2×D6112yes—
157C24—612no—
158C2×D4—1222no—
159C2×D4—2441no—
160C2×D4—2441no—
161C22×C4—612no—
162C22×C4—612no—
163C22×C4—612no—
164C22×C4C22×D6112yes—
165C22×C4C22×D6112yes—
166C22×C4C22×D6111yescharacteristic
167C22×C4C22×D6111yescharacteristic
168C22×C4C22×D6111yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—24no—
171C4⋊C4—41no—
172C4⋊C4—614no—
173C4⋊C4—1224no—
174C4⋊C4—1224no—
175C4⋊C4—2442no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C22⋊C4—1224no—
179C22⋊C4—1224no—
180C22⋊C4—1224no—
181C22⋊C4—1224no—
182C22⋊C4—2442no—
183C22⋊C4—2442no—
184C42—41no—
185C42—1224no—
186C23—1222no—
187C23—1222no—
188C23—1222no—
189C23—1222no—
190C23—1222no—
191C23—1222no—
192C23—1222no—
193C23C23×D6111yescharacteristic
194D4—2444no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—614no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4#1175822212yes—
217C2×C4D4×D6112yes—
218C2×C4#1175822612yes—
219C22—2442no—
220C22—2442no—
221C22—2442no—
222C22—2442no—
223C22—2442no—
224C22—2442no—
225C22—2442no—
226C22C2×D4×D6111yescharacteristic
227C22C2×#1175822211yescharacteristic
228C22C2×#1175822611yescharacteristic
229C22#1451982211yescharacteristic
230C22#1451982311yescharacteristic
231C22#1451982411yescharacteristic
232C22#1451982511yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—1224no—
239C4—2442no—
240C4—2442no—
241C2—4882no—
242C2#1684033911yescharacteristic
243C2#1684035211yescharacteristic
244C2#1684035911yescharacteristic
245C2#1684041511yescharacteristic
246C2#1684043311yescharacteristic
247C2#1684048511yescharacteristic
248C2#1684051611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2727
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14519772C2semidirect
2. #16839697C2semidirect
3. #16839684C2semidirect
6. #16839660C2semidirect
7. #16839659C2semidirect
8. #16839652C2semidirect
9. C61×#389C2semidirect
56. C4⋊Dic61D4semidirect
132. #389D61semidirect
134. C61#2727semidirect