Finite Group Databasebeta

← #21451763

Subgroups — #21451763

Order 7808.

584 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519773C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic, complemented
3#16839678C214yesmaximal, complemented
4#16839677C214yesmaximal, complemented
5#16839665C211yesmaximal, characteristic, complemented
6#16839664C211yesmaximal, characteristic, complemented
7#16839663C211yesmaximal, characteristic, complemented
8#16839608C211yesmaximal, characteristic, complemented
9C61×#390C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C22⋊D61C2212yes—
13#14519773—24no—
14#14519768—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2212yes—
18C2×C22⋊Dic61C2214yes—
19C2×#11758198C2214yes—
20C2×#11758198C2214yes—
21C2×C4×Dic61C2211yescharacteristic
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2212yes—
25C22×D4×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2214yes—
28C2×C42×C61C2211yescharacteristic
29C24×C61C2312yes—
30C23×D61C2312yes—
31C2×D4×C61—22no—
32C2×D4×C61—22no—
33C2×D4×C61—22no—
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—24no—
38C2×C22⋊D61—24no—
39C2×C22⋊D61—44no—
40C2×C22⋊D61—44no—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2311yescharacteristic
45C2×D244—22no—
46C2×D244—22no—
47C2×D244—22no—
48C4⋊C4×C61—22no—
49C22⋊C4×C61—44no—
50C42×C61—22no—
51C22⋊Dic61—44no—
52#11758198—44no—
53#11758198—44no—
54C4⋊Dic61—22no—
55C4⋊Dic61—24no—
56#11758196—24no—
57C4×Dic61—22no—
58C4×Dic61D414yes—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—24no—
63C23×C61—24no—
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—24no—
69C22×D61—24no—
70D4×C61—44no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—24no—
75C2×C4×C61—22no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61#4112yes—
78C2×C4×C61#4112yes—
79C22⋊D61—48no—
80C22⋊D61—48no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—24no—
87C2×Dic61—22no—
88C2×Dic61C2×D412yes—
89C2×Dic61C2×D412yes—
90D244—44no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—44no—
95C22×C61—44no—
96C22×C61C22×D411yescharacteristic
97C22×C61C2×#4111yescharacteristic
98C22×C61C2×#4111yescharacteristic
99C22×C61H(5,𝔽2)12yes—
100C22×C61H(5,𝔽2)12yes—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—42no—
104C2×D61—44no—
105C2×D61—44no—
106C4×C61—42no—
107C4×C61—42no—
108C4×C61#12414yes—
109Dic61—22no—
110Dic61—22no—
111Dic61—42no—
112Dic61—42no—
113#2641—611nomaximal, Sylow
114C2×C61—82no—
115C2×C61C2×#12411yescharacteristic
116C2×C61#53511yescharacteristic
117C2×C61#53511yescharacteristic
118C2×C61#54012yes—
119C2×C61#54012yes—
120D61—82no—
121C2×#127—611no—
122C2×#125—611no—
123#394—614no—
124#394—614no—
125#390—611no—
126#390—611no—
127#390—611no—
128#390D6111yescharacteristic, complemented
129#376—611no—
130C61#264111yescharacteristic, complemented, Sylow
131C22×D4—612no—
132C22×D4—612no—
133C22×D4—611no—
134C22×D4C2×D6111yescharacteristic
135#127—1224no—
136#125—1224no—
137C2×C4⋊C4—611no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4C2×D6111yescharacteristic
141C2×C22⋊C4—614no—
142C2×C22⋊C4—614no—
143C2×C22⋊C4—614no—
144C2×C22⋊C4C2×D6114yes—
145C2×C42—611no—
146C2×C42—611no—
147C2×C42C2×D6111yescharacteristic
148#95—612no—
149#95—612no—
150C24—612no—
151C24C22×D6112yes—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—1224no—
156C2×D4—1224no—
157C2×D4—1222no—
158C2×D4—1222no—
159C2×D4—1222no—
160C2×D4—2444no—
161C2×D4—2444no—
162C22×C4—611no—
163C22×C4—611no—
164C22×C4—612no—
165C22×C4—612no—
166C22×C4C22×D6112yes—
167C22×C4C22×D6112yes—
168C22×C4C22×D6111yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—1224no—
171C4⋊C4—1224no—
172C4⋊C4—1222no—
173C22⋊C4—44no—
174C22⋊C4—2444no—
175C22⋊C4—2444no—
176C22⋊C4—2444no—
177C42—22no—
178C42—614no—
179C42—1222no—
180C23—22no—
181C23—22no—
182C23—22no—
183C23—24no—
184C23—24no—
185C23—1222no—
186C23—1222no—
187C23—1222no—
188C23—1224no—
189C23—1224no—
190C23C23×D6111yescharacteristic
191D4—44no—
192D4—2448no—
193D4—2448no—
194D4—2444no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—612no—
201C2×C4—612no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1224no—
208C2×C4—1222no—
209C2×C4#1175822212yes—
210C2×C4D4×D6112yes—
211C2×C4#1175822412yes—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—44no—
216C22—44no—
217C22—2442no—
218C22—2442no—
219C22—2442no—
220C22—2444no—
221C22—2444no—
222C22C2×D4×D6111yescharacteristic
223C22C2×#1175822411yescharacteristic
224C22C2×#1175822211yescharacteristic
225C22#1451982212yes—
226C22#1451982312yes—
227C4—42no—
228C4—42no—
229C4—1222no—
230C4—1222no—
231C4—2442no—
232C4—2442no—
233C4#1451976314yes—
234C2—82no—
235C2—4882no—
236C2C2×#1451976311yescharacteristic
237C2#1684032511yescharacteristic
238C2#1684033011yescharacteristic
239C2#1684036312yes—
240C2#1684036512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2641
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#14519768C2semidirect
3. #16839678C2semidirect
4. #16839677C2semidirect
5. #16839665C2semidirect
6. #16839664C2semidirect
7. #16839663C2semidirect
8. #16839608C2semidirect
9. C61×#390C2semidirect
128. #390D61semidirect
130. C61#2641semidirect