Finite Group Databasebeta

← #21456733

Subgroups — #21456733

Order 7808.

532 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840310C211yesmaximal, characteristic, complemented
2#127×D61C211yesmaximal, characteristic, complemented
3#16840138C211yesmaximal, characteristic, complemented
4#16840109C211yesmaximal, characteristic, complemented
5#16840108C211yesmaximal, characteristic, complemented
6#16839955C214yesmaximal, complemented
7#16839894C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic, complemented
9C61×#493C211yesmaximal, characteristic, complemented
10C2×#11758224—21no—
11C2×D4×D61—21no—
12C2×D4×D61—21no—
13C2×D4×D61C2212yes—
14C2×#11758199C2214yescomplemented
15#14519777C2211yescharacteristic, complemented
16#14519774C2211yescharacteristic
17#14519773—21no—
18#14519773—21no—
19#14519773C2212yes—
20#14519764—21no—
21#14519748—21no—
22#14519748C2212yes—
23D4×Dic61—21no—
24D4×Dic61C2212yescomplemented
25C42×D61C2211yescharacteristic
26#14519706C2212yescomplemented
27#14519699C2214yescomplemented
28#14519698C2214yescomplemented
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic, complemented
31C2×D8×C61C2214yescomplemented
32#127×C61C2211yescharacteristic
33#127×C61C2211yescharacteristic, complemented
34C4×C8×C61C2211yescharacteristic, complemented
35C23×D61—22no—
36C2×D4×C61—21no—
37C2×D4×C61—21no—
38C2×D4×C61—21no—
39C2×D4×C61—21no—
40C2×D4×C61C2312yes—
41C2×D4×C61C2312yes—
42C2×C22⋊D61—22no—
43C2×C22⋊D61—22no—
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46C22×Dic61—22no—
47#11758224—44no—
48D4×D61—44no—
49D4×D61—44no—
50D4×D61—44no—
51C2×D244—21no—
52C2×D244—21no—
53C2×D244C2312yes—
54C2×C4×D61D411yescharacteristic
55C2×C4×D61D411yescharacteristic
56C2×C4×D61C2311yescharacteristic
57C2×Dic122—21no—
58D8×C61—44no—
59C2×C8×C61C2312yes—
60C42×C61C2311yescharacteristic
61C22⋊Dic61—22no—
62C22⋊Dic61—22no—
63#11758199—44no—
64C4⋊Dic61—21no—
65C4⋊Dic61C2312yes—
66C4×Dic61D411yescharacteristic
67C4×Dic61D411yescharacteristic
68C4×Dic61C2311yescharacteristic
69C2×#92418C2312yes—
70C23×C61—22no—
71C23×C61—22no—
72C22×D61—22no—
73C22×D61—44no—
74C22×D61—44no—
75C22×D61—44no—
76C22×D61C2×D411yescharacteristic
77D4×C61—24no—
78D4×C61—24no—
79D4×C61—42no—
80D4×C61—42no—
81D4×C61—42no—
82D4×C61—42no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2411yescharacteristic
86C22⋊D61—44no—
87C22⋊D61—44no—
88C22⋊D61—44no—
89C22⋊D61—44no—
90C2×Dic61—22no—
91C2×Dic61—44no—
92C2×Dic61C2×D411yescharacteristic
93C2×Dic61C2×D411yescharacteristic
94C2×Dic61C2×D411yescharacteristic
95D244—24no—
96D244—42no—
97D244—42no—
98C4×D61—22no—
99C4×D61—22no—
100C4×D61D814yescomplemented
101Dic122—42no—
102C8×C61—22no—
103#92418—22no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61C22×D411yescharacteristic
111C2×D61—21no—
112C2×D61—21no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—42no—
116C2×D61—88no—
117C2×D61C2×D812yes—
118C4×C61C2×D812yes—
119C4×C61AGL(1,ℤ/8)12yes—
120C4×C61H(5,𝔽2)12yes—
121Dic61—21no—
122Dic61—21no—
123Dic61—42no—
124Dic61C2×D812yes—
125#3205—611nomaximal, Sylow
126C2×C61—82no—
127C2×C61—82no—
128C2×C61#53511yescharacteristic
129C2×C61C22×D811yescharacteristic
130C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
131D61—22no—
132D61—82no—
133#532—611no—
134C2×#127—611no—
135#493—611no—
136#493D6111yescharacteristic, complemented
137#486—611no—
138#486—611no—
139#459—614no—
140#447—614no—
141#431—611no—
142C61#320511yescharacteristic, complemented, Sylow
143C2×#41—1221no—
144C22×D4—612no—
145C22×D4—1221no—
146C22×D4—1221no—
147C2×D8—614no—
148C2×D8C2×D6114yescomplemented
149C4⋊Q8—611no—
150#127—612no—
151#127—611no—
152#127—1221no—
153#127—1221no—
154#127C2×D6111yescharacteristic
155#127C2×D6111yescharacteristic, complemented
156#124—1221no—
157#121—612no—
158#121—1221no—
159C4×D4—612no—
160C4×D4—1221no—
161C2×C42—611no—
162C4⋊C8—612no—
163#102—614no—
164#102—614no—
165C22⋊C8—612no—
166C4×C8—611no—
167C4×C8C2×D6111yescharacteristic, complemented
168C24—1222no—
169#41—2444no—
170C2×Q8—1221no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—612no—
176C2×D4—1222no—
177C2×D4—1222no—
178C2×D4—1222no—
179C2×D4—1222no—
180C2×D4—1221no—
181C2×D4—1221no—
182C2×D4—2444no—
183C2×D4—2444no—
184C2×D4—2444no—
185C2×D4C22×D6112yes—
186C2×D4C22×D6112yes—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—1222no—
191D8—44no—
192D8—2444no—
193C2×C8—612no—
194C2×C8C22×D6112yes—
195C4⋊C4—612no—
196C4⋊C4—1221no—
197C22⋊C4—1222no—
198C22⋊C4—1222no—
199C42—611no—
200C42—611no—
201C42—611no—
202C42C22×D6111yescharacteristic
203C23—22no—
204C23—22no—
205C23—611no—
206C23—1222no—
207C23—2444no—
208C23—2444no—
209C23—2444no—
210Q8—2442no—
211D4—24no—
212D4—24no—
213D4—42no—
214D4—42no—
215D4—42no—
216D4—42no—
217D4—1224no—
218D4—2444no—
219D4—2444no—
220D4—2444no—
221D4—2444no—
222D4—2442no—
223D4—2442no—
224C2×C4—611no—
225C2×C4—614no—
226C2×C4—611no—
227C2×C4—611no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—2444no—
232C2×C4D4×D6111yescharacteristic
233C2×C4D4×D6111yescharacteristic
234C2×C4C23×D6111yescharacteristic
235C8—22no—
236C8—1222no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—612no—
244C22—1221no—
245C22—1221no—
246C22—4888no—
247C22—2442no—
248C22—2442no—
249C22—2442no—
250C22C2×D4×D6111yescharacteristic
251C4—612no—
252C4—1221no—
253C4—1221no—
254C4—2442no—
255C4D8×D6112yes—
256C4#1451980112yes—
257C4#1451982212yes—
258C2—82no—
259C2—82no—
260C2—1222no—
261C2—4882no—
262C2#1684032511yescharacteristic
263C2C2×D8×D6111yescharacteristic
264C2C2×#1451980111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#493C2
socleC22×C61C22×D4
hypercenter#493D61
hypocenterC61#3205
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #16840310C2semidirect
2. #127×D61C2semidirect
3. #16840138C2semidirect
4. #16840109C2semidirect
5. #16840108C2semidirect
6. #16839955C2semidirect
7. #16839894C2semidirect
8. #16839813C2semidirect
9. C61×#493C2semidirect
14. C2×#11758199C22semidirect
15. #14519777C22semidirect
24. D4×Dic61C22semidirect
26. #14519706C22semidirect
27. #14519699C22semidirect
28. #14519698C22semidirect
30. C4×#92418C22semidirect
31. C2×D8×C61C22semidirect
33. #127×C61C22semidirect
34. C4×C8×C61C22semidirect
100. C4×D61D8semidirect
136. #493D61semidirect
142. C61#3205semidirect
148. C2×D8C2×D61semidirect
155. #127C2×D61semidirect
167. C4×C8C2×D61semidirect