Finite Group Databasebeta

← #21455738

Subgroups — #21455738

Order 7808.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840272C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3#16840099C212yesmaximal, complemented
4#16840093C211yesmaximal, characteristic, complemented
5#16840092C211yesmaximal, characteristic, complemented
6#16840079C212yesmaximal, complemented
7#16840073C211yesmaximal, characteristic, complemented
8#16839803C212yesmaximal, complemented
9#16839760C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#480C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C22×C4×D61—21no—
14C22×C4×D61C2211yescharacteristic
15C2×#11758189C2212yes—
16#14519759—21no—
17#14519757C2211yescharacteristic
18#14519756C2211yescharacteristic
19#14519748C2211yescharacteristic
20#14519745—21no—
21D4×Dic61—21no—
22#14519737—21no—
23#14519735C2211yescharacteristic
24C2×C4⋊Dic61C2211yescharacteristic
25C2×#11758196—21no—
26C4⋊C4×D61—21no—
27C4⋊C4×D61—21no—
28C4⋊C4×D61C2212yes—
29C4⋊C4×D61C2212yes—
30#14519710C2212yescomplemented
31#14519709C2212yescomplemented
32#14519708C2212yescomplemented
33#14519702C2212yescomplemented
34#14519700C2212yescomplemented
35#14519698C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yes—
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yescomplemented
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61D411yescharacteristic
44C2×D4×C61—21no—
45C2×D4×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—21no—
49C2×C22⋊D61—21no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61D411yescharacteristic
53#11758224—24no—
54C2×C4×D61—24no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—44no—
58C2×C4×D61D411yescharacteristic
59C2×C4×D61D411yescharacteristic
60C2×C4×D61C2311yescharacteristic
61C2×C4×D61C2311yescharacteristic
62C2×Dic122C2311yescharacteristic
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C22⋊Dic61—21no—
69C22⋊Dic61—21no—
70#11758198—21no—
71#11758198—21no—
72C4⋊Dic61—21no—
73C4⋊Dic61—21no—
74C4⋊Dic61C2312yes—
75C4⋊Dic61C2311yescharacteristic
76#11758196—21no—
77#11758196—22no—
78#11758196—22no—
79C4×Dic61—21no—
80C2×#92418C2312yes—
81#11758189—24no—
82C23×C61—21no—
83C23×C61C2×D411yescharacteristic
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61C2×D411yescharacteristic
88C22×D61C2×D411yescharacteristic
89D4×C61—22no—
90D4×C61—42no—
91C2×C4×C61—22no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61—42no—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2411yescharacteristic
97C22⋊D61—42no—
98C22⋊D61—42no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61C2×D411yescharacteristic
106C2×Dic61C2×D411yescharacteristic
107C4×D61—22no—
108C4×D61—22no—
109C4×D61—22no—
110C4×D61—44no—
111C4×D61—44no—
112C4×D61#4114yes—
113Dic122—22no—
114C8×C61—22no—
115#92418—22no—
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61AGL(1,ℤ/8)12yes—
122C22×C61C22×D411yescharacteristic
123C2×D61—28no—
124C2×D61—21no—
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—21no—
128C2×D61#12312yes—
129C2×D61#13712yes—
130C4×C61—21no—
131C4×C61—42no—
132C4×C61—41no—
133C4×C61C2×#4112yes—
134Dic61—21no—
135Dic61—41no—
136Dic61—42no—
137Dic61—41no—
138Dic61#12312yes—
139#3092—611nomaximal, Sylow
140C2×C61—22no—
141C2×C61—81no—
142C2×C61C2×#12311yescharacteristic
143C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
144C2×C61C2×#13711yescharacteristic
145D61—22no—
146D61—22no—
147#525—611no—
148C22×C4⋊C4—611no—
149#484—612no—
150#483—611no—
151#483—611no—
152#481—612no—
153#480—611no—
154#480D6111yescharacteristic, complemented
155#428—612no—
156#417—612no—
157#407—611no—
158C61#309211yescharacteristic, complemented, Sylow
159C2×#41—611no—
160C23×C4—611no—
161C23×C4—1221no—
162C2×M16—612no—
163#123—1221no—
164C22⋊Q8—611no—
165C22⋊Q8—611no—
166#121—611no—
167#121C2×D6111yescharacteristic
168#120—1221no—
169C4×D4—1221no—
170C4×D4—1221no—
171#117—611no—
172C2×C4⋊C4—611no—
173C2×C4⋊C4—612no—
174C2×C4⋊C4—612no—
175C2×C4⋊C4—1221no—
176C2×C4⋊C4—1221no—
177C2×C4⋊C4—1221no—
178C2×C4⋊C4C2×D6111yescharacteristic
179#107—612no—
180#107C2×D6112yescomplemented
181#106—612no—
182#106—612no—
183#103—612no—
184#103—612no—
185#102—612no—
186#102C2×D6112yescomplemented
187C22⋊C8—611no—
188C22⋊C8—612no—
189C22⋊C8C2×D6111yescharacteristic
190C24—611no—
191#41—1224no—
192C2×Q8—611no—
193C2×D4—21no—
194C2×D4—1221no—
195C2×D4—1221no—
196C2×D4C22×D6111yescharacteristic
197C22×C4—21no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—1224no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4—1221no—
207C22×C4—1221no—
208C22×C4—2444no—
209C22×C4C22×D6111yescharacteristic
210M16—1224no—
211C2×C8—612no—
212C2×C8C22×D6112yes—
213C4⋊C4—21no—
214C4⋊C4—612no—
215C4⋊C4—611no—
216C4⋊C4—1222no—
217C4⋊C4—1222no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4C22×D6112yes—
222C4⋊C4C22×D6111yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—1221no—
225C22⋊C4—1221no—
226C22⋊C4—1221no—
227C22⋊C4—1221no—
228C42—1221no—
229C23—21no—
230C23—611no—
231C23—611no—
232C23—1222no—
233C23—1222no—
234C23—1222no—
235C23D4×D6111yescharacteristic
236Q8—1222no—
237D4—22no—
238D4—42no—
239D4—2442no—
240D4—2442no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—42no—
245C2×C4—611no—
246C2×C4—614no—
247C2×C4—611no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1222no—
255C2×C4—2444no—
256C2×C4—2444no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4D4×D6111yescharacteristic
260C2×C4C23×D6111yescharacteristic
261C8—22no—
262C8—1222no—
263C22—21no—
264C22—21no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—612no—
269C22—612no—
270C22—1228no—
271C22—1221no—
272C22—1221no—
273C22—1221no—
274C22—1221no—
275C22#1451980112yes—
276C22C2×D4×D6111yescharacteristic
277C4—21no—
278C4—42no—
279C4—41no—
280C4—612no—
281C4—1221no—
282C4—2441no—
283C4—2442no—
284C4—2441no—
285C4#41×D6112yes—
286C2—22no—
287C2—81no—
288C2—1222no—
289C2—1222no—
290C2#123×D6111yescharacteristic
291C2C2×#1451980111yescharacteristic
292C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3092
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D61C2semidirect
3. #16840099C2semidirect
4. #16840093C2semidirect
5. #16840092C2semidirect
6. #16840079C2semidirect
7. #16840073C2semidirect
8. #16839803C2semidirect
9. #16839760C2semidirect
10. #16839724C2semidirect
11. C61×#480C2semidirect
30. #14519710C22semidirect
31. #14519709C22semidirect
32. #14519708C22semidirect
33. #14519702C22semidirect
34. #14519700C22semidirect
35. #14519698C22semidirect
40. #107×C61C22semidirect
41. #102×C61C22semidirect
154. #480D61semidirect
158. C61#3092semidirect
180. #107C2×D61semidirect
186. #102C2×D61semidirect