Finite Group Databasebeta

← #21455280

Subgroups — #21455280

Order 7808.

548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14519803C211yesmaximal, characteristic, complemented
2#16840308C211yesmaximal, characteristic, complemented
3C2×D4×Dic61C211yesmaximal, characteristic, complemented
4#16839979C212yesmaximal, complemented
5#16839975C212yesmaximal, complemented
6#16839965C212yesmaximal, complemented
7#16839955C212yesmaximal, complemented
8#16839785C211yesmaximal, characteristic, complemented
9#16839764C211yesmaximal, characteristic, complemented
10#16839763C211yesmaximal, characteristic, complemented
11C2×AGL(1,ℤ/8)×C61C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C23×Dic61—21no—
14#14519803—24no—
15C2×#11758200C2212yes—
16C2×#11758199C2212yes—
17C2×#11758194C2211yescharacteristic
18#14519775C2211yescharacteristic, complemented
19#14519773C2211yescharacteristic, complemented
20#14519766C2211yescharacteristic, complemented
21#14519764C2211yescharacteristic, complemented
22#14519749—21no—
23#14519749—21no—
24D4×Dic61—21no—
25D4×Dic61—21no—
26D4×Dic61C2212yes—
27D4×Dic61C2212yes—
28C4×C22⋊D61—21no—
29C4×C22⋊D61—21no—
30C2×C4⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61—21no—
32C2×C4×Dic61C2211yescharacteristic
33#14519706C2212yescomplemented
34#14519706C2212yescomplemented
35#14519702C2212yescomplemented
36#14519701C2212yescomplemented
37#14519699C2212yescomplemented
38#14519698C2212yescomplemented
39C2×#41×C61C2211yescharacteristic
40C22×D4×C61C2211yescharacteristic
41AGL(1,ℤ/8)×C61—24no—
42C2×SD16×C61C2212yes—
43C2×D8×C61C2212yes—
44C2×M16×C61C2211yescharacteristic
45C24×C61—21no—
46#41×C61—22no—
47#41×C61—22no—
48C2×Q8×C61C2311yescharacteristic
49C2×D4×C61—21no—
50C2×D4×C61—21no—
51C2×D4×C61—22no—
52C2×D4×C61D414yescomplemented
53C2×D4×C61C2311yescharacteristic
54C2×D4×C61C2312yes—
55C22×C4×C61—21no—
56C22×C4×C61C2311yescharacteristic
57C2×C22⋊D61—21no—
58C2×C22⋊D61—21no—
59C2×C22⋊D61—21no—
60C22×Dic61—21no—
61C22×Dic61—22no—
62C22×Dic61—22no—
63C22×Dic61—44no—
64C22×Dic61D411yescharacteristic
65C22×Dic61D411yescharacteristic
66#11758222—22no—
67#11758222—22no—
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×Dic122C2311yescharacteristic
71SD16×C61—24no—
72D8×C61—24no—
73M16×C61—22no—
74C2×C8×C61C2312yes—
75C22⋊Dic61—22no—
76C22⋊Dic61—22no—
77C22⋊Dic61—21no—
78C22⋊Dic61—21no—
79#11758200—24no—
80#11758199—24no—
81#11758198—21no—
82#11758198—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61C2312yes—
85#11758196—21no—
86#11758196—21no—
87C4×Dic61D411yescharacteristic
88C4×Dic61D411yescharacteristic
89C4×Dic61C2311yescharacteristic
90C4×Dic61C2311yescharacteristic
91#11758194—22no—
92C2×#92418C2312yes—
93C23×C61—24no—
94C23×C61—22no—
95C23×C61—21no—
96C23×C61—42no—
97C23×C61—42no—
98C23×C61C2×D411yescharacteristic
99C22×D61—21no—
100Q8×C61—21no—
101Q8×C61—21no—
102D4×C61—24no—
103D4×C61—21no—
104D4×C61—22no—
105D4×C61—21no—
106D4×C61—42no—
107D4×C61C2×D414yes—
108C2×C4×C61—21no—
109C2×C4×C61—42no—
110C2×C4×C61C2×D411yescharacteristic
111C2×C4×C61C2×D412yes—
112C2×C4×C61#4112yes—
113C2×C4×C61C2411yescharacteristic
114C22⋊D61—42no—
115C22⋊D61—42no—
116C22⋊D61—42no—
117C2×Dic61—22no—
118C2×Dic61—21no—
119C2×Dic61—22no—
120C2×Dic61—41no—
121C2×Dic61—44no—
122C2×Dic61—42no—
123C2×Dic61—44no—
124C2×Dic61C2×D411yescharacteristic
125C2×Dic61C2×D411yescharacteristic
126C2×Dic61C2×D411yescharacteristic
127C2×Dic61C2×D411yescharacteristic
128D244—21no—
129D244—21no—
130C4×D61—42no—
131Dic122—21no—
132Dic122—21no—
133C8×C61—22no—
134#92418—22no—
135C22×C61—21no—
136C22×C61—21no—
137C22×C61—24no—
138C22×C61—48no—
139C22×C61—42no—
140C22×C61—42no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—41no—
144C22×C61#12112yes—
145C22×C61C22×D411yescharacteristic
146C2×D61—41no—
147C2×D61—41no—
148C2×D61—41no—
149C4×C61—41no—
150C4×C61#12112yes—
151C4×C61C22×D411yescharacteristic
152C4×C61C2×#4111yescharacteristic
153Dic61—21no—
154Dic61—21no—
155Dic61—21no—
156Dic61—41no—
157Dic61—42no—
158Dic61AGL(1,ℤ/8)12yescomplemented
159#3036—611nomaximal, Sylow
160C2×C61—22no—
161C2×C61—44no—
162C2×C61—81no—
163C2×C61C2×#12111yescharacteristic
164C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
165C2×C61#57511yescharacteristic
166D61—81no—
167C2×AGL(1,ℤ/8)—611no—
168C2×AGL(1,ℤ/8)D6111yescharacteristic, complemented
169#532—611no—
170C2×C4×D4—611no—
171#463—612no—
172#463—612no—
173#461—612no—
174#459—612no—
175#423—611no—
176#417—611no—
177#417—611no—
178C61#303611yescharacteristic, complemented, Sylow
179C2×#41—611no—
180C2×#41C2×D6111yescharacteristic
181C22×D4C2×D6111yescharacteristic
182C23×C4—1221no—
183AGL(1,ℤ/8)—24no—
184AGL(1,ℤ/8)—1224no—
185C2×SD16—612no—
186C2×SD16C2×D6112yes—
187C2×D8—612no—
188C2×D8C2×D6112yes—
189C2×M16—611no—
190C2×M16C2×D6111yescharacteristic
191C4⋊Q8—611no—
192#127—611no—
193#124—611no—
194#124—611no—
195#121—1221no—
196#121—1221no—
197C4×D4—612no—
198C4×D4—612no—
199C4×D4—1221no—
200C4×D4—1221no—
201C4×D4—1221no—
202C4×D4—1221no—
203C2×C4⋊C4—611no—
204C2×C22⋊C4—1221no—
205C2×C42—611no—
206C4⋊C8—612no—
207C4⋊C8—612no—
208#103—612no—
209#103—612no—
210#102—612no—
211#102—612no—
212C24—21no—
213#41—22no—
214#41—22no—
215#41—1222no—
216#41—1222no—
217C2×Q8—611no—
218C2×Q8C22×D6111yescharacteristic
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—22no—
222C2×D4—611no—
223C2×D4—1221no—
224C2×D4—1221no—
225C2×D4—1221no—
226C2×D4C22⋊D6114yescomplemented
227C2×D4C22×D6111yescharacteristic
228C2×D4C22×D6112yes—
229C22×C4—21no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—1222no—
233C22×C4—1222no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—2444no—
237C22×C4C22×D6111yescharacteristic
238SD16—24no—
239SD16—1224no—
240D8—24no—
241D8—1224no—
242M16—22no—
243M16—1222no—
244C2×C8—612no—
245C2×C8C22×D6112yes—
246C4⋊C4—612no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C22⋊C4—1221no—
251C22⋊C4—1221no—
252C22⋊C4—1222no—
253C22⋊C4—1222no—
254C22⋊C4—1221no—
255C22⋊C4—1221no—
256C42—611no—
257C42—611no—
258C42—611no—
259C42—611no—
260C23—22no—
261C23—24no—
262C23—21no—
263C23—42no—
264C23—42no—
265C23—1221no—
266C23D4×D6111yescharacteristic
267Q8—21no—
268Q8—21no—
269Q8—1221no—
270Q8—1221no—
271D4—21no—
272D4—22no—
273D4—21no—
274D4—24no—
275D4—42no—
276D4—1221no—
277D4—1221no—
278D4—2442no—
279D4—2442no—
280D4—2442no—
281D4C2×C22⋊D6114yes—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—611no—
287C2×C4—611no—
288C2×C4—1222no—
289C2×C4—1222no—
290C2×C4—1221no—
291C2×C4—2444no—
292C2×C4—2441no—
293C2×C4—2444no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4D4×D6111yescharacteristic
297C2×C4#1175822412yes—
298C2×C4C2×C22⋊D6112yes—
299C2×C4C23×D6111yescharacteristic
300C8—22no—
301C8—1222no—
302C22—21no—
303C22—21no—
304C22—24no—
305C22—48no—
306C22—42no—
307C22—42no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22—2441no—
312C22—2441no—
313C22—2441no—
314C22#1451974912yes—
315C22C2×D4×D6111yescharacteristic
316C4—41no—
317C4—612no—
318C4—1221no—
319C4—1221no—
320C4—1221no—
321C4—2441no—
322C4—2442no—
323C4#1451974912yes—
324C4C22×C22⋊D6111yescharacteristic
325C4C2×#1175822411yescharacteristic
326C2—22no—
327C2—44no—
328C2—81no—
329C2—4881no—
330C2C2×#1451974911yescharacteristic
331C2AGL(1,ℤ/8)×D6111yescharacteristic
332C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×AGL(1,ℤ/8)×C61C2
socleC22×C61C22×D4
hypercenterC2×AGL(1,ℤ/8)D61
hypocenterC61#3036
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14519803C2semidirect
2. #16840308C2semidirect
3. C2×D4×Dic61C2semidirect
4. #16839979C2semidirect
5. #16839975C2semidirect
6. #16839965C2semidirect
7. #16839955C2semidirect
8. #16839785C2semidirect
9. #16839764C2semidirect
10. #16839763C2semidirect
11. C2×AGL(1,ℤ/8)×C61C2semidirect
18. #14519775C22semidirect
19. #14519773C22semidirect
20. #14519766C22semidirect
21. #14519764C22semidirect
33. #14519706C22semidirect
34. #14519706C22semidirect
35. #14519702C22semidirect
36. #14519701C22semidirect
37. #14519699C22semidirect
38. #14519698C22semidirect
52. C2×D4×C61D4semidirect
158. Dic61AGL(1,ℤ/8)semidirect
168. C2×AGL(1,ℤ/8)D61semidirect
178. C61#3036semidirect
226. C2×D4C22⋊D61semidirect