Finite Group Databasebeta

← #28399430

Subgroups — #28399430

Order 14464.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D113C211yesmaximal, characteristic
2#20299074C211yesmaximal, characteristic, complemented
3#20299070C211yesmaximal, characteristic
4#20298700C211yesmaximal, characteristic, complemented
5#20298699C211yesmaximal, characteristic, complemented
6#20298697C211yesmaximal, characteristic, complemented
7#20298689C211yesmaximal, characteristic, complemented
8C4×#14268634C211yesmaximal, characteristic, complemented
9C4×#14268635C211yesmaximal, characteristic, complemented
10#20298683C211yesmaximal, characteristic, complemented
11#20298635C211yesmaximal, characteristic, complemented
12#20298605C211yesmaximal, characteristic, complemented
13#20298601C211yesmaximal, characteristic
14#20298555C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21SD16×D113C418yescomplemented
22C2×#14268630C2211yescharacteristic
23C2×C8×D113C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic, complemented
25C4×Dic226—21no—
26C4×Dic226C2211yescharacteristic, complemented
27#16813587—21no—
28#16813587C2211yescharacteristic, complemented
29C4×D452C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31#16813584C2211yescharacteristic
32C4×C22⋊D113—21no—
33#16813582—21no—
34#16813580—21no—
35#16813580C2211yescharacteristic
36#16813580C2211yescharacteristic
37#16813579—21no—
38#16813579C2211yescharacteristic
39C2×#14268624—21no—
40C22⋊C4×D113—21no—
41#16813556C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813553C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813545C2211yescharacteristic, complemented
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C4×#11744751C2211yescharacteristic, complemented
52C8×Dic113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic, complemented
55C4×D4×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic
59#97×C113C2211yescharacteristic, complemented
60C23×D113—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113C2×C414yescomplemented
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67D4×D113—22no—
68D4×D113C2×C414yes—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74#14268636C2×C414yescomplemented
75#14268635C2×C414yescomplemented
76#14268634C2×C414yescomplemented
77#14268630—22no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113C2×C414yescomplemented
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626D411yescharacteristic
87#14268626D411yescharacteristic
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C4×Dic113—21no—
99C4×Dic113—21no—
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104SD16×C113C2×C414yescomplemented
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C42×C113—21no—
112C42×C113C2311yescharacteristic
113C23×C113—21no—
114C22×D113—21no—
115C22×D113—24no—
116C22×D113—81no—
117C22×D113—81no—
118C22×D113C2×D411yescharacteristic
119Q8×C113—21no—
120Q8×C113C22×C412yes—
121D4×C113—21no—
122D4×C113C22×C412yes—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—81no—
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2411yescharacteristic
130C22⋊D113—24no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—81no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138D452—21no—
139D452C22×C412yes—
140C4×D113—24no—
141C4×D113—81no—
142C4×D113—81no—
143C4×D113C22×C412yes—
144C4×D113#4112yes—
145Dic226—21no—
146Dic226—24no—
147Dic226C22×C412yes—
148C8×C113—21no—
149C8×C113C22×C412yes—
150#11744751—21no—
151#11744751C22×C412yes—
152C22×C113—22no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113C22×D411yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—22no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—84no—
162C2×D113C4×D412yes—
163C4×C113—22no—
164C4×C113—21no—
165C4×C113—21no—
166C4×C113—41no—
167C4×C113—41no—
168C4×C113C23×C411yescharacteristic
169C4×C113C2×#4111yescharacteristic
170Dic113—22no—
171Dic113—21no—
172Dic113—21no—
173Dic113—41no—
174Dic113—41no—
175Dic113C4×D412yes—
176C2×C113—42no—
177C2×C113C2×C4×D411yescharacteristic
178C2×C113#57711yescharacteristic
179C2×C113#57711yescharacteristic
180D113—22no—
181D113—42no—
182#2949—1131nomaximal, Sylow
183C113#294911yescharacteristic, complemented, Sylow
184C22×SD16—1131no—
185#519—1131no—
186#518—1131no—
187#440—1131no—
188#440—1131no—
189#440—1131no—
190#440D11311yescharacteristic, complemented
191C4×SD16—1131no—
192C4×SD16—1131no—
193C4×SD16—1131no—
194C4×SD16—1131no—
195#427—1131no—
196#419—1131no—
197#418—1131no—
198#405—1131no—
199C22×Q8—1131no—
200C22×D4—1131no—
201C2×SD16—1131no—
202C2×SD16—1131no—
203C2×SD16—1138no—
204C2×SD16—1131no—
205C2×SD16C2×D11311yescharacteristic
206C2×M16—1131no—
207C22×C8—1131no—
208C4×Q8—1131no—
209C4×Q8—1131no—
210C4×Q8—1131no—
211C4×Q8—2261no—
212C4×Q8—2261no—
213C4×Q8C2×D11311yescharacteristic, complemented
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—1131no—
217C4×D4—2261no—
218C4×D4—2261no—
219C4×D4C2×D11311yescharacteristic
220#117—1131no—
221#117—1131no—
222#117—1131no—
223#117—2261no—
224#117—2261no—
225C2×C22⋊C4—2261no—
226C2×C22⋊C4—2261no—
227#107—1131no—
228#107C2×D11311yescharacteristic, complemented
229#106—1131no—
230#106—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103C2×D11311yescharacteristic, complemented
235#102—1131no—
236#102—1131no—
237#102—1131no—
238#102C2×D11311yescharacteristic
239#97—1131no—
240#97C2×D11311yescharacteristic, complemented
241C4×C8—1131no—
242C4×C8—1131no—
243C24—2261no—
244C2×Q8—1134no—
245C2×Q8—1131no—
246C2×Q8—2261no—
247C2×Q8—2262no—
248C2×Q8C22×D11311yescharacteristic
249C2×D4—1134no—
250C2×D4—1131no—
251C2×D4—2262no—
252C2×D4—2261no—
253C2×D4C22×D11311yescharacteristic
254C22×C4—21no—
255C22×C4—1131no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4—2261no—
259C22×C4—2261no—
260SD16—1134no—
261SD16—1134no—
262SD16—1134no—
263SD16C4×D11314yescomplemented
264M16—2262no—
265C2×C8—1131no—
266C2×C8—1134no—
267C2×C8—1131no—
268C2×C8C22×D11311yescharacteristic
269C2×C8C22×D11311yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—1131no—
272C4⋊C4—1131no—
273C4⋊C4—1131no—
274C4⋊C4—1131no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4C22×D11311yescharacteristic
279C4⋊C4C22×D11311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1131no—
282C22⋊C4—1131no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C42—21no—
289C42—1131no—
290C42—2261no—
291C42—2261no—
292C42—2261no—
293C42—2261no—
294C42—2261no—
295C42C22×D11311yescharacteristic
296C23—21no—
297C23—1131no—
298C23—9041no—
299C23—9041no—
300C23—2264no—
301C23—2261no—
302Q8—21no—
303Q8—1132no—
304Q8—2264no—
305Q8—2261no—
306Q8C2×C4×D11312yes—
307D4—21no—
308D4—1132no—
309D4—2264no—
310D4—2261no—
311D4C2×C4×D11312yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—1131no—
317C2×C4—1132no—
318C2×C4—1132no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—9041no—
322C2×C4—9041no—
323C2×C4—9041no—
324C2×C4—2264no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4D4×D11311yescharacteristic
329C2×C4D4×D11311yescharacteristic
330C2×C4C23×D11311yescharacteristic
331C8—21no—
332C8—1132no—
333C8—2261no—
334C8C2×C4×D11312yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—1132no—
339C22—9044no—
340C22—4521no—
341C22—4521no—
342C22—2262no—
343C22—2261no—
344C22—2261no—
345C22C2×D4×D11311yescharacteristic
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—1132no—
352C4—4521no—
353C4—4521no—
354C4—2262no—
355C4—2261no—
356C4—2261no—
357C4C22×C4×D11311yescharacteristic
358C4#41×D11311yescharacteristic
359C2—42no—
360C2—4522no—
361C2—2262no—
362C2C4×D4×D11311yescharacteristic
363C2#2029940711yescharacteristic
364C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
cosocleC2×C4×C113C24
hypercenter#440D113
hypocenterC113#2949
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #20299074C2semidirect
4. #20298700C2semidirect
5. #20298699C2semidirect
6. #20298697C2semidirect
7. #20298689C2semidirect
8. C4×#14268634C2semidirect
9. C4×#14268635C2semidirect
10. #20298683C2semidirect
11. #20298635C2semidirect
12. #20298605C2semidirect
14. #20298555C2semidirect
15. #440×C113C2semidirect
21. SD16×D113C4semidirect
24. Q8×Dic113C22semidirect
26. C4×Dic226C22semidirect
28. #16813587C22semidirect
41. #16813556C22semidirect
42. #16813553C22semidirect
43. #16813553C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813545C22semidirect
50. #16813532C22semidirect
51. C4×#11744751C22semidirect
52. C8×Dic113C22semidirect
54. C4×Q8×C113C22semidirect
56. #107×C113C22semidirect
57. #103×C113C22semidirect
59. #97×C113C22semidirect
64. Q8×D113C2×C4semidirect
74. #14268636C2×C4semidirect
75. #14268635C2×C4semidirect
76. #14268634C2×C4semidirect
80. C8×D113C2×C4semidirect
104. SD16×C113C2×C4semidirect
183. C113#2949semidirect
190. #440D113semidirect
213. C4×Q8C2×D113semidirect
228. #107C2×D113semidirect
234. #103C2×D113semidirect
240. #97C2×D113semidirect
263. SD16C4×D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×SD16×D1132
#202990742
#202990702
#202987002
#202986992
#202986972
#202986892
C4×#142686342
C4×#142686352
#202986832
#202986352
#202986052
#202986012
#202985552
#440×C1132
#2949113