Finite Group Databasebeta

← #28399405

Subgroups — #28399405

Order 14464.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813649C211yesmaximal, characteristic
2#20299080C211yesmaximal, characteristic, complemented
3#20299070C211yesmaximal, characteristic, complemented
4#20298711C211yesmaximal, characteristic, complemented
5#20298707C211yesmaximal, characteristic, complemented
6#20298701C211yesmaximal, characteristic, complemented
7SD16×Dic113C211yesmaximal, characteristic, complemented
8C4×#14268634C211yesmaximal, characteristic, complemented
9#20298680C211yesmaximal, characteristic, complemented
10C4×#14268632C211yesmaximal, characteristic, complemented
11#20298639C211yesmaximal, characteristic, complemented
12#20298593C211yesmaximal, characteristic, complemented
13#102×D113C211yesmaximal, characteristic, complemented
14#20298555C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18#16813649C418yescomplemented
19C2×#14268634C2211yescharacteristic
20C2×D904C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22C2×#14268630C2211yescharacteristic
23C2×C8×D113C2211yescharacteristic
24Q8×Dic113C2211yescharacteristic, complemented
25C4×D452—21no—
26C4×D452C2211yescharacteristic
27C4×D452C2211yescharacteristic, complemented
28D4×Dic113C2211yescharacteristic
29#16813584—21no—
30#16813584C2211yescharacteristic
31#16813584C2211yescharacteristic, complemented
32C4×C22⋊D113—21no—
33#16813582—21no—
34#16813580C2211yescharacteristic
35#16813579—21no—
36#16813579C2211yescharacteristic
37C4⋊C4×D113—21no—
38C4⋊C4×D113C2211yescharacteristic
39C2×#14268624—21no—
40C22⋊C4×D113—21no—
41#16813555C2211yescharacteristic, complemented
42#16813554C2211yescharacteristic, complemented
43#16813553C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic, complemented
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—
61#14268648—22no—
62#14268648C2×C414yescomplemented
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67D4×D113—22no—
68D4×D113C2×C414yescomplemented
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77#14268634C2×C414yescomplemented
78D904C2×C414yescomplemented
79#14268632C2×C414yescomplemented
80#14268630C2×C414yescomplemented
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C8×D113—22no—
84C4⋊Dic113—21no—
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88#14268626D411yescharacteristic
89#14268626D411yescharacteristic
90C22⋊Dic113—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97#14268624D411yescharacteristic
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—21no—
116C22×D113—24no—
117C22×D113—81no—
118C22×D113—81no—
119C22×D113C2×D411yescharacteristic
120Q8×C113—21no—
121Q8×C113C22×C412yes—
122D4×C113—21no—
123D4×C113C22×C412yes—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—81no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—24no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—81no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138D452—24no—
139D452—21no—
140D452—21no—
141D452C22×C412yes—
142D452C22×C412yes—
143C4×D113—24no—
144C4×D113—81no—
145C4×D113—81no—
146C4×D113—81no—
147C4×D113—81no—
148C4×D113—81no—
149C4×D113C22×C412yes—
150C4×D113#4112yes—
151C8×C113—21no—
152C8×C113C22×C412yes—
153#11744751—21no—
154#11744751C22×C412yes—
155C22×C113—22no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—22no—
162C2×D113—22no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—84no—
168C2×D113C4×D412yes—
169C4×C113—22no—
170C4×C113—21no—
171C4×C113—21no—
172C4×C113—41no—
173C4×C113—41no—
174C4×C113C23×C411yescharacteristic
175C4×C113C2×#4111yescharacteristic
176Dic113—21no—
177Dic113—21no—
178Dic113—41no—
179Dic113—41no—
180Dic113C4×D412yes—
181C2×C113—42no—
182C2×C113C2×C4×D411yescharacteristic
183C2×C113#57611yescharacteristic
184C2×C113#57711yescharacteristic
185D113—22no—
186D113—42no—
187D113—42no—
188#2946—1131nomaximal, Sylow
189C113#294611yescharacteristic, complemented, Sylow
190C2×AGL(1,ℤ/8)—1131no—
191#520—1131no—
192#518—1131no—
193#442—1131no—
194#442—1131no—
195#440—1131no—
196#440D11311yescharacteristic, complemented
197C4×SD16—1131no—
198C4×SD16—1131no—
199C4×D8—1131no—
200C4×D8—1131no—
201#428—1131no—
202#416—1131no—
203C2×#102—1131no—
204#405—1131no—
205C2×#41—1131no—
206C22×D4—1131no—
207AGL(1,ℤ/8)—1138no—
208C2×SD16—1131no—
209C2×SD16C2×D11311yescharacteristic
210C2×D8—1131no—
211C2×D8—1131no—
212C2×M16—1131no—
213C22×C8—1131no—
214C4×Q8—1131no—
215C4×Q8C2×D11311yescharacteristic, complemented
216C4×D4—1131no—
217C4×D4—1131no—
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4—1131no—
221C4×D4—2261no—
222C4×D4—2261no—
223C4×D4—2261no—
224C4×D4—2261no—
225C4×D4C2×D11311yescharacteristic
226#117—1131no—
227#117—1131no—
228#117—2261no—
229C2×C4⋊C4—1131no—
230C2×C4⋊C4—2261no—
231C2×C22⋊C4—2261no—
232C2×C22⋊C4—2261no—
233#107—1131no—
234#107C2×D11311yescharacteristic, complemented
235#106—1131no—
236#106—1131no—
237#103—1131no—
238#103C2×D11311yescharacteristic, complemented
239#102—1131no—
240#102—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102C2×D11311yescharacteristic
245#97—1131no—
246#97C2×D11311yescharacteristic, complemented
247C4×C8—1131no—
248C4×C8—1131no—
249C24—2261no—
250#41—1134no—
251#41—2262no—
252C2×Q8C22×D11311yescharacteristic
253C2×D4—1134no—
254C2×D4—1131no—
255C2×D4—1131no—
256C2×D4—2261no—
257C2×D4—2262no—
258C2×D4—2261no—
259C2×D4C22×D11311yescharacteristic
260C22×C4—21no—
261C22×C4—1131no—
262C22×C4—2261no—
263C22×C4—2261no—
264C22×C4—2261no—
265C22×C4—2261no—
266C22×C4—2261no—
267C22×C4—2261no—
268C22×C4—2261no—
269SD16—1134no—
270SD16C4×D11314yescomplemented
271D8—1134no—
272D8—1134no—
273M16—1134no—
274C2×C8—1131no—
275C2×C8—1131no—
276C2×C8—2262no—
277C2×C8C22×D11311yescharacteristic
278C2×C8C22×D11311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—1131no—
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4C22×D11311yescharacteristic
287C4⋊C4C22×D11311yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—1131no—
290C22⋊C4—1131no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C42—21no—
298C42—1131no—
299C42—2261no—
300C42—2261no—
301C42C22×D11311yescharacteristic
302C23—21no—
303C23—1131no—
304C23—9041no—
305C23—9041no—
306C23—2264no—
307C23—2261no—
308C23—2261no—
309Q8—21no—
310Q8C2×C4×D11312yes—
311D4—21no—
312D4—1132no—
313D4—1132no—
314D4—2264no—
315D4—2264no—
316D4—2261no—
317D4—2261no—
318D4C2×C4×D11312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—1131no—
324C2×C4—1132no—
325C2×C4—1132no—
326C2×C4—1131no—
327C2×C4—1131no—
328C2×C4—9041no—
329C2×C4—9041no—
330C2×C4—9041no—
331C2×C4—9041no—
332C2×C4—9041no—
333C2×C4—9041no—
334C2×C4—2264no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4D4×D11311yescharacteristic
338C2×C4D4×D11311yescharacteristic
339C2×C4C23×D11311yescharacteristic
340C8—21no—
341C8—1132no—
342C8—2261no—
343C8C2×C4×D11312yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—1132no—
348C22—9044no—
349C22—4521no—
350C22—4521no—
351C22—4521no—
352C22—4521no—
353C22—2262no—
354C22—2262no—
355C22—2261no—
356C22—2261no—
357C22C2×D4×D11311yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—1132no—
364C4—4521no—
365C4—4521no—
366C4—2261no—
367C4—2261no—
368C4C22×C4×D11311yescharacteristic
369C4#41×D11311yescharacteristic
370C2—42no—
371C2—4522no—
372C2—4522no—
373C2—2262no—
374C2C4×D4×D11311yescharacteristic
375C2#2029940211yescharacteristic
376C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813649C2
cosocleC2×C4×C113C24
hypercenter#440D113
hypocenterC113#2946
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. #20299080C2semidirect
3. #20299070C2semidirect
4. #20298711C2semidirect
5. #20298707C2semidirect
6. #20298701C2semidirect
7. SD16×Dic113C2semidirect
8. C4×#14268634C2semidirect
9. #20298680C2semidirect
10. C4×#14268632C2semidirect
11. #20298639C2semidirect
12. #20298593C2semidirect
13. #102×D113C2semidirect
14. #20298555C2semidirect
15. #440×C113C2semidirect
18. #16813649C4semidirect
24. Q8×Dic113C22semidirect
27. C4×D452C22semidirect
31. #16813584C22semidirect
41. #16813555C22semidirect
42. #16813554C22semidirect
43. #16813553C22semidirect
44. #16813546C22semidirect
46. #16813544C22semidirect
49. #16813542C22semidirect
50. #16813532C22semidirect
51. C4×#11744751C22semidirect
52. C8×Dic113C22semidirect
54. C4×Q8×C113C22semidirect
56. #107×C113C22semidirect
57. #103×C113C22semidirect
59. #97×C113C22semidirect
62. #14268648C2×C4semidirect
68. D4×D113C2×C4semidirect
77. #14268634C2×C4semidirect
78. D904C2×C4semidirect
79. #14268632C2×C4semidirect
80. #14268630C2×C4semidirect
104. SD16×C113C2×C4semidirect
189. C113#2946semidirect
196. #440D113semidirect
215. C4×Q8C2×D113semidirect
234. #107C2×D113semidirect
238. #103C2×D113semidirect
246. #97C2×D113semidirect
270. SD16C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
#202990802
#202990702
#202987112
#202987072
#202987012
SD16×Dic1132
C4×#142686342
#202986802
C4×#142686322
#202986392
#202985932
#102×D1132
#202985552
#440×C1132
#2946113