Finite Group Databasebeta

← #28401337

Subgroups — #28401337

Order 14464.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299105C211yesmaximal, characteristic, complemented
2#121×D113C211yesmaximal, characteristic, complemented
3#20298932C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298919C211yesmaximal, characteristic, complemented
6#20298915C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic, complemented
8#20298831C211yesmaximal, characteristic, complemented
9#20298830C211yesmaximal, characteristic, complemented
10#20298824C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298743C211yesmaximal, characteristic, complemented
13#20298730C211yesmaximal, characteristic, complemented
14C22⋊C8×D113C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113—21no—
17C2×D4×D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C2×#14268634C2211yescharacteristic, complemented
20C2×#14268632C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic, complemented
22C2×C8×D113C2211yescharacteristic, complemented
23#16813603—21no—
24#16813598C2211yescharacteristic
25#16813598C2211yescharacteristic, complemented
26#16813597C2211yescharacteristic
27#16813596C2211yescharacteristic
28#16813595—21no—
29#16813594—21no—
30#16813593C2211yescharacteristic
31#16813593C2211yescharacteristic
32#16813593C2211yescharacteristic, complemented
33#16813590—21no—
34C4×C22⋊D113—21no—
35C4×C22⋊D113—21no—
36#16813581C2211yescharacteristic, complemented
37C4⋊C4×D113C2211yescharacteristic
38C22⋊C4×D113—21no—
39#16813556C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic, complemented
55#121×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113D411yescharacteristic
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68D4×D113—41no—
69D4×D113—41no—
70D4×D113—44no—
71C22×Dic113D411yescharacteristic
72C2×C4×D113—21no—
73C2×C4×D113—41no—
74C2×C4×D113—41no—
75C2×C4×D113D411yescharacteristic
76C2×C4×D113D411yescharacteristic
77C2×C4×D113C2311yescharacteristic
78C2×C4×D113C2311yescharacteristic
79#14268634—41no—
80#14268632—41no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C8×D113—41no—
84C8×D113—41no—
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99C4×Dic113—21no—
100#41×C113—41no—
101#41×C113—41no—
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113—21no—
104C2×D4×C113—21no—
105C2×D4×C113C2311yescharacteristic
106C2×D4×C113C2311yescharacteristic
107C22×C4×C113—21no—
108C22×C4×C113C2311yescharacteristic
109SD16×C113—41no—
110D8×C113—41no—
111C2×C8×C113C2311yescharacteristic
112C2×C8×C113C2311yescharacteristic
113C4⋊C4×C113C2311yescharacteristic
114C22⋊C4×C113—21no—
115C23×C113—21no—
116C23×C113—21no—
117C23×C113C2×D411yescharacteristic
118C22×D113—22no—
119C22×D113—22no—
120C22×D113—21no—
121C22×D113—41no—
122C22×D113—42no—
123C22×D113—42no—
124C22×D113—42no—
125C22×D113C2×D411yescharacteristic
126C22×D113C2×D411yescharacteristic
127Q8×C113—21no—
128Q8×C113—21no—
129D4×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—21no—
133D4×C113—42no—
134D4×C113—42no—
135C2×C4×C113—21no—
136C2×C4×C113—21no—
137C2×C4×C113—21no—
138C2×C4×C113—21no—
139C2×C4×C113—42no—
140C2×C4×C113C2×D411yescharacteristic
141C2×C4×C113C2411yescharacteristic
142C22⋊D113—42no—
143C22⋊D113—42no—
144C22⋊D113—42no—
145C22⋊D113—42no—
146C22⋊D113—42no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150C2×Dic113—41no—
151C2×Dic113C2×D411yescharacteristic
152C2×Dic113C2×D411yescharacteristic
153D452—21no—
154D452—21no—
155D452—42no—
156C4×D113—21no—
157C4×D113—21no—
158C4×D113—21no—
159C4×D113—21no—
160C4×D113—41no—
161C4×D113—41no—
162C4×D113—42no—
163C8×C113—21no—
164C8×C113—21no—
165#11744751—21no—
166#11744751—21no—
167C22×C113—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113C22×D411yescharacteristic
177C2×D113—21no—
178C2×D113—21no—
179C2×D113—21no—
180C2×D113—21no—
181C2×D113—44no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—84no—
186C2×D113#13512yes—
187C2×D113AGL(1,ℤ/8)12yes—
188C4×C113—21no—
189C4×C113—41no—
190C4×C113—41no—
191C4×C113H(5,𝔽2)11yescharacteristic
192C4×C113H(5,𝔽2)11yescharacteristic
193Dic113—21no—
194Dic113—21no—
195Dic113—41no—
196Dic113—41no—
197Dic113—41no—
198C2×C113—41no—
199C2×C113—81no—
200C2×C113—81no—
201C2×C113#53411yescharacteristic
202C2×C113C2×#13511yescharacteristic
203C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
204D113—22no—
205D113—22no—
206D113—81no—
207#3188—1131nomaximal, Sylow
208C113#318811yescharacteristic, complemented, Sylow
209#525—1131no—
210C2×#121—1131no—
211#484—1131no—
212#482—1131no—
213#482—1131no—
214#481—1131no—
215#466—1131no—
216#466—1131no—
217#465—1131no—
218#465—1131no—
219#450—1131no—
220#449—1131no—
221#449D11311yescharacteristic, complemented
222#447—1131no—
223C2×C22⋊C8—1131no—
224C2×#41C2×D11311yescharacteristic, complemented
225C22×D4—1131no—
226C22×D4—2261no—
227C23×C4—1131no—
228C2×SD16—1131no—
229C2×SD16C2×D11311yescharacteristic, complemented
230C2×D8—1131no—
231C2×D8C2×D11311yescharacteristic, complemented
232C22×C8—1131no—
233C22×C8—1131no—
234#123—2261no—
235C22⋊Q8—1131no—
236C22⋊Q8—1131no—
237#121—1131no—
238#121—1131no—
239#121—1131no—
240#121—1131no—
241#121—1131no—
242#121—2261no—
243#121—2261no—
244#121C2×D11311yescharacteristic
245#120—2261no—
246C4×D4—2261no—
247C4×D4—2261no—
248#117—1131no—
249C2×C4⋊C4—1131no—
250C2×C22⋊C4—2261no—
251#107—1131no—
252#107—1131no—
253#106—1131no—
254#106—1131no—
255#103—1131no—
256#103C2×D11311yescharacteristic, complemented
257#102—1131no—
258#102—1131no—
259#102—1131no—
260#102—1131no—
261#102—1131no—
262#102C2×D11311yescharacteristic, complemented
263C22⋊C8—1131no—
264C22⋊C8—1131no—
265C22⋊C8—1131no—
266C22⋊C8C2×D11311yescharacteristic, complemented
267C24—1131no—
268C24—2261no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D11311yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—1131no—
275C2×D4—4524no—
276C2×D4—4521no—
277C2×D4—4521no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4—2261no—
283C2×D4—2261no—
284C2×D4C22×D11311yescharacteristic
285C2×D4C22×D11311yescharacteristic
286C22×C4—21no—
287C22×C4—1131no—
288C22×C4—1131no—
289C22×C4—1131no—
290C22×C4—1131no—
291C22×C4—1131no—
292C22×C4—4521no—
293C22×C4—4521no—
294C22×C4—2261no—
295C22×C4C22×D11311yescharacteristic
296SD16—41no—
297SD16—4521no—
298D8—41no—
299D8—4521no—
300C2×C8—1131no—
301C2×C8—1131no—
302C2×C8—4521no—
303C2×C8—4521no—
304C2×C8C22×D11311yescharacteristic
305C2×C8C22×D11311yescharacteristic
306C4⋊C4—1131no—
307C4⋊C4—1131no—
308C4⋊C4—1131no—
309C4⋊C4—2261no—
310C4⋊C4—2261no—
311C4⋊C4—2261no—
312C4⋊C4C22×D11311yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C22⋊C4—2261no—
319C22⋊C4—2261no—
320C22⋊C4—2261no—
321C22⋊C4—2261no—
322C42—2261no—
323C23—21no—
324C23—21no—
325C23—1131no—
326C23—1131no—
327C23—4521no—
328C23—4522no—
329C23—4522no—
330C23—4522no—
331C23—2262no—
332C23—2262no—
333C23—2261no—
334C23D4×D11311yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—4522no—
344D4—4522no—
345D4—4522no—
346D4—4522no—
347D4—4522no—
348D4—4522no—
349D4—2261no—
350D4—2261no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—1131no—
357C2×C4—1131no—
358C2×C4—4521no—
359C2×C4—4521no—
360C2×C4—4522no—
361C2×C4—4521no—
362C2×C4—2261no—
363C2×C4—2261no—
364C2×C4—2261no—
365C2×C4—2261no—
366C2×C4—2261no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4D4×D11311yescharacteristic
370C2×C4C23×D11311yescharacteristic
371C8—21no—
372C8—21no—
373C8—2261no—
374C8—2261no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—1132no—
385C22—1132no—
386C22—9044no—
387C22—4524no—
388C22—4521no—
389C22—4521no—
390C22—4521no—
391C22—2261no—
392C22—2261no—
393C22—2261no—
394C22—2261no—
395C22C2×D4×D11311yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—4521no—
400C4—4521no—
401C4—4521no—
402C4—2261no—
403C4—2261no—
404C4#1681366711yescharacteristic
405C4#1681366711yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—9041no—
410C2—2262no—
411C2—2262no—
412C2#2029915811yescharacteristic
413C2#135×D11311yescharacteristic
414C2AGL(1,ℤ/8)×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3188
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20299105C2semidirect
2. #121×D113C2semidirect
3. #20298932C2semidirect
4. #20298923C2semidirect
5. #20298919C2semidirect
6. #20298915C2semidirect
7. #20298833C2semidirect
8. #20298831C2semidirect
9. #20298830C2semidirect
10. #20298824C2semidirect
11. #20298747C2semidirect
12. #20298743C2semidirect
13. #20298730C2semidirect
14. C22⋊C8×D113C2semidirect
15. #449×C113C2semidirect
19. C2×#14268634C22semidirect
20. C2×#14268632C22semidirect
21. C2×C8×D113C22semidirect
22. C2×C8×D113C22semidirect
25. #16813598C22semidirect
32. #16813593C22semidirect
36. #16813581C22semidirect
39. #16813556C22semidirect
40. #16813555C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
43. #16813546C22semidirect
44. #16813544C22semidirect
45. #16813544C22semidirect
46. #16813543C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
49. C22⋊#11744751C22semidirect
52. C2×#41×C113C22semidirect
53. C2×SD16×C113C22semidirect
54. C2×D8×C113C22semidirect
56. #103×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
208. C113#3188semidirect
221. #449D113semidirect
224. C2×#41C2×D113semidirect
229. C2×SD16C2×D113semidirect
231. C2×D8C2×D113semidirect
256. #103C2×D113semidirect
262. #102C2×D113semidirect
266. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991052
#121×D1132
#202989322
#202989232
#202989192
#202989152
#202988332
#202988312
#202988302
#202988242
#202987472
#202987432
#202987302
C22⋊C8×D1132
#449×C1132
#3188113