Finite Group Databasebeta

← #28402417

Subgroups — #28402417

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299295C211yesmaximal, characteristic, complemented
2#20299236C211yesmaximal, characteristic, complemented
3#20298954C211yesmaximal, characteristic, complemented
4#20298932C211yesmaximal, characteristic, complemented
5#20298923C211yesmaximal, characteristic, complemented
6#20298900C211yesmaximal, characteristic, complemented
7#20298832C211yesmaximal, characteristic, complemented
8#20298824C211yesmaximal, characteristic, complemented
9#20298815C211yesmaximal, characteristic, complemented
10#20298730C211yesmaximal, characteristic, complemented
11D8×Dic113C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13#20298594C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C2×#14268632C2211yescharacteristic
18C22×#11744751C2211yescharacteristic, complemented
19C2×C8×D113C2211yescharacteristic
20#16813615—21no—
21#16813613C2211yescharacteristic, complemented
22#16813611C2211yescharacteristic
23#16813605—21no—
24#16813603—21no—
25#16813598C2211yescharacteristic
26#16813596C2211yescharacteristic
27#16813594—21no—
28#16813593—21no—
29#16813593C2211yescharacteristic
30#16813590—21no—
31D4×Dic113C2211yescharacteristic
32D4×Dic113C2211yescharacteristic, complemented
33C4×C22⋊D113C2211yescharacteristic
34#16813582—21no—
35#16813581C2211yescharacteristic, complemented
36C4⋊C4×D113C2211yescharacteristic
37C2×#14268624—21no—
38#16813556C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic, complemented
52C2×#41×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64C2×C22⋊D113D411yescharacteristic
65D4×D113—22no—
66D4×D113—41no—
67C22×Dic113—21no—
68C22×Dic113—21no—
69C2×C4×D113—21no—
70C2×C4×D113C2311yescharacteristic
71#14268632—41no—
72C2×#11744751—41no—
73C2×#11744751C2311yescharacteristic
74C2×#11744751C2311yescharacteristic
75C8×D113—41no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80#14268626—21no—
81#14268626—21no—
82#14268626—21no—
83#14268626D411yescharacteristic
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113D411yescharacteristic
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96#41×C113—22no—
97#41×C113—41no—
98C2×Q8×C113C2311yescharacteristic
99C2×D4×C113—21no—
100C2×D4×C113—21no—
101C2×D4×C113C2311yescharacteristic
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104C22×C4×C113C2311yescharacteristic
105SD16×C113—41no—
106D8×C113—22no—
107C2×C8×C113C2311yescharacteristic
108C2×C8×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C23×C113—21no—
112C23×C113—21no—
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113—81no—
118C22×D113C2×D411yescharacteristic
119Q8×C113—21no—
120Q8×C113—21no—
121D4×C113—21no—
122D4×C113—21no—
123D4×C113—21no—
124D4×C113—42no—
125D4×C113—81no—
126D4×C113#4112yes—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—42no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—22no—
135C22⋊D113—42no—
136C22⋊D113—42no—
137C22⋊D113—81no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—81no—
142C2×Dic113—81no—
143C2×Dic113C2×D411yescharacteristic
144C2×Dic113C2×D411yescharacteristic
145C2×Dic113C2×D411yescharacteristic
146D452—21no—
147D452—21no—
148C4×D113—21no—
149C4×D113—21no—
150C4×D113—81no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—22no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—21no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113C22×D411yescharacteristic
165C2×D113—21no—
166C2×D113—21no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—84no—
171C2×D113#13512yes—
172C4×C113—21no—
173C4×C113—41no—
174C4×C113—41no—
175C4×C113C2×#4111yescharacteristic
176C4×C113H(5,𝔽2)11yescharacteristic
177Dic113—21no—
178Dic113—21no—
179Dic113—21no—
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—42no—
184C2×C113—41no—
185C2×C113—81no—
186C2×C113#54611yescharacteristic
187C2×C113C2×#13511yescharacteristic
188C2×C113#57611yescharacteristic
189D113—22no—
190D113—81no—
191#3297—1131nomaximal, Sylow
192C113#329711yescharacteristic, complemented, Sylow
193#553—1131no—
194#546—1131no—
195#488—1131no—
196#484—1131no—
197#482—1131no—
198#478—1131no—
199#466—1131no—
200#465—1131no—
201#463—1131no—
202#449D11311yescharacteristic, complemented
203#447—1131no—
204C4×D8—1131no—
205C8×D4—1131no—
206#416—1131no—
207C2×#102—1131no—
208C2×#41C2×D11311yescharacteristic
209C22×D4—1131no—
210C2×SD16C2×D11311yescharacteristic, complemented
211C2×D8—1131no—
212C2×D8C2×D11311yescharacteristic
213C22×C8—1131no—
214C22×C8—1131no—
215#126—2261no—
216#125—1131no—
217#124—1131no—
218#123—2261no—
219#123—2261no—
220C22⋊Q8—1131no—
221#121—1131no—
222#121—1131no—
223#121—2261no—
224#121—2261no—
225#121C2×D11311yescharacteristic, complemented
226#120—2261no—
227C4×D4—1131no—
228C4×D4—1131no—
229C4×D4—1131no—
230C4×D4—2261no—
231#117—1131no—
232C2×C4⋊C4—1131no—
233C2×C22⋊C4—2261no—
234#107—1131no—
235#107—1131no—
236#106—1131no—
237C4⋊C8—1131no—
238#103—1131no—
239#103—1131no—
240#103C2×D11311yescharacteristic, complemented
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102C2×D11311yescharacteristic
248C22⋊C8—1131no—
249C22⋊C8C2×D11311yescharacteristic, complemented
250C4×C8—1131no—
251C24—2261no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—1131no—
258C2×D4—1131no—
259C2×D4—4521no—
260C2×D4—2261no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4—2262no—
264C2×D4C22×D11311yescharacteristic
265C2×D4C22×D11311yescharacteristic
266C22×C4—21no—
267C22×C4—1131no—
268C22×C4—2261no—
269C22×C4—2261no—
270C22×C4—2261no—
271C22×C4C22×D11311yescharacteristic
272SD16—41no—
273D8—22no—
274D8—4521no—
275C2×C8—1131no—
276C2×C8—1131no—
277C2×C8—4521no—
278C2×C8—4521no—
279C2×C8C22×D11311yescharacteristic
280C2×C8C22×D11311yescharacteristic
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—1131no—
284C4⋊C4—1131no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4—2261no—
289C4⋊C4C22×D11311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—1131no—
292C22⋊C4—1131no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C42—1131no—
302C42—2261no—
303C23—21no—
304C23—21no—
305C23—1131no—
306C23—9041no—
307C23—4522no—
308C23—4522no—
309C23—2261no—
310C23D4×D11311yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—42no—
317D4—81no—
318D4—9041no—
319D4—4522no—
320D4—4522no—
321D4—2262no—
322D4—2261no—
323D4—2261no—
324D4#1426864612yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—1131no—
331C2×C4—1131no—
332C2×C4—1131no—
333C2×C4—9041no—
334C2×C4—9041no—
335C2×C4—9041no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4D4×D11311yescharacteristic
342C2×C4C23×D11311yescharacteristic
343C8—21no—
344C8—21no—
345C8—2261no—
346C8—2261no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—22no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—1132no—
357C22—9044no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—2261no—
362C22—2261no—
363C22C2×D4×D11311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—4521no—
368C4—4521no—
369C4—4521no—
370C4—2261no—
371C4—2261no—
372C4—2261no—
373C4C2×#1426864611yescharacteristic
374C4#1681366711yescharacteristic
375C2—41no—
376C2—42no—
377C2—81no—
378C2—9041no—
379C2—2262no—
380C2#2029923511yescharacteristic
381C2#135×D11311yescharacteristic
382C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3297
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. #20299295C2semidirect
2. #20299236C2semidirect
3. #20298954C2semidirect
4. #20298932C2semidirect
5. #20298923C2semidirect
6. #20298900C2semidirect
7. #20298832C2semidirect
8. #20298824C2semidirect
9. #20298815C2semidirect
10. #20298730C2semidirect
11. D8×Dic113C2semidirect
12. #20298661C2semidirect
13. #20298594C2semidirect
14. #102×D113C2semidirect
15. #449×C113C2semidirect
18. C22×#11744751C22semidirect
21. #16813613C22semidirect
32. D4×Dic113C22semidirect
35. #16813581C22semidirect
38. #16813556C22semidirect
39. #16813555C22semidirect
40. #16813554C22semidirect
41. #16813551C22semidirect
42. #16813546C22semidirect
43. #16813546C22semidirect
48. #16813543C22semidirect
51. C8×Dic113C22semidirect
53. C2×SD16×C113C22semidirect
55. #121×C113C22semidirect
56. #103×C113C22semidirect
58. C22⋊C8×C113C22semidirect
192. C113#3297semidirect
202. #449D113semidirect
210. C2×SD16C2×D113semidirect
225. #121C2×D113semidirect
240. #103C2×D113semidirect
249. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992952
#202992362
#202989542
#202989322
#202989232
#202989002
#202988322
#202988242
#202988152
#202987302
D8×Dic1132
#202986612
#202985942
#102×D1132
#449×C1132
#3297113