Finite Group Databasebeta

← #28402426

Subgroups — #28402426

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#20299294C211yesmaximal, characteristic, complemented
2#20299244C211yesmaximal, characteristic, complemented
3#20298953C211yesmaximal, characteristic, complemented
4#20298934C211yesmaximal, characteristic, complemented
5#20298923C211yesmaximal, characteristic, complemented
6#20298899C211yesmaximal, characteristic, complemented
7#20298834C211yesmaximal, characteristic, complemented
8#20298827C211yesmaximal, characteristic, complemented
9#20298814C211yesmaximal, characteristic, complemented
10#20298745C211yesmaximal, characteristic, complemented
11#20298734C211yesmaximal, characteristic, complemented
12C4×D904C211yesmaximal, characteristic, complemented
13#20298595C211yesmaximal, characteristic, complemented
14C2×#16813544C211yesmaximal, characteristic, complemented
15C8×D4×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×#14268636C2211yescharacteristic, complemented
19C2×D904C2211yescharacteristic
20C2×D904C2211yescharacteristic
21#16813617—21no—
22#16813614C2211yescharacteristic, complemented
23#16813610C2211yescharacteristic
24#16813607—21no—
25#16813604—21no—
26#16813601C2211yescharacteristic
27#16813596C2211yescharacteristic
28#16813596C2211yescharacteristic
29#16813596C2211yescharacteristic, complemented
30#16813595—21no—
31#16813594—21no—
32#16813590—21no—
33C4×D452C2211yescharacteristic
34C4×D452C2211yescharacteristic, complemented
35#16813582—21no—
36#16813581C2211yescharacteristic, complemented
37C2×C4⋊Dic113C2211yescharacteristic
38C22⋊C4×D113—21no—
39#16813556C2211yescharacteristic, complemented
40#16813556C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813544C2211yescharacteristic
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813544C2211yescharacteristic, complemented
52C22×C8×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic, complemented
54C4×D4×C113C2211yescharacteristic
55C4⋊C8×C113C2211yescharacteristic, complemented
56C22⋊C8×C113C2211yescharacteristic
57C22⋊C8×C113C2211yescharacteristic, complemented
58C4×C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—22no—
61#14268647—41no—
62C2×Dic226C2311yescharacteristic
63C2×D452—22no—
64C2×D452—21no—
65C2×D452—41no—
66C2×D452C2311yescharacteristic
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C22×Dic113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77#14268636—41no—
78D904—22no—
79D904—41no—
80C4⋊Dic113—21no—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84C4⋊Dic113C2311yescharacteristic
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97C4×Dic113—21no—
98C2×D4×C113D411yescharacteristic
99C22×C4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101C2×C8×C113—41no—
102C2×C8×C113—41no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113D411yescharacteristic
108C22⋊C4×C113D411yescharacteristic
109C22⋊C4×C113D411yescharacteristic
110C42×C113C2311yescharacteristic
111C23×C113C2×D411yescharacteristic
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—81no—
119D4×C113—22no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—42no—
130C22⋊D113—42no—
131C22⋊D113—81no—
132C22⋊D113—81no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—81no—
139D452—21no—
140D452—21no—
141D452—21no—
142D452—21no—
143D452—21no—
144D452—42no—
145D452#4112yes—
146C4×D113—42no—
147C4×D113—81no—
148C4×D113—81no—
149Dic226—21no—
150Dic226—21no—
151C8×C113—21no—
152C8×C113—21no—
153C8×C113—21no—
154C8×C113—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113#13512yes—
161C22×C113C22×D411yescharacteristic
162C2×D113—22no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—84no—
172C4×C113—21no—
173C4×C113—21no—
174C4×C113—21no—
175C4×C113—21no—
176C4×C113C2×#4111yescharacteristic
177C4×C113H(5,𝔽2)11yescharacteristic
178Dic113—41no—
179Dic113—41no—
180Dic113—41no—
181Dic113—41no—
182Dic113—41no—
183C2×C113—22no—
184C2×C113—41no—
185C2×C113#54611yescharacteristic
186C2×C113C2×#13511yescharacteristic
187C2×C113#57611yescharacteristic
188D113—42no—
189D113—81no—
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#449—1131no—
203#447—1131no—
204C4×D8—1131no—
205C8×D4D11311yescharacteristic, complemented
206#416—1131no—
207C2×#102—1131no—
208C2×#41—1131no—
209C22×D4—1131no—
210C2×SD16—1131no—
211C2×D8—1131no—
212C2×D8—1131no—
213C22×C8C2×D11311yescharacteristic
214C22×C8C2×D11311yescharacteristic, complemented
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—1131no—
224#121—2261no—
225#121—2261no—
226#120—2261no—
227C4×D4—1131no—
228C4×D4—1131no—
229C4×D4—2261no—
230C4×D4C2×D11311yescharacteristic
231#117—1131no—
232C2×C4⋊C4—1131no—
233C2×C22⋊C4—2261no—
234#107—1131no—
235#107—1131no—
236#106—1131no—
237C4⋊C8C2×D11311yescharacteristic, complemented
238#103—1131no—
239#103—1131no—
240#103—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248C22⋊C8C2×D11311yescharacteristic
249C22⋊C8C2×D11311yescharacteristic, complemented
250C4×C8C2×D11311yescharacteristic, complemented
251C24—2261no—
252#41—4521no—
253#41—2262no—
254C2×Q8—1131no—
255C2×D4—1131no—
256C2×D4—1131no—
257C2×D4—1131no—
258C2×D4—4521no—
259C2×D4—2262no—
260C2×D4—2261no—
261C2×D4—2261no—
262C2×D4—2261no—
263C2×D4—2261no—
264C2×D4—2261no—
265C2×D4D45211yescharacteristic
266C22×C4—2261no—
267C22×C4—2261no—
268C22×C4—2261no—
269C22×C4—2261no—
270C22×C4C22×D11311yescharacteristic
271C22×C4C22×D11311yescharacteristic
272SD16—4521no—
273D8—4521no—
274D8—2262no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×D11311yescharacteristic
278C2×C8C22×D11311yescharacteristic
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⋊C4D45211yescharacteristic
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C22⋊C4D45211yescharacteristic
300C22⋊C4D45211yescharacteristic
301C42—2261no—
302C42C22×D11311yescharacteristic
303C23—9041no—
304C23—4522no—
305C23—4522no—
306C23—2261no—
307C23—2261no—
308C23—2261no—
309C23C2×D45211yescharacteristic
310C23C2×D45211yescharacteristic
311Q8—2261no—
312Q8—2261no—
313D4—22no—
314D4—1132no—
315D4—9041no—
316D4—9041no—
317D4—4522no—
318D4—4522no—
319D4—4522no—
320D4—2261no—
321D4—2261no—
322D4—2261no—
323D4—2261no—
324D4—2261no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—9041no—
330C2×C4—9041no—
331C2×C4—9041no—
332C2×C4—4522no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4C2×D45211yescharacteristic
339C2×C4C2×D45211yescharacteristic
340C2×C4C2×D45211yescharacteristic
341C2×C4C2×D45211yescharacteristic
342C2×C4C23×D11311yescharacteristic
343C8—21no—
344C8—21no—
345C8—21no—
346C8—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—9044no—
353C22—4521no—
354C22—4521no—
355C22—4521no—
356C22—4521no—
357C22—4521no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—2262no—
362C22#1681364412yes—
363C22C22×D45211yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—4521no—
369C4—4521no—
370C4—4521no—
371C4—4521no—
372C4—4521no—
373C4#41×D11311yescharacteristic
374C4#1681366711yescharacteristic
375C2—22no—
376C2—41no—
377C2—9041no—
378C2—9041no—
379C2—4522no—
380C2#2029924311yescharacteristic
381C2C2×#1681364411yescharacteristic
382C2#2029940311yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC8×D4×C113C2
socleC22×C113C22×D4
hypercenterC8×D4D113
hypocenterC113#3297
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20299294C2semidirect
2. #20299244C2semidirect
3. #20298953C2semidirect
4. #20298934C2semidirect
5. #20298923C2semidirect
6. #20298899C2semidirect
7. #20298834C2semidirect
8. #20298827C2semidirect
9. #20298814C2semidirect
10. #20298745C2semidirect
11. #20298734C2semidirect
12. C4×D904C2semidirect
13. #20298595C2semidirect
14. C2×#16813544C2semidirect
15. C8×D4×C113C2semidirect
18. C2×#14268636C22semidirect
22. #16813614C22semidirect
29. #16813596C22semidirect
34. C4×D452C22semidirect
36. #16813581C22semidirect
39. #16813556C22semidirect
40. #16813556C22semidirect
41. #16813554C22semidirect
42. #16813547C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
51. #16813544C22semidirect
53. C22×C8×C113C22semidirect
55. C4⋊C8×C113C22semidirect
57. C22⋊C8×C113C22semidirect
58. C4×C8×C113C22semidirect
192. C113#3297semidirect
205. C8×D4D113semidirect
214. C22×C8C2×D113semidirect
237. C4⋊C8C2×D113semidirect
249. C22⋊C8C2×D113semidirect
250. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992942
#202992442
#202989532
#202989342
#202989232
#202988992
#202988342
#202988272
#202988142
#202987452
#202987342
C4×D9042
#202985952
C2×#168135442
C8×D4×C1132
#3297113