Finite Group Databasebeta

← #28402532

Subgroups — #28402532

Order 14464.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299251C211yesmaximal, characteristic, complemented
2#20299243C211yesmaximal, characteristic, complemented
3#20298960C211yesmaximal, characteristic, complemented
4#20298930C211yesmaximal, characteristic, complemented
5#20298918C211yesmaximal, characteristic, complemented
6#20298852C211yesmaximal, characteristic, complemented
7#20298828C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298744C211yesmaximal, characteristic, complemented
10#20298733C211yesmaximal, characteristic, complemented
11#20298708C211yesmaximal, characteristic, complemented
12#20298668C211yesmaximal, characteristic, complemented
13#20298596C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#476×C113C211yesmaximal, characteristic, complemented
16C2×#14268648—21no—
17C2×#14268646C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19C2×#14268636C2211yescharacteristic, complemented
20C2×D904C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22C2×#14268630C2211yescharacteristic, complemented
23C2×C8×D113C2211yescharacteristic
24#16813610C2211yescharacteristic
25#16813607—21no—
26#16813607—21no—
27#16813606—21no—
28#16813602C2211yescharacteristic
29#16813598—21no—
30#16813597C2211yescharacteristic
31#16813597C2211yescharacteristic
32#16813597C2211yescharacteristic, complemented
33#16813596—21no—
34#16813592—21no—
35C4×D452C2211yescharacteristic
36C4×D452C2211yescharacteristic, complemented
37C4⋊C4×D113C2211yescharacteristic
38C4⋊C4×D113C2211yescharacteristic, complemented
39C2×#14268624—21no—
40#16813553C2211yescharacteristic, complemented
41#16813547C2211yescharacteristic, complemented
42#16813545C2211yescharacteristic, complemented
43#16813545C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51#16813533C2211yescharacteristic, complemented
52C4⋊Q8×C113C2211yescharacteristic, complemented
53C4×D4×C113C2211yescharacteristic
54#106×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60#14268648—44no—
61#14268646—22no—
62#14268646—41no—
63C2×Dic226C2311yescharacteristic
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452D411yescharacteristic
68C2×D452C2311yescharacteristic
69C2×D452C2311yescharacteristic
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72D4×D113—22no—
73D4×D113—41no—
74C22×Dic113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113C2311yescharacteristic
79C2×C4×D113C2311yescharacteristic
80#14268636—41no—
81D904—41no—
82#14268632—22no—
83#14268630—41no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C8×D113—41no—
87C4⋊Dic113—21no—
88C4⋊Dic113D411yescharacteristic
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91#14268626—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624D411yescharacteristic
100#14268624D411yescharacteristic
101C2×Q8×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113C2311yescharacteristic
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C22⋊C4×C113—21no—
111C42×C113C2311yescharacteristic
112C23×C113—21no—
113C22×D113—21no—
114C22×D113—21no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113—81no—
118C22×D113C2×D411yescharacteristic
119C22×D113C2×D411yescharacteristic
120Q8×C113—42no—
121D4×C113—21no—
122D4×C113#4112yescomplemented
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—42no—
131C22⋊D113—42no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—42no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137D452—22no—
138D452—21no—
139D452—21no—
140D452—21no—
141D452—21no—
142D452—42no—
143D452—42no—
144D452—81no—
145C4×D113—21no—
146C4×D113—21no—
147C4×D113—21no—
148C4×D113—21no—
149C4×D113—42no—
150C4×D113—42no—
151C4×D113—42no—
152Dic226—21no—
153Dic226—21no—
154C8×C113—21no—
155C8×C113—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—22no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113C22×D411yescharacteristic
162C2×D113—21no—
163C2×D113—21no—
164C2×D113—21no—
165C2×D113—21no—
166C2×D113—21no—
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—84no—
174C2×D113AGL(1,ℤ/8)12yes—
175C4×C113—21no—
176C4×C113—21no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113—41no—
180C4×C113C2×#4111yescharacteristic
181C4×C113H(5,𝔽2)11yescharacteristic
182Dic113—21no—
183Dic113—21no—
184Dic113—41no—
185Dic113—41no—
186C2×C113—42no—
187C2×C113#54611yescharacteristic
188C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C113#57711yescharacteristic
190D113—22no—
191D113—41no—
192D113—81no—
193D113—81no—
194#3306—1131nomaximal, Sylow
195C113#330611yescharacteristic, complemented, Sylow
196#547—1131no—
197#546—1131no—
198#489—1131no—
199#483—1131no—
200#481—1131no—
201#476D11311yescharacteristic, complemented
202#469—1131no—
203#465—1131no—
204#463—1131no—
205#449—1131no—
206#447—1131no—
207#442—1131no—
208#435—1131no—
209#417—1131no—
210C2×#102—1131no—
211C2×#41—1131no—
212C2×#41—2261no—
213C22×D4—1131no—
214C2×SD16—1131no—
215C2×D8—1131no—
216C2×D8—1131no—
217C2×M16—1131no—
218C22×C8—1131no—
219C4⋊Q8C2×D11311yescharacteristic, complemented
220#124—1131no—
221#123—2261no—
222#123—2261no—
223#123—2261no—
224C22⋊Q8—1131no—
225C22⋊Q8—2261no—
226#121—1131no—
227#121—1131no—
228#121—1131no—
229#121—2261no—
230#120—2261no—
231C4×D4—1131no—
232C4×D4—1131no—
233C4×D4C2×D11311yescharacteristic
234C2×C4⋊C4—1131no—
235C2×C4⋊C4—1131no—
236C2×C22⋊C4—2261no—
237#106—1131no—
238#106C2×D11311yescharacteristic, complemented
239#106C2×D11311yescharacteristic, complemented
240C4⋊C8C2×D11311yescharacteristic, complemented
241#103—1131no—
242#103—1131no—
243#103—1131no—
244#102—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102C2×D11311yescharacteristic
250#102C2×D11311yescharacteristic
251C22⋊C8—1131no—
252C22⋊C8—1131no—
253#97—1131no—
254C24—2261no—
255#41—4524no—
256#41—4521no—
257#41—2262no—
258C2×Q8—21no—
259C2×Q8—1131no—
260C2×D4—1131no—
261C2×D4—1131no—
262C2×D4—1131no—
263C2×D4—4521no—
264C2×D4—2261no—
265C2×D4—2261no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2262no—
270C2×D4C22×D11311yescharacteristic
271C22×C4—21no—
272C22×C4—1131no—
273C22×C4—1131no—
274C22×C4—2261no—
275C22×C4—2261no—
276C22×C4—2261no—
277C22×C4—2261no—
278SD16—4521no—
279D8—4521no—
280D8—2262no—
281M16—4521no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8—4521no—
285C2×C8C22×D11311yescharacteristic
286C2×C8C22×D11311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—1131no—
289C4⋊C4—1131no—
290C4⋊C4—2261no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4C22×D11311yescharacteristic
294C4⋊C4C22×D11311yescharacteristic
295C4⋊C4C22×D11311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—1131no—
298C22⋊C4—1131no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C42C22×D11311yescharacteristic
307C23—21no—
308C23—1131no—
309C23—1131no—
310C23—9041no—
311C23—4522no—
312C23—4522no—
313C23—2261no—
314C23—2261no—
315Q8—42no—
316Q8—2261no—
317Q8—2261no—
318D4—21no—
319D4—9041no—
320D4—4522no—
321D4—4522no—
322D4—4522no—
323D4—4522no—
324D4—2262no—
325D4—2261no—
326D4—2261no—
327D4—2261no—
328D4—2261no—
329D4#1426864812yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—81no—
334C2×C4—1131no—
335C2×C4—1131no—
336C2×C4—4522no—
337C2×C4—4522no—
338C2×C4—4522no—
339C2×C4—4522no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4D4×D11311yescharacteristic
347C2×C4D4×D11311yescharacteristic
348C2×C4C23×D11311yescharacteristic
349C8—21no—
350C8—21no—
351C8—2261no—
352C8—2261no—
353C22—22no—
354C22—41no—
355C22—41no—
356C22—1132no—
357C22—9044no—
358C22—4521no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22—4521no—
363C22—4521no—
364C22—2261no—
365C22—2261no—
366C22—2261no—
367C22—2261no—
368C22—2261no—
369C22C2×D4×D11311yescharacteristic
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—4521no—
376C4—4521no—
377C4—2261no—
378C4—2261no—
379C4C2×#1426864811yescharacteristic
380C4#1681366811yescharacteristic
381C2—42no—
382C2—9041no—
383C2—9041no—
384C2—4521no—
385C2—2262no—
386C2#2029923911yescharacteristic
387C2AGL(1,ℤ/8)×D11311yescharacteristic
388C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#476×C113C2
socleC22×C113C22×D4
hypercenter#476D113
hypocenterC113#3306
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #20299251C2semidirect
2. #20299243C2semidirect
3. #20298960C2semidirect
4. #20298930C2semidirect
5. #20298918C2semidirect
6. #20298852C2semidirect
7. #20298828C2semidirect
8. #20298814C2semidirect
9. #20298744C2semidirect
10. #20298733C2semidirect
11. #20298708C2semidirect
12. #20298668C2semidirect
13. #20298596C2semidirect
14. #102×D113C2semidirect
15. #476×C113C2semidirect
19. C2×#14268636C22semidirect
22. C2×#14268630C22semidirect
32. #16813597C22semidirect
36. C4×D452C22semidirect
38. C4⋊C4×D113C22semidirect
40. #16813553C22semidirect
41. #16813547C22semidirect
42. #16813545C22semidirect
43. #16813545C22semidirect
48. #16813542C22semidirect
50. #16813534C22semidirect
51. #16813533C22semidirect
52. C4⋊Q8×C113C22semidirect
54. #106×C113C22semidirect
55. #106×C113C22semidirect
56. C4⋊C8×C113C22semidirect
122. D4×C113#41semidirect
195. C113#3306semidirect
201. #476D113semidirect
219. C4⋊Q8C2×D113semidirect
238. #106C2×D113semidirect
239. #106C2×D113semidirect
240. C4⋊C8C2×D113semidirect
329. D4#14268648semidirect

Maximal subgroups

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

subgroupindex
#202992512
#202992432
#202989602
#202989302
#202989182
#202988522
#202988282
#202988142
#202987442
#202987332
#202987082
#202986682
#202985962
#102×D1132
#476×C1132
#3306113