Finite Group Databasebeta

← #28402539

Subgroups — #28402539

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#20299248C211yesmaximal, characteristic, complemented
2#20299242C211yesmaximal, characteristic, complemented
3#20298956C211yesmaximal, characteristic, complemented
4#20298929C211yesmaximal, characteristic, complemented
5#20298915C211yesmaximal, characteristic, complemented
6#20298886C211yesmaximal, characteristic, complemented
7#20298848C211yesmaximal, characteristic, complemented
8#20298825C211yesmaximal, characteristic, complemented
9#20298811C211yesmaximal, characteristic, complemented
10#20298740C211yesmaximal, characteristic, complemented
11#20298710C211yesmaximal, characteristic, complemented
12#20298666C211yesmaximal, characteristic, complemented
13#20298596C211yesmaximal, characteristic, complemented
14C2×#16813543C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×#14268646C2211yescharacteristic
18C2×#14268635C2211yescharacteristic, complemented
19C2×#14268630C2211yescharacteristic, complemented
20C22×#11744751C2211yescharacteristic
21#16813621C2211yescharacteristic, complemented
22#16813609C2211yescharacteristic
23#16813604—21no—
24#16813603—21no—
25#16813603—21no—
26#16813601C2211yescharacteristic
27#16813599—21no—
28#16813594—21no—
29#16813593C2211yescharacteristic
30#16813593C2211yescharacteristic, complemented
31#16813591—21no—
32D4×Dic113C2211yescharacteristic
33D4×Dic113C2211yescharacteristic, complemented
34C4×C22⋊D113C2211yescharacteristic
35C2×C4⋊Dic113C2211yescharacteristic
36C4⋊C4×D113C2211yescharacteristic, complemented
37C2×C22⋊Dic113—21no—
38#16813554C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813547C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813545C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51#16813532C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61#14268646—44no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113D411yescharacteristic
68C22×Dic113—21no—
69C22×Dic113—21no—
70C22×Dic113—21no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74#14268635—41no—
75#14268630—41no—
76C2×#11744751—41no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93C22⋊Dic113—21no—
94C22⋊Dic113D411yescharacteristic
95#14268624D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C24×C113—21no—
98C2×D4×C113—22no—
99C2×D4×C113—21no—
100C2×D4×C113—21no—
101C2×D4×C113—41no—
102C2×D4×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C2×D4×C113C2311yescharacteristic
105C22×C4×C113C2311yescharacteristic
106D8×C113—22no—
107D8×C113—41no—
108C2×C8×C113C2311yescharacteristic
109C2×C8×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113—21no—
113C23×C113—21no—
114C23×C113—21no—
115C23×C113—42no—
116C23×C113—42no—
117C23×C113—81no—
118C23×C113C2×D411yescharacteristic
119C22×D113C2×D411yescharacteristic
120D4×C113—21no—
121D4×C113—21no—
122D4×C113—21no—
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—42no—
126D4×C113—42no—
127D4×C113#4112yescomplemented
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2411yescharacteristic
133C22⋊D113—22no—
134C22⋊D113—42no—
135C22⋊D113—42no—
136C22⋊D113—81no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—42no—
142C2×Dic113—42no—
143C2×Dic113—42no—
144C2×Dic113—81no—
145C2×Dic113C2×D411yescharacteristic
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148C4×D113—21no—
149C4×D113—21no—
150C4×D113—42no—
151Dic226—21no—
152Dic226—21no—
153Dic226—42no—
154C8×C113—21no—
155C8×C113—21no—
156#11744751—21no—
157#11744751—21no—
158C22×C113—21no—
159C22×C113—21no—
160C22×C113—22no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—84no—
170C22×C113AGL(1,ℤ/8)12yes—
171C22×C113C22×D411yescharacteristic
172C2×D113—21no—
173C2×D113—21no—
174C2×D113—21no—
175C4×C113—21no—
176C4×C113—41no—
177C4×C113C2×#4111yescharacteristic
178C4×C113H(5,𝔽2)11yescharacteristic
179Dic113—21no—
180Dic113—21no—
181Dic113—21no—
182Dic113—41no—
183Dic113—41no—
184Dic113—41no—
185Dic113—41no—
186C2×C113—22no—
187C2×C113—42no—
188C2×C113—81no—
189C2×C113—81no—
190C2×C113#54611yescharacteristic
191C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C113#57711yescharacteristic
193D113—41no—
194#3306—1131nomaximal, Sylow
195C113#330611yescharacteristic, complemented, Sylow
196#547—1131no—
197#546—1131no—
198#489—1131no—
199#483—1131no—
200#481—1131no—
201#476—1131no—
202#469—1131no—
203#465—1131no—
204#463—1131no—
205#449—1131no—
206#447D11311yescharacteristic, complemented
207#442—1131no—
208#435—1131no—
209#417—1131no—
210C2×#102—1131no—
211C2×#41—1131no—
212C2×#41—2261no—
213C22×D4C2×D11311yescharacteristic
214C2×SD16—1131no—
215C2×D8C2×D11311yescharacteristic
216C2×D8C2×D11311yescharacteristic
217C2×M16—1131no—
218C22×C8—1131no—
219C4⋊Q8—1131no—
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—2261no—
229#121C2×D11311yescharacteristic
230#120—2261no—
231C4×D4—1131no—
232C4×D4—1131no—
233C4×D4—1131no—
234C2×C4⋊C4—1131no—
235C2×C4⋊C4—1131no—
236C2×C22⋊C4—2261no—
237#106—1131no—
238#106—1131no—
239#106—1131no—
240C4⋊C8—1131no—
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⋊C8C2×D11311yescharacteristic
253#97—1131no—
254C24—21no—
255#41—4524no—
256#41—4521no—
257#41—2262no—
258C2×Q8—1131no—
259C2×Q8—2261no—
260C2×D4—22no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—1131no—
265C2×D4—2261no—
266C2×D4—2261no—
267C2×D4—2261no—
268C2×D4C22×D11311yescharacteristic
269C2×D4C22×D11311yescharacteristic
270C2×D4C22×D11311yescharacteristic
271C22×C4—1131no—
272C22×C4—2261no—
273C22×C4—2261no—
274C22×C4—2261no—
275C22×C4—2261no—
276C22×C4—2261no—
277C22×C4C22×D11311yescharacteristic
278SD16—4521no—
279D8—22no—
280D8—41no—
281M16—4521no—
282C2×C8—1131no—
283C2×C8—1131no—
284C2×C8—4521no—
285C2×C8C22×D11311yescharacteristic
286C2×C8C22×D11311yescharacteristic
287C4⋊C4—1131no—
288C4⋊C4—1131no—
289C4⋊C4—1131no—
290C4⋊C4—1131no—
291C4⋊C4—2261no—
292C4⋊C4—2261no—
293C4⋊C4—2261no—
294C4⋊C4—2261no—
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—
306C42—1131no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—42no—
311C23—42no—
312C23—81no—
313C23—1131no—
314C23D4×D11311yescharacteristic
315Q8—4522no—
316Q8—2261no—
317Q8—2261no—
318D4—21no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—42no—
325D4—9041no—
326D4—4522no—
327D4—4522no—
328D4—2262no—
329D4#1426864612yescomplemented
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—1131no—
334C2×C4—1131no—
335C2×C4—1131no—
336C2×C4—9041no—
337C2×C4—4522no—
338C2×C4—4522no—
339C2×C4—4522no—
340C2×C4—4522no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4D4×D11311yescharacteristic
348C2×C4C23×D11311yescharacteristic
349C8—21no—
350C8—21no—
351C8—2261no—
352C8—2261no—
353C22—21no—
354C22—21no—
355C22—22no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—84no—
365C22—2261no—
366C22—2261no—
367C22—2261no—
368C22#1681364612yes—
369C22C2×D4×D11311yescharacteristic
370C4—21no—
371C4—41no—
372C4—4521no—
373C4—4521no—
374C4—4521no—
375C4—4521no—
376C4—2261no—
377C4—2261no—
378C4—2261no—
379C4C2×#1426864611yescharacteristic
380C4#1681366711yescharacteristic
381C2—22no—
382C2—42no—
383C2—81no—
384C2—81no—
385C2—4521no—
386C2#2029923511yescharacteristic
387C2C2×#1681364611yescharacteristic
388C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3306
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20299248C2semidirect
2. #20299242C2semidirect
3. #20298956C2semidirect
4. #20298929C2semidirect
5. #20298915C2semidirect
6. #20298886C2semidirect
7. #20298848C2semidirect
8. #20298825C2semidirect
9. #20298811C2semidirect
10. #20298740C2semidirect
11. #20298710C2semidirect
12. #20298666C2semidirect
13. #20298596C2semidirect
14. C2×#16813543C2semidirect
15. #447×C113C2semidirect
18. C2×#14268635C22semidirect
19. C2×#14268630C22semidirect
21. #16813621C22semidirect
30. #16813593C22semidirect
33. D4×Dic113C22semidirect
36. C4⋊C4×D113C22semidirect
38. #16813554C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813547C22semidirect
43. #16813547C22semidirect
44. #16813545C22semidirect
49. #16813543C22semidirect
50. #16813534C22semidirect
51. #16813532C22semidirect
127. D4×C113#41semidirect
195. C113#3306semidirect
206. #447D113semidirect
329. D4#14268646semidirect

Maximal subgroups

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

subgroupindex
#202992482
#202992422
#202989562
#202989292
#202989152
#202988862
#202988482
#202988252
#202988112
#202987402
#202987102
#202986662
#202985962
C2×#168135432
#447×C1132
#3306113