Finite Group Databasebeta

← #28401162

Subgroups — #28401162

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299143C211yesmaximal, characteristic, complemented
2#20299134C211yesmaximal, characteristic, complemented
3#20299006C211yesmaximal, characteristic, complemented
4#20298984C211yesmaximal, characteristic, complemented
5#20298961C211yesmaximal, characteristic, complemented
6#20298959C211yesmaximal, characteristic, complemented
7#20298851C211yesmaximal, characteristic, complemented
8#20298849C211yesmaximal, characteristic, complemented
9#20298846C211yesmaximal, characteristic, complemented
10SD16×Dic113C211yesmaximal, characteristic, complemented
11#20298683C211yesmaximal, characteristic, complemented
12#20298680C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14M16×Dic113C211yesmaximal, characteristic, complemented
15#468×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×#14268634C2211yescharacteristic
18C2×D904C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268631C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813618C2211yescharacteristic
23#16813617—21no—
24#16813613C2211yescharacteristic
25#16813611C2211yescharacteristic
26#16813608—21no—
27#16813606—21no—
28#16813596C2211yescharacteristic
29#16813596C2211yescharacteristic
30#16813594—21no—
31Q8×Dic113C2211yescharacteristic
32D4×Dic113C2211yescharacteristic
33#16813584C2211yescharacteristic
34#16813584C2211yescharacteristic
35#16813582—21no—
36#16813582—21no—
37#16813580—21no—
38C2×C4×Dic113C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813553C2211yescharacteristic
42#16813546C2211yescharacteristic
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813532C2211yescharacteristic
49#16813532C2211yescharacteristic
50C8×Dic113C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C2×M16×C113C2211yescharacteristic
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#107×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—44no—
60C2×Dic226—21no—
61C2×D452C2311yescharacteristic
62C2×D452C2311yescharacteristic
63C2×C22⋊D113—21no—
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C22×Dic113—21no—
68C22×Dic113D411yescharacteristic
69C22×Dic113D411yescharacteristic
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72#14268634—22no—
73D904—22no—
74#14268632—22no—
75#14268631—22no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113—21no—
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91C4×Dic113—21no—
92C4×Dic113D411yescharacteristic
93C4×Dic113D411yescharacteristic
94C4×Dic113C2311yescharacteristic
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113C2311yescharacteristic
100SD16×C113—22no—
101M16×C113—22no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113—21no—
105C4⋊C4×C113C2311yescharacteristic
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C23×C113—21no—
110C23×C113C2×D411yescharacteristic
111C22×D113—21no—
112C22×D113—21no—
113Q8×C113—21no—
114Q8×C113—21no—
115D4×C113—21no—
116D4×C113—21no—
117D4×C113—42no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113—42no—
126C22⋊D113—42no—
127C22⋊D113—42no—
128C22⋊D113—42no—
129C2×Dic113—22no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—41no—
133C2×Dic113—42no—
134C2×Dic113C2×D411yescharacteristic
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138D452—21no—
139D452—21no—
140D452—21no—
141D452—21no—
142C4×D113—42no—
143C4×D113—42no—
144Dic226—42no—
145C8×C113—21no—
146C8×C113#4112yescomplemented
147#11744751—21no—
148#11744751#4112yescomplemented
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—21no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113C22×D411yescharacteristic
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#4111yescharacteristic
167C4×C113C2×#4111yescharacteristic
168Dic113—21no—
169Dic113—21no—
170Dic113—21no—
171Dic113—41no—
172Dic113—41no—
173Dic113AGL(1,ℤ/8)12yes—
174C2×C113—41no—
175C2×C113—81no—
176C2×C113#53211yescharacteristic
177C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
178C2×C113#57511yescharacteristic
179D113—81no—
180D113—81no—
181#3171—1131nomaximal, Sylow
182C113#317111yescharacteristic, complemented, Sylow
183#532—1131no—
184#529—1131no—
185#501—1131no—
186#496—1131no—
187#490—1131no—
188#489—1131no—
189#469—1131no—
190#469—1131no—
191#468—1131no—
192#468D11311yescharacteristic, complemented
193C4×SD16—1131no—
194C4×SD16—1131no—
195C4×D8—1131no—
196C4×D8—1131no—
197C4×M16—1131no—
198C2×#41—2261no—
199C2×SD16—1131no—
200C2×SD16C2×D11311yescharacteristic
201C2×D8—1131no—
202C2×D8—1131no—
203C2×M16—1131no—
204C2×M16C2×D11311yescharacteristic
205C4⋊Q8—1131no—
206#127—1131no—
207#126—2261no—
208#125—1131no—
209#124—1131no—
210#124—2261no—
211#123—2261no—
212C22⋊Q8C2×D11311yescharacteristic
213#121—1131no—
214#121—1131no—
215#121—2261no—
216#121C2×D11311yescharacteristic
217C4×Q8—1131no—
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4—1131no—
221C4×D4—2261no—
222C4×D4—2261no—
223#117—2261no—
224C2×C42—1131no—
225#107—1131no—
226#107C2×D11311yescharacteristic
227#106—1131no—
228#106—1131no—
229#103—1131no—
230#103C2×D11311yescharacteristic
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102C2×D11311yescharacteristic
237#97—1131no—
238#97—1131no—
239C4×C8—1131no—
240C4×C8—1131no—
241#41—4524no—
242C2×Q8—2261no—
243C2×Q8C22×D11311yescharacteristic
244C2×D4—21no—
245C2×D4—1131no—
246C2×D4—1131no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4—2261no—
250C2×D4—2261no—
251C2×D4C22×D11311yescharacteristic
252C22×C4—1131no—
253C22×C4—1131no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4C22×D11311yescharacteristic
258SD16—22no—
259SD16—2262no—
260D8—2262no—
261D8—2262no—
262M16—22no—
263M16—2262no—
264C2×C8—1131no—
265C2×C8—1131no—
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—1131no—
287C42—1131no—
288C42—1131no—
289C42—1131no—
290C42—2261no—
291C23—21no—
292C23—2261no—
293C23—2261no—
294C23D4×D11311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—4522no—
298D4—21no—
299D4—21no—
300D4—42no—
301D4—4522no—
302D4—4522no—
303D4—4522no—
304D4—4522no—
305D4—2261no—
306D4—2261no—
307D4—2261no—
308D4—2261no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—1131no—
317C2×C4—1131no—
318C2×C4—4522no—
319C2×C4—4522no—
320C2×C4—4522no—
321C2×C4—4521no—
322C2×C4—2262no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4D4×D11311yescharacteristic
326C2×C4C23×D11311yescharacteristic
327C8—21no—
328C8—1132no—
329C8—2261no—
330C8#1426864612yescomplemented
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—4521no—
338C22—4521no—
339C22—4521no—
340C22—4521no—
341C22—4521no—
342C22—4521no—
343C22C2×D4×D11311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—1132no—
349C4—4521no—
350C4—4521no—
351C4—2261no—
352C4—2261no—
353C4—2261no—
354C4#41×D11311yescharacteristic
355C4C2×#1426864611yescharacteristic
356C2—41no—
357C2—81no—
358C2—9041no—
359C2—9041no—
360C2#2029914311yescharacteristic
361C2AGL(1,ℤ/8)×D11311yescharacteristic
362C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#468×C113C2
socleC22×C113C22×D4
hypercenter#468D113
hypocenterC113#3171
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #20299143C2semidirect
2. #20299134C2semidirect
3. #20299006C2semidirect
4. #20298984C2semidirect
5. #20298961C2semidirect
6. #20298959C2semidirect
7. #20298851C2semidirect
8. #20298849C2semidirect
9. #20298846C2semidirect
10. SD16×Dic113C2semidirect
11. #20298683C2semidirect
12. #20298680C2semidirect
13. #20298678C2semidirect
14. M16×Dic113C2semidirect
15. #468×C113C2semidirect
146. C8×C113#41semidirect
148. #11744751#41semidirect
182. C113#3171semidirect
192. #468D113semidirect
330. C8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202991432
#202991342
#202990062
#202989842
#202989612
#202989592
#202988512
#202988492
#202988462
SD16×Dic1132
#202986832
#202986802
#202986782
M16×Dic1132
#468×C1132
#3171113