Finite Group Databasebeta

← #28402849

Subgroups — #28402849

Order 14464.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299289C211yesmaximal, characteristic, complemented
2#20299256C211yesmaximal, characteristic
3#20298952C211yesmaximal, characteristic, complemented
4#20298932C211yesmaximal, characteristic, complemented
5#20298921C211yesmaximal, characteristic, complemented
6#20298906C211yesmaximal, characteristic, complemented
7#20298853C211yesmaximal, characteristic, complemented
8#20298841C211yesmaximal, characteristic, complemented
9#20298757C211yesmaximal, characteristic, complemented
10#20298752C211yesmaximal, characteristic, complemented
11C4×#14268637C211yesmaximal, characteristic, complemented
12#20298675C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#20298596C211yesmaximal, characteristic, complemented
15#464×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268637C2211yescharacteristic
19C2×#14268630C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21#16813616—21no—
22#16813614C2211yescharacteristic
23#16813612—21no—
24#16813608—21no—
25#16813607—21no—
26#16813599—21no—
27#16813598C2211yescharacteristic
28#16813598C2211yescharacteristic
29#16813598C2211yescharacteristic
30#16813595—21no—
31#16813593C2211yescharacteristic
32C4×Dic226C2211yescharacteristic
33C4×D452C2211yescharacteristic
34#16813582—21no—
35#16813580C2211yescharacteristic
36#16813579—21no—
37C4⋊C4×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813554C2211yescharacteristic
41#16813547C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813546C2211yescharacteristic
46#16813545C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic
52C2×Q16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54#124×C113C2211yescharacteristic
55C4×Q8×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59#14268646—22no—
60#14268646—41no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113—41no—
65C2×D452D411yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C22×Dic113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113C2311yescharacteristic
72C2×C4×D113C2311yescharacteristic
73#14268637—22no—
74#14268630—41no—
75#14268630—41no—
76C2×#11744751C2311yescharacteristic
77C2×#11744751C2311yescharacteristic
78C4⋊Dic113D411yescharacteristic
79C4⋊Dic113C2311yescharacteristic
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82#14268626—21no—
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88#14268626—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624D411yescharacteristic
95#14268624D411yescharacteristic
96C4×Dic113—21no—
97C4×Dic113—21no—
98C2×Q8×C113C2311yescharacteristic
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113C2311yescharacteristic
101Q16×C113—41no—
102SD16×C113—41no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C22×D113C2×D411yescharacteristic
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117Q8×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—42no—
127C22⋊D113—42no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—42no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—41no—
136C4×D113—21no—
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—21no—
140C4×D113—42no—
141C4×D113—42no—
142Dic226—21no—
143Dic226—42no—
144Dic226#4112yes—
145C8×C113—21no—
146C8×C113—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113C22×D411yescharacteristic
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—21no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113C2×#4111yescharacteristic
165C4×C113H(5,𝔽2)11yescharacteristic
166Dic113—22no—
167Dic113—21no—
168Dic113—21no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172C2×C113—81no—
173C2×C113#54611yescharacteristic
174C2×C113#57511yescharacteristic
175C2×C113#57811yescharacteristic
176D113—41no—
177D113—41no—
178#3327—1131nomaximal, Sylow
179C113#332711yescharacteristic, complemented, Sylow
180#552—1131no—
181#548—1131no—
182#488—1131no—
183#484—1131no—
184#482—1131no—
185#479—1131no—
186#470—1131no—
187#468—1131no—
188#464D11311yescharacteristic, complemented
189#452—1131no—
190#451—1131no—
191C4×Q16—1131no—
192#436—1131no—
193#419—1131no—
194#417—1131no—
195C2×#41—1131no—
196C22×Q8—1131no—
197C2×Q16—1131no—
198C2×Q16C2×D11311yescharacteristic
199C2×SD16C2×D11311yescharacteristic
200C2×M16—1131no—
201C2×M16—1131no—
202#126—2261no—
203#125—1131no—
204#125—2261no—
205#124—2261no—
206#124C2×D11311yescharacteristic
207#123—2261no—
208C22⋊Q8—1131no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212#121—1131no—
213#121—2261no—
214C4×Q8—1131no—
215C4×Q8C2×D11311yescharacteristic
216C4×D4—1131no—
217C4×D4—2261no—
218#117—1131no—
219#117—2261no—
220C2×C4⋊C4—1131no—
221#107—1131no—
222#107—1131no—
223#106—1131no—
224C4⋊C8C2×D11311yescharacteristic
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103C2×D11311yescharacteristic
232#102—1131no—
233#102—1131no—
234#102C2×D11311yescharacteristic
235C22⋊C8—1131no—
236C22⋊C8—1131no—
237C4×C8—1131no—
238#41—4521no—
239#41—2262no—
240C2×Q8—1131no—
241C2×Q8—4521no—
242C2×Q8—2261no—
243C2×Q8—2262no—
244C2×Q8C22×D11311yescharacteristic
245C2×Q8C22×D11311yescharacteristic
246C2×D4—1131no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4C22×D11311yescharacteristic
250C22×C4—1131no—
251C22×C4—1131no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255Q16—41no—
256Q16—2262no—
257SD16—41no—
258M16—4521no—
259M16—4521no—
260C2×C8—1131no—
261C2×C8—1131no—
262C2×C8C22×D11311yescharacteristic
263C2×C8C22×D11311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1131no—
280C22⋊C4—1131no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—2261no—
288C42—2261no—
289C42C22×D11311yescharacteristic
290C23—21no—
291C23—1131no—
292C23—1131no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—1132no—
298Q8—4522no—
299Q8—2261no—
300D4—21no—
301D4—21no—
302D4—4521no—
303D4—4522no—
304D4—4522no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—1131no—
309C2×C4—1131no—
310C2×C4—4522no—
311C2×C4—4522no—
312C2×C4—4522no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4D4×D11311yescharacteristic
322C2×C4D4×D11311yescharacteristic
323C2×C4C23×D11311yescharacteristic
324C8—21no—
325C8—21no—
326C8—2261no—
327C8—2261no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—2261no—
332C22—2261no—
333C22—2261no—
334C22—2261no—
335C22—2261no—
336C22—2261no—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—4521no—
344C4—4521no—
345C4—4521no—
346C4—2261no—
347C4—2261no—
348C4—2262no—
349C4#41×D11311yescharacteristic
350C4#1681366711yescharacteristic
351C2—81no—
352C2—4521no—
353C2—4521no—
354C2#2029924511yescharacteristic
355C2#2029939511yescharacteristic
356C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#464×C113C2
socleC22×C113C22×D4
prime radical#20299256C2
hypercenter#464D113
hypocenterC113#3327
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #20299289C2semidirect
3. #20298952C2semidirect
4. #20298932C2semidirect
5. #20298921C2semidirect
6. #20298906C2semidirect
7. #20298853C2semidirect
8. #20298841C2semidirect
9. #20298757C2semidirect
10. #20298752C2semidirect
11. C4×#14268637C2semidirect
12. #20298675C2semidirect
13. #20298605C2semidirect
14. #20298596C2semidirect
15. #464×C113C2semidirect
179. C113#3327semidirect
188. #464D113semidirect

Maximal subgroups

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

subgroupindex
#202992892
#202992562
#202989522
#202989322
#202989212
#202989062
#202988532
#202988412
#202987572
#202987522
C4×#142686372
#202986752
#202986052
#202985962
#464×C1132
#3327113