Finite Group Databasebeta

← #28400694

Subgroups — #28400694

Order 14464.

424 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299145C211yesmaximal, characteristic
2C4×Q8×D113C211yesmaximal, characteristic, complemented
3#20298913C211yesmaximal, characteristic, complemented
4#20298910C211yesmaximal, characteristic, complemented
5#20298892C211yesmaximal, characteristic, complemented
6#20298891C211yesmaximal, characteristic, complemented
7#20298797C211yesmaximal, characteristic, complemented
8#20298796C211yesmaximal, characteristic, complemented
9#20298738C211yesmaximal, characteristic, complemented
10#20298735C211yesmaximal, characteristic, complemented
11#20298700C211yesmaximal, characteristic, complemented
12#20298698C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298653C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×#14268647—21no—
17C2×Q8×D113C2211yescharacteristic
18C2×#14268636C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21#16813621C2211yescharacteristic
22#16813618C2211yescharacteristic
23#16813608—21no—
24#16813597C2211yescharacteristic
25#16813595—21no—
26#16813593C2211yescharacteristic
27Q8×Dic113C2211yescharacteristic
28C4×Dic226—21no—
29C4×Dic226C2211yescharacteristic
30#16813587—21no—
31#16813587C2211yescharacteristic
32C4×D452C2211yescharacteristic
33C4×C22⋊D113—21no—
34C4⋊C4×D113—21no—
35C4⋊C4×D113C2211yescharacteristic
36C42×D113—21no—
37C42×D113C2211yescharacteristic
38#16813556C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813546C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813533C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59#14268647—44no—
60C2×Dic226—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113—22no—
65C2×D452—21no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113D411yescharacteristic
74C2×C4×D113D411yescharacteristic
75C2×C4×D113C2311yescharacteristic
76#14268636—22no—
77#14268635—22no—
78#14268634—22no—
79C2×#11744751C2311yescharacteristic
80C2×#11744751C2311yescharacteristic
81C4⋊Dic113—21no—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2311yescharacteristic
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94C4×Dic113D411yescharacteristic
95C4×Dic113D411yescharacteristic
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100SD16×C113—22no—
101C2×C8×C113C2311yescharacteristic
102C2×C8×C113C2311yescharacteristic
103C4⋊C4×C113—21no—
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C42×C113C2311yescharacteristic
109C23×C113—21no—
110C22×D113—21no—
111C22×D113C2×D411yescharacteristic
112Q8×C113—21no—
113Q8×C113#4112yescomplemented
114D4×C113—21no—
115D4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—42no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2×D411yescharacteristic
122C2×C4×C113C2411yescharacteristic
123C22⋊D113—42no—
124C22⋊D113—42no—
125C22⋊D113—42no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132D452—21no—
133D452—21no—
134D452—42no—
135C4×D113—24no—
136C4×D113—22no—
137C4×D113—21no—
138C4×D113—21no—
139C4×D113—22no—
140C4×D113—42no—
141C4×D113—42no—
142Dic226—24no—
143Dic226—21no—
144Dic226—42no—
145Dic226#4112yescomplemented
146C8×C113—21no—
147C8×C113—21no—
148#11744751—21no—
149#11744751—21no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113C22×D411yescharacteristic
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113AGL(1,ℤ/8)12yes—
160C4×C113—22no—
161C4×C113—21no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113C2×#4111yescharacteristic
166C4×C113C2×#4111yescharacteristic
167Dic113—21no—
168Dic113—22no—
169Dic113—21no—
170Dic113—41no—
171Dic113—41no—
172Dic113#13712yes—
173C2×C113—81no—
174C2×C113#52511yescharacteristic
175C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C113C2×#13711yescharacteristic
177D113—22no—
178D113—81no—
179#3112—1131nomaximal, Sylow
180C113#311211yescharacteristic, complemented, Sylow
181#532—1131no—
182C2×C4×Q8—1131no—
183#480—1131no—
184#480—1131no—
185#477—1131no—
186#477—1131no—
187#460—1131no—
188#460—1131no—
189#448—1131no—
190#448—1131no—
191#440—1131no—
192#440—1131no—
193#440—1131no—
194#440D11311yescharacteristic, complemented
195#432—1131no—
196C2×#41—2261no—
197C22×Q8—1131no—
198C2×SD16—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16C2×D11311yescharacteristic
202C4⋊Q8—1131no—
203#127—1131no—
204#124—2261no—
205#121—1131no—
206#121—1131no—
207#121—2261no—
208C4×Q8—1131no—
209C4×Q8—1131no—
210C4×Q8—1131no—
211C4×Q8—2261no—
212C4×Q8—2261no—
213C4×Q8C2×D11311yescharacteristic
214C4×D4—1131no—
215C4×D4—2261no—
216C4×D4C2×D11311yescharacteristic
217C2×C4⋊C4—1131no—
218C2×C4⋊C4—2261no—
219C2×C42—1131no—
220C2×C42—2261no—
221#107—1131no—
222#107—1131no—
223#107—1131no—
224#107C2×D11311yescharacteristic
225C4⋊C8—1131no—
226C4⋊C8—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103C2×D11311yescharacteristic
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102C2×D11311yescharacteristic
235C22⋊C8—1131no—
236C22⋊C8—1131no—
237#97—1131no—
238#97C2×D11311yescharacteristic
239#41—4524no—
240C2×Q8—1131no—
241C2×Q8—2261no—
242C2×Q8—2261no—
243C2×Q8—2262no—
244C2×Q8—2262no—
245C2×Q8C22×D11311yescharacteristic
246C2×D4—1131no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4—2261no—
250C2×D4—2261no—
251C2×D4C22×D11311yescharacteristic
252C22×C4—21no—
253C22×C4—1131no—
254C22×C4—1131no—
255C22×C4—1131no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4—2261no—
259SD16—22no—
260SD16—2262no—
261SD16—2262no—
262SD16—2262no—
263C2×C8—1131no—
264C2×C8—1131no—
265C2×C8C22×D11311yescharacteristic
266C2×C8C22×D11311yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C42—21no—
282C42—1131no—
283C42—1131no—
284C42—1131no—
285C42—2261no—
286C42—2261no—
287C42—2261no—
288C42C22×D11311yescharacteristic
289C23—21no—
290C23—1131no—
291C23—2261no—
292Q8—21no—
293Q8—1132no—
294Q8—4522no—
295Q8—2264no—
296Q8—2261no—
297Q8#1426864712yescomplemented
298D4—21no—
299D4—21no—
300D4—4522no—
301D4—4522no—
302D4—4522no—
303D4—4522no—
304D4—2261no—
305D4—2261no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—1131no—
313C2×C4—4522no—
314C2×C4—4522no—
315C2×C4—2262no—
316C2×C4—2262no—
317C2×C4—2264no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4D4×D11311yescharacteristic
324C2×C4D4×D11311yescharacteristic
325C2×C4C23×D11311yescharacteristic
326C8—21no—
327C8—21no—
328C8—2261no—
329C8—2261no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—1132no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22—2261no—
338C22—2261no—
339C22C2×D4×D11311yescharacteristic
340C4—22no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—1132no—
346C4—4521no—
347C4—4521no—
348C4—2261no—
349C4—2262no—
350C4—2261no—
351C4#41×D11311yescharacteristic
352C4C2×#1426864711yescharacteristic
353C2—81no—
354C2—9041no—
355C2—2262no—
356C2#2029910711yescharacteristic
357C2AGL(1,ℤ/8)×D11311yescharacteristic
358C2#137×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radical#20299145C2
hypercenter#440D113
hypocenterC113#3112
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D113C2semidirect
3. #20298913C2semidirect
4. #20298910C2semidirect
5. #20298892C2semidirect
6. #20298891C2semidirect
7. #20298797C2semidirect
8. #20298796C2semidirect
9. #20298738C2semidirect
10. #20298735C2semidirect
11. #20298700C2semidirect
12. #20298698C2semidirect
13. #20298696C2semidirect
14. #20298653C2semidirect
15. #440×C113C2semidirect
113. Q8×C113#41semidirect
145. Dic226#41semidirect
180. C113#3112semidirect
194. #440D113semidirect
297. Q8#14268647semidirect

Maximal subgroups

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

subgroupindex
#202991452
C4×Q8×D1132
#202989132
#202989102
#202988922
#202988912
#202987972
#202987962
#202987382
#202987352
#202987002
#202986982
#202986962
#202986532
#440×C1132
#3112113