Finite Group Databasebeta

← #28402877

Subgroups — #28402877

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299250C211yesmaximal, characteristic, complemented
2#20299249C211yesmaximal, characteristic, complemented
3#20298947C211yesmaximal, characteristic, complemented
4#20298935C211yesmaximal, characteristic, complemented
5#20298877C211yesmaximal, characteristic, complemented
6#20298846C211yesmaximal, characteristic, complemented
7#20298845C211yesmaximal, characteristic, complemented
8#20298802C211yesmaximal, characteristic, complemented
9#20298746C211yesmaximal, characteristic, complemented
10#20298745C211yesmaximal, characteristic, complemented
11#20298680C211yesmaximal, characteristic, complemented
12#20298673C211yesmaximal, characteristic, complemented
13#20298598C211yesmaximal, characteristic, complemented
14#20298597C211yesmaximal, characteristic, complemented
15#484×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268647—21no—
18C2×#14268647C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268634C2211yescharacteristic
21C2×D904C2211yescharacteristic
22C2×#14268631C2211yescharacteristic
23C2×#14268630C2211yescharacteristic
24#16813621C2211yescharacteristic
25#16813620C2211yescharacteristic
26#16813607—21no—
27#16813607—21no—
28#16813605—21no—
29#16813604—21no—
30#16813602C2211yescharacteristic
31#16813600—21no—
32#16813597C2211yescharacteristic
33#16813596C2211yescharacteristic
34#16813595—21no—
35#16813584C2211yescharacteristic
36#16813584C2211yescharacteristic
37C4×C22⋊D113C2211yescharacteristic
38C4⋊C4×D113—21no—
39C4⋊C4×D113C2211yescharacteristic
40#16813555C2211yescharacteristic
41#16813551C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813546C2211yescharacteristic
44#16813545C2211yescharacteristic
45#16813545C2211yescharacteristic
46#16813544C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813534C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#103×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268648—22no—
60#14268648—41no—
61#14268647—22no—
62#14268647—41no—
63#14268647—44no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66C2×D452—21no—
67C2×D452—21no—
68C2×D452C2311yescharacteristic
69C2×D452C2311yescharacteristic
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113D411yescharacteristic
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—21no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113C2311yescharacteristic
79#14268636—41no—
80#14268634—41no—
81D904—22no—
82#14268631—41no—
83#14268630—41no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C4⋊Dic113—21no—
87C4⋊Dic113C2311yescharacteristic
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92#14268626D411yescharacteristic
93C22⋊Dic113D411yescharacteristic
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624—21no—
99#14268624D411yescharacteristic
100C4×Dic113C2311yescharacteristic
101C2×Q8×C113C2311yescharacteristic
102C22×C4×C113—21no—
103C22×C4×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C4⋊C4×C113—21no—
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113C2×D411yescharacteristic
113C22×D113—21no—
114C22×D113—21no—
115C22×D113C2×D411yescharacteristic
116Q8×C113—21no—
117Q8×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—42no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—22no—
128C22⋊D113—42no—
129C22⋊D113—42no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113C2×D411yescharacteristic
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—21no—
136D452—21no—
137D452—21no—
138D452—42no—
139D452—42no—
140D452#4112yescomplemented
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—42no—
144C4×D113—42no—
145C4×D113—42no—
146C4×D113—42no—
147C4×D113—42no—
148Dic226—21no—
149Dic226—21no—
150Dic226—42no—
151C8×C113—21no—
152C8×C113—21no—
153#11744751—21no—
154#11744751—21no—
155C22×C113—21no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113C22×D411yescharacteristic
159C2×D113—21no—
160C2×D113—22no—
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—41no—
168C4×C113—21no—
169C4×C113—41no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113—41no—
173C4×C113C2×#4111yescharacteristic
174C4×C113H(5,𝔽2)11yescharacteristic
175Dic113—21no—
176Dic113—21no—
177Dic113—41no—
178Dic113—41no—
179Dic113AGL(1,ℤ/8)12yes—
180C2×C113—41no—
181C2×C113#54611yescharacteristic
182C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C113#57811yescharacteristic
184D113—41no—
185D113—42no—
186D113—81no—
187#3330—1131nomaximal, Sylow
188C113#333011yescharacteristic, complemented, Sylow
189#547—1131no—
190#547—1131no—
191#487—1131no—
192#484—1131no—
193#484D11311yescharacteristic, complemented
194#474—1131no—
195#468—1131no—
196#468—1131no—
197#461—1131no—
198#449—1131no—
199#449—1131no—
200C4×D8—1131no—
201#436—1131no—
202#417—1131no—
203#417—1131no—
204C2×#41—1131no—
205C2×#41—1131no—
206C2×#41—2261no—
207C2×SD16—1131no—
208C2×SD16—1131no—
209C2×D8—1131no—
210C2×M16—1131no—
211C2×M16—1131no—
212C4⋊Q8—1131no—
213C4⋊Q8—1131no—
214#123—2261no—
215#123—2261no—
216#123—2261no—
217#123—2261no—
218C22⋊Q8—1131no—
219C22⋊Q8—2261no—
220C22⋊Q8C2×D11311yescharacteristic
221#121—1131no—
222#121—1131no—
223#121—2261no—
224C4×D4—1131no—
225C4×D4—1131no—
226C4×D4—1131no—
227C2×C4⋊C4—1131no—
228C2×C4⋊C4—2261no—
229C2×C4⋊C4C2×D11311yescharacteristic
230#107—1131no—
231#107C2×D11311yescharacteristic
232#107C2×D11311yescharacteristic
233C4⋊C8—1131no—
234#103—1131no—
235#103—1131no—
236#103—1131no—
237#103—1131no—
238#103C2×D11311yescharacteristic
239#103C2×D11311yescharacteristic
240#102—1131no—
241#102—1131no—
242#102—1131no—
243#102—1131no—
244C22⋊C8—1131no—
245C22⋊C8C2×D11311yescharacteristic
246C4×C8—1131no—
247#41—4521no—
248#41—4524no—
249#41—4521no—
250#41—2262no—
251#41—2262no—
252C2×Q8—1131no—
253C2×Q8—2261no—
254C2×Q8C22×D11311yescharacteristic
255C2×D4—1131no—
256C2×D4—1131no—
257C2×D4—1131no—
258C2×D4—2261no—
259C2×D4—2261no—
260C2×D4—2261no—
261C2×D4—2261no—
262C22×C4—21no—
263C22×C4—1131no—
264C22×C4—2261no—
265C22×C4—2261no—
266C22×C4—2261no—
267C22×C4—2261no—
268C22×C4—2261no—
269C22×C4C22×D11311yescharacteristic
270SD16—4521no—
271SD16—4521no—
272D8—2262no—
273M16—4521no—
274M16—4521no—
275C2×C8—1131no—
276C2×C8—1131no—
277C2×C8C22×D11311yescharacteristic
278C2×C8C22×D11311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4C22×D11311yescharacteristic
289C4⋊C4C22×D11311yescharacteristic
290C4⋊C4C22×D11311yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—1131no—
293C22⋊C4—1131no—
294C22⋊C4—2261no—
295C22⋊C4—2261no—
296C22⋊C4—2261no—
297C22⋊C4—2261no—
298C22⋊C4—2261no—
299C42—1131no—
300C23—1131no—
301C23—2261no—
302C23—2261no—
303C23D4×D11311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—4522no—
307Q8—2261no—
308Q8—2261no—
309D4—1132no—
310D4—4522no—
311D4—4522no—
312D4—4522no—
313D4—4522no—
314D4—2262no—
315D4—2261no—
316D4—2261no—
317D4—2261no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—1131no—
326C2×C4—1131no—
327C2×C4—1131no—
328C2×C4—4522no—
329C2×C4—4522no—
330C2×C4—4522no—
331C2×C4—4522no—
332C2×C4—4522no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4D4×D11311yescharacteristic
338C2×C4C23×D11311yescharacteristic
339C8—21no—
340C8—21no—
341C8—2261no—
342C8—2261no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—4521no—
347C22—4521no—
348C22—4521no—
349C22—4521no—
350C22—4521no—
351C22—2261no—
352C22—2261no—
353C22—2262no—
354C22—2261no—
355C22C2×D4×D11311yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—1132no—
362C4—4521no—
363C4—4521no—
364C4—2261no—
365C4—2261no—
366C4#41×D11311yescharacteristic
367C4#1681366811yescharacteristic
368C2—41no—
369C2—9041no—
370C2—4522no—
371C2—4521no—
372C2#2029924011yescharacteristic
373C2AGL(1,ℤ/8)×D11311yescharacteristic
374C2#2029941111yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#484×C113C2
socleC22×C113C22×D4
hypercenter#484D113
hypocenterC113#3330
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. #20299250C2semidirect
2. #20299249C2semidirect
3. #20298947C2semidirect
4. #20298935C2semidirect
5. #20298877C2semidirect
6. #20298846C2semidirect
7. #20298845C2semidirect
8. #20298802C2semidirect
9. #20298746C2semidirect
10. #20298745C2semidirect
11. #20298680C2semidirect
12. #20298673C2semidirect
13. #20298598C2semidirect
14. #20298597C2semidirect
15. #484×C113C2semidirect
140. D452#41semidirect
188. C113#3330semidirect
193. #484D113semidirect

Maximal subgroups

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

subgroupindex
#202992502
#202992492
#202989472
#202989352
#202988772
#202988462
#202988452
#202988022
#202987462
#202987452
#202986802
#202986732
#202985982
#202985972
#484×C1132
#3330113