Finite Group Databasebeta

← #28402750

Subgroups — #28402750

Order 14464.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299298C211yesmaximal, characteristic
2Q8×D452C211yesmaximal, characteristic, complemented
3#20298967C211yesmaximal, characteristic, complemented
4#20298941C211yesmaximal, characteristic, complemented
5#20298935C211yesmaximal, characteristic, complemented
6#20298905C211yesmaximal, characteristic, complemented
7#20298843C211yesmaximal, characteristic, complemented
8#20298826C211yesmaximal, characteristic, complemented
9#20298803C211yesmaximal, characteristic, complemented
10#20298735C211yesmaximal, characteristic, complemented
11#20298735C211yesmaximal, characteristic, complemented
12#20298671C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#103×D113C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×Q8×D113C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813622—21no—
23#16813622C2211yescharacteristic
24#16813615—21no—
25#16813614C2211yescharacteristic
26#16813605—21no—
27#16813602—21no—
28#16813602—21no—
29#16813602C2211yescharacteristic
30#16813602C2211yescharacteristic
31#16813595—21no—
32#16813593C2211yescharacteristic
33#16813593C2211yescharacteristic
34C4×D452—21no—
35C4×D452C2211yescharacteristic
36C4×C22⋊D113—21no—
37#16813580C2211yescharacteristic
38C4⋊C4×D113C2211yescharacteristic
39#16813555C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813547C2211yescharacteristic
43#16813547C2211yescharacteristic
44#16813547C2211yescharacteristic
45#16813547C2211yescharacteristic
46#16813546C2211yescharacteristic
47#16813546C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113—22no—
65Q8×D113—41no—
66Q8×D113—41no—
67C2×D452D411yescharacteristic
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113C2311yescharacteristic
74C2×C4×D113C2311yescharacteristic
75#14268635—41no—
76#14268635—41no—
77#14268630—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C8×D113—41no—
81C4⋊Dic113—21no—
82C4⋊Dic113—21no—
83C4⋊Dic113—21no—
84C4⋊Dic113—21no—
85C4⋊Dic113D411yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624D411yescharacteristic
97#14268624D411yescharacteristic
98C4×Dic113—21no—
99C2×Q8×C113C2311yescharacteristic
100C2×D4×C113C2311yescharacteristic
101C22×C4×C113—21no—
102SD16×C113—22no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C4⋊C4×C113C2311yescharacteristic
108C22⋊C4×C113—21no—
109C42×C113—21no—
110C42×C113C2311yescharacteristic
111C23×C113—21no—
112C22×D113C2×D411yescharacteristic
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113#4112yes—
116D4×C113—21no—
117D4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—81no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113—42no—
126C22⋊D113—81no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133D452—22no—
134C4×D113—21no—
135C4×D113—21no—
136C4×D113—21no—
137C4×D113—21no—
138C4×D113—42no—
139C4×D113—42no—
140C4×D113—81no—
141Dic226—21no—
142Dic226—21no—
143Dic226—21no—
144Dic226—21no—
145Dic226—42no—
146Dic226—42no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C2×D113—21no—
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—21no—
159C2×D113—21no—
160C2×D113#13712yes—
161C4×C113—22no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113C2×#4111yescharacteristic
167C4×C113H(5,𝔽2)11yescharacteristic
168Dic113—21no—
169Dic113—21no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—81no—
175C2×C113#54611yescharacteristic
176C2×C113C2×#13711yescharacteristic
177C2×C113#57711yescharacteristic
178D113—22no—
179D113—41no—
180#3320—1131nomaximal, Sylow
181C113#332011yescharacteristic, complemented, Sylow
182#553—1131no—
183D4×Q8—1131no—
184#491—1131no—
185#485—1131no—
186#484—1131no—
187#479—1131no—
188#468—1131no—
189#465—1131no—
190#461—1131no—
191#448—1131no—
192#448—1131no—
193#440D11311yescharacteristic, complemented
194#435—1131no—
195#419—1131no—
196C2×#103—1131no—
197C22×Q8—1131no—
198C22×Q8—1131no—
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×SD16C2×D11311yescharacteristic
202C2×M16—1131no—
203C22×C8—1131no—
204C4⋊Q8—1131no—
205C4⋊Q8—2261no—
206#126—2261no—
207#125—1131no—
208#123—2261no—
209C22⋊Q8—1131no—
210C22⋊Q8—1131no—
211C22⋊Q8—2261no—
212C22⋊Q8—2261no—
213#121—1131no—
214#121—1131no—
215#121—2261no—
216C4×Q8C2×D11311yescharacteristic
217C4×D4—1131no—
218C4×D4—2261no—
219C4×D4—2261no—
220C4×D4C2×D11311yescharacteristic
221#117—1131no—
222C2×C4⋊C4—1131no—
223#107—1131no—
224#107C2×D11311yescharacteristic
225#106—1131no—
226C4⋊C8—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#103—1131no—
233#103—1131no—
234#103—1131no—
235#103C2×D11311yescharacteristic
236#102C2×D11311yescharacteristic
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239#97C2×D11311yescharacteristic
240C2×Q8—1131no—
241C2×Q8—1131no—
242C2×Q8—4521no—
243C2×Q8—4521no—
244C2×Q8—2261no—
245C2×Q8—2261no—
246C2×Q8—2262no—
247C2×Q8—2262no—
248C2×Q8C22×D11311yescharacteristic
249C2×D4—1131no—
250C2×D4—2261no—
251C2×D4—2261no—
252C2×D4C22×D11311yescharacteristic
253C22×C4—21no—
254C22×C4—1131no—
255C22×C4—1131no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4—2261no—
259SD16—22no—
260SD16—4521no—
261SD16—4521no—
262M16—4521no—
263C2×C8—1131no—
264C2×C8—1131no—
265C2×C8—4521no—
266C2×C8C22×D11311yescharacteristic
267C2×C8C22×D11311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—1131no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4—2261no—
276C4⋊C4—2261no—
277C4⋊C4—2261no—
278C4⋊C4—2261no—
279C4⋊C4C22×D11311yescharacteristic
280C4⋊C4C22×D11311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—1131no—
283C22⋊C4—1131no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C42—21no—
290C42—2261no—
291C42C22×D11311yescharacteristic
292C23—21no—
293C23—1131no—
294C23—1131no—
295Q8—21no—
296Q8—4522no—
297Q8—4522no—
298Q8—2261no—
299Q8—2261no—
300Q8—2261no—
301Q8—2261no—
302Q8#1426864712yes—
303D4—21no—
304D4—21no—
305D4—9041no—
306D4—4522no—
307D4—2262no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—9041no—
315C2×C4—4522no—
316C2×C4—4522no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4D4×D11311yescharacteristic
326C2×C4D4×D11311yescharacteristic
327C2×C4C23×D11311yescharacteristic
328C8—21no—
329C8—21no—
330C8—2261no—
331C8—2261no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—1132no—
336C22—2261no—
337C22—2261no—
338C22—2261no—
339C22—2261no—
340C22—2261no—
341C22C2×D4×D11311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—41no—
346C4—41no—
347C4—4521no—
348C4—4521no—
349C4—4521no—
350C4—4521no—
351C4—2261no—
352C4—2261no—
353C4C2×#1426864711yescharacteristic
354C4#1681366811yescharacteristic
355C2—81no—
356C2—4521no—
357C2—2262no—
358C2#2029924411yescharacteristic
359C2#137×D11311yescharacteristic
360C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radical#20299298C2
hypercenter#440D113
hypocenterC113#3320
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. Q8×D452C2semidirect
3. #20298967C2semidirect
4. #20298941C2semidirect
5. #20298935C2semidirect
6. #20298905C2semidirect
7. #20298843C2semidirect
8. #20298826C2semidirect
9. #20298803C2semidirect
10. #20298735C2semidirect
11. #20298735C2semidirect
12. #20298671C2semidirect
13. #20298605C2semidirect
14. #103×D113C2semidirect
15. #440×C113C2semidirect
181. C113#3320semidirect
193. #440D113semidirect

Maximal subgroups

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

subgroupindex
#202992982
Q8×D4522
#202989672
#202989412
#202989352
#202989052
#202988432
#202988262
#202988032
#202987352
#202986712
#202986052
#103×D1132
#440×C1132
#3320113