Finite Group Databasebeta

← #28402141

Subgroups — #28402141

Order 14464.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813651C211yesmaximal, characteristic, complemented
2C22×Dic452C211yesmaximal, characteristic, complemented
3#20299261C211yesmaximal, characteristic, complemented
4#20299254C211yesmaximal, characteristic
5#20298989C211yesmaximal, characteristic, complemented
6#20298857C211yesmaximal, characteristic, complemented
7#20298819C211yesmaximal, characteristic, complemented
8#20298807C211yesmaximal, characteristic, complemented
9#20298761C211yesmaximal, characteristic, complemented
10#20298755C211yesmaximal, characteristic, complemented
11#20298753C211yesmaximal, characteristic, complemented
12#20298736C211yesmaximal, characteristic, complemented
13#20298704C211yesmaximal, characteristic, complemented
14#20298669C211yesmaximal, characteristic, complemented
15#465×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C22×Dic226C2211yescharacteristic
18C22×Dic226C2211yescharacteristic
19C2×Q8×D113C2211yescharacteristic
20#16813651—24no—
21C2×Dic452—24no—
22C2×Dic452C2211yescharacteristic
23C2×Dic452C2211yescharacteristic
24C2×Dic452C2211yescharacteristic
25C2×Dic452C2211yescharacteristic
26C2×#14268637C2211yescharacteristic
27C2×#14268637C2211yescharacteristic
28C2×#14268635C2211yescharacteristic
29C2×#14268635C2211yescharacteristic
30C2×#14268630C2211yescharacteristic
31#16813621—21no—
32#16813620C2211yescharacteristic
33#16813609C2211yescharacteristic
34#16813608—21no—
35#16813602C2211yescharacteristic
36#16813602C2211yescharacteristic
37#16813600—21no—
38#16813599—21no—
39#16813599—21no—
40#16813594—21no—
41#16813587C2211yescharacteristic
42#16813587C2211yescharacteristic
43D4×Dic113—21no—
44C4×C22⋊D113C2211yescharacteristic
45#16813582—21no—
46#16813551C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813545C2211yescharacteristic
51C22⋊#11744751C2211yescharacteristic
52#16813534C2211yescharacteristic
53#16813532C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22×C8×C113C2211yescharacteristic
56C22⋊Q8×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic
58#106×C113C2211yescharacteristic
59#103×C113C2211yescharacteristic
60#102×C113C2211yescharacteristic
61#14268646—22no—
62#14268646—41no—
63C2×Dic226—22no—
64C2×Dic226—22no—
65C2×Dic226—21no—
66C2×Dic226—21no—
67C2×Dic226—21no—
68C2×Dic226—41no—
69C2×Dic226—41no—
70C2×Dic226C2311yescharacteristic
71C2×Dic226C2311yescharacteristic
72C2×Dic226C2311yescharacteristic
73C2×Dic226C2311yescharacteristic
74Q8×D113—22no—
75Q8×D113—41no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113D411yescharacteristic
78C22×Dic113—21no—
79C22×Dic113—21no—
80C22×Dic113—21no—
81C2×C4×D113—21no—
82C2×C4×D113C2311yescharacteristic
83Dic452—22no—
84Dic452—22no—
85Dic452—22no—
86Dic452D414yescomplemented
87#14268637—22no—
88#14268637—41no—
89#14268635—22no—
90#14268635—41no—
91#14268630—22no—
92C2×#11744751C2311yescharacteristic
93C2×#11744751C2311yescharacteristic
94C4⋊Dic113—21no—
95C4⋊Dic113—21no—
96#14268626—21no—
97#14268626—21no—
98#14268626—21no—
99#14268626—21no—
100#14268626D411yescharacteristic
101C22⋊Dic113—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113D411yescharacteristic
104#14268624—21no—
105#14268624—21no—
106#14268624D411yescharacteristic
107C4×Dic113—21no—
108C4×Dic113—21no—
109C4×Dic113C2311yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113C2311yescharacteristic
114SD16×C113—22no—
115C2×C8×C113—22no—
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C4⋊C4×C113—21no—
119C4⋊C4×C113C2311yescharacteristic
120C4⋊C4×C113C2311yescharacteristic
121C22⋊C4×C113—21no—
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113C2×D411yescharacteristic
125C22×D113C2×D411yescharacteristic
126Q8×C113—21no—
127Q8×C113—21no—
128D4×C113—21no—
129D4×C113—21no—
130D4×C113—42no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2411yescharacteristic
138C22⋊D113—22no—
139C22⋊D113—42no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—21no—
144C2×Dic113—42no—
145C2×Dic113—42no—
146C2×Dic113—42no—
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149C2×Dic113C2×D411yescharacteristic
150C4×D113—21no—
151C4×D113—21no—
152C4×D113—42no—
153Dic226—21no—
154Dic226—21no—
155Dic226—21no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—42no—
160Dic226—42no—
161Dic226—42no—
162Dic226C2×D412yes—
163Dic226C2×D412yes—
164C8×C113—21no—
165C8×C113C2×D412yes—
166#11744751—21no—
167#11744751—21no—
168C22×C113—21no—
169C22×C113—21no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113#13712yescomplemented
174C22×C113C22×D411yescharacteristic
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113C22×D411yescharacteristic
183C4×C113H(5,𝔽2)11yescharacteristic
184Dic113—22no—
185Dic113—22no—
186Dic113—21no—
187Dic113—21no—
188Dic113—21no—
189Dic113—41no—
190Dic113—41no—
191C2×C113—22no—
192C2×C113—81no—
193C2×C113D4211yescharacteristic
194C2×C113C2×#13711yescharacteristic
195C2×C113#57811yescharacteristic
196D113—41no—
197#3270—1131nomaximal, Sylow
198C113#327011yescharacteristic, complemented, Sylow
199C2×#137—1131no—
200C22×Q16—1131no—
201D4×Q8—1131no—
202#548—1131no—
203#497—1131no—
204#470—1131no—
205#465D11311yescharacteristic, complemented
206#464—1131no—
207#462—1131no—
208#452—1131no—
209#451—1131no—
210#451—1131no—
211#448—1131no—
212#441—1131no—
213#435—1131no—
214C2×#41—1131no—
215C22×Q8—1131no—
216C22×Q8—1131no—
217C22×Q8—1131no—
218#137—2264no—
219C2×Q16—1131no—
220C2×Q16—1131no—
221C2×Q16—1131no—
222C2×Q16—1131no—
223C2×Q16—1131no—
224C2×Q16—1131no—
225C2×Q16—2264no—
226C2×SD16—1131no—
227C2×SD16—1131no—
228C2×SD16C2×D11311yescharacteristic
229C2×M16—1131no—
230C22×C8C2×D11311yescharacteristic
231C4⋊Q8—1131no—
232C4⋊Q8—2261no—
233#124—1131no—
234#124—2261no—
235C22⋊Q8—1131no—
236C22⋊Q8—1131no—
237C22⋊Q8—2261no—
238C22⋊Q8—2261no—
239C22⋊Q8—2261no—
240C22⋊Q8C2×D11311yescharacteristic
241#121—2261no—
242#121C2×D11311yescharacteristic
243C4×Q8—1131no—
244C4×Q8—1131no—
245C4×D4—1131no—
246C4×D4—2261no—
247C4×D4—2261no—
248#106C2×D11311yescharacteristic
249C4⋊C8—1131no—
250#103—1131no—
251#103—1131no—
252#103—1131no—
253#103—1131no—
254#103C2×D11311yescharacteristic
255#102C2×D11311yescharacteristic
256C22⋊C8—1131no—
257C22⋊C8—1131no—
258#97—1131no—
259#41—4521no—
260#41—2262no—
261C2×Q8—1131no—
262C2×Q8—1131no—
263C2×Q8—1131no—
264C2×Q8—1131no—
265C2×Q8—4521no—
266C2×Q8—4521no—
267C2×Q8—4521no—
268C2×Q8—2261no—
269C2×Q8—2262no—
270C2×Q8—2262no—
271C2×Q8—2262no—
272C2×Q8—2261no—
273C2×Q8—2261no—
274C2×Q8C22×D11311yescharacteristic
275C2×D4—21no—
276C2×D4—1131no—
277C2×D4—2261no—
278C2×D4C22×D11311yescharacteristic
279C22×C4—1131no—
280C22×C4—2261no—
281C22×C4—2261no—
282C22×C4—2261no—
283C22×C4—2261no—
284C22×C4C22×D11311yescharacteristic
285Q16—1134no—
286Q16—4521no—
287Q16—2262no—
288Q16—2262no—
289Q16—2262no—
290Q16—2262no—
291SD16—22no—
292SD16—4521no—
293SD16—2262no—
294M16—2262no—
295C2×C8—22no—
296C2×C8—1131no—
297C2×C8—1131no—
298C2×C8C22×D11311yescharacteristic
299C2×C8C22×D11311yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—1131no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4—2261no—
308C4⋊C4C22×D11311yescharacteristic
309C4⋊C4C22×D11311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—1131no—
313C22⋊C4—1131no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C22⋊C4—2261no—
318C42—1131no—
319C42—2261no—
320C42—2261no—
321C23—21no—
322C23—1131no—
323C23D4×D11311yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—1132no—
327Q8—1132no—
328Q8—4522no—
329Q8—4522no—
330Q8—4522no—
331Q8—2261no—
332Q8—2261no—
333Q8—2261no—
334Q8—2261no—
335Q8—2261no—
336Q8—2261no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—4522no—
341D4—2262no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—1131no—
348C2×C4—1131no—
349C2×C4—1131no—
350C2×C4—4522no—
351C2×C4—4522no—
352C2×C4—4522no—
353C2×C4—4522no—
354C2×C4—2261no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4D4×D11311yescharacteristic
361C2×C4C23×D11311yescharacteristic
362C8—21no—
363C8—2261no—
364C8—2261no—
365C8D4×D11312yes—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—2261no—
372C22—2261no—
373C22—2261no—
374C22#1681365112yescomplemented
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—4521no—
381C4—4521no—
382C4—2261no—
383C4—2261no—
384C4—2261no—
385C4—2262no—
386C4—2262no—
387C4C2×D4×D11311yescharacteristic
388C4#1681366811yescharacteristic
389C2—22no—
390C2—81no—
391C2—4521no—
392C2#2029923211yescharacteristic
393C2C2×#1681365111yescharacteristic
394C2#2029941211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#465×C113C2
socleC22×C113C22×D4
prime radical#20299254C2
hypercenter#465D113
hypocenterC113#3270
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#16813651C2semidirect
2. C22×Dic452C2semidirect
3. #20299261C2semidirect
5. #20298989C2semidirect
6. #20298857C2semidirect
7. #20298819C2semidirect
8. #20298807C2semidirect
9. #20298761C2semidirect
10. #20298755C2semidirect
11. #20298753C2semidirect
12. #20298736C2semidirect
13. #20298704C2semidirect
14. #20298669C2semidirect
15. #465×C113C2semidirect
86. Dic452D4semidirect
173. C22×C113#137semidirect
198. C113#3270semidirect
205. #465D113semidirect
374. C22#16813651semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
C22×Dic4522
#202992612
#202992542
#202989892
#202988572
#202988192
#202988072
#202987612
#202987552
#202987532
#202987362
#202987042
#202986692
#465×C1132
#3270113