Finite Group Databasebeta

← #28401043

Subgroups — #28401043

Order 14464.

564 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813651C211yesmaximal, characteristic, complemented
2C2×#16813649C211yesmaximal, characteristic, complemented
3C2×#16813643C211yesmaximal, characteristic, complemented
4C2×SD16×D113C211yesmaximal, characteristic, complemented
5#20299173C211yesmaximal, characteristic, complemented
6#20299161C211yesmaximal, characteristic, complemented
7#20298990C211yesmaximal, characteristic, complemented
8#20298989C211yesmaximal, characteristic, complemented
9#20298985C211yesmaximal, characteristic, complemented
10#20298984C211yesmaximal, characteristic, complemented
11#20298982C211yesmaximal, characteristic, complemented
12#20298979C211yesmaximal, characteristic, complemented
13#20298969C211yesmaximal, characteristic, complemented
14#20298552C211yesmaximal, characteristic, complemented
15#492×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic
20#16813651—24no—
21#16813649—24no—
22#16813643—24no—
23C2×Dic452C2211yescharacteristic, complemented
24C2×#14268637C2211yescharacteristic, complemented
25C2×#14268637C2211yescharacteristic, complemented
26C2×#14268636C2211yescharacteristic
27C2×#14268636C2211yescharacteristic, complemented
28C2×#14268635C2211yescharacteristic
29C2×#14268635C2211yescharacteristic, complemented
30C2×#14268634C2211yescharacteristic
31C2×#14268634C2211yescharacteristic
32SD16×D113—24no—
33C2×D904C2211yescharacteristic
34C2×#14268632C2211yescharacteristic
35C2×#14268632C2211yescharacteristic, complemented
36C2×#14268630C2211yescharacteristic
37C2×C8×D113C2211yescharacteristic
38#16813620C2211yescharacteristic, complemented
39#16813618C2211yescharacteristic
40#16813611C2211yescharacteristic, complemented
41#16813610C2211yescharacteristic
42#16813610C2211yescharacteristic, complemented
43#16813609C2211yescharacteristic
44#16813607—22no—
45#16813600—22no—
46#16813594—22no—
47#16813590—22no—
48#16813579C2211yescharacteristic
49#16813533C2211yescharacteristic, complemented
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic, complemented
56C4⋊Q8×C113C2211yescharacteristic, complemented
57#127×C113C2211yescharacteristic
58C4×C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268648—22no—
61#14268648—22no—
62#14268646—22no—
63#14268646—22no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66C2×Dic226C2311yescharacteristic
67Q8×D113—22no—
68Q8×D113—22no—
69C2×D452—21no—
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—22no—
75D4×D113—22no—
76D4×D113—22no—
77C22×Dic113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113C2311yescharacteristic
81Dic452—22no—
82#14268637—22no—
83#14268637—22no—
84#14268636—22no—
85#14268636—22no—
86#14268635—22no—
87#14268635—22no—
88#14268634—22no—
89#14268634—22no—
90D904—22no—
91#14268632—22no—
92#14268632—22no—
93#14268630D414yescomplemented
94C2×#11744751C2311yescharacteristic
95C2×#11744751C2311yescharacteristic
96C8×D113D414yescomplemented
97#14268626—22no—
98#14268626D412yes—
99C22⋊Dic113—22no—
100#14268624—22no—
101#14268624—22no—
102#14268624—22no—
103#14268624D412yes—
104C4×Dic113C2311yescharacteristic
105C2×Q8×C113C2311yescharacteristic
106C2×Q8×C113C2311yescharacteristic
107C2×D4×C113—22no—
108C2×D4×C113C2311yescharacteristic
109C2×D4×C113C2311yescharacteristic
110SD16×C113—22no—
111SD16×C113—22no—
112SD16×C113—22no—
113SD16×C113—22no—
114C2×C8×C113C2311yescharacteristic
115C2×C8×C113C2311yescharacteristic
116C4⋊C4×C113—22no—
117C42×C113C2311yescharacteristic
118C23×C113—21no—
119C23×C113—21no—
120C22×D113—21no—
121C22×D113—21no—
122C22×D113—42no—
123C22×D113—82no—
124C22×D113C2×D411yescharacteristic
125Q8×C113—21no—
126Q8×C113—21no—
127Q8×C113—21no—
128Q8×C113—21no—
129D4×C113—21no—
130D4×C113—21no—
131D4×C113—21no—
132D4×C113—21no—
133D4×C113—82no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113C2×D412yes—
137C2×C4×C113C2411yescharacteristic
138C22⋊D113—42no—
139C22⋊D113—42no—
140C22⋊D113—82no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—42no—
144C2×Dic113C2×D412yes—
145C2×Dic113C2×D411yescharacteristic
146D452—21no—
147D452—21no—
148D452—21no—
149D452—21no—
150D452—42no—
151C4×D113—42no—
152C4×D113—42no—
153C4×D113C2×D412yes—
154C4×D113C2×D412yes—
155Dic226—21no—
156Dic226—21no—
157Dic226—21no—
158Dic226—21no—
159Dic226—42no—
160C8×C113C2×D412yes—
161C8×C113C2×D412yes—
162#11744751C2×D412yes—
163#11744751C2×D412yes—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—42no—
167C22×C113—42no—
168C22×C113C22×D411yescharacteristic
169C2×D113—22no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—42no—
173C2×D113—42no—
174C2×D113—84no—
175C2×D113#12712yes—
176C4×C113—22no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113C22×D411yescharacteristic
180C4×C113C22×D411yescharacteristic
181Dic113—22no—
182Dic113—41no—
183Dic113—41no—
184Dic113#12712yes—
185C2×C113—81no—
186C2×C113—81no—
187C2×C113C2×#12711yescharacteristic
188C2×C113#57712yes—
189D113—22no—
190D113—81no—
191D113—81no—
192#3154—1131nomaximal, Sylow
193C113#315411yescharacteristic, complemented, Sylow
194C2×#137—1131no—
195C2×AGL(1,ℤ/8)—1131no—
196C2×#135—1131no—
197C22×SD16—1131no—
198#536—1131no—
199#535—1131no—
200#497—1131no—
201#497—1131no—
202#496—1131no—
203#496—1131no—
204#495—1131no—
205#495—1131no—
206#492—1131no—
207#492D11311yescharacteristic, complemented
208#405—1131no—
209C2×#41—1131no—
210C2×#41—1131no—
211C22×Q8—1131no—
212C22×D4—1131no—
213#137—2264no—
214AGL(1,ℤ/8)—2264no—
215#135—2264no—
216C2×Q16—1131no—
217C2×Q16—1131no—
218C2×Q16—1131no—
219C2×SD16—1131no—
220C2×SD16—1131no—
221C2×SD16—1131no—
222C2×SD16—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×SD16—2264no—
226C2×SD16C2×D11311yescharacteristic
227C2×SD16C2×D11311yescharacteristic
228C2×SD16C2×D11311yescharacteristic, complemented
229C2×SD16C2×D11311yescharacteristic, complemented
230C2×D8—1131no—
231C2×D8—1131no—
232C2×D8—1131no—
233C2×M16—1131no—
234C22×C8—1131no—
235C4⋊Q8—1131no—
236C4⋊Q8C2×D11311yescharacteristic, complemented
237#127—1131no—
238#127C2×D11311yescharacteristic
239#124—1131no—
240#124—1131no—
241#124—1131no—
242#124—1131no—
243#123—2262no—
244C22⋊Q8—2262no—
245#121—2262no—
246#120—2262no—
247#117—1131no—
248#97—1131no—
249#97—1131no—
250C4×C8—1131no—
251C4×C8C2×D11311yescharacteristic, complemented
252C24—2261no—
253#41—2262no—
254#41—2262no—
255#41—2262no—
256#41—2262no—
257C2×Q8—1131no—
258C2×Q8—1131no—
259C2×Q8—2261no—
260C2×Q8—2262no—
261C2×Q8—2262no—
262C2×Q8C22×D11311yescharacteristic
263C2×Q8C22×D11311yescharacteristic
264C2×D4—22no—
265C2×D4—1131no—
266C2×D4—1131no—
267C2×D4—2261no—
268C2×D4—2262no—
269C2×D4—2262no—
270C2×D4—2262no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4C22×D11311yescharacteristic
274C2×D4C22×D11311yescharacteristic
275C22×C4—1131no—
276C22×C4—2261no—
277C22×C4—2261no—
278C22×C4—2261no—
279Q16—2262no—
280Q16—2262no—
281Q16—2262no—
282SD16—22no—
283SD16—22no—
284SD16—22no—
285SD16—22no—
286SD16—2262no—
287SD16—2262no—
288SD16—2262no—
289SD16—2262no—
290SD16—2262no—
291SD16—2262no—
292D8—2262no—
293D8—2262no—
294D8—2262no—
295M16—1134no—
296C2×C8—1131no—
297C2×C8—1131no—
298C2×C8—1134no—
299C2×C8C22×D11311yescharacteristic
300C2×C8C22×D11311yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—1132no—
303C4⋊C4—2262no—
304C22⋊C4—1132no—
305C22⋊C4—2262no—
306C22⋊C4—2262no—
307C22⋊C4—2262no—
308C22⋊C4—2262no—
309C42—1131no—
310C42C22×D11311yescharacteristic
311C23—21no—
312C23—21no—
313C23—1131no—
314C23—9042no—
315C23—4522no—
316C23—2261no—
317C23—2261no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—4522no—
323Q8—2261no—
324Q8—2261no—
325Q8—2261no—
326Q8—2261no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—82no—
332D4—9042no—
333D4—4522no—
334D4—4522no—
335D4—4522no—
336D4—2261no—
337D4—2261no—
338D4—2261no—
339D4—2261no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—1131no—
343C2×C4—1132no—
344C2×C4—1132no—
345C2×C4—1132no—
346C2×C4—4522no—
347C2×C4—4522no—
348C2×C4—4522no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4D4×D11312yes—
352C2×C4C23×D11311yescharacteristic
353C8—1132no—
354C8—1132no—
355C8D4×D11312yes—
356C8D4×D11312yes—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—42no—
361C22—1132no—
362C22—9044no—
363C22—4521no—
364C22—4521no—
365C22—4522no—
366C22—4522no—
367C22—2262no—
368C22C2×D4×D11311yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—1132no—
373C4—4521no—
374C4—4521no—
375C4—2262no—
376C4C2×D4×D11311yescharacteristic
377C4C2×D4×D11311yescharacteristic
378C2—81no—
379C2—81no—
380C2—9041no—
381C2—9041no—
382C2—2262no—
383C2#127×D11311yescharacteristic
384C2#2029940412yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#492×C113C2
socleC22×C113C22×D4
hypercenter#492D113
hypocenterC113#3154
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#16813651C2semidirect
2. C2×#16813649C2semidirect
3. C2×#16813643C2semidirect
4. C2×SD16×D113C2semidirect
5. #20299173C2semidirect
6. #20299161C2semidirect
7. #20298990C2semidirect
8. #20298989C2semidirect
9. #20298985C2semidirect
10. #20298984C2semidirect
11. #20298982C2semidirect
12. #20298979C2semidirect
13. #20298969C2semidirect
14. #20298552C2semidirect
15. #492×C113C2semidirect
23. C2×Dic452C22semidirect
24. C2×#14268637C22semidirect
25. C2×#14268637C22semidirect
27. C2×#14268636C22semidirect
29. C2×#14268635C22semidirect
35. C2×#14268632C22semidirect
38. #16813620C22semidirect
40. #16813611C22semidirect
42. #16813610C22semidirect
49. #16813533C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
54. C2×SD16×C113C22semidirect
55. C2×SD16×C113C22semidirect
56. C4⋊Q8×C113C22semidirect
58. C4×C8×C113C22semidirect
93. #14268630D4semidirect
96. C8×D113D4semidirect
193. C113#3154semidirect
207. #492D113semidirect
228. C2×SD16C2×D113semidirect
229. C2×SD16C2×D113semidirect
236. C4⋊Q8C2×D113semidirect
251. C4×C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136512
C2×#168136492
C2×#168136432
C2×SD16×D1132
#202991732
#202991612
#202989902
#202989892
#202989852
#202989842
#202989822
#202989792
#202989692
#202985522
#492×C1132
#3154113