Finite Group Databasebeta

← #28401049

Subgroups — #28401049

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×#16813654C211yesmaximal, characteristic, complemented
2C2×#16813649C211yesmaximal, characteristic, complemented
3C2×#16813645C211yesmaximal, characteristic, complemented
4C2×SD16×D113C211yesmaximal, characteristic, complemented
5#20299173C211yesmaximal, characteristic, complemented
6#20299166C211yesmaximal, characteristic, complemented
7#20298991C211yesmaximal, characteristic, complemented
8#20298987C211yesmaximal, characteristic, complemented
9#20298984C211yesmaximal, characteristic, complemented
10#20298983C211yesmaximal, characteristic, complemented
11#20298980C211yesmaximal, characteristic, complemented
12#20298972C211yesmaximal, characteristic, complemented
13#20298969C211yesmaximal, characteristic, complemented
14#20298555C211yesmaximal, characteristic, complemented
15#497×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268648C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic
20#16813654—24no—
21#16813649—24no—
22#16813645—24no—
23C2×#14268637C2211yescharacteristic, complemented
24C2×#14268636C2211yescharacteristic
25C2×#14268636C2211yescharacteristic, complemented
26C2×#14268635C2211yescharacteristic
27C2×#14268634C2211yescharacteristic
28C2×#14268634C2211yescharacteristic
29C2×#14268634C2211yescharacteristic, complemented
30C2×#14268634C2211yescharacteristic, complemented
31C2×#14268634C2211yescharacteristic, complemented
32SD16×D113—24no—
33C2×D904C2211yescharacteristic
34C2×D904C2211yescharacteristic, complemented
35C2×#14268632C2211yescharacteristic
36C2×#14268630C2211yescharacteristic
37C2×C8×D113C2211yescharacteristic
38#16813620C2211yescharacteristic, complemented
39#16813619C2211yescharacteristic
40#16813618C2211yescharacteristic
41#16813611C2211yescharacteristic
42#16813611C2211yescharacteristic, complemented
43#16813610C2211yescharacteristic, complemented
44#16813607—22no—
45#16813600—22no—
46#16813595—22no—
47#16813592—22no—
48#16813579C2211yescharacteristic
49#16813532C2211yescharacteristic, complemented
50C4×#11744751C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×Q16×C113C2211yescharacteristic, complemented
53C2×Q16×C113C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic
55C2×SD16×C113C2211yescharacteristic
56C4⋊Q8×C113C2211yescharacteristic, complemented
57#124×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268648—22no—
61#14268648—22no—
62#14268648—22no—
63#14268648—22no—
64C2×Dic226—21no—
65C2×Dic226C2311yescharacteristic
66Q8×D113—22no—
67Q8×D113—22no—
68C2×D452—21no—
69C2×D452—21no—
70C2×D452—22no—
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×D452C2311yescharacteristic
74C2×C22⋊D113—21no—
75C2×C22⋊D113—22no—
76D4×D113—22no—
77D4×D113—22no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113—21no—
81C2×C4×D113C2311yescharacteristic
82#14268637—22no—
83#14268636—22no—
84#14268636—22no—
85#14268635—22no—
86#14268634—22no—
87#14268634—22no—
88#14268634—22no—
89#14268634—22no—
90#14268634—22no—
91D904—22no—
92D904—22no—
93#14268632—22no—
94#14268630D414yescomplemented
95C2×#11744751C2311yescharacteristic
96C2×#11744751C2311yescharacteristic
97C8×D113D414yescomplemented
98#14268626—22no—
99#14268626D412yes—
100#14268624—22no—
101#14268624—22no—
102#14268624—22no—
103#14268624D412yes—
104C4×Dic113C2311yescharacteristic
105C2×Q8×C113C2311yescharacteristic
106C2×Q8×C113C2311yescharacteristic
107C2×Q8×C113C2311yescharacteristic
108C2×D4×C113C2311yescharacteristic
109Q16×C113—22no—
110Q16×C113—22no—
111SD16×C113—22no—
112SD16×C113—22no—
113C2×C8×C113C2311yescharacteristic
114C2×C8×C113C2311yescharacteristic
115C4⋊C4×C113—22no—
116C22⋊C4×C113—22no—
117C42×C113C2311yescharacteristic
118C23×C113—21no—
119C22×D113—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—
129Q8×C113—21no—
130Q8×C113—21no—
131D4×C113—21no—
132D4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113C2×D412yes—
137C2×C4×C113C2411yescharacteristic
138C22⋊D113—42no—
139C22⋊D113—82no—
140C2×Dic113—21no—
141C2×Dic113C2×D412yes—
142C2×Dic113C2×D411yescharacteristic
143D452—21no—
144D452—21no—
145D452—21no—
146D452—21no—
147D452—21no—
148D452—21no—
149D452—42no—
150D452—42no—
151D452—82no—
152C4×D113—42no—
153C4×D113—42no—
154C4×D113—42no—
155C4×D113C2×D412yes—
156C4×D113C2×D412yes—
157Dic226—21no—
158Dic226—21no—
159Dic226—42no—
160C8×C113C2×D412yes—
161C8×C113C2×D412yes—
162#11744751C2×D412yes—
163#11744751C2×D412yes—
164C22×C113—41no—
165C22×C113—42no—
166C22×C113C22×D411yescharacteristic
167C2×D113—22no—
168C2×D113—41no—
169C2×D113—41no—
170C2×D113—41no—
171C2×D113—42no—
172C2×D113—42no—
173C2×D113—42no—
174C2×D113—84no—
175C2×D113#12712yes—
176C4×C113—22no—
177C4×C113—41no—
178C4×C113—41no—
179C4×C113—41no—
180C4×C113C22×D411yescharacteristic
181C4×C113C22×D411yescharacteristic
182Dic113—22no—
183Dic113—41no—
184Dic113#12712yes—
185C2×C113—81no—
186C2×C113C2×#12711yescharacteristic
187C2×C113#57712yes—
188D113—22no—
189D113—81no—
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#497D11311yescharacteristic, complemented
202#496—1131no—
203#496—1131no—
204#495—1131no—
205#495—1131no—
206#492—1131no—
207#492—1131no—
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×Q16C2×D11311yescharacteristic, complemented
218C2×Q16C2×D11311yescharacteristic, complemented
219C2×SD16—1131no—
220C2×SD16—1131no—
221C2×SD16—1131no—
222C2×SD16—1131no—
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×SD16—1131no—
226C2×SD16—1131no—
227C2×SD16—2264no—
228C2×SD16C2×D11311yescharacteristic
229C2×SD16C2×D11311yescharacteristic
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#127—1131no—
239#124—1131no—
240#124—1131no—
241#124—1131no—
242#124C2×D11311yescharacteristic
243#123—2262no—
244C22⋊Q8—2262no—
245#121—2262no—
246#120—2262no—
247#117—1131no—
248#97—1131no—
249#97C2×D11311yescharacteristic, complemented
250C4×C8—1131no—
251C4×C8—1131no—
252C24—2261no—
253#41—2262no—
254#41—2262no—
255#41—2262no—
256#41—2262no—
257C2×Q8—1131no—
258C2×Q8—2261no—
259C2×Q8—2262no—
260C2×Q8—2262no—
261C2×Q8C22×D11311yescharacteristic
262C2×Q8C22×D11311yescharacteristic
263C2×Q8C22×D11311yescharacteristic
264C2×D4—1131no—
265C2×D4—1131no—
266C2×D4—1131no—
267C2×D4—2261no—
268C2×D4—2261no—
269C2×D4—2262no—
270C2×D4—2262no—
271C2×D4—2262no—
272C2×D4—2261no—
273C2×D4—2262no—
274C2×D4C22×D11311yescharacteristic
275C22×C4—1131no—
276C22×C4—2261no—
277C22×C4—2261no—
278C22×C4—2261no—
279Q16—22no—
280Q16—22no—
281Q16—2262no—
282SD16—22no—
283SD16—22no—
284SD16—2262no—
285SD16—2262no—
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—22no—
305C22⋊C4—1132no—
306C22⋊C4—2262no—
307C22⋊C4—2262no—
308C22⋊C4—2262no—
309C42—1131no—
310C42C22×D11311yescharacteristic
311C23—21no—
312C23—1131no—
313C23—9042no—
314C23—4522no—
315C23—2261no—
316C23—2261no—
317C23—2261no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—4522no—
325Q8—2261no—
326Q8—2261no—
327D4—21no—
328D4—21no—
329D4—9042no—
330D4—9042no—
331D4—4522no—
332D4—4522no—
333D4—4522no—
334D4—2261no—
335D4—2261no—
336D4—2261no—
337D4—2261no—
338D4—2261no—
339D4—2261no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—1131no—
344C2×C4—1132no—
345C2×C4—1132no—
346C2×C4—1132no—
347C2×C4—4522no—
348C2×C4—4522no—
349C2×C4—4522no—
350C2×C4—2261no—
351C2×C4D4×D11312yes—
352C2×C4C23×D11311yescharacteristic
353C8—1132no—
354C8—1132no—
355C8D4×D11312yes—
356C8D4×D11312yes—
357C22—41no—
358C22—42no—
359C22—1132no—
360C22—9044no—
361C22—4521no—
362C22—4521no—
363C22—4521no—
364C22—4522no—
365C22—4522no—
366C22—4522no—
367C22—2262no—
368C22C2×D4×D11311yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—1132no—
374C4—4521no—
375C4—2262no—
376C4C2×D4×D11311yescharacteristic
377C4C2×D4×D11311yescharacteristic
378C2—81no—
379C2—9041no—
380C2—9041no—
381C2—9041no—
382C2—2262no—
383C2#127×D11311yescharacteristic
384C2#2029940712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#497×C113C2
socleC22×C113C22×D4
hypercenter#497D113
hypocenterC113#3154
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#16813654C2semidirect
2. C2×#16813649C2semidirect
3. C2×#16813645C2semidirect
4. C2×SD16×D113C2semidirect
5. #20299173C2semidirect
6. #20299166C2semidirect
7. #20298991C2semidirect
8. #20298987C2semidirect
9. #20298984C2semidirect
10. #20298983C2semidirect
11. #20298980C2semidirect
12. #20298972C2semidirect
13. #20298969C2semidirect
14. #20298555C2semidirect
15. #497×C113C2semidirect
23. C2×#14268637C22semidirect
25. C2×#14268636C22semidirect
29. C2×#14268634C22semidirect
30. C2×#14268634C22semidirect
31. C2×#14268634C22semidirect
34. C2×D904C22semidirect
38. #16813620C22semidirect
42. #16813611C22semidirect
43. #16813610C22semidirect
49. #16813532C22semidirect
50. C4×#11744751C22semidirect
51. C8×Dic113C22semidirect
52. C2×Q16×C113C22semidirect
53. C2×Q16×C113C22semidirect
56. C4⋊Q8×C113C22semidirect
58. #97×C113C22semidirect
94. #14268630D4semidirect
97. C8×D113D4semidirect
193. C113#3154semidirect
201. #497D113semidirect
217. C2×Q16C2×D113semidirect
218. C2×Q16C2×D113semidirect
236. C4⋊Q8C2×D113semidirect
249. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136542
C2×#168136492
C2×#168136452
C2×SD16×D1132
#202991732
#202991662
#202989912
#202989872
#202989842
#202989832
#202989802
#202989722
#202989692
#202985552
#497×C1132
#3154113