Finite Group Databasebeta

← #28402104

Subgroups — #28402104

Order 14464.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813650C211yesmaximal, characteristic, complemented
2C2×#16813644C211yesmaximal, characteristic, complemented
3#20299253C211yesmaximal, characteristic, complemented
4#20299244C211yesmaximal, characteristic, complemented
5#20298992C211yesmaximal, characteristic, complemented
6#20298856C211yesmaximal, characteristic, complemented
7#20298827C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298804C211yesmaximal, characteristic, complemented
10#20298762C211yesmaximal, characteristic, complemented
11#20298762C211yesmaximal, characteristic, complemented
12#20298751C211yesmaximal, characteristic, complemented
13#20298745C211yesmaximal, characteristic, complemented
14#20298711C211yesmaximal, characteristic, complemented
15#435×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268647C2211yescharacteristic
18C2×#14268647C2211yescharacteristic, complemented
19C22×D452C2211yescharacteristic
20#16813650—24no—
21#16813644—24no—
22C2×Dic452C2211yescharacteristic, complemented
23C2×Dic452C2211yescharacteristic, complemented
24C2×#14268636C2211yescharacteristic
25C2×#14268636C2211yescharacteristic
26C2×#14268636C2211yescharacteristic
27C2×#14268636C2211yescharacteristic
28C2×#14268636C2211yescharacteristic, complemented
29C2×D904C2211yescharacteristic
30C2×D904C2211yescharacteristic
31#16813622C2211yescharacteristic, complemented
32#16813610C2211yescharacteristic
33#16813607—21no—
34#16813604—21no—
35#16813604—21no—
36#16813601C2211yescharacteristic
37#16813601C2211yescharacteristic
38#16813601C2211yescharacteristic, complemented
39#16813596C2211yescharacteristic
40#16813595—21no—
41#16813593—21no—
42#16813590—21no—
43C4×D452C2211yescharacteristic
44C4×D452C2211yescharacteristic, complemented
45C4⋊C4×D113—21no—
46C22⋊C4×D113—21no—
47#16813554C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813547C2211yescharacteristic, complemented
50#16813547C2211yescharacteristic, complemented
51#16813544C2211yescharacteristic
52#16813544C2211yescharacteristic
53#16813544C2211yescharacteristic, complemented
54C2×M16×C113C2211yescharacteristic
55C22×C8×C113C2211yescharacteristic, complemented
56C4×D4×C113C2211yescharacteristic
57C4⋊C8×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C22⋊C8×C113C2211yescharacteristic, complemented
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268647—22no—
63#14268647—22no—
64#14268647—22no—
65#14268647—41no—
66#14268647—41no—
67#14268647—41no—
68C2×Dic226C2311yescharacteristic
69C2×Dic226C2311yescharacteristic
70C2×Dic226C2311yescharacteristic
71C2×D452—22no—
72C2×D452—21no—
73C2×D452—41no—
74C2×D452C2311yescharacteristic
75C2×D452C2311yescharacteristic
76C2×D452C2311yescharacteristic
77C2×C22⋊D113—21no—
78C2×C22⋊D113—21no—
79C2×C22⋊D113—21no—
80C2×C22⋊D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113—21no—
83C2×C4×D113—21no—
84C2×C4×D113—21no—
85C2×C4×D113—21no—
86Dic452—22no—
87Dic452—41no—
88#14268636—22no—
89#14268636—22no—
90#14268636—22no—
91#14268636—22no—
92#14268636—41no—
93D904—22no—
94D904D414yescomplemented
95C4⋊Dic113—21no—
96C4⋊Dic113—21no—
97C4⋊Dic113C2311yescharacteristic
98C4⋊Dic113C2311yescharacteristic
99#14268626—21no—
100#14268626—21no—
101#14268626—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113—21no—
104C22⋊Dic113—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624—21no—
109#14268624—21no—
110C2×D4×C113D411yescharacteristic
111C22×C4×C113C2311yescharacteristic
112C22×C4×C113C2311yescharacteristic
113M16×C113—22no—
114C2×C8×C113—22no—
115C2×C8×C113C2311yescharacteristic
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C2×C8×C113C2311yescharacteristic
119C4⋊C4×C113D411yescharacteristic
120C22⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C42×C113C2311yescharacteristic
123C23×C113C2×D411yescharacteristic
124C23×C113C2×D411yescharacteristic
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—81no—
131D4×C113—41no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—21no—
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2×D411yescharacteristic
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2×D411yescharacteristic
140C2×C4×C113C2411yescharacteristic
141C22⋊D113—42no—
142C22⋊D113—42no—
143C22⋊D113—42no—
144C22⋊D113—81no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113—21no—
150D452—21no—
151D452—21no—
152D452—21no—
153D452—21no—
154D452—42no—
155D452C2×D412yes—
156D452C2×D412yes—
157C4×D113—42no—
158C4×D113—42no—
159C4×D113—42no—
160C4×D113—42no—
161C4×D113—81no—
162Dic226—21no—
163Dic226—21no—
164Dic226—21no—
165Dic226—21no—
166Dic226—21no—
167Dic226—21no—
168C8×C113—21no—
169C8×C113—21no—
170C8×C113—21no—
171C8×C113C2×D412yes—
172C22×C113—21no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113—21no—
177C22×C113—21no—
178C22×C113C22×D411yescharacteristic
179C2×D113—22no—
180C2×D113—22no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—41no—
184C2×D113—41no—
185C2×D113—41no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—84no—
189C4×C113—21no—
190C4×C113—21no—
191C4×C113—21no—
192C4×C113—21no—
193C4×C113C22×D411yescharacteristic
194C4×C113H(5,𝔽2)11yescharacteristic
195Dic113—41no—
196Dic113—41no—
197Dic113—41no—
198Dic113—41no—
199Dic113—41no—
200C2×C113—41no—
201C2×C113—41no—
202C2×C113D4211yescharacteristic
203C2×C113#57511yescharacteristic
204C2×C113#57711yescharacteristic
205D113—42no—
206D113—42no—
207D113—81no—
208#3267—1131nomaximal, Sylow
209C113#326711yescharacteristic, complemented, Sylow
210C2×AGL(1,ℤ/8)—1131no—
211C2×#135—1131no—
212#547—1131no—
213#546—1131no—
214#497—1131no—
215#470—1131no—
216#465—1131no—
217#463—1131no—
218#461—1131no—
219#452—1131no—
220#452—1131no—
221#450—1131no—
222#449—1131no—
223#442—1131no—
224#435D11311yescharacteristic, complemented
225C2×#41—1131no—
226C2×#41—1131no—
227C2×#41—1131no—
228C22×D4—1131no—
229AGL(1,ℤ/8)—2264no—
230#135—2264no—
231C2×Q16—1131no—
232C2×Q16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—1131no—
236C2×SD16—1131no—
237C2×SD16—1131no—
238C2×D8—1131no—
239C2×D8—1131no—
240C2×M16C2×D11311yescharacteristic
241C22×C8C2×D11311yescharacteristic, complemented
242C4⋊Q8—1131no—
243#124—1131no—
244#123—2261no—
245#123—2261no—
246#123—2261no—
247C22⋊Q8—1131no—
248C22⋊Q8—1131no—
249C22⋊Q8—1131no—
250#121—1131no—
251#121—2261no—
252#121—2261no—
253#120—2261no—
254C4×D4—1131no—
255C4×D4—1131no—
256C4×D4C2×D11311yescharacteristic
257C2×C4⋊C4—2261no—
258C2×C22⋊C4—2261no—
259#106—1131no—
260C4⋊C8C2×D11311yescharacteristic, complemented
261#103—1131no—
262#103—1131no—
263#103—1131no—
264#102—1131no—
265#102—1131no—
266#102—1131no—
267C22⋊C8C2×D11311yescharacteristic
268C22⋊C8C2×D11311yescharacteristic, complemented
269#97C2×D11311yescharacteristic, complemented
270C24—2261no—
271#41—4521no—
272#41—4521no—
273#41—4521no—
274#41—2262no—
275#41—2262no—
276#41—2262no—
277C2×Q8—1131no—
278C2×Q8—1131no—
279C2×Q8—1131no—
280C2×D4—1131no—
281C2×D4—1131no—
282C2×D4—1131no—
283C2×D4—4521no—
284C2×D4—2262no—
285C2×D4—2261no—
286C2×D4—2261no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4—2261no—
290C2×D4D45211yescharacteristic
291C22×C4—2261no—
292C22×C4—2261no—
293C22×C4—2261no—
294C22×C4—2261no—
295C22×C4—2261no—
296C22×C4C22×D11311yescharacteristic
297C22×C4C22×D11311yescharacteristic
298Q16—4521no—
299Q16—2262no—
300SD16—4521no—
301SD16—2262no—
302SD16—2262no—
303SD16—2262no—
304SD16—2262no—
305D8—1134no—
306D8—2262no—
307M16—22no—
308C2×C8—22no—
309C2×C8C22×D11311yescharacteristic
310C2×C8C22×D11311yescharacteristic
311C2×C8C22×D11311yescharacteristic
312C2×C8C22×D11311yescharacteristic
313C4⋊C4—1131no—
314C4⋊C4—1131no—
315C4⋊C4—2261no—
316C4⋊C4—2261no—
317C4⋊C4—2261no—
318C4⋊C4—2261no—
319C4⋊C4—2261no—
320C4⋊C4D45211yescharacteristic
321C22⋊C4—2261no—
322C22⋊C4—2261no—
323C22⋊C4—2261no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C22⋊C4D45211yescharacteristic
330C22⋊C4D45211yescharacteristic
331C42C22×D11311yescharacteristic
332C23—9041no—
333C23—4522no—
334C23—4522no—
335C23—2261no—
336C23—2261no—
337C23—2261no—
338C23C2×D45211yescharacteristic
339C23C2×D45211yescharacteristic
340Q8—2261no—
341Q8—2261no—
342Q8—2261no—
343Q8—2261no—
344Q8—2261no—
345Q8—2261no—
346D4—41no—
347D4—1132no—
348D4—1132no—
349D4—9041no—
350D4—4522no—
351D4—4522no—
352D4—4522no—
353D4—4522no—
354D4—2261no—
355D4—2261no—
356D4—2261no—
357D4—2261no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—9041no—
363C2×C4—4522no—
364C2×C4—4522no—
365C2×C4—4522no—
366C2×C4—4522no—
367C2×C4—2261no—
368C2×C4—2261no—
369C2×C4—2261no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4C2×D45211yescharacteristic
373C2×C4C2×D45211yescharacteristic
374C2×C4C2×D45211yescharacteristic
375C2×C4C2×D45211yescharacteristic
376C2×C4C23×D11311yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D11312yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—9044no—
388C22—4521no—
389C22—4521no—
390C22—4521no—
391C22—4521no—
392C22—4521no—
393C22—4521no—
394C22—4521no—
395C22—2262no—
396C22—2262no—
397C22C22×D45211yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—4521no—
403C4—4521no—
404C4—4521no—
405C4—4521no—
406C4—4521no—
407C4C2×D4×D11311yescharacteristic
408C4#1681366811yescharacteristic
409C2—41no—
410C2—41no—
411C2—9041no—
412C2—4522no—
413C2—4522no—
414C2D4×D45211yescharacteristic
415C2#2029939811yescharacteristic
416C2#2029941011yescharacteristic
subgroupG/H
centerC22C22×D452
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#435×C113C2
socleC22×C113C22×D4
hypercenter#435D113
hypocenterC113#3267
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. C2×#16813644C2semidirect
3. #20299253C2semidirect
4. #20299244C2semidirect
5. #20298992C2semidirect
6. #20298856C2semidirect
7. #20298827C2semidirect
8. #20298814C2semidirect
9. #20298804C2semidirect
10. #20298762C2semidirect
11. #20298762C2semidirect
12. #20298751C2semidirect
13. #20298745C2semidirect
14. #20298711C2semidirect
15. #435×C113C2semidirect
18. C2×#14268647C22semidirect
22. C2×Dic452C22semidirect
23. C2×Dic452C22semidirect
28. C2×#14268636C22semidirect
31. #16813622C22semidirect
38. #16813601C22semidirect
44. C4×D452C22semidirect
47. #16813554C22semidirect
48. #16813547C22semidirect
49. #16813547C22semidirect
50. #16813547C22semidirect
53. #16813544C22semidirect
55. C22×C8×C113C22semidirect
57. C4⋊C8×C113C22semidirect
59. C22⋊C8×C113C22semidirect
60. #97×C113C22semidirect
94. D904D4semidirect
209. C113#3267semidirect
224. #435D113semidirect
241. C22×C8C2×D113semidirect
260. C4⋊C8C2×D113semidirect
268. C22⋊C8C2×D113semidirect
269. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
C2×#168136442
#202992532
#202992442
#202989922
#202988562
#202988272
#202988142
#202988042
#202987622
#202987512
#202987452
#202987112
#435×C1132
#3267113