Finite Group Databasebeta

← #28402254

Subgroups — #28402254

Order 14464.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813643C211yesmaximal, characteristic, complemented
2C2×D8×D113C211yesmaximal, characteristic, complemented
3#20299243C211yesmaximal, characteristic, complemented
4#20299241C211yesmaximal, characteristic, complemented
5#20298980C211yesmaximal, characteristic, complemented
6#20298838C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic, complemented
8#20298814C211yesmaximal, characteristic, complemented
9#20298750C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11#20298746C211yesmaximal, characteristic, complemented
12#20298740C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14#20298663C211yesmaximal, characteristic, complemented
15#463×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic, complemented
17C2×#14268646C2211yescharacteristic, complemented
18C2×D4×D113C2211yescharacteristic
19C2×D4×D113C2211yescharacteristic
20#16813643—24no—
21C2×#14268637C2211yescharacteristic, complemented
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268634C2211yescharacteristic, complemented
25C2×D904C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28D8×D113—24no—
29C2×C8×D113C2211yescharacteristic
30C2×C8×D113C2211yescharacteristic, complemented
31#16813610C2211yescharacteristic, complemented
32#16813606—21no—
33#16813604—21no—
34#16813602C2211yescharacteristic
35#16813598C2211yescharacteristic
36#16813597C2211yescharacteristic, complemented
37#16813596—21no—
38#16813595—21no—
39#16813593C2211yescharacteristic, complemented
40#16813592—21no—
41#16813592—21no—
42C4×D452C2211yescharacteristic
43C4×D452C2211yescharacteristic, complemented
44C2×#14268624—21no—
45C22⋊C4×D113—21no—
46#16813555C2211yescharacteristic, complemented
47#16813547C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic, complemented
49#16813543C2211yescharacteristic, complemented
50#16813542C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic
52#16813534C2211yescharacteristic, complemented
53C4×#11744751C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic
56#124×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic, complemented
58C4⋊C8×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63#14268648—22no—
64#14268648—41no—
65#14268646—22no—
66#14268646—41no—
67C2×Dic226C2311yescharacteristic
68C2×D452—21no—
69C2×D452—21no—
70C2×D452D411yescharacteristic
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77D4×D113—22no—
78D4×D113—22no—
79D4×D113—41no—
80D4×D113—41no—
81C22×Dic113—21no—
82C2×C4×D113—21no—
83C2×C4×D113—21no—
84C2×C4×D113C2311yescharacteristic
85C2×C4×D113C2311yescharacteristic
86#14268637—22no—
87#14268636—22no—
88#14268635—41no—
89#14268634—41no—
90D904—22no—
91#14268632—22no—
92#14268632D414yescomplemented
93C2×#11744751C2311yescharacteristic
94C2×#11744751C2311yescharacteristic
95C8×D113—22no—
96C8×D113—22no—
97C4⋊Dic113—21no—
98C4⋊Dic113D411yescharacteristic
99C4⋊Dic113C2311yescharacteristic
100#14268626—21no—
101C22⋊Dic113—21no—
102#14268624—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624—21no—
108#14268624D411yescharacteristic
109#14268624D411yescharacteristic
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113C2311yescharacteristic
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113—21no—
114SD16×C113—22no—
115D8×C113—22no—
116C2×C8×C113C2311yescharacteristic
117C2×C8×C113C2311yescharacteristic
118C4⋊C4×C113C2311yescharacteristic
119C22⋊C4×C113—21no—
120C22⋊C4×C113—21no—
121C22⋊C4×C113—21no—
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113—21no—
125C22×D113—21no—
126C22×D113—21no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113—81no—
132C22×D113—81no—
133C22×D113C2×D411yescharacteristic
134C22×D113C2×D411yescharacteristic
135Q8×C113—21no—
136Q8×C113—21no—
137D4×C113—21no—
138D4×C113—21no—
139D4×C113—21no—
140D4×C113C2×D412yes—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—81no—
144C2×C4×C113C2×D411yescharacteristic
145C2×C4×C113C2×D411yescharacteristic
146C2×C4×C113C2411yescharacteristic
147C22⋊D113—42no—
148C22⋊D113—42no—
149C22⋊D113—42no—
150C22⋊D113—81no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—42no—
154C2×Dic113C2×D411yescharacteristic
155C2×Dic113C2×D411yescharacteristic
156D452—22no—
157D452—21no—
158D452—21no—
159D452—21no—
160D452—42no—
161D452—81no—
162D452C2×D412yes—
163C4×D113—21no—
164C4×D113—21no—
165C4×D113—21no—
166C4×D113—21no—
167C4×D113—42no—
168C4×D113—81no—
169Dic226—21no—
170Dic226—21no—
171C8×C113—21no—
172C8×C113—21no—
173#11744751—21no—
174#11744751C2×D412yes—
175C22×C113—22no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113C22×D411yescharacteristic
182C2×D113—21no—
183C2×D113—21no—
184C2×D113—21no—
185C2×D113—22no—
186C2×D113—21no—
187C2×D113—21no—
188C2×D113—41no—
189C2×D113—41no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—84no—
194C2×D113—84no—
195C2×D113#13512yescomplemented
196C4×C113—21no—
197C4×C113—21no—
198C4×C113—41no—
199C4×C113—41no—
200C4×C113C22×D411yescharacteristic
201C4×C113H(5,𝔽2)11yescharacteristic
202Dic113—21no—
203Dic113—21no—
204Dic113—41no—
205Dic113—41no—
206C2×C113—42no—
207C2×C113—81no—
208C2×C113D4211yescharacteristic
209C2×C113C2×#13511yescharacteristic
210C2×C113#57611yescharacteristic
211D113—22no—
212D113—41no—
213D113—42no—
214D113—81no—
215#3280—1131nomaximal, Sylow
216C113#328011yescharacteristic, complemented, Sylow
217C2×#135—1131no—
218C22×D8—1131no—
219#546—1131no—
220#546—1131no—
221#495—1131no—
222#467—1131no—
223#466—1131no—
224#463—1131no—
225#463D11311yescharacteristic, complemented
226#450—1131no—
227#450—1131no—
228#449—1131no—
229#449—1131no—
230C4×D8—1131no—
231C8×D4—1131no—
232C2×#41—1131no—
233C2×#41—1131no—
234C22×D4—1131no—
235C22×D4—1131no—
236#135—2264no—
237C2×Q16—1131no—
238C2×SD16—1131no—
239C2×SD16—1131no—
240C2×SD16—1131no—
241C2×SD16C2×D11311yescharacteristic, complemented
242C2×D8—1131no—
243C2×D8—1131no—
244C2×D8—1131no—
245C2×D8—2264no—
246C2×D8C2×D11311yescharacteristic
247C22×C8—1131no—
248C22×C8—1131no—
249#124—1131no—
250#124C2×D11311yescharacteristic, complemented
251#123—2261no—
252#123—2261no—
253C22⋊Q8—1131no—
254C22⋊Q8—1131no—
255#121—1131no—
256#121—1131no—
257#121—2261no—
258#121—2261no—
259#120—2261no—
260#120—2261no—
261C4×D4—1131no—
262C4×D4—1131no—
263C4×D4C2×D11311yescharacteristic, complemented
264C2×C22⋊C4—2261no—
265C2×C22⋊C4—2261no—
266#107—1131no—
267C4⋊C8C2×D11311yescharacteristic, complemented
268#103—1131no—
269#103C2×D11311yescharacteristic, complemented
270#102—1131no—
271#102—1131no—
272#102—1131no—
273#102C2×D11311yescharacteristic, complemented
274C22⋊C8—1131no—
275C22⋊C8—1131no—
276C4×C8—1131no—
277C24—2261no—
278C24—2261no—
279#41—4521no—
280#41—4521no—
281#41—2262no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8C22×D11311yescharacteristic
285C2×D4—1131no—
286C2×D4—1131no—
287C2×D4—1131no—
288C2×D4—4521no—
289C2×D4—4521no—
290C2×D4—2261no—
291C2×D4—2261no—
292C2×D4—2261no—
293C2×D4—2261no—
294C2×D4—2262no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2262no—
298C2×D4C22×D11311yescharacteristic
299C2×D4C22×D11311yescharacteristic
300C22×C4—21no—
301C22×C4—1131no—
302C22×C4—1131no—
303C22×C4—2261no—
304C22×C4—2261no—
305C22×C4—2261no—
306Q16—2262no—
307SD16—22no—
308SD16—4521no—
309SD16—4521no—
310SD16—2262no—
311D8—22no—
312D8—1134no—
313D8—2262no—
314D8—2262no—
315C2×C8—1131no—
316C2×C8—1131no—
317C2×C8—2262no—
318C2×C8—2262no—
319C2×C8C22×D11311yescharacteristic
320C2×C8C22×D11311yescharacteristic
321C4⋊C4—1131no—
322C4⋊C4—1131no—
323C4⋊C4—2261no—
324C4⋊C4—2261no—
325C4⋊C4C22×D11311yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—1131no—
330C22⋊C4—1131no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C22⋊C4—2261no—
337C22⋊C4—2261no—
338C42C22×D11311yescharacteristic
339C23—21no—
340C23—21no—
341C23—1131no—
342C23—1131no—
343C23—9041no—
344C23—9041no—
345C23—4522no—
346C23—4522no—
347C23—4522no—
348C23—4522no—
349C23—2261no—
350C23—2261no—
351Q8—21no—
352Q8—21no—
353Q8—2261no—
354Q8—2261no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—1132no—
359D4—9041no—
360D4—9041no—
361D4—4522no—
362D4—4522no—
363D4—4522no—
364D4—4522no—
365D4—2262no—
366D4—2261no—
367D4—2261no—
368D4—2261no—
369D4D4×D11312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—1131no—
374C2×C4—1131no—
375C2×C4—9041no—
376C2×C4—4522no—
377C2×C4—4522no—
378C2×C4—2261no—
379C2×C4—2261no—
380C2×C4—2261no—
381C2×C4—2261no—
382C2×C4—2261no—
383C2×C4—2261no—
384C2×C4D4×D11311yescharacteristic
385C2×C4D4×D11311yescharacteristic
386C2×C4C23×D11311yescharacteristic
387C8—21no—
388C8—21no—
389C8—1132no—
390C8—2261no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—1132no—
398C22—9044no—
399C22—9044no—
400C22—4521no—
401C22—4521no—
402C22—4521no—
403C22—4521no—
404C22—4521no—
405C22—2261no—
406C22—2261no—
407C22—2262no—
408C22—2261no—
409C22—2261no—
410C22—2261no—
411C22C2×D4×D11311yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—4521no—
417C4—4521no—
418C4—2261no—
419C4—2261no—
420C4C2×D4×D11311yescharacteristic
421C4#1681366811yescharacteristic
422C2—42no—
423C2—81no—
424C2—9041no—
425C2—4522no—
426C2—4521no—
427C2—2262no—
428C2#2029923211yescharacteristic
429C2#135×D11311yescharacteristic
430C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#463×C113C2
socleC22×C113C22×D4
hypercenter#463D113
hypocenterC113#3280
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#16813643C2semidirect
2. C2×D8×D113C2semidirect
3. #20299243C2semidirect
4. #20299241C2semidirect
5. #20298980C2semidirect
6. #20298838C2semidirect
7. #20298833C2semidirect
8. #20298814C2semidirect
9. #20298750C2semidirect
10. #20298747C2semidirect
11. #20298746C2semidirect
12. #20298740C2semidirect
13. C4×#14268632C2semidirect
14. #20298663C2semidirect
15. #463×C113C2semidirect
16. C2×#14268648C22semidirect
17. C2×#14268646C22semidirect
21. C2×#14268637C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268634C22semidirect
30. C2×C8×D113C22semidirect
31. #16813610C22semidirect
36. #16813597C22semidirect
39. #16813593C22semidirect
43. C4×D452C22semidirect
46. #16813555C22semidirect
47. #16813547C22semidirect
48. #16813544C22semidirect
49. #16813543C22semidirect
50. #16813542C22semidirect
52. #16813534C22semidirect
53. C4×#11744751C22semidirect
54. C2×SD16×C113C22semidirect
56. #124×C113C22semidirect
57. C4×D4×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #103×C113C22semidirect
60. #102×C113C22semidirect
92. #14268632D4semidirect
195. C2×D113#135semidirect
216. C113#3280semidirect
225. #463D113semidirect
241. C2×SD16C2×D113semidirect
250. #124C2×D113semidirect
263. C4×D4C2×D113semidirect
267. C4⋊C8C2×D113semidirect
269. #103C2×D113semidirect
273. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136432
C2×D8×D1132
#202992432
#202992412
#202989802
#202988382
#202988332
#202988142
#202987502
#202987472
#202987462
#202987402
C4×#142686322
#202986632
#463×C1132
#3280113