Finite Group Databasebeta

← #28402113

Subgroups — #28402113

Order 14464.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813646C211yesmaximal, characteristic, complemented
2C2×#16813643C211yesmaximal, characteristic, complemented
3#20299268C211yesmaximal, characteristic, complemented
4#20299241C211yesmaximal, characteristic, complemented
5#20298841C211yesmaximal, characteristic, complemented
6#20298831C211yesmaximal, characteristic, complemented
7#20298817C211yesmaximal, characteristic, complemented
8#20298790C211yesmaximal, characteristic, complemented
9#20298757C211yesmaximal, characteristic, complemented
10#20298742C211yesmaximal, characteristic, complemented
11#20298740C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298700C211yesmaximal, characteristic, complemented
14#20298671C211yesmaximal, characteristic, complemented
15#496×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×#14268646C2211yescharacteristic, complemented
19C2×D4×D113C2211yescharacteristic
20#16813646—24no—
21#16813643—24no—
22C2×#14268637C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic
24C2×#14268635C2211yescharacteristic
25C2×#14268632C2211yescharacteristic
26C2×#14268632C2211yescharacteristic
27C2×#14268630C2211yescharacteristic
28C2×C8×D113C2211yescharacteristic, complemented
29#16813618—21no—
30#16813604—21no—
31#16813598C2211yescharacteristic
32#16813595—21no—
33#16813594—21no—
34#16813594—21no—
35#16813593C2211yescharacteristic
36#16813593C2211yescharacteristic
37#16813593C2211yescharacteristic, complemented
38#16813592—21no—
39C4×Dic226C2211yescharacteristic, complemented
40C4×D452C2211yescharacteristic
41C4×D452C2211yescharacteristic
42D4×Dic113—21no—
43C22⋊C4×D113—21no—
44#16813556C2211yescharacteristic, complemented
45C4⋊#11744751C2211yescharacteristic, complemented
46#16813547C2211yescharacteristic, complemented
47#16813546C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic
49#16813543C2211yescharacteristic
50#16813543C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic
53#16813534C2211yescharacteristic, complemented
54C2×SD16×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic, complemented
56C2×D8×C113C2211yescharacteristic
57C2×D8×C113C2211yescharacteristic
58#127×C113C2211yescharacteristic, complemented
59#124×C113C2211yescharacteristic
60#97×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268648—22no—
63#14268648—41no—
64#14268646—22no—
65#14268646—22no—
66#14268646—41no—
67#14268646—41no—
68C2×Dic226C2311yescharacteristic
69C2×D452—21no—
70C2×D452D411yescharacteristic
71C2×D452C2311yescharacteristic
72C2×C22⋊D113—21no—
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78D4×D113—22no—
79D4×D113—41no—
80C22×Dic113—21no—
81C22×Dic113—21no—
82C2×C4×D113—21no—
83C2×C4×D113—21no—
84C2×C4×D113C2311yescharacteristic
85C2×C4×D113C2311yescharacteristic
86#14268637—22no—
87#14268636D414yescomplemented
88#14268635—22no—
89#14268632—22no—
90#14268632—22no—
91#14268630—22no—
92C2×#11744751C2311yescharacteristic
93C2×#11744751C2311yescharacteristic
94C8×D113—22no—
95C4⋊Dic113D411yescharacteristic
96C4⋊Dic113C2311yescharacteristic
97C4⋊Dic113C2311yescharacteristic
98#14268626—21no—
99#14268626—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113—21no—
102C22⋊Dic113—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624D411yescharacteristic
106#14268624D411yescharacteristic
107C4×Dic113—21no—
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113—21no—
110C2×D4×C113—21no—
111C2×D4×C113C2311yescharacteristic
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114SD16×C113—22no—
115SD16×C113—41no—
116D8×C113—22no—
117D8×C113—41no—
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C22⋊C4×C113—21no—
121C22⋊C4×C113—21no—
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C22×D113—21no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—81no—
130C22×D113C2×D411yescharacteristic
131C22×D113C2×D411yescharacteristic
132Q8×C113—21no—
133Q8×C113—21no—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—21no—
137D4×C113—21no—
138D4×C113—21no—
139D4×C113—21no—
140D4×C113—42no—
141D4×C113—81no—
142C2×C4×C113—21no—
143C2×C4×C113C2×D411yescharacteristic
144C2×C4×C113C2×D411yescharacteristic
145C2×C4×C113C2411yescharacteristic
146C22⋊D113—42no—
147C22⋊D113—42no—
148C22⋊D113—42no—
149C22⋊D113—81no—
150C22⋊D113—81no—
151C22⋊D113—81no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—42no—
156C2×Dic113—42no—
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159D452—21no—
160D452—41no—
161D452—42no—
162D452C2×D412yes—
163C4×D113—21no—
164C4×D113—21no—
165C4×D113—21no—
166C4×D113—21no—
167C4×D113—42no—
168C4×D113—81no—
169Dic226—21no—
170Dic226C2×D412yes—
171C8×C113—21no—
172C8×C113C2×D412yes—
173#11744751—21no—
174#11744751—21no—
175C22×C113—41no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113C22×D411yescharacteristic
185C2×D113—21no—
186C2×D113—21no—
187C2×D113—22no—
188C2×D113—21no—
189C2×D113—21no—
190C2×D113—21no—
191C2×D113—21no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—84no—
195C4×C113—21no—
196C4×C113—21no—
197C4×C113—41no—
198C4×C113C22×D411yescharacteristic
199C4×C113H(5,𝔽2)11yescharacteristic
200Dic113—22no—
201Dic113—21no—
202Dic113—21no—
203Dic113—41no—
204Dic113—41no—
205C2×C113—81no—
206C2×C113—81no—
207C2×C113—81no—
208C2×C113D4211yescharacteristic
209C2×C113#57511yescharacteristic
210C2×C113#57611yescharacteristic
211D113—41no—
212D113—41no—
213D113—42no—
214#3268—1131nomaximal, Sylow
215C113#326811yescharacteristic, complemented, Sylow
216C2×AGL(1,ℤ/8)—1131no—
217C2×#135—1131no—
218#550—1131no—
219#546—1131no—
220#496D11311yescharacteristic, complemented
221#468—1131no—
222#466—1131no—
223#464—1131no—
224#459—1131no—
225#452—1131no—
226#449—1131no—
227#449—1131no—
228#447—1131no—
229#440—1131no—
230#435—1131no—
231C2×#41—1131no—
232C2×#41—1131no—
233C2×#41—1131no—
234C22×D4—1131no—
235AGL(1,ℤ/8)—2264no—
236#135—2264no—
237C2×Q16—1131no—
238C2×SD16—1131no—
239C2×SD16—1131no—
240C2×SD16C2×D11311yescharacteristic, complemented
241C2×SD16C2×D11311yescharacteristic, complemented
242C2×D8—1131no—
243C2×D8—1131no—
244C2×D8C2×D11311yescharacteristic
245C2×D8C2×D11311yescharacteristic
246C2×M16—1131no—
247C22×C8—1131no—
248#127—2261no—
249#127C2×D11311yescharacteristic, complemented
250#124C2×D11311yescharacteristic
251#123—2261no—
252C22⋊Q8—1131no—
253#121—1131no—
254#121—1131no—
255#121—1131no—
256#121—2261no—
257#121—2261no—
258#121—2261no—
259#120—2261no—
260C4×Q8—1131no—
261C4×D4—1131no—
262C4×D4—1131no—
263C4×D4—2261no—
264C2×C22⋊C4—2261no—
265#107—1131no—
266C4⋊C8—1131no—
267#103—1131no—
268#103—1131no—
269#102—1131no—
270#102—1131no—
271#102—1131no—
272#102—1131no—
273C22⋊C8—1131no—
274C22⋊C8—1131no—
275#97C2×D11311yescharacteristic, complemented
276C24—2261no—
277#41—4521no—
278#41—4521no—
279#41—4521no—
280#41—2262no—
281#41—2262no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8C22×D11311yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—1131no—
288C2×D4—1131no—
289C2×D4—4521no—
290C2×D4—2261no—
291C2×D4—2261no—
292C2×D4—2262no—
293C2×D4—2261no—
294C2×D4—2261no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4C22×D11311yescharacteristic
299C2×D4C22×D11311yescharacteristic
300C2×D4C22×D11311yescharacteristic
301C22×C4—1131no—
302C22×C4—1131no—
303C22×C4—2261no—
304C22×C4—2261no—
305C22×C4—2261no—
306C22×C4—2261no—
307Q16—2262no—
308SD16—22no—
309SD16—41no—
310SD16—1134no—
311SD16—2262no—
312D8—22no—
313D8—41no—
314D8—2262no—
315D8—2262no—
316M16—2262no—
317C2×C8—1131no—
318C2×C8—1131no—
319C2×C8—2262no—
320C2×C8C22×D11311yescharacteristic
321C2×C8C22×D11311yescharacteristic
322C4⋊C4—1131no—
323C4⋊C4—1131no—
324C4⋊C4—1131no—
325C4⋊C4—2261no—
326C4⋊C4—2261no—
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—
336C42—2261no—
337C42C22×D11311yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—1131no—
342C23—1131no—
343C23—9041no—
344C23—4522no—
345C23—4522no—
346C23—2261no—
347Q8—21no—
348Q8—21no—
349Q8—1132no—
350Q8—2261no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—21no—
357D4—42no—
358D4—81no—
359D4—1132no—
360D4—9041no—
361D4—9041no—
362D4—9041no—
363D4—4521no—
364D4—4522no—
365D4—4522no—
366D4—4522no—
367D4—4522no—
368D4—2261no—
369C2×C4—21no—
370C2×C4—1131no—
371C2×C4—1131no—
372C2×C4—9041no—
373C2×C4—4522no—
374C2×C4—4522no—
375C2×C4—4522no—
376C2×C4—2261no—
377C2×C4—2261no—
378C2×C4—2261no—
379C2×C4—2261no—
380C2×C4—2261no—
381C2×C4—2261no—
382C2×C4—2261no—
383C2×C4D4×D11311yescharacteristic
384C2×C4D4×D11311yescharacteristic
385C2×C4C23×D11311yescharacteristic
386C8—21no—
387C8—2261no—
388C8—2261no—
389C8D4×D11312yes—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—9044no—
400C22—4521no—
401C22—4521no—
402C22—2261no—
403C22—2261no—
404C22—2261no—
405C22—2261no—
406C22—2262no—
407C22—2261no—
408C22—2261no—
409C22C2×D4×D11311yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—4521no—
414C4—4521no—
415C4—2261no—
416C4—2261no—
417C4—2262no—
418C4C2×D4×D11311yescharacteristic
419C4#1681366711yescharacteristic
420C2—81no—
421C2—81no—
422C2—81no—
423C2—4521no—
424C2—4522no—
425C2—4521no—
426C2#2029923311yescharacteristic
427C2#2029939411yescharacteristic
428C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#496×C113C2
socleC22×C113C22×D4
hypercenter#496D113
hypocenterC113#3268
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. C2×#16813643C2semidirect
3. #20299268C2semidirect
4. #20299241C2semidirect
5. #20298841C2semidirect
6. #20298831C2semidirect
7. #20298817C2semidirect
8. #20298790C2semidirect
9. #20298757C2semidirect
10. #20298742C2semidirect
11. #20298740C2semidirect
12. #20298730C2semidirect
13. #20298700C2semidirect
14. #20298671C2semidirect
15. #496×C113C2semidirect
18. C2×#14268646C22semidirect
22. C2×#14268637C22semidirect
28. C2×C8×D113C22semidirect
37. #16813593C22semidirect
39. C4×Dic226C22semidirect
44. #16813556C22semidirect
45. C4⋊#11744751C22semidirect
46. #16813547C22semidirect
47. #16813546C22semidirect
50. #16813543C22semidirect
51. #16813543C22semidirect
53. #16813534C22semidirect
54. C2×SD16×C113C22semidirect
55. C2×SD16×C113C22semidirect
58. #127×C113C22semidirect
60. #97×C113C22semidirect
87. #14268636D4semidirect
215. C113#3268semidirect
220. #496D113semidirect
240. C2×SD16C2×D113semidirect
241. C2×SD16C2×D113semidirect
249. #127C2×D113semidirect
275. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×#168136432
#202992682
#202992412
#202988412
#202988312
#202988172
#202987902
#202987572
#202987422
#202987402
#202987302
#202987002
#202986712
#496×C1132
#3268113