Finite Group Databasebeta

← #28402070

Subgroups — #28402070

Order 14464.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813647C211yesmaximal, characteristic, complemented
2C22×#14268634C211yesmaximal, characteristic, complemented
3D4×D452C211yesmaximal, characteristic, complemented
4#20298988C211yesmaximal, characteristic, complemented
5#20298846C211yesmaximal, characteristic, complemented
6#20298832C211yesmaximal, characteristic, complemented
7#20298810C211yesmaximal, characteristic, complemented
8#20298798C211yesmaximal, characteristic, complemented
9#20298748C211yesmaximal, characteristic, complemented
10#20298743C211yesmaximal, characteristic, complemented
11#20298737C211yesmaximal, characteristic, complemented
12#20298731C211yesmaximal, characteristic, complemented
13#20298696C211yesmaximal, characteristic, complemented
14#20298670C211yesmaximal, characteristic, complemented
15#548×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×D4×D113—21no—
19#16813647—24no—
20C2×#14268634—24no—
21C2×#14268634C2211yescharacteristic
22C2×#14268634C2211yescharacteristic
23C2×#14268634C2211yescharacteristic, complemented
24C2×#14268634C2211yescharacteristic, complemented
25C2×#14268634C2211yescharacteristic, complemented
26C2×#14268634C2211yescharacteristic, complemented
27C2×#14268632C2211yescharacteristic
28C2×#14268632C2211yescharacteristic, complemented
29C2×#14268632C2211yescharacteristic, complemented
30C2×#14268631C2211yescharacteristic, complemented
31C22×#11744751C2211yescharacteristic, complemented
32#16813619C2211yescharacteristic
33#16813597—21no—
34#16813596C2211yescharacteristic
35#16813596C2211yescharacteristic
36#16813592—21no—
37#16813592—21no—
38C4×D452C2211yescharacteristic
39#16813555C2211yescharacteristic, complemented
40C4⋊#11744751C2211yescharacteristic, complemented
41#16813546C2211yescharacteristic, complemented
42#16813546C2211yescharacteristic, complemented
43#16813543C2211yescharacteristic, complemented
44#16813542C2211yescharacteristic
45#16813542C2211yescharacteristic, complemented
46#16813542C2211yescharacteristic, complemented
47C22⋊#11744751C2211yescharacteristic, complemented
48C22⋊#11744751C2211yescharacteristic, complemented
49#16813533C2211yescharacteristic, complemented
50C2×#41×C113C2211yescharacteristic, complemented
51C22×Q8×C113C2211yescharacteristic, complemented
52#124×C113—21no—
53#124×C113C2211yescharacteristic, complemented
54C22⋊Q8×C113—21no—
55C22⋊Q8×C113C2211yescharacteristic, complemented
56#121×C113—21no—
57#121×C113C2211yescharacteristic, complemented
58C4×Q8×C113C2211yescharacteristic, complemented
59C4×D4×C113—21no—
60C4×D4×C113C2211yescharacteristic
61C23×D113—21no—
62C23×D113—21no—
63C2×D452—22no—
64C2×D452—22no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—41no—
70C2×D452—41no—
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×D452C2311yescharacteristic
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76D4×D113—44no—
77C2×C4×D113—21no—
78#14268634—22no—
79#14268634—22no—
80#14268634—22no—
81#14268634—22no—
82#14268634—41no—
83#14268634D414yescomplemented
84#14268632—22no—
85#14268632—22no—
86#14268632—41no—
87#14268631—22no—
88C2×#11744751—22no—
89C2×#11744751C2311yescharacteristic
90C2×#11744751C2311yescharacteristic
91C2×#11744751C2311yescharacteristic
92C2×#11744751C2311yescharacteristic
93C4⋊Dic113C2311yescharacteristic
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#41×C113—22no—
98#41×C113—41no—
99C2×Q8×C113—21no—
100C2×Q8×C113—22no—
101C2×Q8×C113—41no—
102C2×Q8×C113C2311yescharacteristic
103C2×Q8×C113C2311yescharacteristic
104C2×D4×C113—21no—
105C2×D4×C113—21no—
106C2×D4×C113D411yescharacteristic
107C2×D4×C113C2311yescharacteristic
108C22×C4×C113—21no—
109C22×C4×C113—21no—
110C22×C4×C113C2311yescharacteristic
111C22×C4×C113C2311yescharacteristic
112C4⋊C4×C113—21no—
113C4⋊C4×C113—21no—
114C4⋊C4×C113D411yescharacteristic
115C4⋊C4×C113C2311yescharacteristic
116C22⋊C4×C113—21no—
117C22⋊C4×C113—21no—
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C22⋊C4×C113D411yescharacteristic
121C22⋊C4×C113D411yescharacteristic
122C42×C113—21no—
123C42×C113C2311yescharacteristic
124C23×C113—21no—
125C23×C113C2×D411yescharacteristic
126C23×C113C2×D411yescharacteristic
127C22×D113—21no—
128C22×D113—21no—
129C22×D113—21no—
130C22×D113—42no—
131C22×D113—42no—
132C22×D113—42no—
133C22×D113—42no—
134C22×D113—81no—
135C22×D113—81no—
136Q8×C113—21no—
137Q8×C113—21no—
138Q8×C113—21no—
139Q8×C113—42no—
140Q8×C113C2×D412yescomplemented
141D4×C113—22no—
142D4×C113—21no—
143D4×C113—21no—
144D4×C113—42no—
145D4×C113—42no—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—21no—
149C2×C4×C113—21no—
150C2×C4×C113—21no—
151C2×C4×C113—21no—
152C2×C4×C113—21no—
153C2×C4×C113—42no—
154C2×C4×C113—42no—
155C2×C4×C113C2×D411yescharacteristic
156C2×C4×C113C2×D411yescharacteristic
157C2×C4×C113C2×D411yescharacteristic
158C2×C4×C113C2×D411yescharacteristic
159C2×C4×C113C2411yescharacteristic
160C22⋊D113—42no—
161C22⋊D113—42no—
162C2×Dic113—21no—
163D452—21no—
164D452—21no—
165D452—21no—
166D452—21no—
167D452—21no—
168D452—42no—
169D452—42no—
170D452—42no—
171D452—81no—
172D452C2×D412yes—
173C4×D113—42no—
174#11744751—21no—
175#11744751—21no—
176#11744751—21no—
177#11744751C2×D412yescomplemented
178C22×C113—21no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113—21no—
182C22×C113—21no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113AGL(1,ℤ/8)12yescomplemented
187C22×C113C22×D411yescharacteristic
188C2×D113—22no—
189C2×D113—41no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—41no—
195C2×D113—41no—
196C2×D113—41no—
197C2×D113—84no—
198C2×D113—84no—
199C4×C113—21no—
200C4×C113—21no—
201C4×C113—22no—
202C4×C113—21no—
203C4×C113—21no—
204C4×C113—41no—
205C4×C113—41no—
206C4×C113C22×D411yescharacteristic
207C4×C113H(5,𝔽2)11yescharacteristic
208Dic113—41no—
209C2×C113—22no—
210C2×C113—41no—
211C2×C113—81no—
212C2×C113D4211yescharacteristic
213C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C113#57711yescharacteristic
215D113—42no—
216D113—81no—
217D113—81no—
218#3265—1131nomaximal, Sylow
219C113#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—1131no—
221C22×SD16—1131no—
222#548D11311yescharacteristic, complemented
223D42—1131no—
224#496—1131no—
225#468—1131no—
226#466—1131no—
227#463—1131no—
228#460—1131no—
229#450—1131no—
230#449—1131no—
231#448—1131no—
232#447—1131no—
233#440—1131no—
234#435—1131no—
235C2×#41C2×D11311yescharacteristic, complemented
236C22×Q8C2×D11311yescharacteristic, complemented
237C22×D4—1131no—
238C22×D4—1131no—
239C22×D4—2261no—
240AGL(1,ℤ/8)—2264no—
241C2×SD16—1131no—
242C2×SD16—1131no—
243C2×SD16—1131no—
244C2×SD16—1131no—
245C2×SD16—1131no—
246C2×SD16—1131no—
247C2×SD16—2264no—
248C2×D8—1131no—
249C2×D8—1131no—
250C2×D8—1131no—
251C2×M16—1131no—
252C22×C8—1131no—
253#127—1131no—
254#124—21no—
255#124C2×D11311yescharacteristic, complemented
256C22⋊Q8—21no—
257C22⋊Q8C2×D11311yescharacteristic, complemented
258#121—21no—
259#121—1131no—
260#121—1131no—
261#121—2261no—
262#121C2×D11311yescharacteristic, complemented
263#120—2261no—
264#120—2261no—
265C4×Q8C2×D11311yescharacteristic, complemented
266C4×D4—21no—
267C4×D4—1131no—
268C4×D4C2×D11311yescharacteristic
269#107—1131no—
270C4⋊C8—1131no—
271#103—1131no—
272#103—1131no—
273#102—1131no—
274#102—1131no—
275#102—1131no—
276#102—1131no—
277C22⋊C8—1131no—
278C22⋊C8—1131no—
279#97—1131no—
280C24—2261no—
281C24—2261no—
282#41—22no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D11311yescharacteristic
288C2×Q8C22×D11311yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—1131no—
292C2×D4—1131no—
293C2×D4—1131no—
294C2×D4—4521no—
295C2×D4—4521no—
296C2×D4—4524no—
297C2×D4—2262no—
298C2×D4—2262no—
299C2×D4—2261no—
300C2×D4—2261no—
301C2×D4—2261no—
302C2×D4—2261no—
303C2×D4—2261no—
304C2×D4—2261no—
305C2×D4C22⋊D11311yescharacteristic
306C2×D4C22×D11311yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—2261no—
310C22×C4C22×D11311yescharacteristic
311C22×C4C22×D11311yescharacteristic
312SD16—1134no—
313SD16—4521no—
314SD16—2262no—
315SD16—2262no—
316SD16—2262no—
317SD16—2262no—
318D8—4521no—
319D8—2262no—
320D8—2262no—
321M16—2262no—
322C2×C8—1131no—
323C2×C8—1131no—
324C2×C8—1131no—
325C2×C8—1131no—
326C2×C8—2262no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—1131no—
330C4⋊C4C22⋊D11311yescharacteristic
331C4⋊C4C22×D11311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—2261no—
337C22⋊C4—2261no—
338C22⋊C4—2261no—
339C22⋊C4C22⋊D11311yescharacteristic
340C22⋊C4C22⋊D11311yescharacteristic
341C42—21no—
342C42C22×D11311yescharacteristic
343C23—21no—
344C23—9041no—
345C23—9041no—
346C23—4522no—
347C23—4522no—
348C23—4522no—
349C23—4522no—
350C23—2261no—
351C23—2261no—
352C23—2261no—
353C23C2×C22⋊D11311yescharacteristic
354C23C2×C22⋊D11311yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8D4×D11312yescomplemented
360D4—22no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—1132no—
366D4—9041no—
367D4—4522no—
368D4—4522no—
369D4—4522no—
370D4—4522no—
371D4—4522no—
372D4—2261no—
373D4—2261no—
374D4—2261no—
375D4—2261no—
376D4—2261no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—4522no—
387C2×C4—2261no—
388C2×C4C2×C22⋊D11311yescharacteristic
389C2×C4C2×C22⋊D11311yescharacteristic
390C2×C4C2×C22⋊D11311yescharacteristic
391C2×C4C2×C22⋊D11311yescharacteristic
392C2×C4C23×D11311yescharacteristic
393C8—1132no—
394C8—2261no—
395C8—2261no—
396C8—2261no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—9044no—
406C22—9044no—
407C22—4521no—
408C22—4521no—
409C22—4521no—
410C22—4521no—
411C22—4521no—
412C22—4521no—
413C22—4521no—
414C22—4521no—
415C22—2262no—
416C22#1681364712yescomplemented
417C22C22×C22⋊D11311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—22no—
423C4—41no—
424C4—41no—
425C4—4521no—
426C4C2×D4×D11311yescharacteristic
427C4#1681366711yescharacteristic
428C2—22no—
429C2—41no—
430C2—81no—
431C2—9041no—
432C2—9041no—
433C2—4522no—
434C2D4×C22⋊D11311yescharacteristic
435C2C2×#1681364711yescharacteristic
436C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#548×C113C2
socleC22×C113C22×D4
hypercenter#548D113
hypocenterC113#3265
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16813647C2semidirect
2. C22×#14268634C2semidirect
3. D4×D452C2semidirect
4. #20298988C2semidirect
5. #20298846C2semidirect
6. #20298832C2semidirect
7. #20298810C2semidirect
8. #20298798C2semidirect
9. #20298748C2semidirect
10. #20298743C2semidirect
11. #20298737C2semidirect
12. #20298731C2semidirect
13. #20298696C2semidirect
14. #20298670C2semidirect
15. #548×C113C2semidirect
23. C2×#14268634C22semidirect
24. C2×#14268634C22semidirect
25. C2×#14268634C22semidirect
26. C2×#14268634C22semidirect
28. C2×#14268632C22semidirect
29. C2×#14268632C22semidirect
30. C2×#14268631C22semidirect
31. C22×#11744751C22semidirect
39. #16813555C22semidirect
40. C4⋊#11744751C22semidirect
41. #16813546C22semidirect
42. #16813546C22semidirect
43. #16813543C22semidirect
45. #16813542C22semidirect
46. #16813542C22semidirect
47. C22⋊#11744751C22semidirect
48. C22⋊#11744751C22semidirect
49. #16813533C22semidirect
50. C2×#41×C113C22semidirect
51. C22×Q8×C113C22semidirect
53. #124×C113C22semidirect
55. C22⋊Q8×C113C22semidirect
57. #121×C113C22semidirect
58. C4×Q8×C113C22semidirect
83. #14268634D4semidirect
140. Q8×C113C2×D4semidirect
177. #11744751C2×D4semidirect
186. C22×C113AGL(1,ℤ/8)semidirect
219. C113#3265semidirect
222. #548D113semidirect
235. C2×#41C2×D113semidirect
236. C22×Q8C2×D113semidirect
255. #124C2×D113semidirect
257. C22⋊Q8C2×D113semidirect
262. #121C2×D113semidirect
265. C4×Q8C2×D113semidirect
359. Q8D4×D113semidirect
416. C22#16813647semidirect

Maximal subgroups

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

subgroupindex
C2×#168136472
C22×#142686342
D4×D4522
#202989882
#202988462
#202988322
#202988102
#202987982
#202987482
#202987432
#202987372
#202987312
#202986962
#202986702
#548×C1132
#3265113