Finite Group Databasebeta

← #28404240

Subgroups — #28404240

Order 14464.

1658 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×#16813668C211yesmaximal, characteristic, complemented
2C22×#14268648C211yesmaximal, characteristic, complemented
3#20299270C211yesmaximal, characteristic, complemented
4#20299267C211yesmaximal, characteristic, complemented
5#20299259C211yesmaximal, characteristic, complemented
6#20299241C213yesmaximal, complemented
7#20299239C213yesmaximal, complemented
8D4×D452C213yesmaximal, complemented
9#20299232C213yesmaximal, complemented
10#20299178C213yesmaximal, complemented
11#20299166C213yesmaximal, complemented
12#20299107C213yesmaximal, complemented
13#121×D113C213yesmaximal, complemented
14#20299080C211yesmaximal, characteristic, complemented
15#548×C113C211yesmaximal, characteristic, complemented
16#16813668—28no—
17C2×#14268648—28no—
18C2×#14268648C2211yescharacteristic
19C2×#14268648C2211yescharacteristic, complemented
20C2×#14268648C2211yescharacteristic, complemented
21C2×#14268648C2213yescomplemented
22C2×#14268648C2213yescomplemented
23C2×#14268647C2213yescomplemented
24C22×D452C2213yescomplemented
25C22×D452C2213yescomplemented
26C2×D4×D113C2213yescomplemented
27C2×D4×D113C2213yescomplemented
28C2×D4×D113C2216yescomplemented
29C22×C4×D113C2213yescomplemented
30#16813619C2213yescomplemented
31#16813618C2213yescomplemented
32#16813611C2213yescomplemented
33#16813607C2213yescomplemented
34#16813604C2213yescomplemented
35#16813600C2213yescomplemented
36#16813599C2211yescharacteristic, complemented
37#16813598C2213yescomplemented
38#16813597C2213yescomplemented
39#16813597C2213yescomplemented
40#16813597C2216yescomplemented
41#16813596C2213yescomplemented
42#16813596C2213yescomplemented
43#16813595C2216yescomplemented
44#16813595C2213yescomplemented
45#16813595C2216yescomplemented
46#16813594C2213yescomplemented
47#16813593C2213yescomplemented
48#16813592C2213yescomplemented
49#16813592C2216yescomplemented
50#16813592C2216yescomplemented
51#16813590C2213yescomplemented
52Q8×Dic113C2211yescharacteristic, complemented
53C4×D452C2213yescomplemented
54C4×D452C2213yescomplemented
55#16813584C2213yescomplemented
56C4×C22⋊D113C2213yescomplemented
57C4×C22⋊D113C2213yescomplemented
58#16813579C2213yescomplemented
59C4⋊C4×D113C2213yescomplemented
60C22⋊C4×D113C2216yescomplemented
61C2×#41×C113C2211yescharacteristic, complemented
62C22×Q8×C113C2211yescharacteristic, complemented
63#124×C113C2213yescomplemented
64C22⋊Q8×C113C2213yescomplemented
65#121×C113C2213yescomplemented
66C4×Q8×C113C2211yescharacteristic, complemented
67C4×D4×C113C2213yescomplemented
68C23×D113C2313yes—
69C23×D113C2316yes—
70#14268648—24no—
71#14268648—24no—
72#14268648—212no—
73#14268648—212no—
74#14268648D418yescomplemented
75#14268647—212no—
76C2×Dic226C2311yescharacteristic
77C2×D452—212no—
78C2×D452—212no—
79C2×D452C2316yes—
80C2×D452C2313yes—
81C2×D452C2313yes—
82C2×D452C2313yes—
83C2×D452C2313yes—
84C2×D452C2316yes—
85C2×D452C2313yes—
86C2×C22⋊D113C2313yes—
87C2×C22⋊D113C2313yes—
88C2×C22⋊D113C2313yes—
89C2×C22⋊D113C2313yes—
90C2×C22⋊D113C2316yes—
91D4×D113—212no—
92D4×D113—212no—
93D4×D113—412no—
94C22×Dic113C2311yescharacteristic
95C2×C4×D113—212no—
96C2×C4×D113C2313yes—
97C2×C4×D113C2313yes—
98C2×C4×D113C2313yes—
99C2×C4×D113C2313yes—
100C2×C4×D113C2316yes—
101C2×C4×D113C2313yes—
102C4⋊Dic113C2313yes—
103C4⋊Dic113C2311yescharacteristic
104#14268626C2313yes—
105#14268626C2311yescharacteristic
106#14268626C2311yescharacteristic
107#14268626C2313yes—
108C22⋊Dic113C2313yes—
109C22⋊Dic113C2311yescharacteristic
110#14268624C2313yes—
111#14268624C2316yes—
112#14268624C2313yes—
113#14268624C2313yes—
114#14268624C2313yes—
115#14268624C2313yes—
116#14268624C2313yes—
117C4×Dic113C2313yes—
118#41×C113—24no—
119C2×Q8×C113—24no—
120C2×Q8×C113C2313yes—
121C2×Q8×C113C2311yescharacteristic
122C2×D4×C113C2313yes—
123C2×D4×C113C2313yes—
124C22×C4×C113C2313yes—
125C22×C4×C113C2313yes—
126C4⋊C4×C113C2313yes—
127C4⋊C4×C113C2313yes—
128C22⋊C4×C113C2316yes—
129C22⋊C4×C113C2311yescharacteristic
130C22⋊C4×C113C2313yes—
131C42×C113C2313yes—
132C23×C113C2413yes—
133C23×C113C2411yescharacteristic
134C22×D113—26no—
135C22×D113—26no—
136C22×D113—212no—
137C22×D113—43no—
138C22×D113—46no—
139C22×D113—46no—
140C22×D113C2413yes—
141C22×D113C2413yes—
142C22×D113C2413yes—
143Q8×C113—26no—
144Q8×C113C2×D414yescomplemented
145D4×C113—26no—
146D4×C113—26no—
147C2×C4×C113—26no—
148C2×C4×C113—26no—
149C2×C4×C113C2411yescharacteristic
150C2×C4×C113C2413yes—
151C2×C4×C113C2413yes—
152C2×C4×C113C2411yescharacteristic
153C2×C4×C113C2413yes—
154C22⋊D113—26no—
155C22⋊D113—26no—
156C22⋊D113—26no—
157C22⋊D113—46no—
158C22⋊D113—43no—
159C2×Dic113—22no—
160C2×Dic113C2411yescharacteristic
161C2×Dic113C2413yes—
162C2×Dic113C2411yescharacteristic
163C2×Dic113C2411yescharacteristic
164C2×Dic113C2411yescharacteristic
165D452—26no—
166D452—212no—
167D452—26no—
168D452—26no—
169D452—46no—
170D452—43no—
171D452C2×D4112yescomplemented
172C4×D113—26no—
173C4×D113—26no—
174C4×D113—26no—
175C4×D113—26no—
176C4×D113—46no—
177C4×D113C2×D4112yescomplemented
178Dic226—22no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113—23no—
182C22×C113—23no—
183C22×C113—23no—
184C22×C113H(5,𝔽2)12yescomplemented
185C22×C113C2511yescharacteristic
186C2×D113—23no—
187C2×D113—23no—
188C2×D113—23no—
189C2×D113—23no—
190C2×D113—23no—
191C2×D113—23no—
192C2×D113—23no—
193C2×D113—23no—
194C2×D113—412no—
195C2×D113—812no—
196C2×D113C22×D416yes—
197C4×C113—21no—
198C4×C113—23no—
199C4×C113—23no—
200C4×C113—21no—
201C4×C113C22×D416yes—
202Dic113—21no—
203Dic113—21no—
204Dic113—23no—
205Dic113—21no—
206Dic113C22×D412yes—
207C2×C113—22no—
208C2×C113—43no—
209C2×C113C23×D411yescharacteristic
210C2×C113C2×H(5,𝔽2)11yescharacteristic
211C2×C113#58511yescharacteristic
212D113—26no—
213D113—43no—
214D113—43no—
215#3488—1131nomaximal, Sylow
216C113#348811yescharacteristic, complemented, Sylow
217C2×H(5,𝔽2)—1131no—
218C22×#41—1131no—
219#550—1131no—
220#550—1131no—
221#548—1131no—
222#548D11311yescharacteristic, complemented
223#546—1133no—
224#546—1133no—
225D42—1133no—
226D42—1133no—
227#537—1133no—
228#535—1133no—
229#525—1133no—
230C2×#121—1133no—
231#520—1131no—
232H(5,𝔽2)—2268no—
233C2×#41—1131no—
234C2×#41—1133no—
235C2×#41—1133no—
236C2×#41—1131no—
237C2×#41—1131no—
238C2×#41—1133no—
239C2×#41—2268no—
240C2×#41C2×D11311yescharacteristic, complemented
241C22×Q8C2×D11311yescharacteristic, complemented
242C22×D4—1136no—
243C22×D4—1133no—
244C22×D4—1133no—
245C22×D4—1133no—
246C22×D4—1133no—
247C23×C4—1133no—
248#127—1133no—
249#127—1133no—
250#124—1133no—
251#124C2×D11313yescomplemented
252#123—1133no—
253#123—1133no—
254C22⋊Q8—1133no—
255C22⋊Q8—1133no—
256C22⋊Q8—1131no—
257C22⋊Q8C2×D11313yescomplemented
258#121—1133no—
259#121—1133no—
260#121—1133no—
261#121—1133no—
262#121—1133no—
263#121—1136no—
264#121—1133no—
265#121—1136no—
266#121—1133no—
267#121—1136no—
268#121C2×D11313yescomplemented
269#120—1133no—
270#120—1133no—
271#120—1136no—
272#120—1136no—
273C4×Q8—1131no—
274C4×Q8C2×D11311yescharacteristic, complemented
275C4×D4—1133no—
276C4×D4—1133no—
277C4×D4—1133no—
278C4×D4—1133no—
279C4×D4—1133no—
280C4×D4C2×D11313yescomplemented
281#117—1133no—
282C2×C4⋊C4—1133no—
283C2×C22⋊C4—1136no—
284C24—1136no—
285C24—1133no—
286#41—24no—
287#41—1138no—
288#41—22612no—
289#41—22612no—
290#41—22612no—
291#41—2264no—
292#41—2264no—
293C2×Q8—24no—
294C2×Q8—1131no—
295C2×Q8C22×D11313yes—
296C2×Q8C22×D11311yescharacteristic
297C2×D4—1133no—
298C2×D4—1136no—
299C2×D4—1133no—
300C2×D4—1133no—
301C2×D4—1133no—
302C2×D4—1133no—
303C2×D4—1133no—
304C2×D4—1136no—
305C2×D4—1136no—
306C2×D4—1133no—
307C2×D4—1133no—
308C2×D4—1133no—
309C2×D4—45212no—
310C2×D4—22612no—
311C2×D4—22612no—
312C2×D4—22612no—
313C2×D4—22612no—
314C2×D4C22×D11313yes—
315C2×D4C22×D11313yes—
316C22×C4—1133no—
317C22×C4—1131no—
318C22×C4—1136no—
319C22×C4—1133no—
320C22×C4—1133no—
321C22×C4—1133no—
322C22×C4—1133no—
323C22×C4—22612no—
324C22×C4C22×D11313yes—
325C22×C4C22×D11313yes—
326C4⋊C4—1133no—
327C4⋊C4—1133no—
328C4⋊C4—1131no—
329C4⋊C4—1131no—
330C4⋊C4—1131no—
331C4⋊C4—1133no—
332C4⋊C4C22×D11313yes—
333C4⋊C4C22×D11313yes—
334C22⋊C4—1133no—
335C22⋊C4—1131no—
336C22⋊C4—1133no—
337C22⋊C4—1136no—
338C22⋊C4—1133no—
339C22⋊C4—1133no—
340C22⋊C4—1133no—
341C22⋊C4—1133no—
342C22⋊C4—1133no—
343C22⋊C4C22×D11316yes—
344C22⋊C4C22×D11311yescharacteristic
345C22⋊C4C22×D11313yes—
346C42—1133no—
347C42C22×D11313yes—
348C23—1133no—
349C23—1133no—
350C23—1133no—
351C23—4526no—
352C23—4526no—
353C23—4523no—
354C23—22612no—
355C23—2266no—
356C23—2266no—
357C23C23×D11313yes—
358C23C23×D11311yescharacteristic
359Q8—26no—
360Q8—2262no—
361Q8D4×D11314yescomplemented
362D4—26no—
363D4—26no—
364D4—11312no—
365D4—4526no—
366D4—4523no—
367D4—4526no—
368D4—4523no—
369D4—2266no—
370D4—22612no—
371D4—2266no—
372D4—2266no—
373D4—2266no—
374D4—2266no—
375D4—2266no—
376C2×C4—26no—
377C2×C4—26no—
378C2×C4—1131no—
379C2×C4—11312no—
380C2×C4—1131no—
381C2×C4—1133no—
382C2×C4—1131no—
383C2×C4—1131no—
384C2×C4—4526no—
385C2×C4—2266no—
386C2×C4—2266no—
387C2×C4—2262no—
388C2×C4—2266no—
389C2×C4—2266no—
390C2×C4C23×D11311yescharacteristic
391C2×C4C23×D11313yes—
392C2×C4C23×D11313yes—
393C2×C4C23×D11311yescharacteristic
394C2×C4C23×D11313yes—
395C22—21no—
396C22—21no—
397C22—23no—
398C22—23no—
399C22—23no—
400C22—1136no—
401C22—90412no—
402C22—45212no—
403C22—2263no—
404C22—2263no—
405C22—2263no—
406C22—2263no—
407C22—2263no—
408C22—2263no—
409C22—2263no—
410C22—2263no—
411C22#1681366812yescomplemented
412C22C24×D11311yescharacteristic
413C4—21no—
414C4—23no—
415C4—23no—
416C4—21no—
417C4—1132no—
418C4—2261no—
419C4—2261no—
420C4—2263no—
421C4—2261no—
422C4C2×D4×D11316yes—
423C2—22no—
424C2—43no—
425C2—4523no—
426C2—4523no—
427C2—2266no—
428C2C22×D4×D11311yescharacteristic
429C2C2×#1681366811yescharacteristic
430C2#2029943511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#548×C113C2
hypercenter#548D113
hypocenterC113#3488
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16813668C2semidirect
2. C22×#14268648C2semidirect
3. #20299270C2semidirect
4. #20299267C2semidirect
5. #20299259C2semidirect
6. #20299241C2semidirect
7. #20299239C2semidirect
8. D4×D452C2semidirect
9. #20299232C2semidirect
10. #20299178C2semidirect
11. #20299166C2semidirect
12. #20299107C2semidirect
13. #121×D113C2semidirect
14. #20299080C2semidirect
15. #548×C113C2semidirect
19. C2×#14268648C22semidirect
20. C2×#14268648C22semidirect
21. C2×#14268648C22semidirect
22. C2×#14268648C22semidirect
23. C2×#14268647C22semidirect
24. C22×D452C22semidirect
25. C22×D452C22semidirect
26. C2×D4×D113C22semidirect
27. C2×D4×D113C22semidirect
28. C2×D4×D113C22semidirect
29. C22×C4×D113C22semidirect
30. #16813619C22semidirect
31. #16813618C22semidirect
32. #16813611C22semidirect
33. #16813607C22semidirect
34. #16813604C22semidirect
35. #16813600C22semidirect
36. #16813599C22semidirect
37. #16813598C22semidirect
38. #16813597C22semidirect
39. #16813597C22semidirect
40. #16813597C22semidirect
41. #16813596C22semidirect
42. #16813596C22semidirect
43. #16813595C22semidirect
44. #16813595C22semidirect
45. #16813595C22semidirect
46. #16813594C22semidirect
47. #16813593C22semidirect
48. #16813592C22semidirect
49. #16813592C22semidirect
50. #16813592C22semidirect
51. #16813590C22semidirect
52. Q8×Dic113C22semidirect
53. C4×D452C22semidirect
54. C4×D452C22semidirect
55. #16813584C22semidirect
56. C4×C22⋊D113C22semidirect
57. C4×C22⋊D113C22semidirect
58. #16813579C22semidirect
59. C4⋊C4×D113C22semidirect
60. C22⋊C4×D113C22semidirect
61. C2×#41×C113C22semidirect
62. C22×Q8×C113C22semidirect
63. #124×C113C22semidirect
64. C22⋊Q8×C113C22semidirect
65. #121×C113C22semidirect
66. C4×Q8×C113C22semidirect
67. C4×D4×C113C22semidirect
74. #14268648D4semidirect
144. Q8×C113C2×D4semidirect
171. D452C2×D4semidirect
177. C4×D113C2×D4semidirect
184. C22×C113H(5,𝔽2)semidirect
216. C113#3488semidirect
222. #548D113semidirect
240. C2×#41C2×D113semidirect
241. C22×Q8C2×D113semidirect
251. #124C2×D113semidirect
257. C22⋊Q8C2×D113semidirect
268. #121C2×D113semidirect
274. C4×Q8C2×D113semidirect
280. C4×D4C2×D113semidirect
361. Q8D4×D113semidirect
411. C22#16813668semidirect

Maximal subgroups

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

subgroupindex
C2×#168136682
C22×#142686482
#202992702
#202992672
#202992592
#202992412
#202992392
D4×D4522
#202992322
#202991782
#202991662
#202991072
#121×D1132
#202990802
#548×C1132
#3488113