Finite Group Databasebeta

← #28402187

Subgroups — #28402187

Order 14464.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813649C211yesmaximal, characteristic, complemented
2C2×#16813647C211yesmaximal, characteristic, complemented
3#20299267C211yesmaximal, characteristic, complemented
4#20299232C211yesmaximal, characteristic, complemented
5#20298973C211yesmaximal, characteristic, complemented
6#20298850C211yesmaximal, characteristic, complemented
7#20298849C211yesmaximal, characteristic, complemented
8#20298796C211yesmaximal, characteristic, complemented
9#20298792C211yesmaximal, characteristic, complemented
10#20298746C211yesmaximal, characteristic, complemented
11#20298734C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298683C211yesmaximal, characteristic, complemented
14#20298673C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic, complemented
17C22×D452C2211yescharacteristic
18C2×D4×D113—21no—
19C2×D4×D113C2211yescharacteristic
20#16813649—24no—
21#16813647—24no—
22C2×#14268634C2211yescharacteristic
23C2×#14268634C2211yescharacteristic, complemented
24C2×D904C2211yescharacteristic
25C2×D904C2211yescharacteristic, complemented
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic, complemented
28C2×#14268632C2211yescharacteristic, complemented
29C2×#14268631C2211yescharacteristic, complemented
30C2×#14268630C2211yescharacteristic, complemented
31#16813618—21no—
32#16813618C2211yescharacteristic
33#16813618C2211yescharacteristic, complemented
34#16813597C2211yescharacteristic
35#16813596—21no—
36#16813596C2211yescharacteristic, complemented
37#16813595—21no—
38#16813593—21no—
39#16813593C2211yescharacteristic, complemented
40#16813592—21no—
41#16813590—21no—
42Q8×Dic113C2211yescharacteristic, complemented
43#16813584C2211yescharacteristic
44C4×C22⋊D113—21no—
45C4×C22⋊D113C2211yescharacteristic
46#16813553C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813544C2211yescharacteristic
49#16813544C2211yescharacteristic, complemented
50#16813543C2211yescharacteristic, complemented
51#16813542C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53C8×Dic113C2211yescharacteristic, complemented
54C2×#41×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic, complemented
56C2×D8×C113C2211yescharacteristic, complemented
57#121×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63#14268648—22no—
64#14268648—41no—
65C2×D452—22no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—21no—
69C2×D452—41no—
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78C2×C22⋊D113—21no—
79C2×C22⋊D113—21no—
80C2×C22⋊D113D411yescharacteristic
81D4×D113—22no—
82D4×D113—41no—
83D4×D113—44no—
84C2×C4×D113—21no—
85C2×C4×D113—21no—
86C2×C4×D113C2311yescharacteristic
87#14268634—22no—
88#14268634D414yescomplemented
89D904—22no—
90D904—41no—
91#14268632—22no—
92#14268632—22no—
93#14268632—22no—
94#14268631—22no—
95#14268630—22no—
96C2×#11744751C2311yescharacteristic
97C2×#11744751C2311yescharacteristic
98C4⋊Dic113—21no—
99C4⋊Dic113C2311yescharacteristic
100#14268626D411yescharacteristic
101C22⋊Dic113—21no—
102C22⋊Dic113D411yescharacteristic
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624D411yescharacteristic
107C4×Dic113—21no—
108C4×Dic113C2311yescharacteristic
109#41×C113—22no—
110#41×C113—41no—
111C2×Q8×C113C2311yescharacteristic
112C2×D4×C113—21no—
113C2×D4×C113—21no—
114C2×D4×C113C2311yescharacteristic
115C2×D4×C113C2311yescharacteristic
116C22×C4×C113—21no—
117C22×C4×C113C2311yescharacteristic
118SD16×C113—22no—
119D8×C113—41no—
120C2×C8×C113C2311yescharacteristic
121C2×C8×C113C2311yescharacteristic
122C4⋊C4×C113C2311yescharacteristic
123C22⋊C4×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
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—
136C22×D113C2×D411yescharacteristic
137Q8×C113—21no—
138Q8×C113C2×D412yescomplemented
139D4×C113—21no—
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—21no—
143D4×C113—42no—
144D4×C113—42no—
145C2×C4×C113—21no—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—21no—
149C2×C4×C113—42no—
150C2×C4×C113C2×D411yescharacteristic
151C2×C4×C113C2411yescharacteristic
152C22⋊D113—22no—
153C22⋊D113—42no—
154C22⋊D113—42no—
155C22⋊D113—42no—
156C22⋊D113—81no—
157C22⋊D113—81no—
158C22⋊D113—81no—
159C22⋊D113—81no—
160C2×Dic113—21no—
161C2×Dic113C2×D411yescharacteristic
162C2×Dic113C2×D411yescharacteristic
163C2×Dic113C2×D411yescharacteristic
164D452—21no—
165D452—21no—
166D452—21no—
167D452—21no—
168D452—21no—
169D452—42no—
170D452—42no—
171D452—42no—
172D452C2×D412yes—
173C4×D113—21no—
174C4×D113—21no—
175C4×D113—42no—
176C4×D113—42no—
177C8×C113—21no—
178C8×C113—21no—
179#11744751—21no—
180#11744751C2×D412yescomplemented
181C22×C113—21no—
182C22×C113—21no—
183C22×C113—21no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113—41no—
188C22×C113—41no—
189C22×C113—41no—
190C22×C113C22×D411yescharacteristic
191C2×D113—21no—
192C2×D113—22no—
193C2×D113—21no—
194C2×D113—21no—
195C2×D113—41no—
196C2×D113—41no—
197C2×D113—41no—
198C2×D113—41no—
199C2×D113—41no—
200C2×D113—41no—
201C2×D113—41no—
202C2×D113—41no—
203C2×D113—84no—
204C2×D113—84no—
205C4×C113—22no—
206C4×C113—21no—
207C4×C113—41no—
208C4×C113C22×D411yescharacteristic
209C4×C113H(5,𝔽2)11yescharacteristic
210Dic113—21no—
211Dic113—21no—
212Dic113—41no—
213Dic113AGL(1,ℤ/8)12yescomplemented
214C2×C113—41no—
215C2×C113—81no—
216C2×C113—81no—
217C2×C113D4211yescharacteristic
218C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C113#57611yescharacteristic
220D113—41no—
221D113—42no—
222D113—81no—
223D113—81no—
224#3274—1131nomaximal, Sylow
225C113#327411yescharacteristic, complemented, Sylow
226C2×AGL(1,ℤ/8)—1131no—
227C2×AGL(1,ℤ/8)—1131no—
228#550—1131no—
229D42—1131no—
230#493—1131no—
231#469—1131no—
232#469—1131no—
233#460—1131no—
234#459—1131no—
235#449—1131no—
236#449D11311yescharacteristic, complemented
237#447—1131no—
238#447—1131no—
239C4×SD16—1131no—
240#436—1131no—
241C2×#41—1131no—
242C2×#41C2×D11311yescharacteristic, complemented
243C22×D4—1131no—
244C22×D4—1131no—
245C22×D4—2261no—
246AGL(1,ℤ/8)—2264no—
247AGL(1,ℤ/8)—2264no—
248C2×SD16—1131no—
249C2×SD16—1131no—
250C2×SD16C2×D11311yescharacteristic, complemented
251C2×D8—1131no—
252C2×D8—1131no—
253C2×D8—1131no—
254C2×D8—1131no—
255C2×D8—1131no—
256C2×D8C2×D11311yescharacteristic, complemented
257C2×M16—1131no—
258C2×M16—1131no—
259#127—1131no—
260#127—1131no—
261#127—2261no—
262#121—1131no—
263#121—1131no—
264#121—1131no—
265#121—2261no—
266#121—2261no—
267#121—2261no—
268#121C2×D11311yescharacteristic
269#120—2261no—
270#120—2261no—
271C4×Q8—1131no—
272C4×D4—1131no—
273C4×D4—1131no—
274C4×D4—2261no—
275#106—1131no—
276C4⋊C8—1131no—
277#103C2×D11311yescharacteristic, complemented
278#102—1131no—
279#102—1131no—
280#102—1131no—
281#102—1131no—
282#102C2×D11311yescharacteristic, complemented
283C22⋊C8—1131no—
284C22⋊C8C2×D11311yescharacteristic, complemented
285C4×C8—1131no—
286C24—2261no—
287C24—2261no—
288#41—22no—
289#41—41no—
290#41—4521no—
291#41—2262no—
292C2×Q8C22×D11311yescharacteristic
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—1131no—
296C2×D4—1131no—
297C2×D4—1131no—
298C2×D4—1131no—
299C2×D4—4521no—
300C2×D4—4524no—
301C2×D4—4521no—
302C2×D4—2262no—
303C2×D4—2261no—
304C2×D4—2261no—
305C2×D4—2261no—
306C2×D4—2261no—
307C2×D4—2261no—
308C2×D4—2261no—
309C2×D4—2261no—
310C2×D4—2262no—
311C2×D4—2261no—
312C2×D4—2261no—
313C2×D4—2261no—
314C2×D4C22×D11311yescharacteristic
315C2×D4C22×D11311yescharacteristic
316C22×C4—21no—
317C22×C4—1131no—
318C22×C4—2261no—
319C22×C4—2261no—
320C22×C4C22×D11311yescharacteristic
321SD16—22no—
322SD16—1134no—
323SD16—2262no—
324D8—41no—
325D8—4521no—
326D8—2262no—
327D8—2262no—
328D8—2262no—
329D8—2262no—
330M16—2262no—
331M16—2262no—
332C2×C8—1131no—
333C2×C8—1131no—
334C2×C8C22×D11311yescharacteristic
335C2×C8C22×D11311yescharacteristic
336C4⋊C4—1131no—
337C4⋊C4—1131no—
338C4⋊C4—2261no—
339C4⋊C4C22×D11311yescharacteristic
340C22⋊C4—21no—
341C22⋊C4—1131no—
342C22⋊C4—1131no—
343C22⋊C4—2261no—
344C22⋊C4—2261no—
345C22⋊C4—2261no—
346C22⋊C4—2261no—
347C42—1131no—
348C42—2261no—
349C23—21no—
350C23—21no—
351C23—1131no—
352C23—9041no—
353C23—9041no—
354C23—4522no—
355C23—4522no—
356C23—4522no—
357C23—4522no—
358C23—2261no—
359C23—2261no—
360C23—2261no—
361C23D4×D11311yescharacteristic
362Q8—21no—
363Q8D4×D11312yescomplemented
364D4—21no—
365D4—21no—
366D4—21no—
367D4—21no—
368D4—42no—
369D4—42no—
370D4—1132no—
371D4—9041no—
372D4—9041no—
373D4—9041no—
374D4—9041no—
375D4—4522no—
376D4—4522no—
377D4—4522no—
378D4—4522no—
379D4—4522no—
380D4—4522no—
381D4—2262no—
382D4—2261no—
383D4—2261no—
384D4—2261no—
385D4—2261no—
386D4—2261no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—42no—
392C2×C4—1131no—
393C2×C4—1131no—
394C2×C4—1131no—
395C2×C4—4522no—
396C2×C4—4522no—
397C2×C4—2261no—
398C2×C4—2261no—
399C2×C4—2261no—
400C2×C4D4×D11311yescharacteristic
401C2×C4C23×D11311yescharacteristic
402C8—21no—
403C8—21no—
404C8—1132no—
405C8—2261no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—9044no—
416C22—9044no—
417C22—4521no—
418C22—4521no—
419C22—4521no—
420C22—4521no—
421C22—4521no—
422C22—4521no—
423C22—4521no—
424C22—4521no—
425C22—2261no—
426C22—2261no—
427C22—2261no—
428C22—2262no—
429C22C2×D4×D11311yescharacteristic
430C4—21no—
431C4—22no—
432C4—41no—
433C4—1132no—
434C4—4521no—
435C4—2261no—
436C4—2261no—
437C4C2×D4×D11311yescharacteristic
438C4#1681366711yescharacteristic
439C2—41no—
440C2—81no—
441C2—81no—
442C2—9041no—
443C2—9041no—
444C2—4522no—
445C2—4521no—
446C2#2029923011yescharacteristic
447C2AGL(1,ℤ/8)×D11311yescharacteristic
448C2#2029940011yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3274
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#16813649C2semidirect
2. C2×#16813647C2semidirect
3. #20299267C2semidirect
4. #20299232C2semidirect
5. #20298973C2semidirect
6. #20298850C2semidirect
7. #20298849C2semidirect
8. #20298796C2semidirect
9. #20298792C2semidirect
10. #20298746C2semidirect
11. #20298734C2semidirect
12. #20298730C2semidirect
13. #20298683C2semidirect
14. #20298673C2semidirect
15. #449×C113C2semidirect
16. C2×#14268648C22semidirect
23. C2×#14268634C22semidirect
25. C2×D904C22semidirect
27. C2×#14268632C22semidirect
28. C2×#14268632C22semidirect
29. C2×#14268631C22semidirect
30. C2×#14268630C22semidirect
33. #16813618C22semidirect
36. #16813596C22semidirect
39. #16813593C22semidirect
42. Q8×Dic113C22semidirect
46. #16813553C22semidirect
47. #16813551C22semidirect
49. #16813544C22semidirect
50. #16813543C22semidirect
51. #16813542C22semidirect
52. #16813534C22semidirect
53. C8×Dic113C22semidirect
54. C2×#41×C113C22semidirect
55. C2×SD16×C113C22semidirect
56. C2×D8×C113C22semidirect
58. #103×C113C22semidirect
59. #102×C113C22semidirect
60. C22⋊C8×C113C22semidirect
88. #14268634D4semidirect
138. Q8×C113C2×D4semidirect
180. #11744751C2×D4semidirect
213. Dic113AGL(1,ℤ/8)semidirect
225. C113#3274semidirect
236. #449D113semidirect
242. C2×#41C2×D113semidirect
250. C2×SD16C2×D113semidirect
256. C2×D8C2×D113semidirect
277. #103C2×D113semidirect
282. #102C2×D113semidirect
284. C22⋊C8C2×D113semidirect
363. Q8D4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136492
C2×#168136472
#202992672
#202992322
#202989732
#202988502
#202988492
#202987962
#202987922
#202987462
#202987342
#202987302
#202986832
#202986732
#449×C1132
#3274113