Finite Group Databasebeta

← #28402185

Subgroups — #28402185

Order 14464.

520 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×#16813648C211yesmaximal, characteristic, complemented
2C2×#16813646C211yesmaximal, characteristic, complemented
3#20299245C211yesmaximal, characteristic, complemented
4#20299242C211yesmaximal, characteristic, complemented
5#20298981C211yesmaximal, characteristic, complemented
6#20298843C211yesmaximal, characteristic, complemented
7#20298842C211yesmaximal, characteristic, complemented
8#20298812C211yesmaximal, characteristic, complemented
9#20298811C211yesmaximal, characteristic, complemented
10#20298762C211yesmaximal, characteristic, complemented
11#20298761C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298673C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic, complemented
19#16813648—24no—
20#16813646—24no—
21C2×Dic452C2211yescharacteristic, complemented
22C2×#14268636C2211yescharacteristic, complemented
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268635C2211yescharacteristic, complemented
25C2×#14268635C2211yescharacteristic, complemented
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28C2×#14268631C2211yescharacteristic, complemented
29C2×#14268630C2211yescharacteristic, complemented
30#16813609C2211yescharacteristic, complemented
31#16813609C2211yescharacteristic, complemented
32#16813604—21no—
33#16813603—21no—
34#16813602C2211yescharacteristic, complemented
35#16813601C2211yescharacteristic, complemented
36#16813594—21no—
37#16813593—21no—
38#16813593C2211yescharacteristic
39#16813591—21no—
40#16813590—21no—
41D4×Dic113C2211yescharacteristic, complemented
42#16813584C2211yescharacteristic, complemented
43C4×C22⋊D113C2211yescharacteristic
44C2×C22⋊Dic113—21no—
45C22⋊C4×D113—21no—
46#16813555C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813545C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53C8×Dic113C2211yescharacteristic, complemented
54C22×D4×C113C2211yescharacteristic, complemented
55C2×D8×C113C2211yescharacteristic
56C2×D8×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268647—22no—
63#14268647—41no—
64#14268646—22no—
65#14268646—41no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C2×C22⋊D113D411yescharacteristic
74D4×D113—22no—
75D4×D113—41no—
76C22×Dic113—21no—
77C22×Dic113—21no—
78C2×C4×D113—21no—
79C2×C4×D113—21no—
80C2×C4×D113C2311yescharacteristic
81Dic452—41no—
82#14268636—22no—
83#14268635—22no—
84#14268635—22no—
85#14268635—22no—
86#14268632—22no—
87#14268632D414yescomplemented
88#14268631—22no—
89#14268630—22no—
90C2×#11744751C2311yescharacteristic
91C2×#11744751C2311yescharacteristic
92C4⋊Dic113—21no—
93C4⋊Dic113C2311yescharacteristic
94#14268626—21no—
95#14268626D411yescharacteristic
96C22⋊Dic113—21no—
97C22⋊Dic113—21no—
98C22⋊Dic113—21no—
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113—21no—
102C22⋊Dic113—21no—
103C22⋊Dic113D411yescharacteristic
104#14268624—21no—
105#14268624—21no—
106#14268624D411yescharacteristic
107C4×Dic113C2311yescharacteristic
108C24×C113—21no—
109C2×D4×C113—22no—
110C2×D4×C113—21no—
111C2×D4×C113—21no—
112C2×D4×C113—41no—
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115C2×D4×C113C2311yescharacteristic
116C22×C4×C113C2311yescharacteristic
117D8×C113—22no—
118D8×C113—41no—
119C2×C8×C113C2311yescharacteristic
120C2×C8×C113C2311yescharacteristic
121C4⋊C4×C113C2311yescharacteristic
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—42no—
127C23×C113—42no—
128C23×C113—81no—
129C23×C113C2×D411yescharacteristic
130C22×D113—21no—
131C22×D113—42no—
132C22×D113—42no—
133C22×D113—81no—
134C22×D113C2×D411yescharacteristic
135D4×C113—21no—
136D4×C113—21no—
137D4×C113—21no—
138D4×C113—21no—
139D4×C113—21no—
140D4×C113—42no—
141D4×C113—81no—
142D4×C113C2×D412yes—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113C2×D411yescharacteristic
147C2×C4×C113C2411yescharacteristic
148C22⋊D113—41no—
149C22⋊D113—42no—
150C22⋊D113—42no—
151C22⋊D113—42no—
152C22⋊D113—81no—
153C2×Dic113—21no—
154C2×Dic113—21no—
155C2×Dic113—21no—
156C2×Dic113—42no—
157C2×Dic113—81no—
158C2×Dic113C2×D411yescharacteristic
159C2×Dic113C2×D411yescharacteristic
160C2×Dic113C2×D411yescharacteristic
161D452—21no—
162D452C2×D412yes—
163C4×D113—21no—
164C4×D113—21no—
165C4×D113—42no—
166C4×D113—81no—
167Dic226—21no—
168Dic226—21no—
169Dic226—21no—
170Dic226—21no—
171C8×C113—21no—
172C8×C113—21no—
173#11744751—21no—
174#11744751C2×D412yes—
175C22×C113—22no—
176C22×C113—21no—
177C22×C113—21no—
178C22×C113—21no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113—84no—
188C22×C113C22×D411yescharacteristic
189C2×D113—21no—
190C2×D113—22no—
191C2×D113—21no—
192C2×D113—21no—
193C2×D113—41no—
194C2×D113—41no—
195C2×D113—84no—
196C4×C113—21no—
197C4×C113—41no—
198C4×C113C22×D411yescharacteristic
199C4×C113H(5,𝔽2)11yescharacteristic
200Dic113—21no—
201Dic113—21no—
202Dic113—21no—
203Dic113—41no—
204Dic113—41no—
205Dic113—41no—
206C2×C113—41no—
207C2×C113—42no—
208C2×C113—81no—
209C2×C113—81no—
210C2×C113D4211yescharacteristic
211C2×C113#57511yescharacteristic
212C2×C113#57611yescharacteristic
213D113—41no—
214D113—42no—
215#3273—1131nomaximal, Sylow
216C113#327311yescharacteristic, complemented, Sylow
217C2×AGL(1,ℤ/8)—1131no—
218C2×AGL(1,ℤ/8)—1131no—
219#546—1131no—
220#546—1131no—
221#495—1131no—
222#468—1131no—
223#468—1131no—
224#463—1131no—
225#463—1131no—
226#452—1131no—
227#452—1131no—
228#447—1131no—
229#447D11311yescharacteristic, complemented
230C4×D8—1131no—
231#436—1131no—
232C2×#41—1131no—
233C2×#41—1131no—
234C22×D4—1131no—
235C22×D4C2×D11311yescharacteristic, complemented
236AGL(1,ℤ/8)—2264no—
237AGL(1,ℤ/8)—2264no—
238C2×Q16—1131no—
239C2×SD16—1131no—
240C2×SD16—1131no—
241C2×SD16—1131no—
242C2×SD16—1131no—
243C2×D8—1131no—
244C2×D8—1131no—
245C2×D8C2×D11311yescharacteristic
246C2×D8C2×D11311yescharacteristic
247C2×M16—1131no—
248C2×M16—1131no—
249#124—1131no—
250#124—1131no—
251#123—2261no—
252#123—2261no—
253C22⋊Q8—1131no—
254C22⋊Q8—1131no—
255#121—1131no—
256#121—2261no—
257#121—2261no—
258#121C2×D11311yescharacteristic
259#120—2261no—
260#120—2261no—
261C4×D4—1131no—
262C4×D4—1131no—
263C4×D4—1131no—
264C2×C22⋊C4—2261no—
265C2×C22⋊C4—2261no—
266#107—1131no—
267C4⋊C8—1131no—
268#103—1131no—
269#103—1131no—
270#102—1131no—
271#102—1131no—
272#102C2×D11311yescharacteristic, complemented
273#102C2×D11311yescharacteristic, complemented
274C22⋊C8—1131no—
275C22⋊C8C2×D11311yescharacteristic, complemented
276C4×C8—1131no—
277C24—21no—
278C24—2261no—
279#41—4521no—
280#41—4521no—
281#41—2262no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8—1131no—
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—41no—
289C2×D4—1131no—
290C2×D4—1131no—
291C2×D4—4521no—
292C2×D4—2261no—
293C2×D4—2262no—
294C2×D4—2261no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4C22×D11311yescharacteristic
298C2×D4C22×D11311yescharacteristic
299C2×D4C22×D11311yescharacteristic
300C22×C4—1131no—
301C22×C4—2261no—
302C22×C4—2261no—
303C22×C4—2261no—
304C22×C4—2261no—
305C22×C4C22×D11311yescharacteristic
306Q16—4521no—
307SD16—2262no—
308SD16—2262no—
309SD16—2262no—
310SD16—2262no—
311D8—22no—
312D8—41no—
313D8—1134no—
314D8—2262no—
315M16—2262no—
316M16—2262no—
317C2×C8—1131no—
318C2×C8—1131no—
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—1131no—
328C22⋊C4—1131no—
329C22⋊C4—2261no—
330C22⋊C4—2261no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C22⋊C4—2261no—
337C22⋊C4—2261no—
338C42—1131no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—42no—
343C23—42no—
344C23—81no—
345C23—1131no—
346C23—9041no—
347C23—4522no—
348C23—4522no—
349C23—2261no—
350C23D4×D11311yescharacteristic
351Q8—2261no—
352Q8—2261no—
353Q8—2261no—
354Q8—2261no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—21no—
359D4—21no—
360D4—42no—
361D4—81no—
362D4—1132no—
363D4—9041no—
364D4—4522no—
365D4—4522no—
366D4—4521no—
367D4—4522no—
368D4—2261no—
369D4D4×D11312yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—1131no—
374C2×C4—1131no—
375C2×C4—1131no—
376C2×C4—9041no—
377C2×C4—9041no—
378C2×C4—4522no—
379C2×C4—4522no—
380C2×C4—2261no—
381C2×C4—2261no—
382C2×C4—2261no—
383C2×C4—2261no—
384C2×C4—2261no—
385C2×C4D4×D11311yescharacteristic
386C2×C4C23×D11311yescharacteristic
387C8—21no—
388C8—21no—
389C8—1132no—
390C8—2261no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—84no—
404C22—9044no—
405C22—4521no—
406C22—4521no—
407C22—2261no—
408C22—2261no—
409C22—2262no—
410C22—2261no—
411C22C2×D4×D11311yescharacteristic
412C4—21no—
413C4—41no—
414C4—4521no—
415C4—4521no—
416C4—4521no—
417C4—2261no—
418C4—2261no—
419C4—2261no—
420C4C2×D4×D11311yescharacteristic
421C4#1681366711yescharacteristic
422C2—41no—
423C2—42no—
424C2—81no—
425C2—81no—
426C2—4521no—
427C2—4522no—
428C2#2029923011yescharacteristic
429C2#2029939411yescharacteristic
430C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3273
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. C2×#16813646C2semidirect
3. #20299245C2semidirect
4. #20299242C2semidirect
5. #20298981C2semidirect
6. #20298843C2semidirect
7. #20298842C2semidirect
8. #20298812C2semidirect
9. #20298811C2semidirect
10. #20298762C2semidirect
11. #20298761C2semidirect
12. #20298730C2semidirect
13. #20298678C2semidirect
14. #20298673C2semidirect
15. #447×C113C2semidirect
18. C2×D4×D113C22semidirect
21. C2×Dic452C22semidirect
22. C2×#14268636C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268635C22semidirect
25. C2×#14268635C22semidirect
28. C2×#14268631C22semidirect
29. C2×#14268630C22semidirect
30. #16813609C22semidirect
31. #16813609C22semidirect
34. #16813602C22semidirect
35. #16813601C22semidirect
41. D4×Dic113C22semidirect
42. #16813584C22semidirect
46. #16813555C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813545C22semidirect
50. #16813544C22semidirect
51. #16813543C22semidirect
52. #16813534C22semidirect
53. C8×Dic113C22semidirect
54. C22×D4×C113C22semidirect
58. #102×C113C22semidirect
59. #102×C113C22semidirect
60. C22⋊C8×C113C22semidirect
87. #14268632D4semidirect
216. C113#3273semidirect
229. #447D113semidirect
235. C22×D4C2×D113semidirect
272. #102C2×D113semidirect
273. #102C2×D113semidirect
275. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
C2×#168136462
#202992452
#202992422
#202989812
#202988432
#202988422
#202988122
#202988112
#202987622
#202987612
#202987302
#202986782
#202986732
#447×C1132
#3273113