Finite Group Databasebeta

← #28402263

Subgroups — #28402263

Order 14464.

546 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
1C22×#14268634C211yesmaximal, characteristic, complemented
2C2×SD16×D113C211yesmaximal, characteristic, complemented
3Q8×C22⋊D113C211yesmaximal, characteristic, complemented
4#20299232C211yesmaximal, characteristic
5#20298969C211yesmaximal, characteristic, complemented
6#20298830C211yesmaximal, characteristic, complemented
7#20298825C211yesmaximal, characteristic, complemented
8#20298802C211yesmaximal, characteristic, complemented
9#20298796C211yesmaximal, characteristic, complemented
10#20298751C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298738C211yesmaximal, characteristic, complemented
13#20298683C211yesmaximal, characteristic, complemented
14#20298661C211yesmaximal, characteristic, complemented
15#448×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic, complemented
17C22×D452C2211yescharacteristic
18C2×D4×D113—21no—
19C2×D4×D113C2211yescharacteristic
20C2×#14268636C2211yescharacteristic
21C2×#14268636C2211yescharacteristic, complemented
22C2×#14268635C2211yescharacteristic, complemented
23C2×#14268634—24no—
24C2×#14268634C2211yescharacteristic
25C2×#14268634C2211yescharacteristic
26C2×#14268634C2211yescharacteristic, complemented
27C2×#14268634C2211yescharacteristic, complemented
28SD16×D113—24no—
29C22×#11744751C2211yescharacteristic, complemented
30C2×C8×D113C2211yescharacteristic, complemented
31#16813620—21no—
32#16813620C2211yescharacteristic, complemented
33#16813618C2211yescharacteristic
34#16813601—21no—
35#16813601C2211yescharacteristic, complemented
36#16813598—21no—
37#16813598C2211yescharacteristic, complemented
38#16813597C2211yescharacteristic
39#16813595—21no—
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#16813545C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic
50#16813544C2211yescharacteristic, complemented
51#16813543C2211yescharacteristic, complemented
52#16813534C2211yescharacteristic, complemented
53C8×Dic113C2211yescharacteristic, complemented
54C22×Q8×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic, complemented
56C2×SD16×C113C2211yescharacteristic, complemented
57#121×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic, complemented
59#103×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C23×D113—21no—
63C2×Dic226—21no—
64C2×Dic226C2311yescharacteristic
65Q8×D113—22no—
66Q8×D113—41no—
67C2×D452—22no—
68C2×D452—21no—
69C2×D452—21no—
70C2×D452—41no—
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113D411yescharacteristic
77D4×D113—22no—
78D4×D113—41no—
79D4×D113—44no—
80C2×C4×D113—21no—
81C2×C4×D113—21no—
82C2×C4×D113C2311yescharacteristic
83#14268636—22no—
84#14268636—41no—
85#14268635—22no—
86#14268634—22no—
87#14268634—22no—
88#14268634—22no—
89#14268634D414yescomplemented
90C2×#11744751—22no—
91C2×#11744751C2311yescharacteristic
92C2×#11744751C2311yescharacteristic
93C8×D113—22no—
94C4⋊Dic113—21no—
95C4⋊Dic113C2311yescharacteristic
96#14268626—21no—
97#14268626—21no—
98#14268626—21no—
99#14268626—21no—
100#14268626D411yescharacteristic
101C22⋊Dic113—21no—
102C22⋊Dic113D411yescharacteristic
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624D411yescharacteristic
107C4×Dic113—21no—
108C4×Dic113C2311yescharacteristic
109C2×Q8×C113—21no—
110C2×Q8×C113—22no—
111C2×Q8×C113—41no—
112C2×Q8×C113C2311yescharacteristic
113C2×Q8×C113C2311yescharacteristic
114C2×D4×C113—21no—
115C2×D4×C113C2311yescharacteristic
116C22×C4×C113—21no—
117C22×C4×C113C2311yescharacteristic
118SD16×C113—22no—
119SD16×C113—41no—
120C2×C8×C113C2311yescharacteristic
121C2×C8×C113C2311yescharacteristic
122C4⋊C4×C113C2311yescharacteristic
123C22⋊C4×C113—21no—
124C23×C113—21no—
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127C22×D113—21no—
128C22×D113—42no—
129C22×D113—42no—
130C22×D113—42no—
131C22×D113—42no—
132C22×D113—81no—
133C22×D113—81no—
134C22×D113C2×D411yescharacteristic
135Q8×C113—21no—
136Q8×C113—21no—
137Q8×C113—21no—
138Q8×C113—42no—
139Q8×C113C2×D412yescomplemented
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—42no—
143C2×C4×C113—21no—
144C2×C4×C113—21no—
145C2×C4×C113—21no—
146C2×C4×C113—21no—
147C2×C4×C113—21no—
148C2×C4×C113—42no—
149C2×C4×C113C2×D411yescharacteristic
150C2×C4×C113C2411yescharacteristic
151C22⋊D113—42no—
152C22⋊D113—42no—
153C22⋊D113—81no—
154C22⋊D113SD1614yescomplemented
155C2×Dic113—21no—
156C2×Dic113—21no—
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159C2×Dic113C2×D411yescharacteristic
160D452—21no—
161D452—21no—
162D452—21no—
163D452—42no—
164D452—42no—
165D452C2×D412yes—
166C4×D113—21no—
167C4×D113—21no—
168C4×D113—42no—
169C4×D113—42no—
170Dic226—21no—
171Dic226—21no—
172Dic226—42no—
173C8×C113—21no—
174C8×C113—21no—
175#11744751—21no—
176#11744751C2×D412yescomplemented
177C22×C113—21no—
178C22×C113—21no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113C2×SD1612yescomplemented
183C22×C113C22×D411yescharacteristic
184C2×D113—21no—
185C2×D113—21no—
186C2×D113—22no—
187C2×D113—41no—
188C2×D113—41no—
189C2×D113—41no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—84no—
193C2×D113—84no—
194C2×D113C2×SD1612yescomplemented
195C4×C113—22no—
196C4×C113—21no—
197C4×C113—41no—
198C4×C113—41no—
199C4×C113C22×D411yescharacteristic
200C4×C113H(5,𝔽2)11yescharacteristic
201Dic113—21no—
202Dic113—21no—
203Dic113—41no—
204Dic113—41no—
205Dic113C2×SD1612yescomplemented
206C2×C113—22no—
207C2×C113—81no—
208C2×C113D4211yescharacteristic
209C2×C113C22×SD1611yescharacteristic
210C2×C113#57711yescharacteristic
211D113—22no—
212D113—42no—
213D113—81no—
214D4×SD16—1131nomaximal, Sylow
215C113D4×SD1611yescharacteristic, complemented, Sylow
216C22×SD16—1131no—
217C22×SD16—1131no—
218D4×Q8—1131no—
219D42—1131no—
220#492—1131no—
221#465—1131no—
222#465—1131no—
223#461—1131no—
224#460—1131no—
225#450—1131no—
226#450—1131no—
227#448—1131no—
228#448D11311yescharacteristic, complemented
229C4×SD16—1131no—
230C8×D4—1131no—
231C22×Q8—1131no—
232C22×Q8C2×D11311yescharacteristic, complemented
233C22×D4—1131no—
234C22×D4—1131no—
235C22×D4—2261no—
236C2×SD16—1131no—
237C2×SD16—1131no—
238C2×SD16—1131no—
239C2×SD16—1131no—
240C2×SD16—1131no—
241C2×SD16—1131no—
242C2×SD16—1131no—
243C2×SD16—2264no—
244C2×SD16—2264no—
245C2×SD16C2×D11311yescharacteristic, complemented
246C2×SD16C2×D11311yescharacteristic, complemented
247C22×C8—1131no—
248C22×C8—1131no—
249C4⋊Q8—1131no—
250C4⋊Q8—2261no—
251#127—1131no—
252C22⋊Q8—1131no—
253C22⋊Q8—1131no—
254C22⋊Q8—2261no—
255C22⋊Q8—2261no—
256#121—1131no—
257#121—2261no—
258#121C2×D11311yescharacteristic
259#120—2261no—
260#120—2261no—
261C4×Q8—1131no—
262C4×D4—1131no—
263C4×D4—1131no—
264C4×D4—2261no—
265#106—1131no—
266C4⋊C8—1131no—
267#103—1131no—
268#103C2×D11311yescharacteristic, complemented
269#103C2×D11311yescharacteristic, complemented
270#102—1131no—
271#102—1131no—
272#102—1131no—
273C22⋊C8—1131no—
274C22⋊C8C2×D11311yescharacteristic, complemented
275C4×C8—1131no—
276C24—2261no—
277C24—2261no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—1131no—
282C2×Q8—4521no—
283C2×Q8—2261no—
284C2×Q8—2262no—
285C2×Q8C22×D11311yescharacteristic
286C2×Q8C22×D11311yescharacteristic
287C2×D4—21no—
288C2×D4—1131no—
289C2×D4—1131no—
290C2×D4—1131no—
291C2×D4—4521no—
292C2×D4—4524no—
293C2×D4—4521no—
294C2×D4—2262no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4—2261no—
299C2×D4—2262no—
300C2×D4—2261no—
301C2×D4C22×D11311yescharacteristic
302C22×C4—21no—
303C22×C4—1131no—
304C22×C4—2261no—
305C22×C4—2261no—
306C22×C4C22×D11311yescharacteristic
307SD16—22no—
308SD16—41no—
309SD16—1134no—
310SD16—4521no—
311SD16—2262no—
312SD16—2262no—
313SD16—2262no—
314SD16—2262no—
315SD16—2262no—
316C2×C8—1131no—
317C2×C8—1131no—
318C2×C8—2262no—
319C2×C8—2262no—
320C2×C8C22×D11311yescharacteristic
321C2×C8C22×D11311yescharacteristic
322C4⋊C4—1131no—
323C4⋊C4—1131no—
324C4⋊C4—2261no—
325C4⋊C4—2261no—
326C4⋊C4—2261no—
327C4⋊C4—2261no—
328C4⋊C4—2261no—
329C4⋊C4C22×D11311yescharacteristic
330C22⋊C4—21no—
331C22⋊C4—1131no—
332C22⋊C4—1131no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C22⋊C4—2261no—
337C42—1131no—
338C42—2261no—
339C23—21no—
340C23—1131no—
341C23—9041no—
342C23—9041no—
343C23—4522no—
344C23—4522no—
345C23—4522no—
346C23—4522no—
347C23—2261no—
348C23—2261no—
349C23D4×D11311yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—4522no—
355Q8—2261no—
356Q8—2261no—
357Q8D4×D11312yescomplemented
358D4—21no—
359D4—21no—
360D4—42no—
361D4—1134no—
362D4—1132no—
363D4—9041no—
364D4—4522no—
365D4—4522no—
366D4—4522no—
367D4—4522no—
368D4—2261no—
369D4—2261no—
370D4—2261no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—42no—
377C2×C4—1131no—
378C2×C4—1131no—
379C2×C4—1131no—
380C2×C4—4522no—
381C2×C4—4522no—
382C2×C4—2261no—
383C2×C4—2261no—
384C2×C4—2261no—
385C2×C4—2261no—
386C2×C4D4×D11311yescharacteristic
387C2×C4C23×D11311yescharacteristic
388C8—21no—
389C8—21no—
390C8—1132no—
391C8—2261no—
392C22—21no—
393C22—21no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—1132no—
398C22—9044no—
399C22—9044no—
400C22—4521no—
401C22—4521no—
402C22—4521no—
403C22—4521no—
404C22—4521no—
405C22—2262no—
406C22—2261no—
407C22—2261no—
408C22SD16×D11312yescomplemented
409C22C2×D4×D11311yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—41no—
414C4—1132no—
415C4—4521no—
416C4—4521no—
417C4—2261no—
418C4—2261no—
419C4C2×D4×D11311yescharacteristic
420C4#1681366711yescharacteristic
421C2—22no—
422C2—81no—
423C2—9041no—
424C2—4522no—
425C2—2262no—
426C2#2029923011yescharacteristic
427C2C2×SD16×D11311yescharacteristic
428C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#448×C113C2
socleC22×C113C22×D4
prime radical#20299232C2
hypercenter#448D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C22×#14268634C2semidirect
2. C2×SD16×D113C2semidirect
3. Q8×C22⋊D113C2semidirect
5. #20298969C2semidirect
6. #20298830C2semidirect
7. #20298825C2semidirect
8. #20298802C2semidirect
9. #20298796C2semidirect
10. #20298751C2semidirect
11. #20298747C2semidirect
12. #20298738C2semidirect
13. #20298683C2semidirect
14. #20298661C2semidirect
15. #448×C113C2semidirect
16. C2×Q8×D113C22semidirect
21. C2×#14268636C22semidirect
22. C2×#14268635C22semidirect
26. C2×#14268634C22semidirect
27. C2×#14268634C22semidirect
29. C22×#11744751C22semidirect
30. C2×C8×D113C22semidirect
32. #16813620C22semidirect
35. #16813601C22semidirect
37. #16813598C22semidirect
42. Q8×Dic113C22semidirect
46. #16813553C22semidirect
47. #16813551C22semidirect
48. #16813545C22semidirect
50. #16813544C22semidirect
51. #16813543C22semidirect
52. #16813534C22semidirect
53. C8×Dic113C22semidirect
54. C22×Q8×C113C22semidirect
55. C2×SD16×C113C22semidirect
56. C2×SD16×C113C22semidirect
58. #103×C113C22semidirect
59. #103×C113C22semidirect
60. C22⋊C8×C113C22semidirect
89. #14268634D4semidirect
139. Q8×C113C2×D4semidirect
154. C22⋊D113SD16semidirect
176. #11744751C2×D4semidirect
182. C22×C113C2×SD16semidirect
194. C2×D113C2×SD16semidirect
205. Dic113C2×SD16semidirect
215. C113D4×SD16semidirect
228. #448D113semidirect
232. C22×Q8C2×D113semidirect
245. C2×SD16C2×D113semidirect
246. C2×SD16C2×D113semidirect
268. #103C2×D113semidirect
269. #103C2×D113semidirect
274. C22⋊C8C2×D113semidirect
357. Q8D4×D113semidirect
408. C22SD16×D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686342
C2×SD16×D1132
Q8×C22⋊D1132
#202992322
#202989692
#202988302
#202988252
#202988022
#202987962
#202987512
#202987472
#202987382
#202986832
#202986612
#448×C1132
D4×SD16113