Finite Group Databasebeta

← SD16×C22⋊D113 #28402264

Subgroups — SD16×C22⋊D113 #28402264

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
1C2×SD16×D113C211yesmaximal, characteristic, complemented
2Q8×C22⋊D113C211yesmaximal, characteristic, complemented
3D4×C22⋊D113C211yesmaximal, characteristic
4#20298969C211yesmaximal, characteristic, complemented
5#20298827C211yesmaximal, characteristic, complemented
6#20298824C211yesmaximal, characteristic, complemented
7#20298801C211yesmaximal, characteristic, complemented
8#20298796C211yesmaximal, characteristic, complemented
9#20298749C211yesmaximal, characteristic, complemented
10#20298747C211yesmaximal, characteristic, complemented
11#20298737C211yesmaximal, characteristic, complemented
12#20298735C211yesmaximal, characteristic, complemented
13SD16×Dic113C211yesmaximal, characteristic, complemented
14C8×C22⋊D113C211yesmaximal, characteristic, complemented
15C22×SD16×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic, complemented
17C22×C22⋊D113—21no—
18C2×D4×D113C2211yescharacteristic
19C2×#14268636C2211yescharacteristic, complemented
20C2×#14268635C2211yescharacteristic
21C2×#14268635C2211yescharacteristic, complemented
22C2×#14268634C2211yescharacteristic, complemented
23C2×#14268634C2211yescharacteristic, complemented
24SD16×D113—24no—
25C2×C8×D113C2211yescharacteristic, complemented
26#16813620—21no—
27#16813620C2211yescharacteristic, complemented
28#16813618C2211yescharacteristic
29#16813601—21no—
30#16813601C2211yescharacteristic, complemented
31#16813598—21no—
32#16813598C2211yescharacteristic, complemented
33#16813596C2211yescharacteristic
34#16813594—21no—
35#16813593C2211yescharacteristic
36#16813591—21no—
37#16813590—21no—
38Q8×Dic113C2211yescharacteristic, complemented
39D4×Dic113C2211yescharacteristic
40C4×C22⋊D113—21no—
41C4×C22⋊D113C2211yescharacteristic
42#16813554C2211yescharacteristic, complemented
43#16813551C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813546C2211yescharacteristic, complemented
47#16813544C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic
49#16813543C2211yescharacteristic, complemented
50C22⋊#11744751C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52C8×Dic113C2211yescharacteristic, complemented
53C22×Q8×C113C2211yescharacteristic, complemented
54C22×D4×C113C2211yescharacteristic
55C2×SD16×C113—24no—
56C2×SD16×C113C2211yescharacteristic
57C2×SD16×C113C2211yescharacteristic
58C2×SD16×C113C2211yescharacteristic, complemented
59C2×SD16×C113C2211yescharacteristic, complemented
60C22×C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62C2×Dic226—21no—
63C2×Dic226C2311yescharacteristic
64Q8×D113—22no—
65Q8×D113—41no—
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—44no—
73C2×C22⋊D113D411yescharacteristic
74D4×D113—22no—
75D4×D113—41no—
76C22×Dic113—21no—
77C2×C4×D113—21no—
78C2×C4×D113C2311yescharacteristic
79#14268636—22no—
80#14268635—22no—
81#14268635—41no—
82#14268634—22no—
83#14268634—41no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C8×D113—22no—
87C4⋊Dic113—21no—
88C4⋊Dic113C2311yescharacteristic
89C4⋊Dic113C2311yescharacteristic
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93#14268626—21no—
94#14268626D411yescharacteristic
95C22⋊Dic113—21no—
96C22⋊Dic113—21no—
97C22⋊Dic113—21no—
98C22⋊Dic113D411yescharacteristic
99#14268624—21no—
100#14268624—21no—
101#14268624D411yescharacteristic
102C4×Dic113—21no—
103C4×Dic113C2311yescharacteristic
104C24×C113—21no—
105C2×Q8×C113—21no—
106C2×Q8×C113—22no—
107C2×Q8×C113—41no—
108C2×Q8×C113C2311yescharacteristic
109C2×Q8×C113C2311yescharacteristic
110C2×D4×C113—22no—
111C2×D4×C113—21no—
112C2×D4×C113—41no—
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115C22×C4×C113—21no—
116C22×C4×C113C2311yescharacteristic
117SD16×C113—22no—
118SD16×C113—22no—
119SD16×C113—22no—
120SD16×C113D414yescomplemented
121C2×C8×C113—22no—
122C2×C8×C113C2311yescharacteristic
123C2×C8×C113C2311yescharacteristic
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
135Q8×C113—21no—
136Q8×C113—21no—
137Q8×C113—21no—
138Q8×C113—42no—
139Q8×C113C2×D412yescomplemented
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—21no—
143D4×C113—42no—
144D4×C113C2×D412yes—
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—42no—
153C22⋊D113—42no—
154C22⋊D113—42no—
155C22⋊D113—42no—
156C22⋊D113—81no—
157C22⋊D113SD1614yesdirect product factor
158C2×Dic113—21no—
159C2×Dic113—21no—
160C2×Dic113—21no—
161C2×Dic113—42no—
162C2×Dic113C2×D411yescharacteristic
163C2×Dic113C2×D411yescharacteristic
164C2×Dic113C2×D411yescharacteristic
165D452—21no—
166D452—21no—
167C4×D113—21no—
168C4×D113—21no—
169C4×D113—42no—
170Dic226—21no—
171Dic226—21no—
172Dic226—42no—
173C8×C113—21no—
174C8×C113C2×D412yescomplemented
175#11744751—21no—
176#11744751—21no—
177C22×C113—21no—
178C22×C113—21no—
179C22×C113—22no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113—41no—
185C22×C113—84no—
186C22×C113C2×SD1612yescomplemented
187C22×C113C22×D411yescharacteristic
188C2×D113—21no—
189C2×D113—21no—
190C2×D113—41no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—84no—
194C2×D113C2×SD1612yescomplemented
195C4×C113—22no—
196C4×C113—21no—
197C4×C113—41no—
198C4×C113C22×D411yescharacteristic
199C4×C113H(5,𝔽2)11yescharacteristic
200Dic113—21no—
201Dic113—21no—
202Dic113—41no—
203Dic113—41no—
204Dic113—41no—
205Dic113C2×SD1612yescomplemented
206C2×C113—22no—
207C2×C113—42no—
208C2×C113—81no—
209C2×C113D4211yescharacteristic
210C2×C113C22×SD1611yescharacteristic
211C2×C113#57711yescharacteristic
212D113—22no—
213D113—81no—
214D4×SD16—1131nomaximal, Sylow
215C113D4×SD1611yescharacteristic, complemented, Sylow
216C22×SD16—1131no—
217C22×SD16D11311yescharacteristic, complemented
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#448—1131no—
229C4×SD16—1131no—
230C8×D4—1131no—
231C22×Q8—1131no—
232C22×Q8C2×D11311yescharacteristic, complemented
233C22×D4—1131no—
234C22×D4—2261no—
235C22×D4C2×D11311yescharacteristic
236C2×SD16—24no—
237C2×SD16—1131no—
238C2×SD16—1131no—
239C2×SD16—1131no—
240C2×SD16—1131no—
241C2×SD16—1131no—
242C2×SD16—2264no—
243C2×SD16C2×D11311yescharacteristic
244C2×SD16C2×D11311yescharacteristic
245C2×SD16C2×D11311yescharacteristic, complemented
246C2×SD16C2×D11311yescharacteristic, complemented
247C22×C8—1131no—
248C22×C8C2×D11311yescharacteristic, complemented
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—1131no—
258#121—2261no—
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#103—1131no—
269#103—1131no—
270#102—1131no—
271#102—1131no—
272#102—1131no—
273C22⋊C8—1131no—
274C22⋊C8—1131no—
275C4×C8—1131no—
276C24—21no—
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—22no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—1131no—
291C2×D4—1131no—
292C2×D4—4524no—
293C2×D4—4521no—
294C2×D4—2261no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2261no—
298C2×D4—2261no—
299C2×D4—2262no—
300C2×D4C22×D11311yescharacteristic
301C2×D4C22×D11311yescharacteristic
302C22×C4—21no—
303C22×C4—1131no—
304C22×C4—2261no—
305C22×C4—2261no—
306C22×C4C22×D11311yescharacteristic
307SD16—22no—
308SD16—22no—
309SD16—22no—
310SD16—4521no—
311SD16—4521no—
312SD16—2262no—
313SD16—2262no—
314SD16—2262no—
315SD16C22⋊D11314yesdirect product factor
316C2×C8—22no—
317C2×C8—1131no—
318C2×C8—1131no—
319C2×C8—2262no—
320C2×C8C22×D11311yescharacteristic
321C2×C8C22×D11311yescharacteristic
322C4⋊C4—1131no—
323C4⋊C4—1131no—
324C4⋊C4—1131no—
325C4⋊C4—2261no—
326C4⋊C4—2261no—
327C4⋊C4—2261no—
328C4⋊C4—2261no—
329C4⋊C4—2261no—
330C22⋊C4—1131no—
331C22⋊C4—1131no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C22⋊C4—2261no—
337C42—1131no—
338C42—2261no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—1131no—
345C23—9041no—
346C23—4522no—
347C23—4522no—
348C23—2261no—
349C23D4×D11311yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—4522no—
355Q8—2261no—
356Q8—2261no—
357Q8C2×C22⋊D11312yescomplemented
358D4—21no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—1134no—
363D4—9041no—
364D4—4522no—
365D4—4522no—
366D4—4522no—
367D4—4522no—
368D4—2261no—
369D4—2261no—
370D4C2×C22⋊D11312yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—1131no—
377C2×C4—1131no—
378C2×C4—1131no—
379C2×C4—4522no—
380C2×C4—4522no—
381C2×C4—2261no—
382C2×C4—2261no—
383C2×C4—2261no—
384C2×C4—2261no—
385C2×C4—2261no—
386C2×C4D4×D11311yescharacteristic
387C2×C4C23×D11311yescharacteristic
388C8—21no—
389C8—2261no—
390C8—2261no—
391C8C2×C22⋊D11312yescomplemented
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—1132no—
402C22—9044no—
403C22—4521no—
404C22—4521no—
405C22—4521no—
406C22—2261no—
407C22—2261no—
408C22SD16×D11312yescomplemented
409C22C2×D4×D11311yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—1132no—
414C4—4521no—
415C4—4521no—
416C4—4521no—
417C4—2261no—
418C4—2261no—
419C4C22×C22⋊D11311yescharacteristic
420C4#1681366711yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—9041no—
425C2—2262no—
426C2D4×C22⋊D11311yescharacteristic
427C2C2×SD16×D11311yescharacteristic
428C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×SD16×C113C2
socleC22×C113C22×D4
prime radicalD4×C22⋊D113C2
hypercenterC22×SD16D113
hypocenterC113D4×SD16
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D113C2semidirect
2. Q8×C22⋊D113C2semidirect
4. #20298969C2semidirect
5. #20298827C2semidirect
6. #20298824C2semidirect
7. #20298801C2semidirect
8. #20298796C2semidirect
9. #20298749C2semidirect
10. #20298747C2semidirect
11. #20298737C2semidirect
12. #20298735C2semidirect
13. SD16×Dic113C2semidirect
14. C8×C22⋊D113C2semidirect
15. C22×SD16×C113C2semidirect
16. C2×Q8×D113C22semidirect
19. C2×#14268636C22semidirect
21. C2×#14268635C22semidirect
22. C2×#14268634C22semidirect
23. C2×#14268634C22semidirect
25. C2×C8×D113C22semidirect
27. #16813620C22semidirect
30. #16813601C22semidirect
32. #16813598C22semidirect
38. Q8×Dic113C22semidirect
42. #16813554C22semidirect
43. #16813551C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813546C22semidirect
47. #16813544C22semidirect
49. #16813543C22semidirect
50. C22⋊#11744751C22semidirect
51. #16813534C22semidirect
52. C8×Dic113C22semidirect
53. C22×Q8×C113C22semidirect
58. C2×SD16×C113C22semidirect
59. C2×SD16×C113C22semidirect
60. C22×C8×C113C22semidirect
120. SD16×C113D4semidirect
139. Q8×C113C2×D4semidirect
157. C22⋊D113SD16direct (N × H)
174. C8×C113C2×D4semidirect
186. C22×C113C2×SD16semidirect
194. C2×D113C2×SD16semidirect
205. Dic113C2×SD16semidirect
215. C113D4×SD16semidirect
217. C22×SD16D113semidirect
232. C22×Q8C2×D113semidirect
245. C2×SD16C2×D113semidirect
246. C2×SD16C2×D113semidirect
248. C22×C8C2×D113semidirect
315. SD16C22⋊D113direct (N × H)
357. Q8C2×C22⋊D113semidirect
391. C8C2×C22⋊D113semidirect
408. C22SD16×D113semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1132
Q8×C22⋊D1132
D4×C22⋊D1132
#202989692
#202988272
#202988242
#202988012
#202987962
#202987492
#202987472
#202987372
#202987352
SD16×Dic1132
C8×C22⋊D1132
C22×SD16×C1132
D4×SD16113