Finite Group Databasebeta

← SD16×C22⋊D149 #34056381

Subgroups — SD16×C22⋊D149 #34056381

Order 19072.

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×D149C211yesmaximal, characteristic, complemented
2Q8×C22⋊D149C211yesmaximal, characteristic, complemented
3D4×C22⋊D149C211yesmaximal, characteristic
4#23749996C211yesmaximal, characteristic, complemented
5#23749854C211yesmaximal, characteristic, complemented
6#23749851C211yesmaximal, characteristic, complemented
7#23749828C211yesmaximal, characteristic, complemented
8#23749823C211yesmaximal, characteristic, complemented
9#23749776C211yesmaximal, characteristic, complemented
10#23749774C211yesmaximal, characteristic, complemented
11#23749764C211yesmaximal, characteristic, complemented
12#23749762C211yesmaximal, characteristic, complemented
13SD16×Dic149C211yesmaximal, characteristic, complemented
14C8×C22⋊D149C211yesmaximal, characteristic, complemented
15C22×SD16×C149C211yesmaximal, characteristic, complemented
16C2×Q8×D149C2211yescharacteristic, complemented
17C22×C22⋊D149—21no—
18C2×D4×D149C2211yescharacteristic
19C2×#14558725C2211yescharacteristic, complemented
20C2×#14558724C2211yescharacteristic
21C2×#14558724C2211yescharacteristic, complemented
22C2×#14558723C2211yescharacteristic, complemented
23C2×#14558723C2211yescharacteristic, complemented
24SD16×D149—24no—
25C2×C8×D149C2211yescharacteristic, complemented
26#18011909—21no—
27#18011909C2211yescharacteristic, complemented
28#18011907C2211yescharacteristic
29#18011890—21no—
30#18011890C2211yescharacteristic, complemented
31#18011887—21no—
32#18011887C2211yescharacteristic, complemented
33#18011885C2211yescharacteristic
34#18011883—21no—
35#18011882C2211yescharacteristic
36#18011880—21no—
37#18011879—21no—
38Q8×Dic149C2211yescharacteristic, complemented
39D4×Dic149C2211yescharacteristic
40C4×C22⋊D149—21no—
41C4×C22⋊D149C2211yescharacteristic
42#18011843C2211yescharacteristic, complemented
43#18011840C2211yescharacteristic, complemented
44#18011836C2211yescharacteristic, complemented
45#18011835C2211yescharacteristic, complemented
46#18011835C2211yescharacteristic, complemented
47#18011833C2211yescharacteristic, complemented
48#18011832C2211yescharacteristic
49#18011832C2211yescharacteristic, complemented
50C22⋊#11924746C2211yescharacteristic, complemented
51#18011823C2211yescharacteristic, complemented
52C8×Dic149C2211yescharacteristic, complemented
53C22×Q8×C149C2211yescharacteristic, complemented
54C22×D4×C149C2211yescharacteristic
55C2×SD16×C149—24no—
56C2×SD16×C149C2211yescharacteristic
57C2×SD16×C149C2211yescharacteristic
58C2×SD16×C149C2211yescharacteristic, complemented
59C2×SD16×C149C2211yescharacteristic, complemented
60C22×C8×C149C2211yescharacteristic, complemented
61C23×D149—21no—
62C2×Dic298—21no—
63C2×Dic298C2311yescharacteristic
64Q8×D149—22no—
65Q8×D149—41no—
66C2×D596C2311yescharacteristic
67C2×C22⋊D149—21no—
68C2×C22⋊D149—21no—
69C2×C22⋊D149—21no—
70C2×C22⋊D149—21no—
71C2×C22⋊D149—21no—
72C2×C22⋊D149—44no—
73C2×C22⋊D149D411yescharacteristic
74D4×D149—22no—
75D4×D149—41no—
76C22×Dic149—21no—
77C2×C4×D149—21no—
78C2×C4×D149C2311yescharacteristic
79#14558725—22no—
80#14558724—22no—
81#14558724—41no—
82#14558723—22no—
83#14558723—41no—
84C2×#11924746C2311yescharacteristic
85C2×#11924746C2311yescharacteristic
86C8×D149—22no—
87C4⋊Dic149—21no—
88C4⋊Dic149C2311yescharacteristic
89C4⋊Dic149C2311yescharacteristic
90#14558715—21no—
91#14558715—21no—
92#14558715—21no—
93#14558715—21no—
94#14558715D411yescharacteristic
95C22⋊Dic149—21no—
96C22⋊Dic149—21no—
97C22⋊Dic149—21no—
98C22⋊Dic149D411yescharacteristic
99#14558713—21no—
100#14558713—21no—
101#14558713D411yescharacteristic
102C4×Dic149—21no—
103C4×Dic149C2311yescharacteristic
104C24×C149—21no—
105C2×Q8×C149—21no—
106C2×Q8×C149—22no—
107C2×Q8×C149—41no—
108C2×Q8×C149C2311yescharacteristic
109C2×Q8×C149C2311yescharacteristic
110C2×D4×C149—22no—
111C2×D4×C149—21no—
112C2×D4×C149—41no—
113C2×D4×C149C2311yescharacteristic
114C2×D4×C149C2311yescharacteristic
115C22×C4×C149—21no—
116C22×C4×C149C2311yescharacteristic
117SD16×C149—22no—
118SD16×C149—22no—
119SD16×C149—22no—
120SD16×C149D414yescomplemented
121C2×C8×C149—22no—
122C2×C8×C149C2311yescharacteristic
123C2×C8×C149C2311yescharacteristic
124C22×D149—21no—
125C22×D149—42no—
126C22×D149—42no—
127C22×D149—81no—
128C22×D149C2×D411yescharacteristic
129Dic298—21no—
130Dic298—21no—
131Dic298—42no—
132D596—21no—
133D596—21no—
134C22⋊D149—42no—
135C22⋊D149—42no—
136C22⋊D149—42no—
137C22⋊D149—42no—
138C22⋊D149—81no—
139C22⋊D149SD1614yesdirect product factor
140C2×Dic149—21no—
141C2×Dic149—21no—
142C2×Dic149—21no—
143C2×Dic149—42no—
144C2×Dic149C2×D411yescharacteristic
145C2×Dic149C2×D411yescharacteristic
146C2×Dic149C2×D411yescharacteristic
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—42no—
150#11924746—21no—
151#11924746—21no—
152C23×C149—21no—
153C23×C149—21no—
154C23×C149—42no—
155C23×C149—42no—
156C23×C149—81no—
157C23×C149C2×D411yescharacteristic
158Q8×C149—21no—
159Q8×C149—21no—
160Q8×C149—21no—
161Q8×C149—42no—
162Q8×C149C2×D412yescomplemented
163D4×C149—21no—
164D4×C149—21no—
165D4×C149—21no—
166D4×C149—42no—
167D4×C149C2×D412yes—
168C2×C4×C149—21no—
169C2×C4×C149—21no—
170C2×C4×C149—21no—
171C2×C4×C149—21no—
172C2×C4×C149—42no—
173C2×C4×C149C2×D411yescharacteristic
174C2×C4×C149C2411yescharacteristic
175C8×C149—21no—
176C8×C149C2×D412yescomplemented
177C22×C149—21no—
178C22×C149—21no—
179C22×C149—22no—
180C22×C149—41no—
181C22×C149—41no—
182C22×C149—41no—
183C22×C149—41no—
184C22×C149—41no—
185C22×C149—84no—
186C22×C149C2×SD1612yescomplemented
187C22×C149C22×D411yescharacteristic
188C2×D149—21no—
189C2×D149—21no—
190C2×D149—41no—
191C2×D149—41no—
192C2×D149—41no—
193C2×D149—84no—
194C2×D149C2×SD1612yescomplemented
195C4×C149—21no—
196C4×C149—22no—
197C4×C149—41no—
198C4×C149C22×D411yescharacteristic
199C4×C149H(5,𝔽2)11yescharacteristic
200Dic149—21no—
201Dic149—21no—
202Dic149—41no—
203Dic149—41no—
204Dic149—41no—
205Dic149C2×SD1612yescomplemented
206C2×C149—22no—
207C2×C149—42no—
208C2×C149—81no—
209C2×C149D4211yescharacteristic
210C2×C149C22×SD1611yescharacteristic
211C2×C149#57711yescharacteristic
212D149—22no—
213D149—81no—
214C149D4×SD1611yescharacteristic, complemented, Sylow
215D4×SD16—1491nomaximal, Sylow
216C22×SD16—1491no—
217C22×SD16D14911yescharacteristic, complemented
218D4×Q8—1491no—
219D42—1491no—
220#492—1491no—
221#465—1491no—
222#465—1491no—
223#461—1491no—
224#460—1491no—
225#450—1491no—
226#450—1491no—
227#448—1491no—
228#448—1491no—
229C4×SD16—1491no—
230C8×D4—1491no—
231C22×Q8—1491no—
232C22×Q8C2×D14911yescharacteristic, complemented
233C22×D4—2981no—
234C22×D4—1491no—
235C22×D4C2×D14911yescharacteristic
236C2×SD16—24no—
237C2×SD16—2984no—
238C2×SD16—1491no—
239C2×SD16—1491no—
240C2×SD16—1491no—
241C2×SD16—1491no—
242C2×SD16—1491no—
243C2×SD16C2×D14911yescharacteristic
244C2×SD16C2×D14911yescharacteristic
245C2×SD16C2×D14911yescharacteristic, complemented
246C2×SD16C2×D14911yescharacteristic, complemented
247C22×C8—1491no—
248C22×C8C2×D14911yescharacteristic, complemented
249C4⋊Q8—2981no—
250C4⋊Q8—1491no—
251#127—1491no—
252C22⋊Q8—2981no—
253C22⋊Q8—2981no—
254C22⋊Q8—1491no—
255C22⋊Q8—1491no—
256#121—2981no—
257#121—1491no—
258#121—1491no—
259#120—2981no—
260#120—2981no—
261C4×Q8—1491no—
262C4×D4—2981no—
263C4×D4—1491no—
264C4×D4—1491no—
265#106—1491no—
266C4⋊C8—1491no—
267#103—1491no—
268#103—1491no—
269#103—1491no—
270#102—1491no—
271#102—1491no—
272#102—1491no—
273C22⋊C8—1491no—
274C22⋊C8—1491no—
275C4×C8—1491no—
276C24—21no—
277C24—2981no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—2981no—
282C2×Q8—2982no—
283C2×Q8—5961no—
284C2×Q8—1491no—
285C2×Q8C22×D14911yescharacteristic
286C2×Q8C22×D14911yescharacteristic
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—2982no—
291C2×D4—2981no—
292C2×D4—2981no—
293C2×D4—2981no—
294C2×D4—2981no—
295C2×D4—2981no—
296C2×D4—5961no—
297C2×D4—5964no—
298C2×D4—1491no—
299C2×D4—1491no—
300C2×D4C22×D14911yescharacteristic
301C2×D4C22×D14911yescharacteristic
302C22×C4—21no—
303C22×C4—2981no—
304C22×C4—2981no—
305C22×C4—1491no—
306C22×C4C22×D14911yescharacteristic
307SD16—22no—
308SD16—22no—
309SD16—22no—
310SD16—2982no—
311SD16—2982no—
312SD16—2982no—
313SD16—5961no—
314SD16—5961no—
315SD16C22⋊D14914yesdirect product factor
316C2×C8—22no—
317C2×C8—2982no—
318C2×C8—1491no—
319C2×C8—1491no—
320C2×C8C22×D14911yescharacteristic
321C2×C8C22×D14911yescharacteristic
322C4⋊C4—2981no—
323C4⋊C4—2981no—
324C4⋊C4—2981no—
325C4⋊C4—2981no—
326C4⋊C4—2981no—
327C4⋊C4—1491no—
328C4⋊C4—1491no—
329C4⋊C4—1491no—
330C22⋊C4—2981no—
331C22⋊C4—2981no—
332C22⋊C4—2981no—
333C22⋊C4—2981no—
334C22⋊C4—2981no—
335C22⋊C4—1491no—
336C22⋊C4—1491no—
337C42—2981no—
338C42—1491no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—2981no—
345C23—5962no—
346C23—5962no—
347C23—1491no—
348C23—11921no—
349C23D4×D14911yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—2981no—
355Q8—2981no—
356Q8—5962no—
357Q8C2×C22⋊D14912yescomplemented
358D4—21no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—2981no—
363D4—2981no—
364D4—5962no—
365D4—5962no—
366D4—5962no—
367D4—5962no—
368D4—1494no—
369D4—11921no—
370D4C2×C22⋊D14912yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—2981no—
377C2×C4—2981no—
378C2×C4—2981no—
379C2×C4—2981no—
380C2×C4—2981no—
381C2×C4—5962no—
382C2×C4—5962no—
383C2×C4—1491no—
384C2×C4—1491no—
385C2×C4—1491no—
386C2×C4D4×D14911yescharacteristic
387C2×C4C23×D14911yescharacteristic
388C8—21no—
389C8—2981no—
390C8—2981no—
391C8C2×C22⋊D14912yescomplemented
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—2981no—
402C22—2981no—
403C22—5961no—
404C22—5961no—
405C22—5961no—
406C22—1492no—
407C22—11924no—
408C22SD16×D14912yescomplemented
409C22C2×D4×D14911yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—2981no—
414C4—2981no—
415C4—5961no—
416C4—5961no—
417C4—5961no—
418C4—1492no—
419C4C22×C22⋊D14911yescharacteristic
420C4#1801195611yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—2982no—
425C2—11921no—
426C2D4×C22⋊D14911yescharacteristic
427C2C2×SD16×D14911yescharacteristic
428C2#2375043111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC22×SD16×C149C2
socleC22×C149C22×D4
prime radicalD4×C22⋊D149C2
hypercenterC22×SD16D149
hypocenterC149D4×SD16
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D149C2semidirect
2. Q8×C22⋊D149C2semidirect
4. #23749996C2semidirect
5. #23749854C2semidirect
6. #23749851C2semidirect
7. #23749828C2semidirect
8. #23749823C2semidirect
9. #23749776C2semidirect
10. #23749774C2semidirect
11. #23749764C2semidirect
12. #23749762C2semidirect
13. SD16×Dic149C2semidirect
14. C8×C22⋊D149C2semidirect
15. C22×SD16×C149C2semidirect
16. C2×Q8×D149C22semidirect
19. C2×#14558725C22semidirect
21. C2×#14558724C22semidirect
22. C2×#14558723C22semidirect
23. C2×#14558723C22semidirect
25. C2×C8×D149C22semidirect
27. #18011909C22semidirect
30. #18011890C22semidirect
32. #18011887C22semidirect
38. Q8×Dic149C22semidirect
42. #18011843C22semidirect
43. #18011840C22semidirect
44. #18011836C22semidirect
45. #18011835C22semidirect
46. #18011835C22semidirect
47. #18011833C22semidirect
49. #18011832C22semidirect
50. C22⋊#11924746C22semidirect
51. #18011823C22semidirect
52. C8×Dic149C22semidirect
53. C22×Q8×C149C22semidirect
58. C2×SD16×C149C22semidirect
59. C2×SD16×C149C22semidirect
60. C22×C8×C149C22semidirect
120. SD16×C149D4semidirect
139. C22⋊D149SD16direct (N × H)
162. Q8×C149C2×D4semidirect
176. C8×C149C2×D4semidirect
186. C22×C149C2×SD16semidirect
194. C2×D149C2×SD16semidirect
205. Dic149C2×SD16semidirect
214. C149D4×SD16semidirect
217. C22×SD16D149semidirect
232. C22×Q8C2×D149semidirect
245. C2×SD16C2×D149semidirect
246. C2×SD16C2×D149semidirect
248. C22×C8C2×D149semidirect
315. SD16C22⋊D149direct (N × H)
357. Q8C2×C22⋊D149semidirect
391. C8C2×C22⋊D149semidirect
408. C22SD16×D149semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1492
Q8×C22⋊D1492
D4×C22⋊D1492
#237499962
#237498542
#237498512
#237498282
#237498232
#237497762
#237497742
#237497642
#237497622
SD16×Dic1492
C8×C22⋊D1492
C22×SD16×C1492
D4×SD16149