Finite Group Databasebeta

← SD16×C22⋊D151 #34080800

Subgroups — SD16×C22⋊D151 #34080800

Order 19328.

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×D151C211yesmaximal, characteristic, complemented
2Q8×C22⋊D151C211yesmaximal, characteristic, complemented
3D4×C22⋊D151C211yesmaximal, characteristic
4#23752583C211yesmaximal, characteristic, complemented
5#23752441C211yesmaximal, characteristic, complemented
6#23752438C211yesmaximal, characteristic, complemented
7#23752415C211yesmaximal, characteristic, complemented
8#23752410C211yesmaximal, characteristic, complemented
9#23752363C211yesmaximal, characteristic, complemented
10#23752361C211yesmaximal, characteristic, complemented
11#23752351C211yesmaximal, characteristic, complemented
12#23752349C211yesmaximal, characteristic, complemented
13SD16×Dic151C211yesmaximal, characteristic, complemented
14C8×C22⋊D151C211yesmaximal, characteristic, complemented
15C22×SD16×C151C211yesmaximal, characteristic, complemented
16C2×Q8×D151C2211yescharacteristic, complemented
17C22×C22⋊D151—21no—
18C2×D4×D151C2211yescharacteristic
19C2×#14558993C2211yescharacteristic, complemented
20C2×#14558992C2211yescharacteristic
21C2×#14558992C2211yescharacteristic, complemented
22C2×#14558991C2211yescharacteristic, complemented
23C2×#14558991C2211yescharacteristic, complemented
24SD16×D151—24no—
25C2×C8×D151C2211yescharacteristic, complemented
26#18012737—21no—
27#18012737C2211yescharacteristic, complemented
28#18012735C2211yescharacteristic
29#18012718—21no—
30#18012718C2211yescharacteristic, complemented
31#18012715—21no—
32#18012715C2211yescharacteristic, complemented
33#18012713C2211yescharacteristic
34#18012711—21no—
35#18012710C2211yescharacteristic
36#18012708—21no—
37#18012707—21no—
38Q8×Dic151C2211yescharacteristic, complemented
39D4×Dic151C2211yescharacteristic
40C4×C22⋊D151—21no—
41C4×C22⋊D151C2211yescharacteristic
42#18012671C2211yescharacteristic, complemented
43Dic151⋊C8C2211yescharacteristic, complemented
44#18012664C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012663C2211yescharacteristic, complemented
47#18012661C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic, complemented
50C22⋊(C151⋊C8)C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52C8×Dic151C2211yescharacteristic, complemented
53C22×Q8×C151C2211yescharacteristic, complemented
54C22×D4×C151C2211yescharacteristic
55C2×SD16×C151—24no—
56C2×SD16×C151C2211yescharacteristic
57C2×SD16×C151C2211yescharacteristic
58C2×SD16×C151C2211yescharacteristic, complemented
59C2×SD16×C151C2211yescharacteristic, complemented
60C22×C8×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C2×Dic302—21no—
63C2×Dic302C2311yescharacteristic
64Q8×D151—22no—
65Q8×D151—41no—
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—44no—
73C2×C22⋊D151D411yescharacteristic
74D4×D151—22no—
75D4×D151—41no—
76C22×Dic151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79#14558993—22no—
80#14558992—22no—
81#14558992—41no—
82#14558991—22no—
83#14558991—41no—
84C2×C151⋊C8C2311yescharacteristic
85C2×C151⋊C8C2311yescharacteristic
86C8×D151—22no—
87C4⋊Dic151—21no—
88C4⋊Dic151C2311yescharacteristic
89C4⋊Dic151C2311yescharacteristic
90Dic151⋊C4—21no—
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93Dic151⋊C4—21no—
94Dic151⋊C4D411yescharacteristic
95C22⋊Dic151—21no—
96C22⋊Dic151—21no—
97C22⋊Dic151—21no—
98C22⋊Dic151D411yescharacteristic
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4D411yescharacteristic
102C4×Dic151—21no—
103C4×Dic151C2311yescharacteristic
104C24×C151—21no—
105C2×Q8×C151—21no—
106C2×Q8×C151—22no—
107C2×Q8×C151—41no—
108C2×Q8×C151C2311yescharacteristic
109C2×Q8×C151C2311yescharacteristic
110C2×D4×C151—22no—
111C2×D4×C151—21no—
112C2×D4×C151—41no—
113C2×D4×C151C2311yescharacteristic
114C2×D4×C151C2311yescharacteristic
115C22×C4×C151—21no—
116C22×C4×C151C2311yescharacteristic
117SD16×C151—22no—
118SD16×C151—22no—
119SD16×C151—22no—
120SD16×C151D414yescomplemented
121C2×C8×C151—22no—
122C2×C8×C151C2311yescharacteristic
123C2×C8×C151C2311yescharacteristic
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—81no—
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302—21no—
131Dic302—42no—
132D604—21no—
133D604—21no—
134C22⋊D151—42no—
135C22⋊D151—42no—
136C22⋊D151—42no—
137C22⋊D151—42no—
138C22⋊D151—81no—
139C22⋊D151SD1614yesdirect product factor
140C2×Dic151—21no—
141C2×Dic151—21no—
142C2×Dic151—21no—
143C2×Dic151—42no—
144C2×Dic151C2×D411yescharacteristic
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C4×D151—21no—
148C4×D151—21no—
149C4×D151—42no—
150C151⋊C8—21no—
151C151⋊C8—21no—
152C23×C151—21no—
153C23×C151—21no—
154C23×C151—42no—
155C23×C151—42no—
156C23×C151—81no—
157C23×C151C2×D411yescharacteristic
158Q8×C151—21no—
159Q8×C151—21no—
160Q8×C151—21no—
161Q8×C151—42no—
162Q8×C151C2×D412yescomplemented
163D4×C151—21no—
164D4×C151—21no—
165D4×C151—21no—
166D4×C151—42no—
167D4×C151C2×D412yes—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—42no—
173C2×C4×C151C2×D411yescharacteristic
174C2×C4×C151C2411yescharacteristic
175C8×C151—21no—
176C8×C151C2×D412yescomplemented
177C22×C151—21no—
178C22×C151—21no—
179C22×C151—22no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151—41no—
185C22×C151—84no—
186C22×C151C2×SD1612yescomplemented
187C22×C151C22×D411yescharacteristic
188C2×D151—21no—
189C2×D151—21no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—84no—
194C2×D151C2×SD1612yescomplemented
195C4×C151—21no—
196C4×C151—22no—
197C4×C151—41no—
198C4×C151C22×D411yescharacteristic
199C4×C151H(5,𝔽2)11yescharacteristic
200Dic151—21no—
201Dic151—21no—
202Dic151—41no—
203Dic151—41no—
204Dic151—41no—
205Dic151C2×SD1612yescomplemented
206C2×C151—22no—
207C2×C151—42no—
208C2×C151—81no—
209C2×C151D4211yescharacteristic
210C2×C151C22×SD1611yescharacteristic
211C2×C151#57711yescharacteristic
212D151—22no—
213D151—81no—
214C151D4×SD1611yescharacteristic, complemented, Sylow
215D4×SD16—1511nomaximal, Sylow
216C22×SD16—1511no—
217C22×SD16D15111yescharacteristic, complemented
218D4×Q8—1511no—
219D42—1511no—
220#492—1511no—
221#465—1511no—
222#465—1511no—
223#461—1511no—
224#460—1511no—
225#450—1511no—
226#450—1511no—
227#448—1511no—
228#448—1511no—
229C4×SD16—1511no—
230C8×D4—1511no—
231C22×Q8—1511no—
232C22×Q8C2×D15111yescharacteristic, complemented
233C22×D4—3021no—
234C22×D4—1511no—
235C22×D4C2×D15111yescharacteristic
236C2×SD16—24no—
237C2×SD16—3024no—
238C2×SD16—1511no—
239C2×SD16—1511no—
240C2×SD16—1511no—
241C2×SD16—1511no—
242C2×SD16—1511no—
243C2×SD16C2×D15111yescharacteristic
244C2×SD16C2×D15111yescharacteristic
245C2×SD16C2×D15111yescharacteristic, complemented
246C2×SD16C2×D15111yescharacteristic, complemented
247C22×C8—1511no—
248C22×C8C2×D15111yescharacteristic, complemented
249C4⋊Q8—3021no—
250C4⋊Q8—1511no—
251#127—1511no—
252C22⋊Q8—3021no—
253C22⋊Q8—3021no—
254C22⋊Q8—1511no—
255C22⋊Q8—1511no—
256#121—3021no—
257#121—1511no—
258#121—1511no—
259#120—3021no—
260#120—3021no—
261C4×Q8—1511no—
262C4×D4—3021no—
263C4×D4—1511no—
264C4×D4—1511no—
265#106—1511no—
266C4⋊C8—1511no—
267#103—1511no—
268#103—1511no—
269#103—1511no—
270#102—1511no—
271#102—1511no—
272#102—1511no—
273C22⋊C8—1511no—
274C22⋊C8—1511no—
275C4×C8—1511no—
276C24—21no—
277C24—3021no—
278C2×Q8—21no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—3021no—
282C2×Q8—3022no—
283C2×Q8—6041no—
284C2×Q8—1511no—
285C2×Q8C22×D15111yescharacteristic
286C2×Q8C22×D15111yescharacteristic
287C2×D4—22no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—3022no—
291C2×D4—3021no—
292C2×D4—3021no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—3021no—
296C2×D4—6041no—
297C2×D4—6044no—
298C2×D4—1511no—
299C2×D4—1511no—
300C2×D4C22×D15111yescharacteristic
301C2×D4C22×D15111yescharacteristic
302C22×C4—21no—
303C22×C4—3021no—
304C22×C4—3021no—
305C22×C4—1511no—
306C22×C4C22×D15111yescharacteristic
307SD16—22no—
308SD16—22no—
309SD16—22no—
310SD16—3022no—
311SD16—3022no—
312SD16—3022no—
313SD16—6041no—
314SD16—6041no—
315SD16C22⋊D15114yesdirect product factor
316C2×C8—22no—
317C2×C8—3022no—
318C2×C8—1511no—
319C2×C8—1511no—
320C2×C8C22×D15111yescharacteristic
321C2×C8C22×D15111yescharacteristic
322C4⋊C4—3021no—
323C4⋊C4—3021no—
324C4⋊C4—3021no—
325C4⋊C4—3021no—
326C4⋊C4—3021no—
327C4⋊C4—1511no—
328C4⋊C4—1511no—
329C4⋊C4—1511no—
330C22⋊C4—3021no—
331C22⋊C4—3021no—
332C22⋊C4—3021no—
333C22⋊C4—3021no—
334C22⋊C4—3021no—
335C22⋊C4—1511no—
336C22⋊C4—1511no—
337C42—3021no—
338C42—1511no—
339C23—21no—
340C23—21no—
341C23—42no—
342C23—42no—
343C23—81no—
344C23—3021no—
345C23—6042no—
346C23—6042no—
347C23—1511no—
348C23—12081no—
349C23D4×D15111yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—21no—
353Q8—42no—
354Q8—3021no—
355Q8—3021no—
356Q8—6042no—
357Q8C2×C22⋊D15112yescomplemented
358D4—21no—
359D4—21no—
360D4—21no—
361D4—42no—
362D4—3021no—
363D4—3021no—
364D4—6042no—
365D4—6042no—
366D4—6042no—
367D4—6042no—
368D4—1514no—
369D4—12081no—
370D4C2×C22⋊D15112yes—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—3021no—
377C2×C4—3021no—
378C2×C4—3021no—
379C2×C4—3021no—
380C2×C4—3021no—
381C2×C4—6042no—
382C2×C4—6042no—
383C2×C4—1511no—
384C2×C4—1511no—
385C2×C4—1511no—
386C2×C4D4×D15111yescharacteristic
387C2×C4C23×D15111yescharacteristic
388C8—21no—
389C8—3021no—
390C8—3021no—
391C8C2×C22⋊D15112yescomplemented
392C22—21no—
393C22—21no—
394C22—22no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—84no—
401C22—3021no—
402C22—3021no—
403C22—6041no—
404C22—6041no—
405C22—6041no—
406C22—1512no—
407C22—12084no—
408C22SD16×D15112yescomplemented
409C22C2×D4×D15111yescharacteristic
410C4—21no—
411C4—22no—
412C4—41no—
413C4—3021no—
414C4—3021no—
415C4—6041no—
416C4—6041no—
417C4—6041no—
418C4—1512no—
419C4C22×C22⋊D15111yescharacteristic
420C4#1801278411yescharacteristic
421C2—22no—
422C2—42no—
423C2—81no—
424C2—3022no—
425C2—12081no—
426C2D4×C22⋊D15111yescharacteristic
427C2C2×SD16×D15111yescharacteristic
428C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×SD16×C151C2
socleC22×C151C22×D4
prime radicalD4×C22⋊D151C2
hypercenterC22×SD16D151
hypocenterC151D4×SD16
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D151C2semidirect
2. Q8×C22⋊D151C2semidirect
4. #23752583C2semidirect
5. #23752441C2semidirect
6. #23752438C2semidirect
7. #23752415C2semidirect
8. #23752410C2semidirect
9. #23752363C2semidirect
10. #23752361C2semidirect
11. #23752351C2semidirect
12. #23752349C2semidirect
13. SD16×Dic151C2semidirect
14. C8×C22⋊D151C2semidirect
15. C22×SD16×C151C2semidirect
16. C2×Q8×D151C22semidirect
19. C2×#14558993C22semidirect
21. C2×#14558992C22semidirect
22. C2×#14558991C22semidirect
23. C2×#14558991C22semidirect
25. C2×C8×D151C22semidirect
27. #18012737C22semidirect
30. #18012718C22semidirect
32. #18012715C22semidirect
38. Q8×Dic151C22semidirect
42. #18012671C22semidirect
43. Dic151⋊C8C22semidirect
44. #18012664C22semidirect
45. #18012663C22semidirect
46. #18012663C22semidirect
47. #18012661C22semidirect
49. #18012660C22semidirect
50. C22⋊(C151⋊C8)C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. C8×Dic151C22semidirect
53. C22×Q8×C151C22semidirect
58. C2×SD16×C151C22semidirect
59. C2×SD16×C151C22semidirect
60. C22×C8×C151C22semidirect
120. SD16×C151D4semidirect
139. C22⋊D151SD16direct (N × H)
162. Q8×C151C2×D4semidirect
176. C8×C151C2×D4semidirect
186. C22×C151C2×SD16semidirect
194. C2×D151C2×SD16semidirect
205. Dic151C2×SD16semidirect
214. C151D4×SD16semidirect
217. C22×SD16D151semidirect
232. C22×Q8C2×D151semidirect
245. C2×SD16C2×D151semidirect
246. C2×SD16C2×D151semidirect
248. C22×C8C2×D151semidirect
315. SD16C22⋊D151direct (N × H)
357. Q8C2×C22⋊D151semidirect
391. C8C2×C22⋊D151semidirect
408. C22SD16×D151semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1512
Q8×C22⋊D1512
D4×C22⋊D1512
#237525832
#237524412
#237524382
#237524152
#237524102
#237523632
#237523612
#237523512
#237523492
SD16×Dic1512
C8×C22⋊D1512
C22×SD16×C1512
D4×SD16151