Finite Group Databasebeta

← C2×C3×A4×SD16 #11919788

Subgroups — C2×C3×A4×SD16 #11919788

Order 1152.

936 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×A4C211yesmaximal, characteristic, complemented
2C2×C3×D4×A4C211yesmaximal, characteristic
3C3×A4×SD16C214yesmaximal, direct product factor
4C2×C3×C8×A4C211yesmaximal, characteristic, complemented
5C23×C3×SD16C311yesmaximal, characteristic, complemented
6C2×A4×SD16C313yesmaximal, direct product factor
7C23×C3×A4—21no—
8C3×Q8×A4—21no—
9C3×Q8×A4C2212yescomplemented
10C3×D4×A4—21no—
11C3×D4×A4C2212yes—
12C2×C3×C4×A4—21no—
13C2×C3×C4×A4C2211yescharacteristic
14C2×C32×SD16—41nomaximal
15C3×C8×A4C2212yescomplemented
16C23×C3×Q8C2×C311yescharacteristic, complemented
17C23×C3×D4C2×C311yescharacteristic
18C2×Q8×A4C2×C313yescomplemented
19C2×D4×A4C2×C313yes—
20C22×C3×SD16—31no—
21C22×C3×SD16—31no—
22C22×C3×SD16—31no—
23C22×C3×SD16—31no—
24C22×C3×SD16—34no—
25C22×C3×SD16C2×C314yescomplemented
26C23×C3×C8C2×C311yescharacteristic, complemented
27A4×SD16C2×C3112yesdirect product factor
28C2×C8×A4C2×C313yescomplemented
29C22×C3×A4—22no—
30C22×C3×A4—42no—
31C22×C3×A4D411yescharacteristic
32C2×C32×Q8—41no—
33C2×C32×D4—41no—
34C3×C4×A4—22no—
35C3×C4×A4D411yescharacteristic
36C3×C4×A4C2311yescharacteristic
37C32×SD16—44no—
38C2×C32×C8—41no—
39C23×SD16C3211yescharacteristic, complemented, Sylow
40C25×C3—21no—
41C23×A4—23no—
42C22×C3×Q8—21no—
43C22×C3×Q8—31no—
44C22×C3×Q8—32no—
45C22×C3×Q8—31no—
46C22×C3×Q8—61no—
47C22×C3×Q8—61no—
48C22×C3×Q8C22×C312yescomplemented
49C22×C3×D4—21no—
50C22×C3×D4—31no—
51C22×C3×D4—31no—
52C22×C3×D4—32no—
53C22×C3×D4—61no—
54C22×C3×D4—61no—
55C22×C3×D4C22×C312yes—
56C23×C3×C4—21no—
57C23×C3×C4C22×C311yescharacteristic
58Q8×A4—23no—
59Q8×A4C22×C316yescomplemented
60D4×A4—23no—
61D4×A4C22×C316yes—
62C2×C4×A4—23no—
63C2×C4×A4C22×C313yes—
64C2×C3×SD16—34no—
65C2×C3×SD16—34no—
66C2×C3×SD16—32no—
67C2×C3×SD16—34no—
68C2×C3×SD16—31no—
69C2×C3×SD16—31no—
70C2×C3×SD16—34no—
71C2×C3×SD16—34no—
72C2×C3×SD16—34no—
73C2×C3×SD16—34no—
74C2×C3×SD16—34no—
75C2×C3×SD16—31no—
76C2×C3×SD16—43no—
77C2×C3×SD16A411yescharacteristic, direct product factor
78C22×C3×C8—31no—
79C22×C3×C8—31no—
80C22×C3×C8—32no—
81C22×C3×C8C22×C312yescomplemented
82C8×A4C22×C316yescomplemented
83C23×C32—81no—
84C2×C3×A4—42no—
85C2×C3×A4SD1612yesdirect product factor
86C2×C3×A4C2×D411yescharacteristic
87C32×Q8—42no—
88C32×Q8—81no—
89C32×D4—42no—
90C32×D4—81no—
91C2×C32×C4—41no—
92C2×C32×C4—81no—
93C32×C8—42no—
94C23×Q8C2×C3211yescharacteristic, complemented
95C23×D4C2×C3211yescharacteristic
96C22×SD16—31no—
97C22×SD16—31no—
98C22×SD16—31no—
99C22×SD16—31no—
100C22×SD16—34no—
101C22×SD16C2×C3214yescomplemented
102C23×C8C2×C3211yescharacteristic, complemented
103C24×C3—22no—
104C24×C3—42no—
105C24×C3—61no—
106C24×C3—62no—
107C24×C3—61no—
108C24×C3—122no—
109C24×C3C3×D411yescharacteristic
110C22×A4—26no—
111C22×A4—46no—
112C22×A4C3×D413yes—
113C2×C3×Q8—32no—
114C2×C3×Q8—32no—
115C2×C3×Q8—32no—
116C2×C3×Q8—32no—
117C2×C3×Q8—31no—
118C2×C3×Q8—43no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C2×C3×Q8—61no—
122C2×C3×Q8—62no—
123C2×C3×Q8—61no—
124C2×C3×Q8—62no—
125C2×C3×Q8—61no—
126C2×C3×Q8—64no—
127C2×C3×Q8—61no—
128C2×C3×Q8C2×A411yescharacteristic, complemented
129C2×C3×D4—32no—
130C2×C3×D4—32no—
131C2×C3×D4—32no—
132C2×C3×D4—32no—
133C2×C3×D4—31no—
134C2×C3×D4—43no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×C3×D4—64no—
140C2×C3×D4—61no—
141C2×C3×D4—62no—
142C2×C3×D4—61no—
143C2×C3×D4—62no—
144C2×C3×D4C2×A411yescharacteristic
145C22×C3×C4—22no—
146C22×C3×C4—31no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—61no—
151C22×C3×C4—62no—
152C22×C3×C4—61no—
153C22×C3×C4C3×D411yescharacteristic
154C22×C3×C4C23×C311yescharacteristic
155C4×A4—26no—
156C4×A4C3×D413yes—
157C4×A4C23×C313yes—
158C3×SD16—38no—
159C3×SD16—34no—
160C3×SD16—34no—
161C3×SD16—34no—
162C3×SD16—412no—
163C3×SD16C2×A414yesdirect product factor
164C2×C3×C8—32no—
165C2×C3×C8—31no—
166C2×C3×C8—32no—
167C2×C3×C8—32no—
168C2×C3×C8—32no—
169C2×C3×C8—43no—
170C2×C3×C8C2×A411yescharacteristic, complemented
171C22×C32—41no—
172C22×C32—82no—
173C22×C32—162no—
174C3×A4C2×SD1611yescharacteristic, direct product factor
175C32×C4—41no—
176C32×C4—41no—
177C32×C4—82no—
178C25—21no—
179C22×Q8—21no—
180C22×Q8—31no—
181C22×Q8—32no—
182C22×Q8—31no—
183C22×Q8—61no—
184C22×Q8—61no—
185C22×Q8C22×C3212yescomplemented
186C22×D4—21no—
187C22×D4—31no—
188C22×D4—31no—
189C22×D4—32no—
190C22×D4—61no—
191C22×D4—61no—
192C22×D4C22×C3212yes—
193C23×C4—21no—
194C23×C4C22×C3211yescharacteristic
195C2×SD16—34no—
196C2×SD16—34no—
197C2×SD16—32no—
198C2×SD16—34no—
199C2×SD16—31no—
200C2×SD16—31no—
201C2×SD16—34no—
202C2×SD16—34no—
203C2×SD16—34no—
204C2×SD16—34no—
205C2×SD16—34no—
206C2×SD16—31no—
207C2×SD16C3×A411yescharacteristic, direct product factor
208C22×C8—31no—
209C22×C8—31no—
210C22×C8—32no—
211C22×C8C22×C3212yescomplemented
212C23×C3—21no—
213C23×C3—31no—
214C23×C3—32no—
215C23×C3—31no—
216C23×C3—42no—
217C23×C3—62no—
218C23×C3—62no—
219C23×C3—62no—
220C23×C3—62no—
221C23×C3—61no—
222C23×C3—83no—
223C23×C3—122no—
224C23×C3—122no—
225C23×C3—122no—
226C23×C3—124no—
227C23×C3—122no—
228C23×C3—122no—
229C23×C3—124no—
230C23×C3C3×SD1612yescomplemented
231C23×C3C2×C3×D411yescharacteristic
232C2×A4—46no—
233C2×A4C3×SD1616yesdirect product factor
234C2×A4C2×C3×D413yes—
235C3×Q8—21no—
236C3×Q8—32no—
237C3×Q8—46no—
238C3×Q8—62no—
239C3×Q8—62no—
240C3×Q8—62no—
241C3×Q8—62no—
242C3×Q8—61no—
243C3×Q8—83no—
244C3×Q8C22×A412yescomplemented
245C3×D4—21no—
246C3×D4—32no—
247C3×D4—46no—
248C3×D4—62no—
249C3×D4—62no—
250C3×D4—62no—
251C3×D4—62no—
252C3×D4—61no—
253C3×D4—83no—
254C3×D4C22×A412yes—
255C2×C3×C4—21no—
256C2×C3×C4—32no—
257C2×C3×C4—31no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—43no—
265C2×C3×C4—62no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4—61no—
269C2×C3×C4—62no—
270C2×C3×C4—83no—
271C2×C3×C4C22×A411yescharacteristic
272C3×C8—32no—
273C3×C8—46no—
274C3×C8C22×A412yescomplemented
275C2×C32—41no—
276C2×C32—42no—
277C2×C32—162no—
278C24—22no—
279C24—42no—
280C24—61no—
281C24—62no—
282C24—61no—
283C24—122no—
284C24C32×D411yescharacteristic
285C2×Q8—32no—
286C2×Q8—32no—
287C2×Q8—32no—
288C2×Q8—32no—
289C2×Q8—31no—
290C2×Q8—61no—
291C2×Q8—61no—
292C2×Q8—61no—
293C2×Q8—62no—
294C2×Q8—61no—
295C2×Q8—62no—
296C2×Q8—61no—
297C2×Q8—64no—
298C2×Q8—61no—
299C2×Q8C2×C3×A411yescharacteristic, complemented
300C2×D4—32no—
301C2×D4—32no—
302C2×D4—32no—
303C2×D4—32no—
304C2×D4—31no—
305C2×D4—61no—
306C2×D4—61no—
307C2×D4—61no—
308C2×D4—61no—
309C2×D4—64no—
310C2×D4—61no—
311C2×D4—62no—
312C2×D4—61no—
313C2×D4—62no—
314C2×D4C2×C3×A411yescharacteristic
315C22×C4—22no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—31no—
320C22×C4—61no—
321C22×C4—62no—
322C22×C4—61no—
323C22×C4C32×D411yescharacteristic
324C22×C4C23×C3211yescharacteristic
325SD16—38no—
326SD16—34no—
327SD16—34no—
328SD16—34no—
329SD16C2×C3×A414yesdirect product factor
330C2×C8—32no—
331C2×C8—31no—
332C2×C8—32no—
333C2×C8—32no—
334C2×C8—32no—
335C2×C8C2×C3×A411yescharacteristic, complemented
336C22×C3—22no—
337C22×C3—32no—
338C22×C3—31no—
339C22×C3—32no—
340C22×C3—31no—
341C22×C3—31no—
342C22×C3—32no—
343C22×C3—32no—
344C22×C3—42no—
345C22×C3—43no—
346C22×C3—62no—
347C22×C3—86no—
348C22×C3—122no—
349C22×C3—122no—
350C22×C3—124no—
351C22×C3—122no—
352C22×C3—122no—
353C22×C3—124no—
354C22×C3—122no—
355C22×C3—166no—
356C22×C3C2×C3×SD1611yescharacteristic, complemented
357C22×C3D4×A411yescharacteristic
358A4C2×C3×SD1613yesdirect product factor
359C3×C4—22no—
360C3×C4—31no—
361C3×C4—31no—
362C3×C4—43no—
363C3×C4—43no—
364C3×C4—62no—
365C3×C4—86no—
366C3×C4D4×A411yescharacteristic
367C3×C4C23×A411yescharacteristic
368C32—41noSylow
369C23—21no—
370C23—31no—
371C23—32no—
372C23—31no—
373C23—42no—
374C23—62no—
375C23—62no—
376C23—62no—
377C23—62no—
378C23—61no—
379C23—122no—
380C23—122no—
381C23—122no—
382C23—124no—
383C23—122no—
384C23—122no—
385C23—124no—
386C23C32×SD1612yescomplemented
387C23C2×C32×D411yescharacteristic
388Q8—21no—
389Q8—32no—
390Q8—62no—
391Q8—62no—
392Q8—62no—
393Q8—62no—
394Q8—61no—
395Q8C22×C3×A412yescomplemented
396D4—21no—
397D4—32no—
398D4—62no—
399D4—62no—
400D4—62no—
401D4—62no—
402D4—61no—
403D4C22×C3×A412yes—
404C2×C4—21no—
405C2×C4—32no—
406C2×C4—31no—
407C2×C4—31no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—61no—
417C2×C4—62no—
418C2×C4C22×C3×A411yescharacteristic
419C8—32no—
420C8C22×C3×A412yescomplemented
421C2×C3—32no—
422C2×C3—31no—
423C2×C3—31no—
424C2×C3—42no—
425C2×C3—43no—
426C2×C3—46no—
427C2×C3—122no—
428C2×C3—166no—
429C2×C3A4×SD1612yesdirect product factor
430C2×C3C2×D4×A411yescharacteristic
431C22—22no—
432C22—32no—
433C22—31no—
434C22—32no—
435C22—31no—
436C22—31no—
437C22—32no—
438C22—32no—
439C22—42no—
440C22—62no—
441C22—122no—
442C22—122no—
443C22—124no—
444C22—122no—
445C22—122no—
446C22—124no—
447C22—122no—
448C22C2×C32×SD1611yescharacteristic, complemented
449C22C3×D4×A411yescharacteristic
450C4—22no—
451C4—31no—
452C4—31no—
453C4—62no—
454C4C3×D4×A411yescharacteristic
455C4C23×C3×A411yescharacteristic
456C3—43no—
457C3C2×A4×SD1611yescharacteristic, direct product factor
458C2—31no—
459C2—32no—
460C2—31no—
461C2—42no—
462C2—122no—
463C2C3×A4×SD1612yesdirect product factor
464C2C2×C3×D4×A411yescharacteristic
subgroupG/H
centerC22×C3D4×A4
commutator, cosocleC22×C4C23×C32
FrattiniC4C23×C3×A4
FittingC23×C3×SD16C3
socleC24×C3C3×D4
prime radicalC2×C3×D4×A4C2
hypercenterC2×C3×SD16A4
hypocenterC22C2×C32×SD16
LCSG ▷ C22×C4 ▷ C23 ▷ C22
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×A4C2semidirect
3. C3×A4×SD16C2direct (N × H)
4. C2×C3×C8×A4C2semidirect
5. C23×C3×SD16C3semidirect
6. C2×A4×SD16C3direct (N × H)
9. C3×Q8×A4C22semidirect
15. C3×C8×A4C22semidirect
16. C23×C3×Q8C2×C3semidirect
18. C2×Q8×A4C2×C3semidirect
25. C22×C3×SD16C2×C3semidirect
26. C23×C3×C8C2×C3semidirect
27. A4×SD16C2×C3direct (N × H)
28. C2×C8×A4C2×C3semidirect
39. C23×SD16C32semidirect
48. C22×C3×Q8C22×C3semidirect
59. Q8×A4C22×C3semidirect
77. C2×C3×SD16A4direct (N × H)
81. C22×C3×C8C22×C3semidirect
82. C8×A4C22×C3semidirect
85. C2×C3×A4SD16direct (N × H)
94. C23×Q8C2×C32semidirect
101. C22×SD16C2×C32semidirect
102. C23×C8C2×C32semidirect
128. C2×C3×Q8C2×A4semidirect
163. C3×SD16C2×A4direct (N × H)
170. C2×C3×C8C2×A4semidirect
174. C3×A4C2×SD16direct (N × H)
185. C22×Q8C22×C32semidirect
207. C2×SD16C3×A4direct (N × H)
211. C22×C8C22×C32semidirect
230. C23×C3C3×SD16semidirect
233. C2×A4C3×SD16direct (N × H)
244. C3×Q8C22×A4semidirect
274. C3×C8C22×A4semidirect
299. C2×Q8C2×C3×A4semidirect
329. SD16C2×C3×A4direct (N × H)
335. C2×C8C2×C3×A4semidirect
356. C22×C3C2×C3×SD16semidirect
358. A4C2×C3×SD16direct (N × H)
386. C23C32×SD16semidirect
395. Q8C22×C3×A4semidirect
420. C8C22×C3×A4semidirect
429. C2×C3A4×SD16direct (N × H)
448. C22C2×C32×SD16semidirect
457. C3C2×A4×SD16direct (N × H)
463. C2C3×A4×SD16direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×Q8×A42
C2×C3×D4×A42
C3×A4×SD162
C2×C3×C8×A42
C23×C3×SD163
C2×A4×SD163
C2×C32×SD164