Finite Group Databasebeta

← D3×A4×Q16 #11923327

Subgroups — D3×A4×Q16 #11923327

Order 1152.

706 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 87 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
1D3×Q8×A4C212yesmaximal
2C3×A4×Q16C211yesmaximal, characteristic, complemented
3A4×#216C212yesmaximal, complemented
4A4×Dic12C211yesmaximal, characteristic, complemented
5D3×C8×A4C211yesmaximal, characteristic
6C22×D3×Q16C311yesmaximal, characteristic, complemented
7C2×A4×Q16—31nomaximal
8C3×Q8×A4C2212yes—
9C4×D3×A4—22no—
10C4×D3×A4C2211yescharacteristic
11A4×Dic6—22no—
12A4×Dic6C2212yes—
13C3×D3×Q16—41nomaximal
14C3×C8×A4C2211yescharacteristic
15A4×C3⋊C8C2211yescharacteristic
16C22×D3×Q8C2×C312yes—
17C2×Q8×A4—32no—
18C22×C3×Q16C2×C311yescharacteristic, complemented
19C22×#216C2×C312yescomplemented
20C2×D3×Q16—31no—
21C2×D3×Q16—31no—
22C2×D3×Q16—31no—
23C2×D3×Q16—32no—
24C2×D3×Q16—31no—
25C2×D3×Q16—32no—
26C22×Dic12C2×C311yescharacteristic, complemented
27C22×D3×C8C2×C311yescharacteristic
28A4×Q16—21no—
29A4×Q16—32no—
30A4×Q16—31no—
31A4×Q16D311yescharacteristic, direct product factor
32C2×C8×A4—31no—
33C2×D3×A4D411yescharacteristic
34C3×D3×Q8—42no—
35C3×C4×A4—22no—
36C3×C4×A4C2311yescharacteristic
37Dic3×A4—22no—
38Dic3×A4D411yescharacteristic
39C32×Q16—41no—
40C3×#216—42no—
41C3×Dic12—41no—
42C3×D3×C8—41no—
43C23×Q16—31noSylow
44C22×C3×Q8C22×C312yes—
45C2×D3×Q8—32no—
46C2×D3×Q8—32no—
47C2×D3×Q8—32no—
48C2×D3×Q8—32no—
49C2×D3×Q8—62no—
50C2×D3×Q8—62no—
51C22×C4×D3—22no—
52C22×C4×D3C22×C311yescharacteristic
53C22×Dic6—22no—
54C22×Dic6C22×C312yes—
55Q8×A4—22no—
56Q8×A4—32no—
57Q8×A4—62no—
58Q8×A4C2×D312yes—
59C2×C4×A4—31no—
60C2×C4×A4—62no—
61C2×C3×Q16—31no—
62C2×C3×Q16—31no—
63C2×C3×Q16—32no—
64C2×C3×Q16—121no—
65C22×C3×C8C22×C311yescharacteristic
66C2×#216—32no—
67C2×#216—32no—
68C2×#216—32no—
69C2×#216—32no—
70C22×C3⋊C8C22×C311yescharacteristic
71D3×Q16—34no—
72D3×Q16—34no—
73D3×Q16—32no—
74D3×Q16—32no—
75D3×Q16—32no—
76D3×Q16—32no—
77D3×Q16—31no—
78D3×Q16—32no—
79D3×Q16—31no—
80D3×Q16—31no—
81D3×Q16A411yescharacteristic, direct product factor
82C2×Dic12—31no—
83C2×Dic12—32no—
84C2×Dic12—31no—
85C2×D3×C8—31no—
86C2×D3×C8—31no—
87C2×D3×C8—31no—
88C2×D3×C8—31no—
89C8×A4—21no—
90C8×A4—31no—
91C8×A4C2×D311yescharacteristic
92C2×C3×A4C2×D411yescharacteristic
93D3×A4Q1612yesdirect product factor
94C32×Q8—42no—
95C3×C4×D3—41no—
96C3×C4×D3—82no—
97C3×Dic6—42no—
98C3×Dic6—82no—
99C32×C8—41no—
100C3×C3⋊C8—41no—
101C23×Q8—32no—
102C22×Q16—32no—
103C22×Q16—31no—
104C22×Q16—91no—
105C22×Q16—91no—
106C22×Q16—91no—
107C22×Q16—91no—
108C22×Q16—92no—
109C22×Q16—92no—
110C22×Q16C3×D311yescharacteristic, complemented
111C23×C8—31no—
112C23×D3C3×D411yescharacteristic
113C22×A4—31no—
114C2×C3×Q8—32no—
115C2×C3×Q8—32no—
116C2×C3×Q8—62no—
117C2×C3×Q8—122no—
118C22×C3×C4—22no—
119C22×C3×C4C23×C311yescharacteristic
120C22×Dic3—22no—
121C22×Dic3C3×D411yescharacteristic
122D3×Q8—34no—
123D3×Q8—32no—
124D3×Q8—32no—
125D3×Q8—32no—
126D3×Q8—62no—
127D3×Q8—62no—
128D3×Q8—64no—
129D3×Q8—64no—
130D3×Q8—62no—
131D3×Q8—62no—
132D3×Q8C2×A412yes—
133C2×C4×D3—31no—
134C2×C4×D3—31no—
135C2×C4×D3—31no—
136C2×C4×D3—31no—
137C2×C4×D3—62no—
138C2×C4×D3—62no—
139C2×C4×D3—62no—
140C2×C4×D3—62no—
141C2×Dic6—32no—
142C2×Dic6—32no—
143C2×Dic6—62no—
144C2×Dic6—62no—
145C2×Dic6—62no—
146C2×Dic6—62no—
147C2×Dic6—62no—
148C4×A4—22no—
149C4×A4—21no—
150C4×A4—31no—
151C4×A4—42no—
152C4×A4—62no—
153C4×A4C22×D311yescharacteristic
154C3×Q16—32no—
155C3×Q16—32no—
156C3×Q16—31no—
157C3×Q16—41no—
158C3×Q16—81no—
159C3×Q16—121no—
160C3×Q16—122no—
161C3×Q16C2×A411yescharacteristic, complemented
162C2×C3×C8—31no—
163C2×C3×C8—31no—
164C2×C3×C8—121no—
165#216—34no—
166#216—32no—
167#216—32no—
168#216—32no—
169#216C2×A412yescomplemented
170C2×C3⋊C8—31no—
171C2×C3⋊C8—31no—
172Dic12—32no—
173Dic12—32no—
174Dic12—31no—
175Dic12C2×A411yescharacteristic, complemented
176D3×C8—32no—
177D3×C8—31no—
178D3×C8—31no—
179D3×C8—31no—
180D3×C8C2×A411yescharacteristic
181C2×C3×D3—41no—
182C3×A4C2×Q1611yescharacteristic, complemented
183C32×C4—41no—
184C32×C4—82no—
185C3×Dic3—41no—
186C3×Dic3—82no—
187C22×Q8—32no—
188C22×Q8—62no—
189C22×Q8—92no—
190C22×Q8—92no—
191C22×Q8—92no—
192C22×Q8—92no—
193C22×Q8—182no—
194C22×Q8—182no—
195C22×Q8C2×C3×D312yes—
196C23×C4—31no—
197C23×C4—62no—
198C2×Q16—31no—
199C2×Q16—31no—
200C2×Q16—31no—
201C2×Q16—32no—
202C2×Q16—91no—
203C2×Q16—91no—
204C2×Q16—91no—
205C2×Q16—92no—
206C2×Q16—92no—
207C2×Q16—91no—
208C2×Q16—92no—
209C2×Q16—92no—
210C2×Q16—92no—
211C2×Q16—92no—
212C2×Q16—94no—
213C2×Q16—94no—
214C2×Q16—92no—
215C2×Q16—91no—
216C2×Q16—92no—
217C2×Q16—92no—
218C2×Q16—92no—
219C22×C8—31no—
220C22×C8—91no—
221C22×C8—91no—
222C22×C8—91no—
223C22×C8—91no—
224C22×C8C2×C3×D311yescharacteristic
225C23×C3C2×C3×D411yescharacteristic
226C22×D3—31no—
227C22×D3—31no—
228C22×D3—32no—
229C22×D3C3×Q1612yescomplemented
230C2×A4—21no—
231C2×A4—32no—
232C2×A4D3×D411yescharacteristic
233C3×Q8—32no—
234C3×Q8—42no—
235C3×Q8—62no—
236C3×Q8—62no—
237C3×Q8—82no—
238C3×Q8—122no—
239C3×Q8—242no—
240C3×Q8C22×A412yes—
241C2×C3×C4—31no—
242C2×C3×C4—31no—
243C2×C3×C4—62no—
244C2×C3×C4—62no—
245C2×C3×C4—121no—
246C2×C3×C4—242no—
247C2×Dic3—31no—
248C2×Dic3—31no—
249C2×Dic3—62no—
250C2×Dic3—62no—
251C4×D3—22no—
252C4×D3—32no—
253C4×D3—31no—
254C4×D3—31no—
255C4×D3—31no—
256C4×D3—62no—
257C4×D3—62no—
258C4×D3—64no—
259C4×D3—62no—
260C4×D3C22×A411yescharacteristic
261Dic6—22no—
262Dic6—32no—
263Dic6—62no—
264Dic6—62no—
265Dic6—62no—
266Dic6—64no—
267Dic6—62no—
268Dic6—62no—
269Dic6C22×A412yes—
270C3×C8—31no—
271C3×C8—41no—
272C3×C8—81no—
273C3×C8—121no—
274C3×C8C22×A411yescharacteristic
275C3⋊C8—31no—
276C3⋊C8C22×A411yescharacteristic
277C2×C32—41no—
278C3×D3—42no—
279C24—31no—
280C2×Q8—32no—
281C2×Q8—32no—
282C2×Q8—32no—
283C2×Q8—62no—
284C2×Q8—92no—
285C2×Q8—92no—
286C2×Q8—92no—
287C2×Q8—92no—
288C2×Q8—94no—
289C2×Q8—92no—
290C2×Q8—182no—
291C2×Q8—182no—
292C2×Q8—182no—
293C2×Q8—182no—
294C2×Q8—182no—
295C2×Q8—182no—
296C2×Q8—182no—
297C2×Q8—182no—
298C2×Q8—184no—
299C2×Q8—184no—
300C2×Q8—182no—
301C22×C4—22no—
302C22×C4—31no—
303C22×C4—62no—
304C22×C4—91no—
305C22×C4—91no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—182no—
309C22×C4—182no—
310C22×C4—182no—
311C22×C4—182no—
312C22×C4C22×C3×D311yescharacteristic
313Q16—32no—
314Q16—32no—
315Q16—32no—
316Q16—31no—
317Q16—31no—
318Q16—92no—
319Q16—92no—
320Q16—92no—
321Q16—92no—
322Q16—94no—
323Q16—92no—
324Q16—91no—
325Q16D3×A411yescharacteristic, direct product factor
326C2×C8—31no—
327C2×C8—31no—
328C2×C8—31no—
329C2×C8—91no—
330C2×C8—91no—
331C2×C8—91no—
332C2×C8—92no—
333C2×C8—91no—
334C2×C8—91no—
335C22×C3—31no—
336C22×C3—31no—
337C22×C3—121no—
338C22×C3C2×C3×Q1611yescharacteristic, complemented
339C2×D3—32no—
340C2×D3—31no—
341C2×D3—32no—
342C2×D3—32no—
343C2×D3—32no—
344C2×D3D4×A411yescharacteristic
345A4—21no—
346A4D3×Q1611yescharacteristic, direct product factor
347C3×C4—22no—
348C3×C4—31no—
349C3×C4—41no—
350C3×C4—62no—
351C3×C4—82no—
352C3×C4—81no—
353C3×C4—121no—
354C3×C4—162no—
355C3×C4—242no—
356C3×C4C23×A411yescharacteristic
357Dic3—22no—
358Dic3—31no—
359Dic3—62no—
360Dic3D4×A411yescharacteristic
361C32—41noSylow
362C23—32no—
363C23—91no—
364C23—91no—
365C23—92no—
366C23C3×D3×D411yescharacteristic
367Q8—32no—
368Q8—32no—
369Q8—62no—
370Q8—62no—
371Q8—62no—
372Q8—92no—
373Q8—182no—
374Q8—182no—
375Q8—182no—
376Q8—182no—
377Q8—182no—
378Q8—184no—
379Q8C2×D3×A412yes—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—62no—
384C2×C4—62no—
385C2×C4—62no—
386C2×C4—91no—
387C2×C4—91no—
388C2×C4—91no—
389C2×C4—92no—
390C2×C4—91no—
391C2×C4—91no—
392C2×C4—182no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—184no—
397C2×C4—182no—
398C8—31no—
399C8—31no—
400C8—91no—
401C8C2×D3×A411yescharacteristic
402C2×C3—31no—
403C2×C3—31no—
404C2×C3—41no—
405C2×C3—81no—
406C2×C3—122no—
407C2×C3C2×D4×A411yescharacteristic
408D3—32no—
409D3A4×Q1612yesdirect product factor
410C22—31no—
411C22—31no—
412C22—31no—
413C22—92no—
414C22—92no—
415C22—92no—
416C22—92no—
417C22—91no—
418C22C3×D3×Q1611yescharacteristic, complemented
419C4—22no—
420C4—31no—
421C4—31no—
422C4—62no—
423C4—62no—
424C4—91no—
425C4—182no—
426C4C22×D3×A411yescharacteristic
427C3—41no—
428C3—81no—
429C3C2×A4×Q1611yescharacteristic, complemented
430C2—31no—
431C2—31no—
432C2—32no—
433C2—92no—
434C2D3×D4×A411yescharacteristic
subgroupG/H
centerC2D3×D4×A4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC4C22×D3×A4
FittingC22×C3×Q16C2×C3
socleC23×C3C2×C3×D4
prime radicalC2×D3×A4D4
hypercenterQ16D3×A4
hypocenterC22×C3C2×C3×Q16
LCSG ▷ C22×C3×C4 ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C2 ◁ C4 ◁ Q16

Complements

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

NH ≅ G/Ntype
2. C3×A4×Q16C2semidirect
3. A4×#216C2semidirect
4. A4×Dic12C2semidirect
6. C22×D3×Q16C3semidirect
18. C22×C3×Q16C2×C3semidirect
19. C22×#216C2×C3semidirect
26. C22×Dic12C2×C3semidirect
31. A4×Q16D3direct (N × H)
81. D3×Q16A4direct (N × H)
93. D3×A4Q16direct (N × H)
110. C22×Q16C3×D3semidirect
161. C3×Q16C2×A4semidirect
169. #216C2×A4semidirect
175. Dic12C2×A4semidirect
182. C3×A4C2×Q16semidirect
229. C22×D3C3×Q16semidirect
325. Q16D3×A4direct (N × H)
338. C22×C3C2×C3×Q16semidirect
346. A4D3×Q16direct (N × H)
409. D3A4×Q16direct (N × H)
418. C22C3×D3×Q16semidirect
429. C3C2×A4×Q16semidirect

Maximal subgroups

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

subgroupindex
D3×Q8×A42
C3×A4×Q162
A4×#2162
A4×Dic122
D3×C8×A42
C22×D3×Q163
C2×A4×Q163
C3×D3×Q164