Finite Group Databasebeta

← C2×A4×Dic3⋊C4 #11923343

Subgroups — C2×A4×Dic3⋊C4 #11923343

Order 1152.

1190 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C22×C3×C4×A4C211yesmaximal, characteristic
2C22×Dic3×A4C211yesmaximal, characteristic
3C22×Dic3×A4C211yesmaximal, characteristic
4A4×Dic3⋊C4C214yesmaximal, direct product factor
5C23×Dic3⋊C4C311yesmaximal, characteristic, complemented
6C2×A4×C4⋊C4—31nomaximal
7C23×C3×A4C2211yescharacteristic
8C2×C3×C4×A4—22no—
9C2×C3×C4×A4C2212yes—
10C2×Dic3×A4—22no—
11C2×Dic3×A4C414yescomplemented
12C2×Dic3×A4C2212yes—
13C2×Dic3×A4C2212yes—
14C2×C3×Dic3⋊C4—41nomaximal
15C24×C3×C4C2×C311yescharacteristic
16C24×Dic3C2×C311yescharacteristic
17C24×Dic3C2×C311yescharacteristic
18C22×C4×A4—21no—
19C22×C4×A4—31no—
20C22×C4×A4—31no—
21C22×C4×A4D311yescharacteristic
22C22×Dic3⋊C4—31no—
23C22×Dic3⋊C4—31no—
24C22×Dic3⋊C4—31no—
25C22×Dic3⋊C4—31no—
26C22×Dic3⋊C4—34no—
27C22×Dic3⋊C4C2×C314yescomplemented
28A4×C4⋊C4—34no—
29C22×C3×A4C2×C412yes—
30C22×C3×A4D412yes—
31C22×C3×A4Q812yes—
32C22×C3×A4C2311yescharacteristic
33C22×C32×C4—41no—
34C22×C3×Dic3—41no—
35C22×C3×Dic3—41no—
36C3×C4×A4—22no—
37Dic3×A4—22no—
38Dic3×A4C2×C414yescomplemented
39C3×Dic3⋊C4—44no—
40C23×C4⋊C4—31noSylow
41C25×C3C22×C311yescharacteristic
42C23×A4—21no—
43C23×A4C2×D311yescharacteristic
44C23×C3×C4—22no—
45C23×C3×C4—31no—
46C23×C3×C4—31no—
47C23×C3×C4—32no—
48C23×C3×C4—62no—
49C23×C3×C4C22×C312yes—
50C23×Dic3—22no—
51C23×Dic3—31no—
52C23×Dic3—34no—
53C23×Dic3—31no—
54C23×Dic3—32no—
55C23×Dic3—31no—
56C23×Dic3—31no—
57C23×Dic3—32no—
58C23×Dic3—62no—
59C23×Dic3C3×C414yescomplemented
60C23×Dic3C22×C312yes—
61C23×Dic3C22×C312yes—
62C2×C4×A4—24no—
63C2×C4×A4—22no—
64C2×C4×A4—22no—
65C2×C4×A4—34no—
66C2×C4×A4—32no—
67C2×C4×A4—32no—
68C2×C4×A4—62no—
69C2×C4×A4C2×D312yes—
70C2×C3×C4⋊C4—121no—
71C2×Dic3⋊C4—32no—
72C2×Dic3⋊C4—34no—
73C2×Dic3⋊C4—34no—
74C2×Dic3⋊C4—34no—
75C2×Dic3⋊C4—31no—
76C2×Dic3⋊C4—31no—
77C2×Dic3⋊C4—31no—
78C2×Dic3⋊C4—34no—
79C2×Dic3⋊C4—34no—
80C2×Dic3⋊C4—34no—
81C2×Dic3⋊C4—34no—
82C2×Dic3⋊C4—34no—
83C2×Dic3⋊C4A411yescharacteristic, direct product factor
84C23×C32—41no—
85C2×C3×A4C4⋊C414yescomplemented
86C2×C3×A4C22×C411yescharacteristic
87C2×C3×A4C2×D411yescharacteristic
88C2×C3×A4C2×Q811yescharacteristic
89C2×C32×C4—42no—
90C2×C32×C4—82no—
91C2×C3×Dic3—44no—
92C2×C3×Dic3—42no—
93C2×C3×Dic3—42no—
94C2×C3×Dic3—82no—
95C24×C4—31no—
96C24×C4—31no—
97C24×C4C3×D311yescharacteristic
98C22×C4⋊C4—34no—
99C22×C4⋊C4—91no—
100C22×C4⋊C4—94no—
101C22×C4⋊C4—91no—
102C22×C4⋊C4—91no—
103C22×C4⋊C4—91no—
104C24×C3—32no—
105C24×C3—32no—
106C24×C3—31no—
107C24×C3—32no—
108C24×C3—31no—
109C24×C3C2×C3×C412yes—
110C24×C3C3×D412yes—
111C24×C3C3×Q812yes—
112C24×C3C23×C311yescharacteristic
113C22×A4—22no—
114C22×A4—22no—
115C22×A4—22no—
116C22×A4—21no—
117C22×A4Dic612yes—
118C22×A4C4×D312yes—
119C22×A4#6712yes—
120C22×A4C22×D311yescharacteristic
121C22×C3×C4—22no—
122C22×C3×C4—32no—
123C22×C3×C4—31no—
124C22×C3×C4—32no—
125C22×C3×C4—32no—
126C22×C3×C4—32no—
127C22×C3×C4—41no—
128C22×C3×C4—62no—
129C22×C3×C4—62no—
130C22×C3×C4—64no—
131C22×C3×C4—64no—
132C22×C3×C4—62no—
133C22×C3×C4—62no—
134C22×C3×C4—62no—
135C22×C3×C4—81no—
136C22×C3×C4—121no—
137C22×C3×C4—121no—
138C22×C3×C4C2×A411yescharacteristic
139C22×Dic3—22no—
140C22×Dic3—32no—
141C22×Dic3—34no—
142C22×Dic3—38no—
143C22×Dic3—31no—
144C22×Dic3—34no—
145C22×Dic3—34no—
146C22×Dic3—32no—
147C22×Dic3—32no—
148C22×Dic3—32no—
149C22×Dic3—34no—
150C22×Dic3—38no—
151C22×Dic3—34no—
152C22×Dic3—32no—
153C22×Dic3—31no—
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—62no—
158C22×Dic3—62no—
159C22×Dic3—64no—
160C22×Dic3—64no—
161C22×Dic3—62no—
162C22×Dic3—62no—
163C22×Dic3—62no—
164C22×Dic3C2×C3×C414yescomplemented
165C22×Dic3C2×A411yescharacteristic
166C22×Dic3C2×A411yescharacteristic
167C4×A4—24no—
168C4×A4—22no—
169C4×A4—34no—
170C4×A4—62no—
171C3×C4⋊C4—124no—
172Dic3⋊C4—38no—
173Dic3⋊C4—34no—
174Dic3⋊C4—34no—
175Dic3⋊C4—34no—
176Dic3⋊C4C2×A414yesdirect product factor
177C22×C32—42no—
178C22×C32—42no—
179C22×C32—42no—
180C22×C32—41no—
181C3×A4C2×C4⋊C411yescharacteristic, complemented
182C32×C4—82no—
183C3×Dic3—44no—
184C3×Dic3—82no—
185C25C2×C3×D311yescharacteristic
186C23×C4—22no—
187C23×C4—31no—
188C23×C4—31no—
189C23×C4—32no—
190C23×C4—34no—
191C23×C4—32no—
192C23×C4—32no—
193C23×C4—62no—
194C23×C4—62no—
195C23×C4—91no—
196C23×C4—91no—
197C23×C4—92no—
198C23×C4—91no—
199C23×C4—94no—
200C23×C4—92no—
201C23×C4—91no—
202C23×C4—182no—
203C23×C4C2×C3×D312yes—
204C2×C4⋊C4—31no—
205C2×C4⋊C4—94no—
206C2×C4⋊C4—94no—
207C2×C4⋊C4—91no—
208C2×C4⋊C4—91no—
209C2×C4⋊C4—94no—
210C2×C4⋊C4—94no—
211C2×C4⋊C4—92no—
212C2×C4⋊C4—94no—
213C2×C4⋊C4—91no—
214C2×C4⋊C4—94no—
215C2×C4⋊C4—94no—
216C2×C4⋊C4—94no—
217C23×C3—32no—
218C23×C3—31no—
219C23×C3—32no—
220C23×C3—31no—
221C23×C3—34no—
222C23×C3—34no—
223C23×C3—32no—
224C23×C3—34no—
225C23×C3—31no—
226C23×C3—32no—
227C23×C3—32no—
228C23×C3—32no—
229C23×C3—38no—
230C23×C3—32no—
231C23×C3—32no—
232C23×C3—32no—
233C23×C3—32no—
234C23×C3—32no—
235C23×C3—32no—
236C23×C3—31no—
237C23×C3—31no—
238C23×C3—41no—
239C23×C3—81no—
240C23×C3C3×C4⋊C414yescomplemented
241C23×C3C22×C3×C411yescharacteristic
242C23×C3C2×C3×D411yescharacteristic
243C23×C3C2×C3×Q811yescharacteristic
244C23×C3C22×A411yescharacteristic
245C2×A4—24no—
246C2×A4—21no—
247C2×A4—21no—
248C2×A4—21no—
249C2×A4Dic3⋊C414yesdirect product factor
250C2×A4C2×Dic611yescharacteristic
251C2×A4C2×C4×D311yescharacteristic
252C2×A4C2×#6711yescharacteristic
253C2×C3×C4—22no—
254C2×C3×C4—32no—
255C2×C3×C4—42no—
256C2×C3×C4—62no—
257C2×C3×C4—64no—
258C2×C3×C4—62no—
259C2×C3×C4—64no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—62no—
263C2×C3×C4—82no—
264C2×C3×C4—84no—
265C2×C3×C4—82no—
266C2×C3×C4—122no—
267C2×C3×C4—124no—
268C2×C3×C4—122no—
269C2×C3×C4—242no—
270C2×C3×C4C22×A412yes—
271C2×Dic3—22no—
272C2×Dic3—38no—
273C2×Dic3—34no—
274C2×Dic3—34no—
275C2×Dic3—32no—
276C2×Dic3—34no—
277C2×Dic3—38no—
278C2×Dic3—34no—
279C2×Dic3—34no—
280C2×Dic3—32no—
281C2×Dic3—62no—
282C2×Dic3—64no—
283C2×Dic3—62no—
284C2×Dic3—64no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—62no—
288C2×Dic3C4×A414yescomplemented
289C2×Dic3C22×A412yes—
290C2×Dic3C22×A412yes—
291C2×C32—41no—
292C2×C32—41no—
293C2×C32—41no—
294C2×C32—44no—
295C24—31no—
296C24—32no—
297C24—32no—
298C24—32no—
299C24—31no—
300C24C3×Dic612yes—
301C24C3×C4×D312yes—
302C24C3×#6712yes—
303C24C22×C3×D311yescharacteristic
304C22×C4—22no—
305C22×C4—31no—
306C22×C4—32no—
307C22×C4—31no—
308C22×C4—31no—
309C22×C4—32no—
310C22×C4—32no—
311C22×C4—32no—
312C22×C4—34no—
313C22×C4—62no—
314C22×C4—62no—
315C22×C4—64no—
316C22×C4—64no—
317C22×C4—62no—
318C22×C4—62no—
319C22×C4—62no—
320C22×C4—62no—
321C22×C4—92no—
322C22×C4—92no—
323C22×C4—94no—
324C22×C4—94no—
325C22×C4—92no—
326C22×C4—92no—
327C22×C4—92no—
328C22×C4—98no—
329C22×C4—94no—
330C22×C4—91no—
331C22×C4—92no—
332C22×C4—98no—
333C22×C4—94no—
334C22×C4—94no—
335C22×C4—92no—
336C22×C4—91no—
337C22×C4—92no—
338C22×C4—182no—
339C22×C4—182no—
340C22×C4—184no—
341C22×C4—184no—
342C22×C4—182no—
343C22×C4—182no—
344C22×C4—182no—
345C22×C4D3×A411yescharacteristic
346C4⋊C4—34no—
347C4⋊C4—94no—
348C4⋊C4—94no—
349C4⋊C4—98no—
350C4⋊C4—94no—
351C22×C3—34no—
352C22×C3—31no—
353C22×C3—31no—
354C22×C3—31no—
355C22×C3—34no—
356C22×C3—32no—
357C22×C3—34no—
358C22×C3—34no—
359C22×C3—32no—
360C22×C3—31no—
361C22×C3—31no—
362C22×C3—32no—
363C22×C3—31no—
364C22×C3—31no—
365C22×C3—32no—
366C22×C3—31no—
367C22×C3—31no—
368C22×C3—34no—
369C22×C3—34no—
370C22×C3—34no—
371C22×C3—34no—
372C22×C3—42no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3—41no—
376C22×C3—82no—
377C22×C3—82no—
378C22×C3—82no—
379C22×C3—81no—
380C22×C3C2×C3×C4⋊C411yescharacteristic, complemented
381C22×C3C2×C4×A412yes—
382C22×C3D4×A412yes—
383C22×C3Q8×A412yes—
384C22×C3C23×A411yescharacteristic
385A4—21no—
386A4C2×Dic3⋊C411yescharacteristic, direct product factor
387C3×C4—22no—
388C3×C4—62no—
389C3×C4—82no—
390C3×C4—84no—
391C3×C4—124no—
392C3×C4—242no—
393Dic3—22no—
394Dic3—34no—
395Dic3—62no—
396Dic3C2×C4×A414yescomplemented
397C32—41noSylow
398C23—32no—
399C23—31no—
400C23—32no—
401C23—31no—
402C23—32no—
403C23—34no—
404C23—34no—
405C23—34no—
406C23—31no—
407C23—32no—
408C23—32no—
409C23—38no—
410C23—32no—
411C23—32no—
412C23—32no—
413C23—32no—
414C23—32no—
415C23—32no—
416C23—32no—
417C23—31no—
418C23—31no—
419C23C3×Dic3⋊C414yescomplemented
420C23C2×C3×Dic611yescharacteristic
421C23C2×C3×C4×D311yescharacteristic
422C23C2×C3×#6711yescharacteristic
423C23C2×D3×A411yescharacteristic
424C2×C4—22no—
425C2×C4—34no—
426C2×C4—32no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—64no—
432C2×C4—64no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—94no—
438C2×C4—94no—
439C2×C4—98no—
440C2×C4—98no—
441C2×C4—94no—
442C2×C4—94no—
443C2×C4—92no—
444C2×C4—94no—
445C2×C4—92no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—184no—
449C2×C4—184no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4C2×D3×A412yes—
454C2×C3—34no—
455C2×C3—31no—
456C2×C3—31no—
457C2×C3—31no—
458C2×C3—31no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—44no—
462C2×C3—41no—
463C2×C3—81no—
464C2×C3—81no—
465C2×C3—84no—
466C2×C3—81no—
467C2×C3A4×C4⋊C414yescomplemented
468C2×C3C22×C4×A411yescharacteristic
469C2×C3C2×D4×A411yescharacteristic
470C2×C3C2×Q8×A411yescharacteristic
471C22—34no—
472C22—31no—
473C22—31no—
474C22—31no—
475C22—34no—
476C22—32no—
477C22—34no—
478C22—34no—
479C22—31no—
480C22—32no—
481C22—31no—
482C22—31no—
483C22—32no—
484C22—31no—
485C22—34no—
486C22—34no—
487C22—34no—
488C22—34no—
489C22—31no—
490C22—32no—
491C22—31no—
492C22C2×C3×Dic3⋊C411yescharacteristic, complemented
493C22A4×Dic612yes—
494C22C4×D3×A412yes—
495C22A4×#6712yes—
496C22C22×D3×A411yescharacteristic
497C4—22no—
498C4—34no—
499C4—62no—
500C4—62no—
501C4—94no—
502C4—182no—
503C3—41no—
504C3—81no—
505C3C2×A4×C4⋊C411yescharacteristic, complemented
506C2—31no—
507C2—34no—
508C2—31no—
509C2—31no—
510C2—31no—
511C2A4×Dic3⋊C414yesdirect product factor
512C2C2×A4×Dic611yescharacteristic
513C2C2×C4×D3×A411yescharacteristic
514C2C2×A4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×A4
commutatorC23×C3C22×C3×C4
FrattiniC22C22×D3×A4
FittingC24×C3×C4C2×C3
socleC25×C3C22×C3
prime radicalC23×C3×A4C22
cosocleC24×C3C23×C3
hypercenterC22×C4D3×A4
hypocenterC22×C3C2×C3×C4⋊C4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. A4×Dic3⋊C4C2direct (N × H)
5. C23×Dic3⋊C4C3semidirect
11. C2×Dic3×A4C4semidirect
27. C22×Dic3⋊C4C2×C3semidirect
38. Dic3×A4C2×C4semidirect
59. C23×Dic3C3×C4semidirect
83. C2×Dic3⋊C4A4direct (N × H)
85. C2×C3×A4C4⋊C4semidirect
164. C22×Dic3C2×C3×C4semidirect
176. Dic3⋊C4C2×A4direct (N × H)
181. C3×A4C2×C4⋊C4semidirect
240. C23×C3C3×C4⋊C4semidirect
249. C2×A4Dic3⋊C4direct (N × H)
288. C2×Dic3C4×A4semidirect
380. C22×C3C2×C3×C4⋊C4semidirect
386. A4C2×Dic3⋊C4direct (N × H)
396. Dic3C2×C4×A4semidirect
419. C23C3×Dic3⋊C4semidirect
467. C2×C3A4×C4⋊C4semidirect
492. C22C2×C3×Dic3⋊C4semidirect
505. C3C2×A4×C4⋊C4semidirect
511. C2A4×Dic3⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×A42
C22×Dic3×A42
A4×Dic3⋊C42
C23×Dic3⋊C43
C2×A4×C4⋊C43
C2×C3×Dic3⋊C44