Finite Group Databasebeta

← C3×#85480 #11922764

Subgroups — C3×#85480 #11922764

Order 1152.

852 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 100 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
2C2×C3×A4⋊Q8C211yesmaximal, characteristic, complemented
3C3×#5432C212yesmaximal
4C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
5C3×SL(2,ℤ/4)⋊C4C212yesmaximal, complemented
6#85480C311yesmaximal, characteristic, direct product factor
7C3×#2848—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C2×C3×C4×A4—22no—
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×SL(2,ℤ/4)C2212yes—
13C2×C3×SL(2,ℤ/4)C2212yes—
14C3×A4⋊Q8—22no—
15C3×#924—41nomaximal
16C24×C3×C4D311yescharacteristic
17C22×C4×A4—21no—
18C22×C4×A4C2×C311yescharacteristic
19C2×A4⋊Q8C2×C311yescharacteristic, complemented
20C2×C3×C22⋊Q8—31no—
21C2×C3×C22⋊Q8—31no—
22C2×C3×C22⋊Q8—31no—
23#5432C2×C312yes—
24C4⋊SL(2,ℤ/4)C2×C311yescharacteristic, complemented
25SL(2,ℤ/4)⋊C4C2×C312yescomplemented
26C3×#385—32no—
27C3×#385—32no—
28C3×#385—32no—
29C3×#380—31no—
30C3×#380—31no—
31C3×#380—31no—
32C3×#379—32no—
33C22×C3×A4—21no—
34C22×C3×A4—21no—
35C22×C3×A4Q812yescomplemented
36C22×C3×A4C2311yescharacteristic
37C22×C32×C4—41no—
38C2×C3×Dic6—41no—
39C3×C4×A4—21no—
40C3×C4×A4D412yes—
41C3×SL(2,ℤ/4)—22no—
42C3×SL(2,ℤ/4)—22no—
43C3×#217—42no—
44C3×C4⋊Dic3—41no—
45C3×Dic3⋊C4—42no—
46#2848—31noSylow
47C25×C3C2×D311yescharacteristic
48C23×A4—21no—
49C23×A4C22×C311yescharacteristic
50C22×C3×Q8—31no—
51C23×C3×C4—22no—
52C23×C3×C4—31no—
53C23×C3×C4—31no—
54C23×C3×C4—31no—
55C23×C3×C4—31no—
56C23×C3×C4—62no—
57C23×C3×C4C2×D311yescharacteristic
58C23×C3×C4C2×D311yescharacteristic
59C2×C4×A4—24no—
60C2×C4×A4—22no—
61C2×C4×A4—21no—
62C2×C4×A4—21no—
63C2×C4×A4C22×C311yescharacteristic
64C2×C4×A4C22×C311yescharacteristic
65C2×SL(2,ℤ/4)C22×C312yes—
66C2×SL(2,ℤ/4)C22×C312yes—
67A4⋊Q8—22no—
68C3×C22⋊Q8—62no—
69C3×C22⋊Q8—64no—
70C3×C22⋊Q8—61no—
71C3×C22⋊Q8—61no—
72C3×C22⋊Q8—61no—
73C3×C22⋊Q8—62no—
74C3×C22⋊Q8—61no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C22⋊C4—32no—
82C2×C3×C22⋊C4—32no—
83C2×C3×C22⋊C4—32no—
84C2×C3×C22⋊C4—32no—
85C2×C3×C22⋊C4—32no—
86C2×C3×C22⋊C4—32no—
87#924—41no—
88C3×#95—32no—
89C3×#95—32no—
90C3×#95—32no—
91C23×C32—41no—
92C2×C3×A4—22no—
93C2×C3×A4C2×D411yescharacteristic
94C2×C3×A4C2×Q811yescharacteristic
95C2×C3×A4#4111yescharacteristic
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4—82no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C3×Dic6—82no—
102C24×C4C3×D311yescharacteristic
103C2×C22⋊Q8—31no—
104C2×C22⋊Q8—31no—
105C2×C22⋊Q8—31no—
106#385—32no—
107#385—32no—
108#385—32no—
109#380—31no—
110#380—31no—
111#380—31no—
112#379—32no—
113C24×C3—21no—
114C24×C3—21no—
115C24×C3—31no—
116C24×C3—31no—
117C24×C3—32no—
118C24×C3—61no—
119C24×C3—61no—
120C24×C3Dic612yescomplemented
121C24×C3C22×D311yescharacteristic
122C22×A4—22no—
123C22×A4—22no—
124C22×A4—21no—
125C22×A4—21no—
126C22×A4—22no—
127C22×A4—21no—
128C22×A4C3×Q812yescomplemented
129C22×A4C23×C311yescharacteristic
130C2×C3×Q8—61no—
131C2×C3×Q8—62no—
132C2×C3×Q8—62no—
133C2×C3×Q8—61no—
134C22×C3×C4—21no—
135C22×C3×C4—31no—
136C22×C3×C4—31no—
137C22×C3×C4—31no—
138C22×C3×C4—32no—
139C22×C3×C4—34no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—32no—
145C22×C3×C4—32no—
146C22×C3×C4—32no—
147C22×C3×C4—32no—
148C22×C3×C4—41no—
149C22×C3×C4—62no—
150C22×C3×C4—62no—
151C22×C3×C4—61no—
152C22×C3×C4—61no—
153C22×C3×C4—62no—
154C22×C3×C4—62no—
155C22×C3×C4—62no—
156C22×C3×C4—62no—
157C22×C3×C4—62no—
158C22×C3×C4—81no—
159C22×C3×C4#6712yes—
160C22×C3×C4S411yescharacteristic
161C2×Dic6—41no—
162C4×A4—22no—
163C4×A4—21no—
164C4×A4—22no—
165C4×A4C3×D412yes—
166SL(2,ℤ/4)—22no—
167SL(2,ℤ/4)—22no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—62no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—64no—
172C3×C4⋊C4—64no—
173C3×C4⋊C4—62no—
174C3×C4⋊C4—62no—
175C3×C4⋊C4—61no—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—64no—
178C3×C22⋊C4—64no—
179C3×C22⋊C4—62no—
180C3×C22⋊C4—64no—
181C3×C22⋊C4—62no—
182C3×C22⋊C4—62no—
183C3×C22⋊C4—62no—
184C3×C22⋊C4—62no—
185#217—42no—
186C4⋊Dic3—41no—
187Dic3⋊C4—42no—
188C22×C32—42no—
189C22×C32—41no—
190C22×C32—81no—
191C22×C32—81no—
192C3×A4C22⋊Q811yescharacteristic, complemented
193C32×C4—42no—
194C32×C4—81no—
195C3×Dic3—82no—
196C3×Dic3—82no—
197C25C2×C3×D311yescharacteristic
198C22×Q8—31no—
199C23×C4—22no—
200C23×C4—31no—
201C23×C4—31no—
202C23×C4—31no—
203C23×C4—31no—
204C23×C4—62no—
205C23×C4C2×C3×D311yescharacteristic
206C23×C4C2×C3×D311yescharacteristic
207C22⋊Q8—62no—
208C22⋊Q8—64no—
209C22⋊Q8—61no—
210C22⋊Q8—61no—
211C22⋊Q8—61no—
212C22⋊Q8—62no—
213C22⋊Q8—61no—
214C2×C4⋊C4—31no—
215C2×C4⋊C4—31no—
216C2×C4⋊C4—31no—
217C2×C4⋊C4—32no—
218C2×C4⋊C4—32no—
219C2×C4⋊C4—32no—
220C2×C22⋊C4—32no—
221C2×C22⋊C4—32no—
222C2×C22⋊C4—32no—
223C2×C22⋊C4—32no—
224C2×C22⋊C4—32no—
225C2×C22⋊C4—32no—
226#95—32no—
227#95—32no—
228#95—32no—
229C23×C3—22no—
230C23×C3—31no—
231C23×C3—31no—
232C23×C3—31no—
233C23×C3—32no—
234C23×C3—31no—
235C23×C3—32no—
236C23×C3—32no—
237C23×C3—32no—
238C23×C3—32no—
239C23×C3—31no—
240C23×C3—41no—
241C23×C3—61no—
242C23×C3—61no—
243C23×C3—61no—
244C23×C3—61no—
245C23×C3—62no—
246C23×C3—61no—
247C23×C3—61no—
248C23×C3—62no—
249C23×C3—62no—
250C23×C3—61no—
251C23×C3—64no—
252C23×C3—81no—
253C23×C3C2×Dic611yescharacteristic
254C23×C3#23511yescharacteristic
255C23×C3C2×#6711yescharacteristic
256C23×C3C2×S411yescharacteristic
257C2×A4—24no—
258C2×A4—22no—
259C2×A4—21no—
260C2×A4—21no—
261C2×A4—21no—
262C2×A4C2×C3×D411yescharacteristic
263C2×A4C2×C3×Q811yescharacteristic
264C2×A4C3×#4111yescharacteristic
265C3×Q8—122no—
266C3×Q8—122no—
267C2×C3×C4—22no—
268C2×C3×C4—31no—
269C2×C3×C4—32no—
270C2×C3×C4—32no—
271C2×C3×C4—32no—
272C2×C3×C4—32no—
273C2×C3×C4—31no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—62no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—62no—
281C2×C3×C4—64no—
282C2×C3×C4—62no—
283C2×C3×C4—61no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—82no—
297C2×C3×C4—84no—
298C2×C3×C4—81no—
299C2×C3×C4—81no—
300C2×C3×C4C2×S411yescharacteristic
301C2×C3×C4C2×S411yescharacteristic
302C2×Dic3—42no—
303C2×Dic3—42no—
304Dic6—82no—
305C2×C32—41no—
306C2×C32—41no—
307C2×C32—41no—
308C2×C32—82no—
309C24—21no—
310C24—21no—
311C24—31no—
312C24—31no—
313C24—32no—
314C24—61no—
315C24—61no—
316C24C3×Dic612yescomplemented
317C24C22×C3×D311yescharacteristic
318C2×Q8—61no—
319C2×Q8—62no—
320C2×Q8—62no—
321C2×Q8—61no—
322C22×C4—21no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—32no—
327C22×C4—34no—
328C22×C4—31no—
329C22×C4—31no—
330C22×C4—31no—
331C22×C4—31no—
332C22×C4—32no—
333C22×C4—32no—
334C22×C4—32no—
335C22×C4—32no—
336C22×C4—62no—
337C22×C4—62no—
338C22×C4—61no—
339C22×C4—61no—
340C22×C4—62no—
341C22×C4—62no—
342C22×C4—62no—
343C22×C4—62no—
344C22×C4—62no—
345C22×C4C3×#6712yes—
346C22×C4C3×S411yescharacteristic
347C4⋊C4—61no—
348C4⋊C4—62no—
349C4⋊C4—62no—
350C4⋊C4—64no—
351C4⋊C4—64no—
352C4⋊C4—62no—
353C4⋊C4—62no—
354C4⋊C4—61no—
355C22⋊C4—62no—
356C22⋊C4—64no—
357C22⋊C4—62no—
358C22⋊C4—62no—
359C22⋊C4—64no—
360C22⋊C4—64no—
361C22⋊C4—62no—
362C22⋊C4—62no—
363C22⋊C4—62no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—31no—
367C22×C3—31no—
368C22×C3—31no—
369C22×C3—31no—
370C22×C3—31no—
371C22×C3—31no—
372C22×C3—31no—
373C22×C3—31no—
374C22×C3—31no—
375C22×C3—34no—
376C22×C3—32no—
377C22×C3—41no—
378C22×C3—42no—
379C22×C3—62no—
380C22×C3—62no—
381C22×C3—62no—
382C22×C3—62no—
383C22×C3—61no—
384C22×C3—62no—
385C22×C3—62no—
386C22×C3—62no—
387C22×C3—61no—
388C22×C3—61no—
389C22×C3—81no—
390C22×C3—81no—
391C22×C3—82no—
392C22×C3—82no—
393C22×C3—81no—
394C22×C3—82no—
395C22×C3#92411yescharacteristic, complemented
396C22×C3A4⋊Q812yescomplemented
397C22×C3C22×S411yescharacteristic
398A4—21no—
399A4C3×C22⋊Q811yescharacteristic, complemented
400C3×C4—21no—
401C3×C4—32no—
402C3×C4—42no—
403C3×C4—61no—
404C3×C4—81no—
405C3×C4—82no—
406C3×C4—82no—
407C3×C4—122no—
408C3×C4—122no—
409C3×C4—122no—
410C3×C4—122no—
411C3×C4GL(2,ℤ/4)12yes—
412Dic3—82no—
413Dic3—82no—
414C32—41noSylow
415C23—22no—
416C23—31no—
417C23—31no—
418C23—31no—
419C23—32no—
420C23—31no—
421C23—32no—
422C23—32no—
423C23—31no—
424C23—32no—
425C23—32no—
426C23—61no—
427C23—61no—
428C23—61no—
429C23—61no—
430C23—62no—
431C23—61no—
432C23—61no—
433C23—62no—
434C23—62no—
435C23—61no—
436C23—64no—
437C23C2×C3×Dic611yescharacteristic
438C23C3×#23511yescharacteristic
439C23C2×C3×#6711yescharacteristic
440C23C2×C3×S411yescharacteristic
441Q8—122no—
442Q8—122no—
443C2×C4—22no—
444C2×C4—31no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—31no—
450C2×C4—62no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—62no—
455C2×C4—64no—
456C2×C4—62no—
457C2×C4—61no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—62no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4C2×C3×S411yescharacteristic
471C2×C4C2×C3×S411yescharacteristic
472C2×C3—22no—
473C2×C3—31no—
474C2×C3—31no—
475C2×C3—31no—
476C2×C3—31no—
477C2×C3—41no—
478C2×C3—41no—
479C2×C3—41no—
480C2×C3—62no—
481C2×C3—82no—
482C2×C3—84no—
483C2×C3—81no—
484C2×C3—81no—
485C2×C3—81no—
486C2×C3C2×A4⋊Q811yescharacteristic
487C2×C3#591211yescharacteristic
488C2×C3C2×GL(2,ℤ/4)11yescharacteristic
489C22—21no—
490C22—21no—
491C22—31no—
492C22—31no—
493C22—31no—
494C22—31no—
495C22—31no—
496C22—31no—
497C22—31no—
498C22—31no—
499C22—31no—
500C22—34no—
501C22—32no—
502C22—62no—
503C22—62no—
504C22—62no—
505C22—62no—
506C22—61no—
507C22—62no—
508C22—62no—
509C22—62no—
510C22—61no—
511C22—61no—
512C22C3×#92411yescharacteristic, complemented
513C22C3×A4⋊Q812yescomplemented
514C22C22×C3×S411yescharacteristic
515C4—21no—
516C4—32no—
517C4—61no—
518C4—122no—
519C4—122no—
520C4—122no—
521C4—122no—
522C4C3×GL(2,ℤ/4)12yes—
523C3—41no—
524C3—81no—
525C3#8548011yescharacteristic, direct product factor
526C2—22no—
527C2—31no—
528C2—31no—
529C2—31no—
530C2—31no—
531C2—62no—
532C2C2×C3×A4⋊Q811yescharacteristic
533C2C3×#591211yescharacteristic
534C2C2×C3×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC24×C3×C4D3
socleC24×C3C22×D3
prime radicalC23×C3×A4C22
hypercenterC22×C3×C4S4
hypocenterA4C3×C22⋊Q8
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×A4⋊Q8C2semidirect
4. C3×C4⋊SL(2,ℤ/4)C2semidirect
5. C3×SL(2,ℤ/4)⋊C4C2semidirect
6. #85480C3direct (N × H)
19. C2×A4⋊Q8C2×C3semidirect
24. C4⋊SL(2,ℤ/4)C2×C3semidirect
25. SL(2,ℤ/4)⋊C4C2×C3semidirect
35. C22×C3×A4Q8semidirect
120. C24×C3Dic6semidirect
128. C22×A4C3×Q8semidirect
192. C3×A4C22⋊Q8semidirect
316. C24C3×Dic6semidirect
395. C22×C3#924semidirect
396. C22×C3A4⋊Q8semidirect
399. A4C3×C22⋊Q8semidirect
512. C22C3×#924semidirect
513. C22C3×A4⋊Q8semidirect
525. C3#85480direct (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
C2×C3×A4⋊Q82
C3×#54322
C3×C4⋊SL(2,ℤ/4)2
C3×SL(2,ℤ/4)⋊C42
#854803
C3×#28483
C3×#9244