Finite Group Databasebeta

← C3×#85313 #11922597

Subgroups — C3×#85313 #11922597

Order 1152.

570 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×A4×C4⋊C4C211yesmaximal, characteristic, complemented
2C3×(C2×S4)⋊C4C211yesmaximal, characteristic
3C3×(C2×S4)⋊C4C211yesmaximal, characteristic
4C3×(C2×S4)⋊C4C211yesmaximal, characteristic
5C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
6C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
7C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
8#85313C311yesmaximal, characteristic, direct product factor
9C3×#2481—31nomaximal
10C22×C3×S4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3×C4×A4C2211yescharacteristic
14C2×C3×SL(2,ℤ/4)C2211yescharacteristic
15C2×C3×SL(2,ℤ/4)C2211yescharacteristic
16C2×C3×SL(2,ℤ/4)C2211yescharacteristic
17C3×#898—41nomaximal
18C2×C3×#126—31no—
19C22×C3×C4⋊C4D311yescharacteristic, complemented
20A4×C4⋊C4—21no—
21A4×C4⋊C4C2×C311yescharacteristic, complemented
22(C2×S4)⋊C4C2×C311yescharacteristic
23(C2×S4)⋊C4C2×C311yescharacteristic
24(C2×S4)⋊C4C2×C311yescharacteristic
25C4⋊SL(2,ℤ/4)C2×C311yescharacteristic, complemented
26SL(2,ℤ/4)⋊C4C2×C311yescharacteristic, complemented
27C4×SL(2,ℤ/4)C2×C311yescharacteristic, complemented
28C3×#400—31no—
29C3×#400—31no—
30C3×#397—31no—
31C3×#396—31no—
32C3×#388—31no—
33C3×#387—31no—
34C3×#387—31no—
35C3×#386—31no—
36C3×#386—31no—
37C3×#386—31no—
38C3×#385—31no—
39C3×#380—31no—
40C3×C4×C22⋊C4—31no—
41C22×C3×A4C2311yescharacteristic
42C2×C3×S4—21no—
43C2×C3×S4—21no—
44C2×C3×S4—21no—
45C3×C4×A4—21no—
46C3×C4×A4—21no—
47C3×C4×A4—21no—
48C3×SL(2,ℤ/4)—21no—
49C3×SL(2,ℤ/4)—21no—
50C3×SL(2,ℤ/4)—21no—
51C32×C4⋊C4—41no—
52C3×(C2×D3)⋊C4—41no—
53C3×(C2×D3)⋊C4—41no—
54C3×(C2×D3)⋊C4—41no—
55C3×C4⋊Dic3—41no—
56C3×Dic3⋊C4—41no—
57C3×C4×Dic3—41no—
58#2481—31noSylow
59C22×S4C22×C311yescharacteristic
60C22×C3×D4—31no—
61C23×C3×C4C2×D311yescharacteristic
62C23×C3×C4C2×D311yescharacteristic
63C23×C3×C4C2×D311yescharacteristic
64C2×C4×A4—21no—
65C2×C4×A4—21no—
66C2×C4×A4—21no—
67C2×C4×A4C22×C311yescharacteristic
68C2×C4×A4C22×C311yescharacteristic
69C2×C4×A4C22×C311yescharacteristic
70C2×SL(2,ℤ/4)C22×C311yescharacteristic
71C2×SL(2,ℤ/4)C22×C311yescharacteristic
72C2×SL(2,ℤ/4)C22×C311yescharacteristic
73C3×#126—61no—
74C3×#126—61no—
75C3×#126—61no—
76C3×#126—61no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C22⋊C4—31no—
86C2×C3×C22⋊C4—31no—
87C2×C3×C22⋊C4—31no—
88C2×C3×C22⋊C4—31no—
89C2×C3×C22⋊C4—31no—
90C2×C3×C22⋊C4—31no—
91C2×C3×C22⋊C4—31no—
92C2×C3×C22⋊C4—31no—
93C2×C3×C22⋊C4—31no—
94C2×C3×C42—31no—
95C2×C3×C42—31no—
96#898—41no—
97C3×#95—31no—
98C3×#95—31no—
99C3×#95—31no—
100C3×#95—31no—
101C3×#95—31no—
102C3×#95—31no—
103C3×#95—31no—
104C3×#95—31no—
105C3×#95—31no—
106C3×#95—31no—
107C3×#95—31no—
108C3×#95—31no—
109C22×C3×D3—41no—
110C2×C3×A4#4111yescharacteristic
111C2×C3×A4#4111yescharacteristic
112C2×C3×A4#4111yescharacteristic
113C3×S4—41no—
114C2×C32×C4—41no—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—41no—
120C2×#126—31no—
121C22×C4⋊C4C3×D311yescharacteristic, complemented
122#400—31no—
123#400—31no—
124#397—31no—
125#396—31no—
126#388—31no—
127#387—31no—
128#387—31no—
129#386—31no—
130#386—31no—
131#386—31no—
132#385—31no—
133#380—31no—
134C4×C22⋊C4—31no—
135C24×C3—31no—
136C24×C3C22×D311yescharacteristic
137C22×A4—21no—
138C22×A4C23×C311yescharacteristic
139C2×S4—21no—
140C2×S4—21no—
141C2×S4—21no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C4×A4—22no—
168C4×A4—21no—
169C4×A4—21no—
170C4×A4—21no—
171C4×A4—41no—
172C4×A4—41no—
173SL(2,ℤ/4)—21no—
174SL(2,ℤ/4)—21no—
175SL(2,ℤ/4)—21no—
176C3×C4⋊C4—31no—
177C3×C4⋊C4—31no—
178C3×C4⋊C4—31no—
179C3×C4⋊C4—41no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—62no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—81no—
187C3×C4⋊C4—121no—
188C3×C4⋊C4S411yescharacteristic, complemented
189C3×C22⋊C4—62no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C22⋊C4—121no—
203C3×C22⋊C4—121no—
204C3×C42—61no—
205C3×C42—61no—
206C3×C42—121no—
207(C2×D3)⋊C4—41no—
208(C2×D3)⋊C4—41no—
209(C2×D3)⋊C4—41no—
210C4⋊Dic3—41no—
211Dic3⋊C4—41no—
212C4×Dic3—41no—
213C22×C32—41no—
214C2×C3×D3—81no—
215C2×C3×D3—81no—
216C2×C3×D3—81no—
217C3×A4#12611yescharacteristic, complemented
218C32×C4—81no—
219C32×C4—81no—
220C32×C4—81no—
221C3×Dic3—81no—
222C3×Dic3—81no—
223C3×Dic3—81no—
224C22×D4—31no—
225C23×C4C2×C3×D311yescharacteristic
226C23×C4C2×C3×D311yescharacteristic
227C23×C4C2×C3×D311yescharacteristic
228#126—61no—
229#126—61no—
230#126—61no—
231#126—61no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—31no—
234C2×C4⋊C4—31no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—31no—
238C2×C4⋊C4—31no—
239C2×C4⋊C4—31no—
240C2×C22⋊C4—31no—
241C2×C22⋊C4—31no—
242C2×C22⋊C4—31no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—31no—
246C2×C22⋊C4—31no—
247C2×C22⋊C4—31no—
248C2×C22⋊C4—31no—
249C2×C42—31no—
250C2×C42—31no—
251#95—31no—
252#95—31no—
253#95—31no—
254#95—31no—
255#95—31no—
256#95—31no—
257#95—31no—
258#95—31no—
259#95—31no—
260#95—31no—
261#95—31no—
262#95—31no—
263C23×C3—31no—
264C23×C3—31no—
265C23×C3—31no—
266C23×C3—31no—
267C23×C3—61no—
268C23×C3—61no—
269C23×C3—61no—
270C23×C3—61no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3#23511yescharacteristic
275C23×C3#23711yescharacteristic
276C23×C3#23911yescharacteristic
277C22×D3—41no—
278C2×A4—21no—
279C2×A4—21no—
280C2×A4—21no—
281C2×A4C3×#4111yescharacteristic
282C2×A4C3×#4111yescharacteristic
283C2×A4C3×#4111yescharacteristic
284S4—41no—
285C3×D4—121no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C2×C3×C4—32no—
290C2×C3×C4—31no—
291C2×C3×C4—31no—
292C2×C3×C4—31no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—61no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—61no—
316C2×C3×C4—61no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—81no—
329C2×C3×C4—81no—
330C2×C3×C4—81no—
331C2×C3×C4C2×S411yescharacteristic
332C2×C3×C4C2×S411yescharacteristic
333C2×C3×C4C2×S411yescharacteristic
334C2×Dic3—41no—
335C2×Dic3—41no—
336C2×Dic3—41no—
337C2×C32—41no—
338C2×C32—41no—
339C2×C32—41no—
340C3×D3—161no—
341C24—31no—
342C24C22×C3×D311yescharacteristic
343C2×D4—61no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—31no—
353C22×C4—31no—
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4—61no—
368C4⋊C4—31no—
369C4⋊C4—31no—
370C4⋊C4—31no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—62no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—121no—
378C4⋊C4C3×S411yescharacteristic, complemented
379C22⋊C4—61no—
380C22⋊C4—61no—
381C22⋊C4—61no—
382C22⋊C4—62no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—61no—
389C22⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—121no—
393C22⋊C4—121no—
394C42—61no—
395C42—61no—
396C42—121no—
397C22×C3—31no—
398C22×C3—31no—
399C22×C3—31no—
400C22×C3—31no—
401C22×C3—31no—
402C22×C3—31no—
403C22×C3—31no—
404C22×C3—31no—
405C22×C3—31no—
406C22×C3—41no—
407C22×C3—61no—
408C22×C3—81no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3—121no—
413C22×C3—121no—
414C22×C3—121no—
415C22×C3—121no—
416C22×C3#89811yescharacteristic, complemented
417C22×C3C22×S411yescharacteristic
418C2×D3—81no—
419C2×D3—81no—
420C2×D3—81no—
421A4—21no—
422A4C3×#12611yescharacteristic, complemented
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—61no—
427C3×C4—61no—
428C3×C4—61no—
429C3×C4—81no—
430C3×C4—81no—
431C3×C4—81no—
432C3×C4—82no—
433C3×C4—121no—
434C3×C4—121no—
435C3×C4—121no—
436C3×C4—121no—
437C3×C4—121no—
438C3×C4—121no—
439C3×C4—121no—
440C3×C4—161no—
441C3×C4—161no—
442Dic3—81no—
443Dic3—81no—
444Dic3—81no—
445C32—41noSylow
446C23—31no—
447C23—31no—
448C23—31no—
449C23—31no—
450C23—61no—
451C23—61no—
452C23—61no—
453C23—61no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23C3×#23511yescharacteristic
458C23C3×#23711yescharacteristic
459C23C3×#23911yescharacteristic
460D4—121no—
461D4—121no—
462D4—121no—
463D4—121no—
464C2×C4—32no—
465C2×C4—31no—
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4C2×C3×S411yescharacteristic
501C2×C4C2×C3×S411yescharacteristic
502C2×C4C2×C3×S411yescharacteristic
503C2×C3—31no—
504C2×C3—31no—
505C2×C3—31no—
506C2×C3—31no—
507C2×C3—41no—
508C2×C3—41no—
509C2×C3—41no—
510C2×C3—81no—
511C2×C3—81no—
512C2×C3—81no—
513C2×C3—241no—
514C2×C3#591211yescharacteristic
515C2×C3#591411yescharacteristic
516C2×C3#591911yescharacteristic
517D3—161no—
518C22—31no—
519C22—31no—
520C22—31no—
521C22—31no—
522C22—31no—
523C22—31no—
524C22—31no—
525C22—31no—
526C22—31no—
527C22—61no—
528C22—121no—
529C22—121no—
530C22—121no—
531C22—121no—
532C22—121no—
533C22—121no—
534C22—121no—
535C22C3×#89811yescharacteristic, complemented
536C22C22×C3×S411yescharacteristic
537C4—21no—
538C4—21no—
539C4—21no—
540C4—61no—
541C4—61no—
542C4—61no—
543C4—121no—
544C4—121no—
545C4—121no—
546C4—121no—
547C4—121no—
548C4—121no—
549C4—121no—
550C3—41no—
551C3—81no—
552C3#8531311yescharacteristic, direct product factor
553C2—31no—
554C2—31no—
555C2—31no—
556C2—31no—
557C2—241no—
558C2C3×#591211yescharacteristic
559C2C3×#591411yescharacteristic
560C2C3×#591911yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
prime radicalC22×C3×S4C22
hypercenterC3×C4⋊C4S4
hypocenterA4C3×#126
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×A4×C4⋊C4C2semidirect
5. C3×C4⋊SL(2,ℤ/4)C2semidirect
6. C3×SL(2,ℤ/4)⋊C4C2semidirect
7. C3×C4×SL(2,ℤ/4)C2semidirect
8. #85313C3direct (N × H)
19. C22×C3×C4⋊C4D3semidirect
21. A4×C4⋊C4C2×C3semidirect
25. C4⋊SL(2,ℤ/4)C2×C3semidirect
26. SL(2,ℤ/4)⋊C4C2×C3semidirect
27. C4×SL(2,ℤ/4)C2×C3semidirect
121. C22×C4⋊C4C3×D3semidirect
188. C3×C4⋊C4S4semidirect
217. C3×A4#126semidirect
378. C4⋊C4C3×S4semidirect
416. C22×C3#898semidirect
422. A4C3×#126semidirect
535. C22C3×#898semidirect
552. C3#85313direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×C4⋊C42
C3×(C2×S4)⋊C42
C3×C4⋊SL(2,ℤ/4)2
C3×SL(2,ℤ/4)⋊C42
C3×C4×SL(2,ℤ/4)2
#853133
C3×#24813
C3×#8984