Finite Group Databasebeta

← C3×#85304 #11922589

Subgroups — C3×#85304 #11922589

Order 1152.

536 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 80 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
2C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic
3C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
4C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
5C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
6C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic
7C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic
8#85304C311yesmaximal, characteristic, direct product factor
9C3×#2473—31nomaximal
10C2×C3×C4×A4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×C4×A4C2211yescharacteristic
13C2×C3×SL(2,ℤ/4)C2211yescharacteristic
14C2×C3×SL(2,ℤ/4)C2211yescharacteristic
15C2×C3×SL(2,ℤ/4)C2211yescharacteristic
16C2×C3×SL(2,ℤ/4)C2211yescharacteristic
17C3×#889—41nomaximal
18C2×C3×#125—31no—
19C22×C3×C4⋊C4D311yescharacteristic
20A4×C4⋊C4—21no—
21A4×C4⋊C4C2×C311yescharacteristic
22C4⋊SL(2,ℤ/4)C2×C311yescharacteristic
23SL(2,ℤ/4)⋊C4C2×C311yescharacteristic
24SL(2,ℤ/4)⋊C4C2×C311yescharacteristic
25SL(2,ℤ/4)⋊C4C2×C311yescharacteristic
26SL(2,ℤ/4)⋊C4C2×C311yescharacteristic
27C4×SL(2,ℤ/4)C2×C311yescharacteristic
28C3×#400—31no—
29C3×#398—31no—
30C3×#398—31no—
31C3×#398—31no—
32C3×#389—31no—
33C3×#387—31no—
34C3×#387—31no—
35C3×#385—31no—
36C3×#385—31no—
37C3×#385—31no—
38C3×#385—31no—
39C3×#380—31no—
40C3×C4×C22⋊C4—31no—
41C22×C3×A4C2311yescharacteristic
42C3×C4×A4—21no—
43C3×C4×A4—21no—
44C3×C4×A4—21no—
45C3×SL(2,ℤ/4)—21no—
46C3×SL(2,ℤ/4)—21no—
47C3×SL(2,ℤ/4)—21no—
48C3×SL(2,ℤ/4)Q812yes—
49C32×C4⋊C4—41no—
50C3×C4⋊Dic3—41no—
51C3×Dic3⋊C4—41no—
52C3×Dic3⋊C4—41no—
53C3×Dic3⋊C4—41no—
54C3×Dic3⋊C4—41no—
55C3×C4×Dic3—41no—
56#2473—31noSylow
57C23×C3×C4C2×D311yescharacteristic
58C23×C3×C4C2×D311yescharacteristic
59C23×C3×C4C2×D311yescharacteristic
60C2×C4×A4—21no—
61C2×C4×A4—21no—
62C2×C4×A4—21no—
63C2×C4×A4C22×C311yescharacteristic
64C2×C4×A4C22×C311yescharacteristic
65C2×C4×A4C22×C311yescharacteristic
66C2×SL(2,ℤ/4)C22×C311yescharacteristic
67C2×SL(2,ℤ/4)C22×C311yescharacteristic
68C2×SL(2,ℤ/4)C22×C311yescharacteristic
69C2×SL(2,ℤ/4)C22×C311yescharacteristic
70C3×#125—61no—
71C3×#125—61no—
72C3×#125—61no—
73C3×#125—61no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—31no—
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×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C22⋊C4—31no—
89C2×C3×C22⋊C4—31no—
90C2×C3×C22⋊C4—31no—
91C2×C3×C22⋊C4—31no—
92C2×C3×C42—31no—
93C2×C3×C42—31no—
94#889—41no—
95C3×#95—31no—
96C3×#95—31no—
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—
107C2×C3×A4C2×Q811yescharacteristic
108C2×C3×A4#4111yescharacteristic
109C2×C3×A4#4111yescharacteristic
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C3×Dic3—41no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—41no—
117C2×#125—31no—
118C22×C4⋊C4C3×D311yescharacteristic
119#400—31no—
120#398—31no—
121#398—31no—
122#398—31no—
123#389—31no—
124#387—31no—
125#387—31no—
126#385—31no—
127#385—31no—
128#385—31no—
129#385—31no—
130#380—31no—
131C4×C22⋊C4—31no—
132C24×C3C22×D311yescharacteristic
133C22×A4—21no—
134C22×A4C23×C311yescharacteristic
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—31no—
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—31no—
142C22×C3×C4—31no—
143C22×C3×C4—31no—
144C22×C3×C4—31no—
145C22×C3×C4—31no—
146C22×C3×C4—31no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—61no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C4×A4—22no—
156C4×A4—21no—
157C4×A4—21no—
158C4×A4—21no—
159C4×A4—41no—
160C4×A4—41no—
161SL(2,ℤ/4)—21no—
162SL(2,ℤ/4)—21no—
163SL(2,ℤ/4)—21no—
164SL(2,ℤ/4)C3×Q812yes—
165C3×C4⋊C4—31no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—41no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—62no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—81no—
183C3×C4⋊C4—121no—
184C3×C4⋊C4—121no—
185C3×C4⋊C4—121no—
186C3×C4⋊C4S411yescharacteristic
187C3×C22⋊C4—32no—
188C3×C22⋊C4—32no—
189C3×C22⋊C4—61no—
190C3×C22⋊C4—61no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C42—61no—
196C3×C42—61no—
197C3×C42—121no—
198C4⋊Dic3—41no—
199Dic3⋊C4—41no—
200Dic3⋊C4—41no—
201Dic3⋊C4—41no—
202Dic3⋊C4—41no—
203C4×Dic3—41no—
204C22×C32—41no—
205C3×A4#12511yescharacteristic, complemented
206C32×C4—81no—
207C32×C4—81no—
208C32×C4—81no—
209C3×Dic3—42no—
210C3×Dic3—81no—
211C3×Dic3—81no—
212C3×Dic3—81no—
213C23×C4C2×C3×D311yescharacteristic
214C23×C4C2×C3×D311yescharacteristic
215C23×C4C2×C3×D311yescharacteristic
216#125—61no—
217#125—61no—
218#125—61no—
219#125—61no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4—31no—
222C2×C4⋊C4—31no—
223C2×C4⋊C4—31no—
224C2×C4⋊C4—31no—
225C2×C4⋊C4—31no—
226C2×C4⋊C4—31no—
227C2×C4⋊C4—31no—
228C2×C4⋊C4—31no—
229C2×C4⋊C4—31no—
230C2×C4⋊C4—31no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233C2×C4⋊C4—31no—
234C2×C22⋊C4—31no—
235C2×C22⋊C4—31no—
236C2×C22⋊C4—31no—
237C2×C22⋊C4—31no—
238C2×C42—31no—
239C2×C42—31no—
240#95—31no—
241#95—31no—
242#95—31no—
243#95—31no—
244#95—31no—
245#95—31no—
246#95—31no—
247#95—31no—
248#95—31no—
249#95—31no—
250#95—31no—
251#95—31no—
252C23×C3—31no—
253C23×C3—31no—
254C23×C3—31no—
255C23×C3—31no—
256C23×C3#23511yescharacteristic
257C23×C3#23711yescharacteristic
258C23×C3D3×Q811yescharacteristic
259C2×A4—21no—
260C2×A4—21no—
261C2×A4—21no—
262C2×A4C2×C3×Q811yescharacteristic
263C2×A4C3×#4111yescharacteristic
264C2×A4C3×#4111yescharacteristic
265C2×C3×C4—32no—
266C2×C3×C4—32no—
267C2×C3×C4—32no—
268C2×C3×C4—31no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—61no—
285C2×C3×C4—61no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—61no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
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—81no—
308C2×C3×C4—81no—
309C2×C3×C4—81no—
310C2×C3×C4C2×S411yescharacteristic
311C2×C3×C4C2×S411yescharacteristic
312C2×C3×C4C2×S411yescharacteristic
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×C32—41no—
318C2×C32—41no—
319C2×C32—41no—
320C24C22×C3×D311yescharacteristic
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—31no—
329C22×C4—31no—
330C22×C4—31no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—61no—
339C22×C4—61no—
340C22×C4—61no—
341C4⋊C4—31no—
342C4⋊C4—31no—
343C4⋊C4—31no—
344C4⋊C4—61no—
345C4⋊C4—61no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—62no—
351C4⋊C4—62no—
352C4⋊C4—61no—
353C4⋊C4—61no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—121no—
358C4⋊C4—121no—
359C4⋊C4—121no—
360C4⋊C4C3×S411yescharacteristic
361C22⋊C4—32no—
362C22⋊C4—32no—
363C22⋊C4—61no—
364C22⋊C4—61no—
365C22⋊C4—61no—
366C22⋊C4—61no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C42—61no—
370C42—61no—
371C42—121no—
372C22×C3—31no—
373C22×C3—31no—
374C22×C3—31no—
375C22×C3—31no—
376C22×C3—31no—
377C22×C3—31no—
378C22×C3—31no—
379C22×C3—31no—
380C22×C3—31no—
381C22×C3—41no—
382C22×C3—61no—
383C22×C3—81no—
384C22×C3#88911yescharacteristic, complemented
385C22×C3C22×S411yescharacteristic
386A4—21no—
387A4C3×#12511yescharacteristic, complemented
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—62no—
392C3×C4—61no—
393C3×C4—61no—
394C3×C4—61no—
395C3×C4—62no—
396C3×C4—81no—
397C3×C4—81no—
398C3×C4—81no—
399C3×C4—82no—
400C3×C4—121no—
401C3×C4—121no—
402C3×C4—121no—
403C3×C4—121no—
404C3×C4—121no—
405C3×C4—121no—
406C3×C4—161no—
407C3×C4—161no—
408Dic3—42no—
409Dic3—81no—
410Dic3—81no—
411Dic3—81no—
412C32—41noSylow
413C23—31no—
414C23—31no—
415C23—31no—
416C23—31no—
417C23C3×#23511yescharacteristic
418C23C3×#23711yescharacteristic
419C23C3×D3×Q811yescharacteristic
420C2×C4—32no—
421C2×C4—32no—
422C2×C4—32no—
423C2×C4—31no—
424C2×C4—31no—
425C2×C4—31no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4—61no—
432C2×C4—61no—
433C2×C4—61no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4C2×C3×S411yescharacteristic
460C2×C4C2×C3×S411yescharacteristic
461C2×C4C2×C3×S411yescharacteristic
462C2×C3—31no—
463C2×C3—31no—
464C2×C3—31no—
465C2×C3—31no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—81no—
470C2×C3—81no—
471C2×C3—81no—
472C2×C3#591211yescharacteristic
473C2×C3#591411yescharacteristic
474C2×C3Q8×S411yescharacteristic
475C22—31no—
476C22—31no—
477C22—31no—
478C22—31no—
479C22—31no—
480C22—31no—
481C22—31no—
482C22—31no—
483C22—31no—
484C22—61no—
485C22C3×#88911yescharacteristic, complemented
486C22C22×C3×S411yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—62no—
491C4—61no—
492C4—61no—
493C4—61no—
494C4—62no—
495C4—121no—
496C4—121no—
497C4—121no—
498C4—121no—
499C4—121no—
500C4—121no—
501C3—41no—
502C3—81no—
503C3#8530411yescharacteristic, direct product factor
504C2—31no—
505C2—31no—
506C2—31no—
507C2—31no—
508C2C3×#591211yescharacteristic
509C2C3×#591411yescharacteristic
510C2C3×Q8×S411yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
prime radicalC22×C3×A4C23
hypercenterC3×C4⋊C4S4
hypocenterA4C3×#125
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
8. #85304C3direct (N × H)
205. C3×A4#125semidirect
384. C22×C3#889semidirect
387. A4C3×#125semidirect
485. C22C3×#889semidirect
503. C3#85304direct (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×C4⋊SL(2,ℤ/4)2
C3×SL(2,ℤ/4)⋊C42
C3×C4×SL(2,ℤ/4)2
#853043
C3×#24733
C3×#8894