Finite Group Databasebeta

← C3×#85491 #11922777

Subgroups — C3×#85491 #11922777

Order 1152.

908 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×C3×D4×A4C211yesmaximal, characteristic
2C22×C3×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
3C3×#5432C211yesmaximal, characteristic, complemented
4C3×#5432C212yesmaximal, complemented
5C3×SL(2,ℤ/4)⋊C4C212yesmaximal, complemented
6#85491C311yesmaximal, characteristic, direct product factor
7C3×#2405—31nomaximal
8C23×C3×A4C2211yescharacteristic
9C23×C3×A4C2211yescharacteristic
10C3×D4×A4—22no—
11C2×C3×C4×A4C2211yescharacteristic
12C2×C3×SL(2,ℤ/4)—22no—
13C2×C3×SL(2,ℤ/4)C2212yes—
14C2×C3×SL(2,ℤ/4)C2212yes—
15C3×#935—41nomaximal
16C23×C3×D4D311yescharacteristic
17C2×D4×A4—21no—
18C2×D4×A4C2×C311yescharacteristic
19C22×SL(2,ℤ/4)C2×C311yescharacteristic, complemented
20C2×C3×#123—31no—
21C2×C3×#123—31no—
22C22×C3×C22⋊C4—31no—
23#5432C2×C312yescomplemented
24#5432C2×C311yescharacteristic, complemented
25SL(2,ℤ/4)⋊C4C2×C312yescomplemented
26C3×#394—32no—
27C3×#394—32no—
28C3×#386—31no—
29C3×#386—31no—
30C3×#385—32no—
31C3×#379—32no—
32C3×#379—31no—
33C22×C3×A4—22no—
34C22×C3×A4—21no—
35C22×C3×A4—22no—
36C22×C3×A4D412yes—
37C22×C3×A4C2311yescharacteristic
38C2×C32×D4—41no—
39C22×C3×Dic3—41no—
40C3×C4×A4—21no—
41C3×SL(2,ℤ/4)—22no—
42C3×SL(2,ℤ/4)—22no—
43C3×#217—41no—
44C3×#217—42no—
45C3×Dic3⋊C4—42no—
46#2405—31noSylow
47C25×C3C2×D311yescharacteristic
48C25×C3C2×D311yescharacteristic
49C23×A4—21no—
50C23×A4—21no—
51C23×A4C22×C311yescharacteristic
52C23×A4C22×C311yescharacteristic
53C22×C3×D4—22no—
54C22×C3×D4—31no—
55C22×C3×D4—31no—
56C22×C3×D4—31no—
57C22×C3×D4—31no—
58C22×C3×D4—62no—
59C23×C3×C4—31no—
60C23×C3×C4—31no—
61C23×C3×C4C2×D311yescharacteristic
62D4×A4—24no—
63D4×A4—22no—
64C2×C4×A4—21no—
65C2×C4×A4C22×C311yescharacteristic
66C2×SL(2,ℤ/4)—22no—
67C2×SL(2,ℤ/4)C22×C312yes—
68C2×SL(2,ℤ/4)C22×C312yes—
69C3×#123—64no—
70C3×#123—61no—
71C3×#123—61no—
72C3×#123—61no—
73C3×#123—61no—
74C2×C3×C4⋊C4—32no—
75C2×C3×C4⋊C4—32no—
76C2×C3×C22⋊C4—31no—
77C2×C3×C22⋊C4—31no—
78C2×C3×C22⋊C4—32no—
79C2×C3×C22⋊C4—32no—
80C2×C3×C22⋊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—62no—
87C2×C3×C22⋊C4—62no—
88#935—41no—
89C3×#95—32no—
90C3×#95—32no—
91C23×C32—41no—
92C23×C32—41no—
93C2×C3×A4—22no—
94C2×C3×A4—41no—
95C2×C3×A4C2×D411yescharacteristic
96C2×C3×A4#4112yes—
97C32×D4—82no—
98C2×C32×C4—41no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—82no—
102C23×D4C3×D311yescharacteristic
103C2×#123—31no—
104C2×#123—31no—
105C22×C22⋊C4—31no—
106#394—32no—
107#394—32no—
108#386—31no—
109#386—31no—
110#385—32no—
111#379—31no—
112#379—32no—
113C24×C3—22no—
114C24×C3—22no—
115C24×C3—21no—
116C24×C3—31no—
117C24×C3—31no—
118C24×C3—31no—
119C24×C3—32no—
120C24×C3—31no—
121C24×C3—61no—
122C24×C3—62no—
123C24×C3—62no—
124C24×C3#6712yes—
125C24×C3C22×D311yescharacteristic
126C22×A4—22no—
127C22×A4—22no—
128C22×A4—21no—
129C22×A4—22no—
130C22×A4—22no—
131C22×A4—21no—
132C22×A4—42no—
133C22×A4—42no—
134C22×A4C3×D412yes—
135C22×A4C23×C311yescharacteristic
136C2×C3×D4—34no—
137C2×C3×D4—31no—
138C2×C3×D4—31no—
139C2×C3×D4—31no—
140C2×C3×D4—41no—
141C2×C3×D4—61no—
142C2×C3×D4—62no—
143C2×C3×D4—62no—
144C2×C3×D4—62no—
145C2×C3×D4—62no—
146C2×C3×D4—62no—
147C2×C3×D4—62no—
148C2×C3×D4—62no—
149C2×C3×D4—81no—
150C2×C3×D4S411yescharacteristic
151C22×C3×C4—21no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—32no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—32no—
158C22×C3×C4—61no—
159C22×C3×C4—62no—
160C22×C3×C4—62no—
161C22×C3×C4—62no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4—122no—
165C22×Dic3—41no—
166C4×A4—22no—
167C4×A4—21no—
168SL(2,ℤ/4)—22no—
169SL(2,ℤ/4)—22no—
170C3×C4⋊C4—64no—
171C3×C4⋊C4—62no—
172C3×C4⋊C4—62no—
173C3×C22⋊C4—62no—
174C3×C22⋊C4—62no—
175C3×C22⋊C4—64no—
176C3×C22⋊C4—62no—
177C3×C22⋊C4—64no—
178C3×C22⋊C4—61no—
179C3×C22⋊C4—62no—
180C3×C22⋊C4—62no—
181C3×C22⋊C4—62no—
182C3×C22⋊C4—61no—
183C3×C22⋊C4—62no—
184C3×C22⋊C4—122no—
185C3×C22⋊C4—122no—
186C3×C22⋊C4—122no—
187#217—41no—
188#217—42no—
189Dic3⋊C4—42no—
190C22×C32—42no—
191C22×C32—41no—
192C22×C32—81no—
193C22×C32—82no—
194C22×C32—82no—
195C3×A4#12311yescharacteristic, complemented
196C32×C4—81no—
197C3×Dic3—82no—
198C3×Dic3—82no—
199C25C2×C3×D311yescharacteristic
200C25C2×C3×D311yescharacteristic
201C22×D4—22no—
202C22×D4—31no—
203C22×D4—31no—
204C22×D4—31no—
205C22×D4—31no—
206C22×D4—62no—
207C23×C4—31no—
208C23×C4—31no—
209C23×C4C2×C3×D311yescharacteristic
210#123—64no—
211#123—61no—
212#123—61no—
213#123—61no—
214#123—61no—
215C2×C4⋊C4—32no—
216C2×C4⋊C4—32no—
217C2×C22⋊C4—32no—
218C2×C22⋊C4—31no—
219C2×C22⋊C4—31no—
220C2×C22⋊C4—32no—
221C2×C22⋊C4—32no—
222C2×C22⋊C4—32no—
223C2×C22⋊C4—32no—
224C2×C22⋊C4—32no—
225C2×C22⋊C4—32no—
226C2×C22⋊C4—32no—
227C2×C22⋊C4—62no—
228C2×C22⋊C4—62no—
229#95—32no—
230#95—32no—
231C23×C3—22no—
232C23×C3—31no—
233C23×C3—31no—
234C23×C3—32no—
235C23×C3—32no—
236C23×C3—32no—
237C23×C3—32no—
238C23×C3—31no—
239C23×C3—32no—
240C23×C3—31no—
241C23×C3—41no—
242C23×C3—41no—
243C23×C3—41no—
244C23×C3—62no—
245C23×C3—62no—
246C23×C3—62no—
247C23×C3—61no—
248C23×C3—61no—
249C23×C3—62no—
250C23×C3—61no—
251C23×C3—62no—
252C23×C3—62no—
253C23×C3—62no—
254C23×C3—64no—
255C23×C3—62no—
256C23×C3—62no—
257C23×C3—61no—
258C23×C3—81no—
259C23×C3—81no—
260C23×C3—122no—
261C23×C3—121no—
262C23×C3—122no—
263C23×C3—122no—
264C23×C3#23712yes—
265C23×C3C2×#6711yescharacteristic
266C23×C3C2×S411yescharacteristic
267C23×C3C2×S411yescharacteristic
268C2×A4—22no—
269C2×A4—22no—
270C2×A4—21no—
271C2×A4—42no—
272C2×A4—42no—
273C2×A4—41no—
274C2×A4C2×C3×D411yescharacteristic
275C2×A4C3×#4112yes—
276C3×D4—22no—
277C3×D4—62no—
278C3×D4—62no—
279C3×D4—64no—
280C3×D4—62no—
281C3×D4—82no—
282C3×D4—84no—
283C2×C3×C4—32no—
284C2×C3×C4—31no—
285C2×C3×C4—41no—
286C2×C3×C4—61no—
287C2×C3×C4—61no—
288C2×C3×C4—61no—
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—62no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—81no—
302C2×C3×C4—122no—
303C2×C3×C4—124no—
304C2×C3×C4—122no—
305C2×C3×C4C2×S411yescharacteristic
306C2×Dic3—42no—
307C2×Dic3—42no—
308C2×Dic3—82no—
309C2×C32—42no—
310C2×C32—41no—
311C2×C32—82no—
312C2×C32—161no—
313C24—22no—
314C24—22no—
315C24—21no—
316C24—31no—
317C24—31no—
318C24—31no—
319C24—32no—
320C24—31no—
321C24—61no—
322C24—62no—
323C24—62no—
324C24C3×#6712yes—
325C24C22×C3×D311yescharacteristic
326C2×D4—34no—
327C2×D4—31no—
328C2×D4—31no—
329C2×D4—31no—
330C2×D4—61no—
331C2×D4—62no—
332C2×D4—62no—
333C2×D4—62no—
334C2×D4—62no—
335C2×D4—62no—
336C2×D4—62no—
337C2×D4—62no—
338C2×D4C3×S411yescharacteristic
339C22×C4—21no—
340C22×C4—31no—
341C22×C4—31no—
342C22×C4—32no—
343C22×C4—32no—
344C22×C4—32no—
345C22×C4—32no—
346C22×C4—61no—
347C22×C4—62no—
348C22×C4—62no—
349C22×C4—62no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—122no—
353C4⋊C4—64no—
354C4⋊C4—62no—
355C4⋊C4—62no—
356C22⋊C4—62no—
357C22⋊C4—64no—
358C22⋊C4—62no—
359C22⋊C4—64no—
360C22⋊C4—61no—
361C22⋊C4—62no—
362C22⋊C4—62no—
363C22⋊C4—61no—
364C22⋊C4—62no—
365C22⋊C4—62no—
366C22⋊C4—62no—
367C22⋊C4—122no—
368C22⋊C4—122no—
369C22⋊C4—122no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—21no—
373C22×C3—32no—
374C22×C3—31no—
375C22×C3—32no—
376C22×C3—32no—
377C22×C3—31no—
378C22×C3—31no—
379C22×C3—32no—
380C22×C3—42no—
381C22×C3—41no—
382C22×C3—62no—
383C22×C3—62no—
384C22×C3—64no—
385C22×C3—61no—
386C22×C3—62no—
387C22×C3—62no—
388C22×C3—64no—
389C22×C3—62no—
390C22×C3—62no—
391C22×C3—61no—
392C22×C3—82no—
393C22×C3—81no—
394C22×C3—82no—
395C22×C3—82no—
396C22×C3—82no—
397C22×C3—81no—
398C22×C3—121no—
399C22×C3—121no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—121no—
403C22×C3—121no—
404C22×C3—162no—
405C22×C3—162no—
406C22×C3#93511yescharacteristic, complemented
407C22×C3GL(2,ℤ/4)12yes—
408C22×C3C22×S411yescharacteristic
409A4—21no—
410A4C3×#12311yescharacteristic, complemented
411C3×C4—21no—
412C3×C4—61no—
413C3×C4—81no—
414C3×C4—82no—
415C3×C4—122no—
416C3×C4—122no—
417C3×C4—122no—
418C3×C4—122no—
419Dic3—82no—
420Dic3—82no—
421C32—41noSylow
422C23—22no—
423C23—31no—
424C23—31no—
425C23—32no—
426C23—32no—
427C23—32no—
428C23—32no—
429C23—31no—
430C23—32no—
431C23—31no—
432C23—41no—
433C23—62no—
434C23—62no—
435C23—62no—
436C23—61no—
437C23—61no—
438C23—62no—
439C23—61no—
440C23—62no—
441C23—62no—
442C23—62no—
443C23—64no—
444C23—62no—
445C23—62no—
446C23—61no—
447C23—122no—
448C23—121no—
449C23—122no—
450C23—122no—
451C23C3×#23712yes—
452C23C2×C3×#6711yescharacteristic
453C23C2×C3×S411yescharacteristic
454C23C2×C3×S411yescharacteristic
455D4—22no—
456D4—62no—
457D4—62no—
458D4—64no—
459D4—62no—
460C2×C4—32no—
461C2×C4—31no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—62no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—122no—
478C2×C4—124no—
479C2×C4—122no—
480C2×C4C2×C3×S411yescharacteristic
481C2×C3—22no—
482C2×C3—31no—
483C2×C3—32no—
484C2×C3—31no—
485C2×C3—41no—
486C2×C3—42no—
487C2×C3—41no—
488C2×C3—62no—
489C2×C3—82no—
490C2×C3—82no—
491C2×C3—81no—
492C2×C3—121no—
493C2×C3—162no—
494C2×C3—161no—
495C2×C3—162no—
496C2×C3#591412yes—
497C2×C3C2×GL(2,ℤ/4)11yescharacteristic
498C22—22no—
499C22—22no—
500C22—21no—
501C22—32no—
502C22—31no—
503C22—32no—
504C22—32no—
505C22—31no—
506C22—31no—
507C22—32no—
508C22—62no—
509C22—62no—
510C22—64no—
511C22—61no—
512C22—62no—
513C22—62no—
514C22—64no—
515C22—62no—
516C22—62no—
517C22—61no—
518C22—121no—
519C22—121no—
520C22—122no—
521C22—122no—
522C22—121no—
523C22—121no—
524C22C3×#93511yescharacteristic, complemented
525C22C3×GL(2,ℤ/4)12yes—
526C22C22×C3×S411yescharacteristic
527C4—21no—
528C4—61no—
529C4—122no—
530C4—122no—
531C4—122no—
532C4—122no—
533C3—41no—
534C3—81no—
535C3#8549111yescharacteristic, direct product factor
536C2—22no—
537C2—31no—
538C2—32no—
539C2—31no—
540C2—41no—
541C2—62no—
542C2—121no—
543C2C3×#591412yes—
544C2C2×C3×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC22×C3C22×S4
commutator, cosocleC22×A4C23×C3
FrattiniC22C22×C3×S4
FittingC23×C3×D4D3
socleC24×C3C22×D3
prime radicalC2×C3×D4×A4C2
hypercenterC2×C3×D4S4
hypocenterA4C3×#123
LCSG ▷ C22×A4 ▷ A4
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×SL(2,ℤ/4)C2semidirect
3. C3×#5432C2semidirect
4. C3×#5432C2semidirect
5. C3×SL(2,ℤ/4)⋊C4C2semidirect
6. #85491C3direct (N × H)
19. C22×SL(2,ℤ/4)C2×C3semidirect
23. #5432C2×C3semidirect
24. #5432C2×C3semidirect
25. SL(2,ℤ/4)⋊C4C2×C3semidirect
195. C3×A4#123semidirect
406. C22×C3#935semidirect
410. A4C3×#123semidirect
524. C22C3×#935semidirect
535. C3#85491direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C22×C3×SL(2,ℤ/4)2
C3×#54322
C3×SL(2,ℤ/4)⋊C42
#854913
C3×#24053
C3×#9354