Finite Group Databasebeta

← #11921968

Subgroups — #11921968

Order 1152.

736 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 75 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⋊S4)⋊C4C211yesmaximal, characteristic
2C4×Dic3×A4C211yesmaximal, characteristic, complemented
3#10593647C211yesmaximal, characteristic
4C3×SL(2,ℤ/4)⋊C4C211yesmaximal, characteristic, complemented
5#10593242C211yesmaximal, characteristic
6SL(2,ℤ/4)⋊Dic3C211yesmaximal, characteristic, complemented
7Dic3×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
8#85287—31nomaximal
9#74377—31nomaximal
10C22×C3⋊S4C2211yescharacteristic
11C2×C3×C4×A4C2211yescharacteristic
12C2×Dic3×A4C2211yescharacteristic
13C2×Dic3×A4C2211yescharacteristic
14C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
15C2×C3×SL(2,ℤ/4)C2211yescharacteristic
16C2×C3×SL(2,ℤ/4)C2211yescharacteristic
17(C3⋊S4)⋊C4C414yescomplemented
18#63836—41nomaximal
19C2×C4×S4—31no—
20C22×C4×Dic3D311yescharacteristic, complemented
21C2×#892—31no—
22C2×#67⋊C4—31no—
23C42×A4—31no—
24(C2×S4)⋊C4—31no—
25(C2×S4)⋊C4—31no—
26(C2×S4)⋊C4—61no—
27SL(2,ℤ/4)⋊C4—31no—
28SL(2,ℤ/4)⋊C4D311yescharacteristic, complemented
29C4×SL(2,ℤ/4)—31no—
30C3×#385—31no—
31#5213—31no—
32#4990—31no—
33#4978—31no—
34Dic3×C4⋊C4—31no—
35#4958—31no—
36#4950—31no—
37Dic3×C22⋊C4—31no—
38#4670—31no—
39#4666—31no—
40#4655—31no—
41#4648—31no—
42C22×C3×A4C2311yescharacteristic
43C2×C3⋊S4—21no—
44C2×C3⋊S4—21no—
45C2×C3⋊S4C2×C412yes—
46C3×C4×A4—21no—
47C2×#624—41no—
48Dic3×A4—21no—
49Dic3×A4C2×C412yes—
50C3⋊SL(2,ℤ/4)—21no—
51C3×SL(2,ℤ/4)—21no—
52C3×SL(2,ℤ/4)C2×C412yes—
53#3752—41no—
54C3×Dic3⋊C4—41no—
55C3×C4×Dic3—41no—
56Dic3⋊Dic3—41no—
57#3722—41no—
58Dic32—41no—
59#2290—91noSylow
60C22×S4—31no—
61C22×S4—61no—
62C23×C3×C4C2×D311yescharacteristic
63C22×#67—31no—
64C23×Dic3C2×D311yescharacteristic
65C23×Dic3C2×D311yescharacteristic
66C22×C4×D3—31no—
67C2×C4×A4—21no—
68C2×C4×A4—31no—
69C2×C4×A4—31no—
70C2×C4×A4C2×D311yescharacteristic
71C2×SL(2,ℤ/4)—31no—
72C2×SL(2,ℤ/4)—61no—
73C2×SL(2,ℤ/4)C2×D311yescharacteristic
74C2×SL(2,ℤ/4)C2×D311yescharacteristic
75C4×S4—34no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C22⋊C4—31no—
79C2×C3×C22⋊C4—31no—
80C2×#217—31no—
81C2×(C2×D3)⋊C4—31no—
82C2×(C2×D3)⋊C4—31no—
83C2×(C2×D3)⋊C4—31no—
84C2×(C2×D3)⋊C4—31no—
85C2×(C2×D3)⋊C4—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×Dic3⋊C4—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—31no—
96#892—61no—
97#892—61no—
98#892—61no—
99#892—61no—
100#67⋊C4—34no—
101#67⋊C4—34no—
102#872—121no—
103C3×#95—31no—
104C3×#95—31no—
105C3⋊#95—31no—
106C3⋊#95—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C22×C3⋊D3—41no—
114C2×C3×A4C22×C411yescharacteristic
115C2×C3×A4#4111yescharacteristic
116C2×C3×A4#4111yescharacteristic
117C3⋊S4—22no—
118C2×C32×C4—41no—
119C2×C3⋊Dic3—41no—
120C2×C3×Dic3—41no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—41no—
123C2×C3×Dic3—41no—
124#624—44no—
125C2×C4×D4—91no—
126C2×#117—91no—
127C22×C42—31no—
128#388—91no—
129#388—91no—
130#387—91no—
131#387—91no—
132#386—91no—
133#386—91no—
134#385—31no—
135#385—91no—
136C4×C4⋊C4—91no—
137C4×C22⋊C4—91no—
138C4×C22⋊C4—91no—
139#376—91no—
140C24×C3C22×D311yescharacteristic
141C23×D3—31no—
142C22×A4—21no—
143C22×A4C22×D311yescharacteristic
144C2×S4—32no—
145C2×S4—62no—
146C2×S4—61no—
147C2×S4—61no—
148C2×S4—121no—
149C2×S4—121no—
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—61no—
158C2×#67—32no—
159C2×#67—32no—
160C2×#67—61no—
161C2×#67—61no—
162C2×#67—61no—
163C2×#67—61no—
164C22×Dic3—21no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—31no—
168C22×Dic3—32no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—61no—
174C22×Dic3C4×D312yes—
175C2×C4×D3—34no—
176C2×C4×D3—61no—
177C2×C4×D3—62no—
178C2×C4×D3—61no—
179C2×C4×D3—121no—
180C4×A4—21no—
181C4×A4—32no—
182C4×A4—41no—
183C4×A4—61no—
184SL(2,ℤ/4)—21no—
185SL(2,ℤ/4)—61no—
186SL(2,ℤ/4)—121no—
187SL(2,ℤ/4)C4×D312yes—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—62no—
190C3×C4⋊C4—61no—
191C3×C22⋊C4—32no—
192C3×C22⋊C4—32no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C42—121no—
196#217—61no—
197#217—61no—
198(C2×D3)⋊C4—34no—
199(C2×D3)⋊C4—61no—
200(C2×D3)⋊C4—62no—
201(C2×D3)⋊C4—61no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—61no—
204(C2×D3)⋊C4—61no—
205(C2×D3)⋊C4—121no—
206(C2×D3)⋊C4—121no—
207(C2×D3)⋊C4—241no—
208C4⋊Dic3—61no—
209C4⋊Dic3—62no—
210C4⋊Dic3—61no—
211Dic3⋊C4—34no—
212Dic3⋊C4—41no—
213Dic3⋊C4—121no—
214C4×Dic3—34no—
215C4×Dic3—31no—
216C4×Dic3—31no—
217C4×Dic3—31no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—62no—
221C4×Dic3—61no—
222C4×Dic3—121no—
223C4×Dic3S411yescharacteristic, complemented
224C22×C32—41no—
225C2×C3⋊D3—42no—
226C2×C3⋊D3—81no—
227C2×C3⋊D3—81no—
228C3×A4#11711yescharacteristic, complemented
229C32×C4—81no—
230C3⋊Dic3—81no—
231C3×Dic3—42no—
232C3×Dic3—42no—
233C3×Dic3—81no—
234C3×Dic3—81no—
235C22×D4—91no—
236C23×C4—31no—
237C23×C4—31no—
238C23×C4—91no—
239C23×C4D3211yescharacteristic
240C4×D4—94no—
241C4×D4—94no—
242#117—181no—
243#117—181no—
244#117—181no—
245#117—181no—
246C2×C4⋊C4—31no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C22⋊C4—31no—
252C2×C22⋊C4—31no—
253C2×C22⋊C4—91no—
254C2×C22⋊C4—91no—
255C2×C22⋊C4—91no—
256C2×C22⋊C4—91no—
257C2×C22⋊C4—91no—
258C2×C22⋊C4—91no—
259C2×C42—91no—
260C2×C42—91no—
261C2×C42—91no—
262C2×C42—91no—
263C2×C42—91no—
264C2×C42—91no—
265C2×C42—91no—
266#95—31no—
267#95—31no—
268#95—91no—
269#95—91no—
270#95—91no—
271#95—91no—
272#95—91no—
273#95—91no—
274#95—91no—
275#95—91no—
276C23×C3—31no—
277C23×C3—31no—
278C23×C3—31no—
279C23×C3—31no—
280C23×C3C2×C4×D311yescharacteristic
281C23×C3#23511yescharacteristic
282C23×C3#23511yescharacteristic
283C22×D3—32no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—61no—
288C22×D3—61no—
289C22×D3—61no—
290C22×D3—121no—
291C22×D3—241no—
292C2×A4—21no—
293C2×A4—21no—
294C2×A4—21no—
295C2×A4C2×C4×D311yescharacteristic
296C2×A4#23711yescharacteristic
297C2×A4#23911yescharacteristic
298S4—62no—
299S4—122no—
300C2×C3×C4—32no—
301C2×C3×C4—32no—
302C2×C3×C4—32no—
303C2×C3×C4—31no—
304C2×C3×C4—41no—
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—81no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4C2×S411yescharacteristic
322#67—62no—
323#67—62no—
324#67—62no—
325#67—62no—
326C2×Dic3—31no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—31no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—61no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—241no—
349C2×Dic3C2×S411yescharacteristic
350C2×Dic3C2×S411yescharacteristic
351C4×D3—64no—
352C4×D3—64no—
353C4×D3—124no—
354C2×C32—41no—
355C2×C32—41no—
356C2×C32—41no—
357C3⋊D3—82no—
358C24—91no—
359C24C2×D3211yescharacteristic
360C2×D4—92no—
361C2×D4—92no—
362C2×D4—181no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—181no—
366C22×C4—21no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—31no—
373C22×C4—32no—
374C22×C4—61no—
375C22×C4—61no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4—94no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4—92no—
382C22×C4—91no—
383C22×C4—91no—
384C22×C4—91no—
385C22×C4—181no—
386C22×C4—181no—
387C22×C4—182no—
388C22×C4—181no—
389C4⋊C4—61no—
390C4⋊C4—62no—
391C4⋊C4—61no—
392C4⋊C4—94no—
393C4⋊C4—181no—
394C4⋊C4—181no—
395C4⋊C4—182no—
396C22⋊C4—32no—
397C22⋊C4—32no—
398C22⋊C4—61no—
399C22⋊C4—61no—
400C22⋊C4—94no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C22⋊C4—182no—
404C22⋊C4—181no—
405C22⋊C4—182no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C42—31no—
410C42—91no—
411C42—91no—
412C42—94no—
413C42—91no—
414C42—181no—
415C42—181no—
416C42—181no—
417C42—182no—
418C22×C3—31no—
419C22×C3—31no—
420C22×C3—31no—
421C22×C3—31no—
422C22×C3—31no—
423C22×C3—31no—
424C22×C3—31no—
425C22×C3—31no—
426C22×C3—31no—
427C22×C3—41no—
428C22×C3—61no—
429C22×C3—81no—
430C22×C3#87211yescharacteristic, complemented
431C22×C3C22×S411yescharacteristic
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—122no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—242no—
441C2×D3—241no—
442C2×D3—241no—
443C2×D3—481no—
444C2×D3—481no—
445A4—21no—
446A4#89211yescharacteristic, complemented
447C3×C4—21no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—61no—
451C3×C4—81no—
452C3×C4—122no—
453C3×C4—121no—
454C3×C4—121no—
455C3×C4—161no—
456C3×C4—241no—
457Dic3—21no—
458Dic3—32no—
459Dic3—42no—
460Dic3—62no—
461Dic3—61no—
462Dic3—81no—
463Dic3—121no—
464Dic3—121no—
465Dic3—241no—
466Dic3—481no—
467Dic3C4×S412yes—
468C32—41noSylow
469C23—31no—
470C23—31no—
471C23—31no—
472C23—31no—
473C23—92no—
474C23—181no—
475C23—181no—
476C23—181no—
477C23—181no—
478C23—181no—
479C23—181no—
480C23#379911yescharacteristic
481C23C4×D3211yescharacteristic
482C23#380411yescharacteristic
483D4—182no—
484D4—182no—
485D4—182no—
486D4—182no—
487C2×C4—31no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—31no—
492C2×C4—31no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—61no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—61no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—92no—
507C2×C4—92no—
508C2×C4—91no—
509C2×C4—92no—
510C2×C4—92no—
511C2×C4—92no—
512C2×C4—91no—
513C2×C4—184no—
514C2×C4—184no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—181no—
519C2×C4—181no—
520C2×C4—181no—
521C2×C4—181no—
522C2×C4—181no—
523C2×C4—181no—
524C2×C4—181no—
525C2×C4—181no—
526C2×C4—181no—
527C2×C4D3×S411yescharacteristic
528C2×C3—31no—
529C2×C3—31no—
530C2×C3—31no—
531C2×C3—31no—
532C2×C3—41no—
533C2×C3—41no—
534C2×C3—41no—
535C2×C3—81no—
536C2×C3—81no—
537C2×C3—81no—
538C2×C3C2×C4×S411yescharacteristic
539C2×C3#591211yescharacteristic
540C2×C3#591211yescharacteristic
541D3—122no—
542D3—242no—
543D3—482no—
544C22—31no—
545C22—31no—
546C22—31no—
547C22—31no—
548C22—31no—
549C22—31no—
550C22—31no—
551C22—31no—
552C22—31no—
553C22—61no—
554C22—182no—
555C22—182no—
556C22—182no—
557C22—361no—
558C22—361no—
559C22—361no—
560C22—361no—
561C22#6383611yescharacteristic, complemented
562C22C2×D3×S411yescharacteristic
563C4—21no—
564C4—32no—
565C4—62no—
566C4—61no—
567C4—62no—
568C4—61no—
569C4—92no—
570C4—121no—
571C4—121no—
572C4—182no—
573C4—181no—
574C4—361no—
575C4—361no—
576C3—41no—
577C3—81no—
578C3#8528711yescharacteristic, complemented
579C2—31no—
580C2—31no—
581C2—31no—
582C2—31no—
583C2—362no—
584C2#1059642811yescharacteristic
585C2C4×D3×S411yescharacteristic
586C2#1059646311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC22×C3⋊S4C22
cosocleC22×C3×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4#117
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C4×Dic3×A4C2semidirect
4. C3×SL(2,ℤ/4)⋊C4C2semidirect
6. SL(2,ℤ/4)⋊Dic3C2semidirect
7. Dic3×SL(2,ℤ/4)C2semidirect
17. (C3⋊S4)⋊C4C4semidirect
20. C22×C4×Dic3D3semidirect
28. SL(2,ℤ/4)⋊C4D3semidirect
223. C4×Dic3S4semidirect
228. C3×A4#117semidirect
430. C22×C3#872semidirect
446. A4#892semidirect
561. C22#63836semidirect
578. C3#85287semidirect

Maximal subgroups

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

subgroupindex
C2×(C3⋊S4)⋊C42
C4×Dic3×A42
#105936472
C3×SL(2,ℤ/4)⋊C42
#105932422
SL(2,ℤ/4)⋊Dic32
Dic3×SL(2,ℤ/4)2
#852873
#743773
#638364