Finite Group Databasebeta

← #11921918

Subgroups — #11921918

Order 1152.

582 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C4×Dic3×A4C211yesmaximal, characteristic, complemented
2#10593645C211yesmaximal, characteristic, complemented
3C3×(C2×S4)⋊C4C211yesmaximal, characteristic
4(C2×S4)⋊Dic3C211yesmaximal, characteristic
5(C2×S4)⋊Dic3C211yesmaximal, characteristic
6SL(2,ℤ/4)⋊Dic3C211yesmaximal, characteristic, complemented
7#10593238C211yesmaximal, characteristic, complemented
8#85291—31nomaximal
9#74870—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#63859—41nomaximal
18C22×C4×Dic3D311yescharacteristic, complemented
19C2×#879—31no—
20C42×A4—31no—
21(C2×S4)⋊C4—31no—
22(C2×S4)⋊C4—31no—
23(C2×S4)⋊C4D311yescharacteristic
24SL(2,ℤ/4)⋊C4—31no—
25SL(2,ℤ/4)⋊C4—31no—
26SL(2,ℤ/4)⋊C4—31no—
27SL(2,ℤ/4)⋊C4—61no—
28C3×#386—31no—
29#5220—31no—
30#5220—31no—
31#5210—31no—
32#4951—31no—
33#4950—31no—
34#4946—31no—
35#4945—31no—
36#4944—31no—
37#4655—31no—
38#4653—31no—
39#4652—31no—
40#4651—31no—
41C22×C3×A4C2311yescharacteristic
42C2×C3×S4—21no—
43C2×C3×S4—21no—
44C2×C3×S4—21no—
45C3×C4×A4—21no—
46Dic3×A4—21no—
47Dic3×A4—21no—
48C3⋊SL(2,ℤ/4)—21no—
49C3⋊SL(2,ℤ/4)—21no—
50C3×SL(2,ℤ/4)—21no—
51#3750—41no—
52C3×(C2×D3)⋊C4—41no—
53C3×C4×Dic3—41no—
54#3724—41no—
55Dic3⋊Dic3—41no—
56(C2×D3)⋊Dic3—41no—
57(C2×D3)⋊Dic3—41no—
58#2852—91noSylow
59C22×S4C2×D311yescharacteristic
60C22×C3×D4—31no—
61C23×C3×C4C2×D311yescharacteristic
62C23×Dic3C2×D311yescharacteristic
63C23×Dic3C2×D311yescharacteristic
64C2×C4×A4—21no—
65C2×C4×A4—31no—
66C2×C4×A4—31no—
67C2×C4×A4C2×D311yescharacteristic
68C2×SL(2,ℤ/4)—31no—
69C2×SL(2,ℤ/4)—31no—
70C2×SL(2,ℤ/4)—61no—
71C2×SL(2,ℤ/4)—61no—
72C2×SL(2,ℤ/4)C2×D311yescharacteristic
73C2×C3×C22⋊C4—31no—
74C2×C3×C22⋊C4—31no—
75C2×C3×C22⋊C4—31no—
76C2×#217—31no—
77C2×#217—31no—
78C2×#217—31no—
79C2×#217—31no—
80C2×#217—31no—
81C2×#217—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×Dic3⋊C4—31no—
85C2×Dic3⋊C4—31no—
86C2×Dic3⋊C4—31no—
87C2×Dic3⋊C4—31no—
88C2×C4×Dic3—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92#879—61no—
93#879—61no—
94#879—61no—
95#879—61no—
96#876—121no—
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×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—41no—
120C2×#126—91no—
121C22×C42—31no—
122#388—91no—
123#388—91no—
124#388—91no—
125#387—91no—
126#387—91no—
127#387—91no—
128#386—31no—
129#386—91no—
130#386—91no—
131#385—91no—
132#385—91no—
133#385—91no—
134#383—91no—
135C24×C3—31no—
136C24×C3C22×D311yescharacteristic
137C22×A4—21no—
138C22×A4C22×D311yescharacteristic
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—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—61no—
155C22×Dic3—21no—
156C22×Dic3—21no—
157C22×Dic3—31no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—31no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C4×A4—21no—
168C4×A4—41no—
169C4×A4—61no—
170C4×A4—61no—
171SL(2,ℤ/4)—21no—
172SL(2,ℤ/4)—62no—
173SL(2,ℤ/4)—61no—
174SL(2,ℤ/4)—61no—
175SL(2,ℤ/4)—121no—
176C3×C22⋊C4—61no—
177C3×C22⋊C4—62no—
178C3×C22⋊C4—61no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C42—121no—
182#217—61no—
183#217—61no—
184#217—62no—
185#217—62no—
186#217—61no—
187#217—61no—
188#217—61no—
189#217—61no—
190#217—61no—
191#217—61no—
192(C2×D3)⋊C4—41no—
193(C2×D3)⋊C4—121no—
194(C2×D3)⋊C4—121no—
195C4⋊Dic3—61no—
196C4⋊Dic3—62no—
197C4⋊Dic3—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—62no—
200Dic3⋊C4—61no—
201Dic3⋊C4—62no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—121no—
205Dic3⋊C4—121no—
206Dic3⋊C4—121no—
207Dic3⋊C4—241no—
208C4×Dic3—31no—
209C4×Dic3—31no—
210C4×Dic3—31no—
211C4×Dic3—61no—
212C4×Dic3S411yescharacteristic, complemented
213C22×C32—41no—
214C2×C3×D3—81no—
215C2×C3×D3—81no—
216C2×C3×D3—81no—
217C3×A4#12611yescharacteristic, complemented
218C32×C4—81no—
219C3⋊Dic3—81no—
220C3⋊Dic3—81no—
221C3×Dic3—81no—
222C3×Dic3—81no—
223C3×Dic3—81no—
224C22×D4—31no—
225C23×C4—31no—
226C23×C4—31no—
227C23×C4D3211yescharacteristic
228#126—181no—
229#126—181no—
230#126—181no—
231#126—181no—
232C2×C4⋊C4—91no—
233C2×C4⋊C4—91no—
234C2×C4⋊C4—91no—
235C2×C4⋊C4—91no—
236C2×C4⋊C4—91no—
237C2×C4⋊C4—91no—
238C2×C22⋊C4—31no—
239C2×C22⋊C4—31no—
240C2×C22⋊C4—31no—
241C2×C22⋊C4—91no—
242C2×C22⋊C4—91no—
243C2×C22⋊C4—91no—
244C2×C22⋊C4—91no—
245C2×C22⋊C4—91no—
246C2×C22⋊C4—91no—
247C2×C42—91no—
248C2×C42—91no—
249C2×C42—91no—
250C2×C42—91no—
251#95—31no—
252#95—31no—
253#95—91no—
254#95—91no—
255#95—91no—
256#95—91no—
257#95—91no—
258#95—91no—
259#95—91no—
260#95—91no—
261#95—91no—
262#95—91no—
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#23511yescharacteristic
276C23×C3#23511yescharacteristic
277C22×D3—41no—
278C2×A4—21no—
279C2×A4—21no—
280C2×A4—21no—
281C2×A4#23511yescharacteristic
282C2×A4#23711yescharacteristic
283C2×A4#23711yescharacteristic
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—41no—
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—81no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4C2×S411yescharacteristic
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—31no—
311C2×Dic3—31no—
312C2×Dic3—41no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—241no—
334C2×Dic3—241no—
335C2×Dic3C2×S411yescharacteristic
336C2×Dic3C2×S411yescharacteristic
337C2×C32—41no—
338C2×C32—41no—
339C2×C32—41no—
340C3×D3—161no—
341C24—31no—
342C24C2×D3211yescharacteristic
343C2×D4—61no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C22×C4—21no—
350C22×C4—31no—
351C22×C4—31no—
352C22×C4—31no—
353C22×C4—31no—
354C22×C4—31no—
355C22×C4—61no—
356C22×C4—61no—
357C22×C4—61no—
358C22×C4—91no—
359C22×C4—91no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—91no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—91no—
366C22×C4—181no—
367C22×C4—181no—
368C4⋊C4—181no—
369C4⋊C4—181no—
370C4⋊C4—181no—
371C4⋊C4—182no—
372C4⋊C4—181no—
373C4⋊C4—181no—
374C4⋊C4—182no—
375C4⋊C4—182no—
376C4⋊C4—181no—
377C22⋊C4—61no—
378C22⋊C4—62no—
379C22⋊C4—61no—
380C22⋊C4—61no—
381C22⋊C4—61no—
382C22⋊C4—181no—
383C22⋊C4—181no—
384C22⋊C4—181no—
385C22⋊C4—181no—
386C22⋊C4—182no—
387C22⋊C4—182no—
388C22⋊C4—181no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C42—31no—
393C42—91no—
394C42—91no—
395C42—91no—
396C42—181no—
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#87611yescharacteristic, complemented
417C22×C3C22×S411yescharacteristic
418C2×D3—81no—
419C2×D3—81no—
420C2×D3—81no—
421A4—21no—
422A4#87911yescharacteristic, complemented
423C3×C4—21no—
424C3×C4—61no—
425C3×C4—81no—
426C3×C4—121no—
427C3×C4—121no—
428C3×C4—121no—
429C3×C4—161no—
430C3×C4—241no—
431C3×C4—241no—
432Dic3—21no—
433Dic3—21no—
434Dic3—61no—
435Dic3—61no—
436Dic3—81no—
437Dic3—121no—
438Dic3—121no—
439Dic3—121no—
440Dic3—121no—
441Dic3—241no—
442Dic3—241no—
443Dic3—242no—
444Dic3—481no—
445C32—41noSylow
446C23—31no—
447C23—31no—
448C23—31no—
449C23—31no—
450C23—61no—
451C23—61no—
452C23—61no—
453C23—61no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23#379511yescharacteristic
458C23#379811yescharacteristic
459C23#380411yescharacteristic
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—92no—
481C2×C4—92no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4D3×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#591211yescharacteristic
516C2×C3#591211yescharacteristic
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—
535C22#6385911yescharacteristic, complemented
536C22C2×D3×S411yescharacteristic
537C4—21no—
538C4—61no—
539C4—61no—
540C4—61no—
541C4—121no—
542C4—121no—
543C4—121no—
544C4—181no—
545C4—181no—
546C4—361no—
547C4—361no—
548C4—361no—
549C4—361no—
550C3—41no—
551C3—81no—
552C3#8529111yescharacteristic, complemented
553C2—31no—
554C2—31no—
555C2—31no—
556C2—31no—
557C2—241no—
558C2#1059642611yescharacteristic
559C2#1059642711yescharacteristic
560C2#1059646311yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, cosocleC22×C3×A4C23
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
prime radicalC22×C3×S4C22
hypercenterC2×C4D3×S4
hypocenterC3×A4#126
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C4×Dic3×A4C2semidirect
2. #10593645C2semidirect
6. SL(2,ℤ/4)⋊Dic3C2semidirect
7. #10593238C2semidirect
18. C22×C4×Dic3D3semidirect
212. C4×Dic3S4semidirect
217. C3×A4#126semidirect
416. C22×C3#876semidirect
422. A4#879semidirect
535. C22#63859semidirect
552. C3#85291semidirect

Maximal subgroups

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

subgroupindex
C4×Dic3×A42
#105936452
C3×(C2×S4)⋊C42
(C2×S4)⋊Dic32
SL(2,ℤ/4)⋊Dic32
#105932382
#852913
#748703
#638594