Finite Group Databasebeta

← #11922844

Subgroups — #11922844

Order 1152.

702 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 83 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×C22⋊C4C211yesmaximal, characteristic
2#10593666C211yesmaximal, characteristic
3#10593666C211yesmaximal, characteristic
4C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic, complemented
5#10593645C211yesmaximal, characteristic, complemented
6#10593645C211yesmaximal, characteristic, complemented
7C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
8#85294—33nomaximal
9#82112—31nomaximal
10C23×C3×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
17#64088—41nomaximal
18C22×C3×C22⋊C4D311yescharacteristic
19C2×#879—31no—
20A4×C22⋊C4D313yes—
21#5432—33no—
22#5432—33no—
23C4⋊SL(2,ℤ/4)—33no—
24SL(2,ℤ/4)⋊C4—33no—
25SL(2,ℤ/4)⋊C4—33no—
26C4×SL(2,ℤ/4)—33no—
27#5247—31no—
28#5247—31no—
29#5212—31no—
30#5210—31no—
31#5210—31no—
32C4×#217—31no—
33#4953—31no—
34#4952—31no—
35#4952—31no—
36#4951—31no—
37#4948—31no—
38#4945—31no—
39#4944—31no—
40C22×C3×A4—21no—
41C22×C3×A4—21no—
42C22×C3×A4—21no—
43C22×C3×A4C2311yescharacteristic
44C3×C4×A4—21no—
45C3×C4×A4—21no—
46C3⋊SL(2,ℤ/4)—21no—
47C3⋊SL(2,ℤ/4)—21no—
48C3⋊SL(2,ℤ/4)—21no—
49C3⋊SL(2,ℤ/4)—21no—
50C32×C22⋊C4—41no—
51#3757—41no—
52#3757—41no—
53C4⋊(C3⋊Dic3)—41no—
54#3750—41no—
55#3750—41no—
56C4×C3⋊Dic3—41no—
57#2480—91noSylow
58C25×C3C2×D311yescharacteristic
59C23×A4C2×D313yes—
60C23×C3×C4C2×D311yescharacteristic
61C23×C3×C4C2×D311yescharacteristic
62C2×C4×A4C2×D313yes—
63C2×C4×A4C2×D313yes—
64C2×SL(2,ℤ/4)—33no—
65C2×SL(2,ℤ/4)—33no—
66C2×SL(2,ℤ/4)—33no—
67C2×SL(2,ℤ/4)—33no—
68C2×C3×C22⋊C4—31no—
69C2×C3×C22⋊C4—31no—
70C2×C3×C22⋊C4—31no—
71C2×C3×C22⋊C4—31no—
72C2×#217—31no—
73C2×#217—31no—
74C2×#217—31no—
75C2×#217—31no—
76C2×#217—31no—
77C2×#217—31no—
78C2×#217—31no—
79C2×#217—31no—
80C2×#217—31no—
81C2×#217—31no—
82C2×#217—31no—
83C2×#217—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×Dic3⋊C4—31no—
87C2×Dic3⋊C4—31no—
88C2×Dic3⋊C4—31no—
89C2×Dic3⋊C4—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92#879—61no—
93#879—61no—
94#879—61no—
95#879—61no—
96#879—123no—
97C3⋊#95—31no—
98C3⋊#95—31no—
99C3⋊#95—31no—
100C3⋊#95—31no—
101C3⋊#95—31no—
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—31no—
105C23×C32—41no—
106C2×C3×A4—41no—
107C2×C3×A4#4111yescharacteristic
108C2×C3×A4#4111yescharacteristic
109C2×C3×A4#4111yescharacteristic
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3—41no—
116C2×#126—91no—
117C22×C22⋊C4C3⋊D311yescharacteristic
118#397—91no—
119#397—91no—
120#397—91no—
121#396—91no—
122#388—91no—
123#388—91no—
124#388—91no—
125#385—91no—
126#385—91no—
127#380—91no—
128#379—91no—
129#379—91no—
130C4×C22⋊C4—91no—
131C24×C3—21no—
132C24×C3—21no—
133C24×C3—21no—
134C24×C3—31no—
135C24×C3—31no—
136C24×C3—61no—
137C24×C3—61no—
138C24×C3—61no—
139C24×C3C22×D311yescharacteristic
140C22×A4—23no—
141C22×A4—23no—
142C22×A4—23no—
143C22×A4C22×D313yes—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—31no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×Dic3—31no—
153C22×Dic3—31no—
154C22×Dic3—31no—
155C22×Dic3—31no—
156C22×Dic3—31no—
157C22×Dic3—31no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C4×A4—23no—
161C4×A4—23no—
162SL(2,ℤ/4)—63no—
163SL(2,ℤ/4)—63no—
164SL(2,ℤ/4)—63no—
165SL(2,ℤ/4)—63no—
166C3×C22⋊C4—31no—
167C3×C22⋊C4—31no—
168C3×C22⋊C4—31no—
169C3×C22⋊C4—43no—
170C3×C22⋊C4—61no—
171C3×C22⋊C4S411yescharacteristic
172#217—61no—
173#217—61no—
174#217—61no—
175#217—61no—
176#217—61no—
177#217—61no—
178#217—62no—
179#217—62no—
180#217—61no—
181#217—61no—
182#217—61no—
183#217—61no—
184#217—61no—
185#217—61no—
186#217—123no—
187#217—123no—
188#217—121no—
189#217—121no—
190#217—121no—
191#217—121no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—123no—
195C4⋊Dic3—121no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—123no—
201Dic3⋊C4—123no—
202Dic3⋊C4—121no—
203Dic3⋊C4—121no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—123no—
207C4×Dic3—121no—
208C22×C32—41no—
209C22×C32—81no—
210C22×C32—81no—
211C22×C32—81no—
212C3×A4#12611yescharacteristic, complemented
213C32×C4—81no—
214C32×C4—81no—
215C3⋊Dic3—81no—
216C3⋊Dic3—81no—
217C3⋊Dic3—81no—
218C3⋊Dic3—81no—
219C25C2×C3⋊D311yescharacteristic
220C23×C4C2×C3⋊D311yescharacteristic
221C23×C4C2×C3⋊D311yescharacteristic
222#126—181no—
223#126—181no—
224#126—181no—
225#126—181no—
226C2×C4⋊C4—91no—
227C2×C4⋊C4—91no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—91no—
231C2×C4⋊C4—91no—
232C2×C22⋊C4—31no—
233C2×C22⋊C4—31no—
234C2×C22⋊C4—31no—
235C2×C22⋊C4—31no—
236C2×C22⋊C4—91no—
237C2×C22⋊C4—91no—
238C2×C22⋊C4—91no—
239C2×C22⋊C4—91no—
240C2×C22⋊C4—91no—
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×C22⋊C4—91no—
248C2×C42—91no—
249C2×C42—91no—
250#95—91no—
251#95—91no—
252#95—91no—
253#95—91no—
254#95—91no—
255#95—91no—
256#95—91no—
257#95—91no—
258C23×C3—31no—
259C23×C3—31no—
260C23×C3—31no—
261C23×C3—31no—
262C23×C3—32no—
263C23×C3—31no—
264C23×C3—41no—
265C23×C3—43no—
266C23×C3—61no—
267C23×C3—61no—
268C23×C3—61no—
269C23×C3—61no—
270C23×C3—61no—
271C23×C3—61no—
272C23×C3—61no—
273C23×C3—61no—
274C23×C3—61no—
275C23×C3—61no—
276C23×C3—61no—
277C23×C3—121no—
278C23×C3—121no—
279C23×C3—121no—
280C23×C3—122no—
281C23×C3#23511yescharacteristic
282C23×C3#23711yescharacteristic
283C23×C3#23711yescharacteristic
284C23×C3C2×S411yescharacteristic
285C2×A4—43no—
286C2×A4#23513yes—
287C2×A4#23713yes—
288C2×A4#23713yes—
289C2×C3×C4—31no—
290C2×C3×C4—31no—
291C2×C3×C4—43no—
292C2×C3×C4—43no—
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×C4C2×S411yescharacteristic
302C2×C3×C4C2×S411yescharacteristic
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—61no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
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—123no—
328C2×Dic3—123no—
329C2×Dic3—123no—
330C2×Dic3—123no—
331C2×C32—41no—
332C2×C32—41no—
333C2×C32—41no—
334C2×C32—161no—
335C24—21no—
336C24—21no—
337C24—21no—
338C24—31no—
339C24—31no—
340C24—61no—
341C24—61no—
342C24—61no—
343C24C22×C3⋊D311yescharacteristic
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—31no—
347C22×C4—31no—
348C22×C4—31no—
349C22×C4—31no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—91no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—91no—
359C22×C4—91no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4—181no—
363C4⋊C4—181no—
364C4⋊C4—181no—
365C4⋊C4—181no—
366C4⋊C4—361no—
367C4⋊C4—361no—
368C4⋊C4—361no—
369C22⋊C4—31no—
370C22⋊C4—31no—
371C22⋊C4—31no—
372C22⋊C4—61no—
373C22⋊C4—181no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C22⋊C4—181no—
377C22⋊C4—181no—
378C22⋊C4—181no—
379C22⋊C4—182no—
380C22⋊C4—182no—
381C22⋊C4—181no—
382C22⋊C4—181no—
383C22⋊C4—181no—
384C22⋊C4—181no—
385C22⋊C4—181no—
386C22⋊C4—181no—
387C22⋊C4—361no—
388C22⋊C4—361no—
389C22⋊C4—361no—
390C22⋊C4—361no—
391C22⋊C4C3⋊S411yescharacteristic
392C42—181no—
393C42—181no—
394C42—361no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
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—31no—
407C22×C3—43no—
408C22×C3—61no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—61no—
412C22×C3—61no—
413C22×C3—61no—
414C22×C3—83no—
415C22×C3—83no—
416C22×C3—83no—
417C22×C3—121no—
418C22×C3—121no—
419C22×C3—121no—
420C22×C3—121no—
421C22×C3—121no—
422C22×C3—121no—
423C22×C3#87911yescharacteristic, complemented
424C22×C3C22×S411yescharacteristic
425A4#87913yescomplemented
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—61no—
429C3×C4—61no—
430C3×C4—83no—
431C3×C4—83no—
432Dic3—121no—
433Dic3—121no—
434Dic3—121no—
435Dic3—121no—
436Dic3—121no—
437Dic3—121no—
438Dic3—121no—
439Dic3—121no—
440Dic3—243no—
441Dic3—243no—
442Dic3—243no—
443Dic3—243no—
444C32—41noSylow
445C23—31no—
446C23—31no—
447C23—31no—
448C23—31no—
449C23—32no—
450C23—31no—
451C23—41no—
452C23—61no—
453C23—61no—
454C23—61no—
455C23—61no—
456C23—61no—
457C23—61no—
458C23—61no—
459C23—61no—
460C23—61no—
461C23—61no—
462C23—61no—
463C23—121no—
464C23—121no—
465C23—121no—
466C23—122no—
467C23#382811yescharacteristic
468C23#383011yescharacteristic
469C23#383011yescharacteristic
470C23C2×C3⋊S411yescharacteristic
471C2×C4—31no—
472C2×C4—31no—
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—181no—
482C2×C4—181no—
483C2×C4—181no—
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×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4C2×C3⋊S411yescharacteristic
506C2×C4C2×C3⋊S411yescharacteristic
507C2×C3—31no—
508C2×C3—31no—
509C2×C3—31no—
510C2×C3—31no—
511C2×C3—41no—
512C2×C3—43no—
513C2×C3—43no—
514C2×C3—43no—
515C2×C3—121no—
516C2×C3—163no—
517C2×C3#591211yescharacteristic
518C2×C3#591411yescharacteristic
519C2×C3#591411yescharacteristic
520C22—21no—
521C22—21no—
522C22—21no—
523C22—31no—
524C22—31no—
525C22—31no—
526C22—31no—
527C22—31no—
528C22—31no—
529C22—31no—
530C22—31no—
531C22—31no—
532C22—61no—
533C22—62no—
534C22—62no—
535C22—61no—
536C22—61no—
537C22—61no—
538C22—121no—
539C22—121no—
540C22—121no—
541C22—121no—
542C22—121no—
543C22—121no—
544C22#6408811yescharacteristic, complemented
545C22C22×C3⋊S411yescharacteristic
546C4—21no—
547C4—21no—
548C4—61no—
549C4—61no—
550C4—361no—
551C4—361no—
552C4—361no—
553C4—361no—
554C4—361no—
555C4—361no—
556C4—361no—
557C4—361no—
558C3—43no—
559C3#8529411yescharacteristic, complemented
560C2—31no—
561C2—31no—
562C2—31no—
563C2—31no—
564C2—41no—
565C2—121no—
566C2#1059657511yescharacteristic
567C2#1059657711yescharacteristic
568C2#1059657711yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutator, cosocleC22×C3×A4C23
FittingC22×C3×C22⋊C4D3
socleC24×C3C22×D3
prime radicalC23×C3×A4C22
hypercenterC22⋊C4C3⋊S4
hypocenterC3×A4#126
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C4⋊(C3⋊SL(2,ℤ/4))C2semidirect
5. #10593645C2semidirect
6. #10593645C2semidirect
7. C4×C3⋊SL(2,ℤ/4)C2semidirect
212. C3×A4#126semidirect
423. C22×C3#879semidirect
425. A4#879semidirect
544. C22#64088semidirect
559. C3#85294semidirect

Maximal subgroups

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

subgroupindex
C3×A4×C22⋊C42
#105936662
C4⋊(C3⋊SL(2,ℤ/4))2
#105936452
C4×C3⋊SL(2,ℤ/4)2
#852943
#821123
#640884