Finite Group Databasebeta

← #11921958

Subgroups — #11921958

Order 1152.

648 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 71 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×A4⋊Q8C211yesmaximal, characteristic
2C2×#64204C211yesmaximal, characteristic
3A4×Dic3⋊C4C211yesmaximal, characteristic
4#10593645C211yesmaximal, characteristic
5Dic3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
6#10593238C211yesmaximal, characteristic
7Dic3×SL(2,ℤ/4)C211yesmaximal, characteristic
8#85303—31nomaximal
9#82763—31nomaximal
10C2×C3×C4×A4C2211yescharacteristic
11C2×Dic3×A4C2211yescharacteristic
12C2×Dic3×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×A4⋊Q8—22no—
18#64204—22no—
19#63839—41nomaximal
20C2×A4⋊Q8—31no—
21C2×A4⋊Q8D311yescharacteristic
22C2×C3×C22⋊Q8—31no—
23C2×#944—31no—
24C22×Dic3⋊C4D311yescharacteristic
25C2×#878—31no—
26A4×C4⋊C4—31no—
27C4⋊SL(2,ℤ/4)—31no—
28SL(2,ℤ/4)⋊C4—31no—
29SL(2,ℤ/4)⋊C4—31no—
30SL(2,ℤ/4)⋊C4—61no—
31C4×SL(2,ℤ/4)—31no—
32#5230—31no—
33#5210—31no—
34#4983—31no—
35#4981—31no—
36#4979—31no—
37#4976—31no—
38#4976—31no—
39#4975—31no—
40#4946—31no—
41#4942—31no—
42Dic3×C22⋊C4—31no—
43C22×C3×A4C2311yescharacteristic
44C2×C3×Dic6—41no—
45C3×C4×A4—21no—
46C2×#627—41no—
47Dic3×A4—21no—
48Dic3×A4Q812yescomplemented
49C3⋊SL(2,ℤ/4)—21no—
50C3⋊SL(2,ℤ/4)Q812yescomplemented
51C3×SL(2,ℤ/4)—21no—
52C3×SL(2,ℤ/4)D412yes—
53#3750—41no—
54C3×Dic3⋊C4—41no—
55#3724—41no—
56Dic3⋊Dic3—41no—
57Dic32—41no—
58#2440—91noSylow
59C22×C3×Q8—31no—
60C23×C3×C4C2×D311yescharacteristic
61C23×Dic3C2×D311yescharacteristic
62C23×Dic3C2×D311yescharacteristic
63C22×Dic6—31no—
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×SL(2,ℤ/4)C2×D311yescharacteristic
74A4⋊Q8—22no—
75A4⋊Q8—62no—
76C3×C22⋊Q8—62no—
77C3×C22⋊Q8—62no—
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C22⋊C4—31no—
82C2×C3×C22⋊C4—31no—
83C2×#217—31no—
84C2×#217—31no—
85#944—61no—
86#944—61no—
87#944—61no—
88#944—61no—
89C2×C4⋊Dic3—31no—
90C2×Dic3⋊C4—31no—
91C2×Dic3⋊C4—31no—
92C2×Dic3⋊C4—31no—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4—31no—
96C2×Dic3⋊C4—31no—
97C2×Dic3⋊C4—31no—
98C2×Dic3⋊C4—31no—
99C2×Dic3⋊C4—31no—
100C2×Dic3⋊C4—31no—
101C2×Dic3⋊C4—31no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—31no—
104#888—121no—
105#878—62no—
106#878—62no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—31no—
114C3⋊#95—31no—
115C2×C3×A4C2×D411yescharacteristic
116C2×C3×A4C2×Q811yescharacteristic
117C2×C3×A4C2×Q811yescharacteristic
118C2×C32×C4—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—41no—
123C2×C3×Dic3—41no—
124C2×C3×Dic3—41no—
125C3×Dic6—82no—
126#627—82no—
127C2×C4⋊Q8—91no—
128C2×C22⋊Q8—31no—
129C2×C22⋊Q8—91no—
130C22×C4⋊C4—31no—
131#398—91no—
132#398—91no—
133#395—91no—
134#395—91no—
135#389—91no—
136#389—91no—
137#385—91no—
138#385—91no—
139#384—91no—
140#380—91no—
141C4×C22⋊C4—91no—
142C24×C3C22×D311yescharacteristic
143C22×A4—21no—
144C22×A4C22×D311yescharacteristic
145C2×C3×Q8—61no—
146C2×C3×Q8—62no—
147C2×C3×Q8—61no—
148C2×C3×Q8—121no—
149C22×C3×C4—21no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—61no—
157C22×Dic3—21no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C22×Dic3—32no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—31no—
167C22×Dic3—61no—
168C22×Dic3Dic612yescomplemented
169C2×Dic6—41no—
170C2×Dic6—61no—
171C2×Dic6—62no—
172C2×Dic6—61no—
173C2×Dic6—121no—
174C2×Dic6—121no—
175C4×A4—21no—
176C4×A4—32no—
177C4×A4—41no—
178C4×A4—61no—
179SL(2,ℤ/4)—21no—
180SL(2,ℤ/4)—32no—
181SL(2,ℤ/4)—62no—
182SL(2,ℤ/4)—61no—
183SL(2,ℤ/4)—121no—
184SL(2,ℤ/4)#6712yes—
185C3×C4⋊C4—62no—
186C3×C4⋊C4—62no—
187C3×C4⋊C4—62no—
188C3×C4⋊C4—121no—
189C3×C22⋊C4—32no—
190C3×C22⋊C4—32no—
191C3×C22⋊C4—61no—
192C3×C22⋊C4—61no—
193#217—32no—
194#217—32no—
195#217—61no—
196#217—61no—
197C4⋊Dic3—62no—
198C4⋊Dic3—121no—
199Dic3⋊C4—31no—
200Dic3⋊C4—31no—
201Dic3⋊C4—31no—
202Dic3⋊C4—61no—
203Dic3⋊C4—62no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—62no—
207Dic3⋊C4—62no—
208Dic3⋊C4—61no—
209Dic3⋊C4—61no—
210Dic3⋊C4—61no—
211Dic3⋊C4—61no—
212Dic3⋊C4—121no—
213Dic3⋊C4—121no—
214Dic3⋊C4—121no—
215Dic3⋊C4—121no—
216Dic3⋊C4—241no—
217Dic3⋊C4S411yescharacteristic
218C4×Dic3—62no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—121no—
222C22×C32—41no—
223C3×A4C4⋊Q811yescharacteristic, complemented
224C32×C4—81no—
225C3⋊Dic3—42no—
226C3⋊Dic3—81no—
227C3×Dic3—42no—
228C3×Dic3—42no—
229C3×Dic3—81no—
230C3×Dic3—81no—
231C22×Q8—31no—
232C22×Q8—91no—
233C23×C4—31no—
234C23×C4—31no—
235C23×C4D3211yescharacteristic
236C4⋊Q8—181no—
237C4⋊Q8—181no—
238C4⋊Q8—181no—
239C4⋊Q8—181no—
240C22⋊Q8—62no—
241C22⋊Q8—62no—
242C22⋊Q8—182no—
243C22⋊Q8—182no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—31no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—91no—
254C2×C4⋊C4—91no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—91no—
260C2×C22⋊C4—31no—
261C2×C22⋊C4—31no—
262C2×C22⋊C4—91no—
263C2×C22⋊C4—91no—
264C2×C42—91no—
265C2×C42—91no—
266#95—91no—
267#95—91no—
268#95—91no—
269#95—91no—
270#95—91no—
271#95—91no—
272#95—91no—
273#95—91no—
274C23×C3—31no—
275C23×C3—31no—
276C23×C3—31no—
277C23×C3—31no—
278C23×C3C2×Dic611yescharacteristic
279C23×C3D3×D411yescharacteristic
280C23×C3D3×Q811yescharacteristic
281C2×A4—21no—
282C2×A4—21no—
283C2×A4—21no—
284C2×A4D3×Q811yescharacteristic
285C2×A4D3×Q811yescharacteristic
286C2×A4C2×#6711yescharacteristic
287C3×Q8—122no—
288C3×Q8—122no—
289C2×C3×C4—32no—
290C2×C3×C4—32no—
291C2×C3×C4—31no—
292C2×C3×C4—41no—
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—121no—
309C2×C3×C4—121no—
310C2×C3×C4C2×S411yescharacteristic
311C2×Dic3—31no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—32no—
315C2×Dic3—32no—
316C2×Dic3—32no—
317C2×Dic3—31no—
318C2×Dic3—41no—
319C2×Dic3—41no—
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—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—121no—
336C2×Dic3—121no—
337C2×Dic3—241no—
338C2×Dic3—241no—
339C2×Dic3C2×S411yescharacteristic
340C2×Dic3C2×S411yescharacteristic
341Dic6—82no—
342Dic6—122no—
343Dic6—122no—
344Dic6—242no—
345C2×C32—41no—
346C2×C32—41no—
347C2×C32—41no—
348C24C2×D3211yescharacteristic
349C2×Q8—62no—
350C2×Q8—61no—
351C2×Q8—61no—
352C2×Q8—121no—
353C2×Q8—181no—
354C2×Q8—182no—
355C2×Q8—181no—
356C2×Q8—361no—
357C22×C4—21no—
358C22×C4—31no—
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—32no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4—91no—
368C22×C4—91no—
369C22×C4—91no—
370C22×C4—92no—
371C22×C4—91no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4—181no—
377C4⋊C4—31no—
378C4⋊C4—62no—
379C4⋊C4—62no—
380C4⋊C4—62no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—182no—
388C4⋊C4—182no—
389C4⋊C4—182no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—182no—
394C4⋊C4—181no—
395C4⋊C4—361no—
396C4⋊C4—361no—
397C22⋊C4—32no—
398C22⋊C4—32no—
399C22⋊C4—61no—
400C22⋊C4—61no—
401C22⋊C4—92no—
402C22⋊C4—92no—
403C22⋊C4—181no—
404C22⋊C4—181no—
405C42—181no—
406C42—181no—
407C42—182no—
408C22×C3—31no—
409C22×C3—31no—
410C22×C3—31no—
411C22×C3—31no—
412C22×C3—31no—
413C22×C3—31no—
414C22×C3—31no—
415C22×C3—31no—
416C22×C3—31no—
417C22×C3—41no—
418C22×C3—61no—
419C22×C3—81no—
420C22×C3#88811yescharacteristic, complemented
421C22×C3C22×S411yescharacteristic
422A4—21no—
423A4#94411yescharacteristic, complemented
424C3×C4—21no—
425C3×C4—62no—
426C3×C4—62no—
427C3×C4—61no—
428C3×C4—81no—
429C3×C4—122no—
430C3×C4—121no—
431C3×C4—121no—
432C3×C4—161no—
433C3×C4—241no—
434Dic3—21no—
435Dic3—32no—
436Dic3—42no—
437Dic3—62no—
438Dic3—61no—
439Dic3—62no—
440Dic3—81no—
441Dic3—122no—
442Dic3—121no—
443Dic3—121no—
444Dic3—242no—
445Dic3—241no—
446Dic3—481no—
447Dic3A4⋊Q812yescomplemented
448C32—41noSylow
449C23—31no—
450C23—31no—
451C23—31no—
452C23—31no—
453C23D3×Dic611yescharacteristic
454C23#379711yescharacteristic
455C23D3×#6711yescharacteristic
456Q8—122no—
457Q8—122no—
458Q8—362no—
459Q8—362no—
460C2×C4—31no—
461C2×C4—32no—
462C2×C4—32no—
463C2×C4—31no—
464C2×C4—31no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
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—92no—
480C2×C4—92no—
481C2×C4—91no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—92no—
485C2×C4—91no—
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×C4D3×S411yescharacteristic
502C2×C3—31no—
503C2×C3—31no—
504C2×C3—31no—
505C2×C3—31no—
506C2×C3—41no—
507C2×C3—41no—
508C2×C3—41no—
509C2×C3—81no—
510C2×C3—81no—
511C2×C3—81no—
512C2×C3C2×A4⋊Q811yescharacteristic
513C2×C3D4×S411yescharacteristic
514C2×C3Q8×S411yescharacteristic
515C22—31no—
516C22—31no—
517C22—31no—
518C22—31no—
519C22—31no—
520C22—31no—
521C22—31no—
522C22—31no—
523C22—31no—
524C22—61no—
525C22#6383911yescharacteristic, complemented
526C22C2×D3×S411yescharacteristic
527C4—21no—
528C4—32no—
529C4—62no—
530C4—61no—
531C4—62no—
532C4—61no—
533C4—92no—
534C4—121no—
535C4—121no—
536C4—182no—
537C4—182no—
538C4—181no—
539C4—361no—
540C4—361no—
541C3—41no—
542C3—81no—
543C3#8530311yescharacteristic, complemented
544C2—31no—
545C2—31no—
546C2—31no—
547C2—31no—
548C2(C3⋊S4)⋊Q811yescharacteristic
549C2D3×A4⋊Q811yescharacteristic
550C2#67×S411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, prime radical, cosocleC22×C3×A4C23
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
hypercenterC2×C4D3×S4
hypocenterC3×A4C4⋊Q8
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
48. Dic3×A4Q8semidirect
50. C3⋊SL(2,ℤ/4)Q8semidirect
168. C22×Dic3Dic6semidirect
223. C3×A4C4⋊Q8semidirect
420. C22×C3#888semidirect
423. A4#944semidirect
447. Dic3A4⋊Q8semidirect
525. C22#63839semidirect
543. C3#85303semidirect

Maximal subgroups

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

subgroupindex
C2×C3×A4⋊Q82
C2×#642042
A4×Dic3⋊C42
#105936452
Dic3⋊SL(2,ℤ/4)2
#105932382
Dic3×SL(2,ℤ/4)2
#853033
#827633
#638394