Finite Group Databasebeta

← #11921980

Subgroups — #11921980

Order 1152.

708 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 65 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, complemented
2C2×(C3⋊S4)⋊C4C211yesmaximal, characteristic
3A4×Dic3⋊C4C211yesmaximal, characteristic, complemented
4#10593647C211yesmaximal, characteristic
5#10593242C211yesmaximal, characteristic
6SL(2,ℤ/4)⋊Dic3C211yesmaximal, characteristic, complemented
7#10593238C211yesmaximal, characteristic, complemented
8#85311—31nomaximal
9#82764—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
17C3×A4⋊Q8—22no—
18(C3⋊S4)⋊C4—22no—
19#63888—41nomaximal
20C2×C4×S4—31no—
21C2×A4⋊Q8D311yescharacteristic, complemented
22C2×C3×C22⋊Q8—31no—
23C2×#946—31no—
24C22×Dic3⋊C4D311yescharacteristic, complemented
25C2×#67⋊C4—31no—
26A4×C4⋊C4—31no—
27(C2×S4)⋊C4—31no—
28(C2×S4)⋊C4—31no—
29(C2×S4)⋊C4—61no—
30SL(2,ℤ/4)⋊C4—31no—
31SL(2,ℤ/4)⋊C4—31no—
32#5230—31no—
33#5213—31no—
34#4994—31no—
35#4993—31no—
36#4989—31no—
37#4982—31no—
38#4978—31no—
39#4972—31no—
40#4958—31no—
41#4950—31no—
42#4946—31no—
43C22×C3×A4C2311yescharacteristic
44C2×C3⋊S4—21no—
45C2×C3⋊S4—21no—
46C2×C3⋊S4Q812yescomplemented
47C2×C3×Dic6—41no—
48C3×C4×A4—21no—
49C2×#624—41no—
50Dic3×A4—21no—
51Dic3×A4—21no—
52C3⋊SL(2,ℤ/4)—21no—
53C3×SL(2,ℤ/4)—21no—
54C3×SL(2,ℤ/4)D412yes—
55#3752—41no—
56C3×Dic3⋊C4—41no—
57#3724—41no—
58Dic3⋊Dic3—41no—
59#3722—41no—
60#2449—91noSylow
61C22×S4—31no—
62C22×S4—61no—
63C22×C3×Q8—31no—
64C23×C3×C4C2×D311yescharacteristic
65C22×#67—31no—
66C23×Dic3C2×D311yescharacteristic
67C23×Dic3C2×D311yescharacteristic
68C22×C4×D3—31no—
69C2×C4×A4—21no—
70C2×C4×A4—31no—
71C2×C4×A4—31no—
72C2×C4×A4C2×D311yescharacteristic
73C2×SL(2,ℤ/4)—31no—
74C2×SL(2,ℤ/4)—61no—
75C2×SL(2,ℤ/4)C2×D311yescharacteristic
76C2×SL(2,ℤ/4)C2×D311yescharacteristic
77C4×S4—62no—
78A4⋊Q8—22no—
79C3×C22⋊Q8—62no—
80C3×C22⋊Q8—62no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C22⋊C4—31no—
85C2×C3×C22⋊C4—31no—
86C2×#217—31no—
87#946—61no—
88#946—61no—
89#946—61no—
90#946—61no—
91C2×(C2×D3)⋊C4—31no—
92C2×(C2×D3)⋊C4—31no—
93C2×(C2×D3)⋊C4—31no—
94C2×(C2×D3)⋊C4—31no—
95C2×(C2×D3)⋊C4—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×Dic3⋊C4—31no—
99C2×Dic3⋊C4—31no—
100C2×Dic3⋊C4—31no—
101C2×Dic3⋊C4—31no—
102C2×Dic3⋊C4—31no—
103C2×Dic3⋊C4—31no—
104C2×Dic3⋊C4—31no—
105C2×C4×Dic3—31no—
106#896—121no—
107#67⋊C4—62no—
108#67⋊C4—62no—
109C3⋊#95—31no—
110C3⋊#95—31no—
111C3⋊#95—31no—
112C3⋊#95—31no—
113C3⋊#95—31no—
114C3⋊#95—31no—
115C3⋊#95—31no—
116C3⋊#95—31no—
117C22×C3⋊D3—41no—
118C2×C3×A4C2×D411yescharacteristic
119C2×C3×A4C2×Q811yescharacteristic
120C2×C3×A4#4111yescharacteristic
121C3⋊S4—22no—
122C2×C32×C4—41no—
123C2×C3⋊Dic3—41no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C3×Dic6—82no—
129#624—82no—
130C2×C22⋊Q8—31no—
131C2×C22⋊Q8—91no—
132C2×C4×D4—91no—
133C22×C4⋊C4—31no—
134#399—91no—
135#398—91no—
136#396—91no—
137#395—91no—
138#389—91no—
139#387—91no—
140#386—91no—
141#386—91no—
142#385—91no—
143#385—91no—
144#385—91no—
145C24×C3C22×D311yescharacteristic
146C23×D3—31no—
147C22×A4—21no—
148C22×A4C22×D311yescharacteristic
149C2×S4—32no—
150C2×S4—62no—
151C2×S4—61no—
152C2×S4—61no—
153C2×S4—121no—
154C2×S4—121no—
155C2×C3×Q8—61no—
156C2×C3×Q8—62no—
157C2×C3×Q8—61no—
158C2×C3×Q8—121no—
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C2×#67—32no—
168C2×#67—32no—
169C2×#67—61no—
170C2×#67—61no—
171C2×#67—61no—
172C2×#67—61no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C2×C4×D3—61no—
185C2×C4×D3—62no—
186C2×C4×D3—61no—
187C2×C4×D3—121no—
188C2×C4×D3—121no—
189C2×Dic6—41no—
190C4×A4—21no—
191C4×A4—41no—
192C4×A4—61no—
193C4×A4—61no—
194SL(2,ℤ/4)—21no—
195SL(2,ℤ/4)—61no—
196SL(2,ℤ/4)—121no—
197SL(2,ℤ/4)#6712yes—
198C3×C4⋊C4—62no—
199C3×C4⋊C4—62no—
200C3×C4⋊C4—62no—
201C3×C4⋊C4—121no—
202C3×C22⋊C4—32no—
203C3×C22⋊C4—32no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206#217—61no—
207#217—61no—
208(C2×D3)⋊C4—62no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—62no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—121no—
215(C2×D3)⋊C4—121no—
216(C2×D3)⋊C4—121no—
217(C2×D3)⋊C4—241no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221Dic3⋊C4—31no—
222Dic3⋊C4—31no—
223Dic3⋊C4—31no—
224Dic3⋊C4—61no—
225Dic3⋊C4—61no—
226Dic3⋊C4—62no—
227Dic3⋊C4—61no—
228Dic3⋊C4—121no—
229Dic3⋊C4—121no—
230Dic3⋊C4—121no—
231Dic3⋊C4S411yescharacteristic, complemented
232C4×Dic3—62no—
233C22×C32—41no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—81no—
236C2×C3⋊D3—81no—
237C3×A4C22⋊Q811yescharacteristic, complemented
238C32×C4—81no—
239C3⋊Dic3—81no—
240C3×Dic3—42no—
241C3×Dic3—81no—
242C3×Dic3—81no—
243C3×Dic3—81no—
244C22×Q8—31no—
245C22×D4—91no—
246C23×C4—31no—
247C23×C4—31no—
248C23×C4—91no—
249C23×C4D3211yescharacteristic
250C22⋊Q8—62no—
251C22⋊Q8—62no—
252C22⋊Q8—181no—
253C22⋊Q8—181no—
254C22⋊Q8—181no—
255C22⋊Q8—181no—
256C4×D4—182no—
257C4×D4—182no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—31no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—91no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—91no—
266C2×C4⋊C4—91no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C22⋊C4—31no—
271C2×C22⋊C4—31no—
272C2×C22⋊C4—91no—
273C2×C22⋊C4—91no—
274C2×C22⋊C4—91no—
275C2×C22⋊C4—91no—
276C2×C22⋊C4—91no—
277C2×C22⋊C4—91no—
278C2×C42—91no—
279#95—91no—
280#95—91no—
281#95—91no—
282#95—91no—
283#95—91no—
284#95—91no—
285#95—91no—
286#95—91no—
287C23×C3—31no—
288C23×C3—31no—
289C23×C3—31no—
290C23×C3—31no—
291C23×C3#23511yescharacteristic
292C23×C3D3×D411yescharacteristic
293C23×C3D3×Q811yescharacteristic
294C22×D3—32no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—61no—
300C22×D3—61no—
301C22×D3—121no—
302C22×D3—241no—
303C2×A4—21no—
304C2×A4—21no—
305C2×A4—21no—
306C2×A4D3×Q811yescharacteristic
307C2×A4#23911yescharacteristic
308C2×A4C2×#6711yescharacteristic
309S4—62no—
310S4—122no—
311C3×Q8—122no—
312C3×Q8—122no—
313C2×C3×C4—32no—
314C2×C3×C4—32no—
315C2×C3×C4—31no—
316C2×C3×C4—41no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—61no—
323C2×C3×C4—61no—
324C2×C3×C4—61no—
325C2×C3×C4—61no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4—61no—
329C2×C3×C4—61no—
330C2×C3×C4—61no—
331C2×C3×C4—81no—
332C2×C3×C4—121no—
333C2×C3×C4—121no—
334C2×C3×C4C2×S411yescharacteristic
335#67—62no—
336#67—62no—
337#67—62no—
338#67—62no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—31no—
342C2×Dic3—31no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—61no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—121no—
361C2×Dic3—241no—
362C2×Dic3C2×S411yescharacteristic
363C2×Dic3C2×S411yescharacteristic
364C4×D3—122no—
365C4×D3—122no—
366C4×D3—242no—
367Dic6—82no—
368C2×C32—41no—
369C2×C32—41no—
370C2×C32—41no—
371C3⋊D3—82no—
372C24—91no—
373C24C2×D3211yescharacteristic
374C2×Q8—62no—
375C2×Q8—61no—
376C2×Q8—61no—
377C2×Q8—121no—
378C2×D4—92no—
379C2×D4—92no—
380C2×D4—181no—
381C2×D4—181no—
382C2×D4—181no—
383C2×D4—181no—
384C22×C4—21no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—31no—
391C22×C4—61no—
392C22×C4—61no—
393C22×C4—61no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—91no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—181no—
402C22×C4—182no—
403C22×C4—181no—
404C22×C4—181no—
405C22×C4—181no—
406C22×C4—361no—
407C4⋊C4—31no—
408C4⋊C4—62no—
409C4⋊C4—62no—
410C4⋊C4—62no—
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—181no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C4⋊C4—182no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—182no—
421C4⋊C4—361no—
422C22⋊C4—32no—
423C22⋊C4—32no—
424C22⋊C4—61no—
425C22⋊C4—61no—
426C22⋊C4—181no—
427C22⋊C4—182no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—182no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C22⋊C4—361no—
435C42—182no—
436C22×C3—31no—
437C22×C3—31no—
438C22×C3—31no—
439C22×C3—31no—
440C22×C3—31no—
441C22×C3—31no—
442C22×C3—31no—
443C22×C3—31no—
444C22×C3—31no—
445C22×C3—41no—
446C22×C3—61no—
447C22×C3—81no—
448C22×C3#89611yescharacteristic, complemented
449C22×C3C22×S411yescharacteristic
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—122no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—242no—
459C2×D3—241no—
460C2×D3—241no—
461C2×D3—481no—
462C2×D3—481no—
463A4—21no—
464A4#94611yescharacteristic, complemented
465C3×C4—21no—
466C3×C4—62no—
467C3×C4—62no—
468C3×C4—61no—
469C3×C4—81no—
470C3×C4—121no—
471C3×C4—121no—
472C3×C4—161no—
473C3×C4—241no—
474C3×C4—241no—
475Dic3—21no—
476Dic3—21no—
477Dic3—42no—
478Dic3—62no—
479Dic3—61no—
480Dic3—61no—
481Dic3—81no—
482Dic3—121no—
483Dic3—121no—
484Dic3—241no—
485Dic3—481no—
486C32—41noSylow
487C23—31no—
488C23—31no—
489C23—31no—
490C23—31no—
491C23—92no—
492C23—181no—
493C23—181no—
494C23—181no—
495C23—181no—
496C23—181no—
497C23—181no—
498C23#379711yescharacteristic
499C23#379911yescharacteristic
500C23D3×#6711yescharacteristic
501Q8—122no—
502Q8—122no—
503D4—182no—
504D4—182no—
505D4—182no—
506D4—182no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—31no—
510C2×C4—31no—
511C2×C4—31no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—92no—
527C2×C4—92no—
528C2×C4—91no—
529C2×C4—91no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—181no—
542C2×C4—181no—
543C2×C4—181no—
544C2×C4—181no—
545C2×C4—362no—
546C2×C4—362no—
547C2×C4D3×S411yescharacteristic
548C2×C3—31no—
549C2×C3—31no—
550C2×C3—31no—
551C2×C3—31no—
552C2×C3—41no—
553C2×C3—41no—
554C2×C3—41no—
555C2×C3—81no—
556C2×C3—81no—
557C2×C3—81no—
558C2×C3#591211yescharacteristic
559C2×C3D4×S411yescharacteristic
560C2×C3Q8×S411yescharacteristic
561D3—122no—
562D3—242no—
563D3—482no—
564C22—31no—
565C22—31no—
566C22—31no—
567C22—31no—
568C22—31no—
569C22—31no—
570C22—31no—
571C22—31no—
572C22—31no—
573C22—61no—
574C22—182no—
575C22—182no—
576C22—182no—
577C22—361no—
578C22—361no—
579C22—361no—
580C22—361no—
581C22#6388811yescharacteristic, complemented
582C22C2×D3×S411yescharacteristic
583C4—21no—
584C4—62no—
585C4—61no—
586C4—61no—
587C4—62no—
588C4—61no—
589C4—121no—
590C4—121no—
591C4—182no—
592C4—181no—
593C4—181no—
594C4—361no—
595C4—361no—
596C3—41no—
597C3—81no—
598C3#8531111yescharacteristic, complemented
599C2—31no—
600C2—31no—
601C2—31no—
602C2—31no—
603C2—362no—
604C2(C3⋊S4)⋊Q811yescharacteristic
605C2#1059642811yescharacteristic
606C2#67×S411yescharacteristic
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×A4C22⋊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
1. C2×C3×A4⋊Q8C2semidirect
3. A4×Dic3⋊C4C2semidirect
6. SL(2,ℤ/4)⋊Dic3C2semidirect
7. #10593238C2semidirect
21. C2×A4⋊Q8D3semidirect
24. C22×Dic3⋊C4D3semidirect
46. C2×C3⋊S4Q8semidirect
231. Dic3⋊C4S4semidirect
237. C3×A4C22⋊Q8semidirect
448. C22×C3#896semidirect
464. A4#946semidirect
581. C22#63888semidirect
598. C3#85311semidirect

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×(C3⋊S4)⋊C42
A4×Dic3⋊C42
#105936472
#105932422
SL(2,ℤ/4)⋊Dic32
#105932382
#853113
#827643
#638884