Finite Group Databasebeta

← #11906276

Subgroups — #11906276

Order 1152.

2028 conjugacy classes of subgroups.

The subgroup lattice has 701 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596040C211yesmaximal, characteristic, complemented
2C3×#5572C211yesmaximal, characteristic
3C3×#5570C211yesmaximal, characteristic, complemented
4Q8×#627C211yesmaximal, characteristic, complemented
5D3×Q8×Dic3C211yesmaximal, characteristic
6#10595351C211yesmaximal, characteristic, complemented
7#10595347C211yesmaximal, characteristic
8#10594505C213yesmaximal
9#10594477C213yesmaximal
10#10594322C213yesmaximal, complemented
11#10594321C213yesmaximal, complemented
12#10593954C213yesmaximal
13#10593926C213yesmaximal
14#10593856C213yesmaximal, complemented
15#10593851C213yesmaximal, complemented
16#87032—31nomaximal
17#85875—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22#64099C2213yes—
23#64097C2213yes—
24#64079C2213yes—
25C4×#634C2213yes—
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×#892C2213yes—
30C3×#890C2213yes—
31C3×#890C2213yes—
32C3×#887C2213yes—
33C3×#872C2213yes—
34C3×#869C2213yes—
35C3×C4×Dic6C2213yes—
36C3×C4×Dic6C2213yes—
37#63919C2213yes—
38#63919C2213yes—
39#63918C2216yes—
40#63918C2213yes—
41#63918C2213yes—
42C4×#627C2213yes—
43C4×#627C2213yes—
44#63899C2211yescharacteristic
45#63899C2216yes—
46#63896C2213yes—
47#63893C2213yes—
48D3×C4⋊Dic3C2213yes—
49#63887C2213yes—
50C4×D3×Dic3C2213yes—
51#63869C2213yes—
52#63869C2213yes—
53#63867C2216yes—
54#63855C2213yes—
55#63846C2216yes—
56#63846C2213yes—
57#63845C2213yes—
58#63844C2216yes—
59#63843C2213yes—
60#63843C2213yes—
61Dic3×Dic6C2213yes—
62Dic3×Dic6C2213yes—
63#63841C2213yes—
64#63840C2213yes—
65#63839C2216yes—
66#63839C2213yes—
67#63837C2216yes—
68C3×#557—31no—
69C3×#519—31no—
70#5812—31no—
71C2×Q8×Dic3—31no—
72#5729—33no—
73#5722—33no—
74#5689—33no—
75#5688—33no—
76#5685—33no—
77#5685—33no—
78#5578—33no—
79#5572—31no—
80#5572D311yescharacteristic
81C4×D3×Q8—31no—
82#5570—33no—
83#5570D311yescharacteristic, complemented
84#5569—31no—
85#5569—31no—
86#5569—31no—
87#5569—31no—
88#5569—33no—
89#5569—33no—
90#5569—61no—
91#5567—33no—
92Q8×Dic6—31no—
93Q8×Dic6—31no—
94Q8×Dic6—33no—
95#5519—33no—
96#5519—33no—
97#5517—33no—
98#5517—33no—
99C2×C32×Q8C2311yescharacteristic
100C2×#634C2313yes—
101C3×D3×Q8Q818yescomplemented
102C2×C3×C4×D3C2313yes—
103C2×C3×Dic6C2313yes—
104C2×C3×Dic6C2313yes—
105C2×#627C2311yescharacteristic
106C2×#627C2316yes—
107C2×#627C2313yes—
108C2×D3×Dic3C2311yescharacteristic
109C2×D3×Dic3C2313yes—
110C32×C4⋊C4C2313yes—
111C32×C42C2313yes—
112C4⋊(C3⋊Dic3)C2313yes—
113C4⋊(C3⋊Dic3)C2313yes—
114C4⋊(C3⋊Dic3)C2313yes—
115#3750C2311yescharacteristic
116#3750C2313yes—
117#3750C2316yes—
118C4×C3⋊Dic3C2313yes—
119C4×C3⋊Dic3C2313yes—
120C3×(C2×D3)⋊C4C2313yes—
121C3×(C2×D3)⋊C4C2311yescharacteristic
122C3×C4⋊Dic3C2316yes—
123C3×C4⋊Dic3C2313yes—
124C3×C4⋊Dic3C2313yes—
125C3×C4⋊Dic3C2313yes—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4C2313yes—
128C3×Dic3⋊C4C2313yes—
129C3×Dic3⋊C4C2313yes—
130C3×Dic3⋊C4C2313yes—
131C3×C4×Dic3C2316yes—
132C3×C4×Dic3C2313yes—
133C3×C4×Dic3C2313yes—
134C3×C4×Dic3C2313yes—
135#3724C2313yes—
136#3724C2316yes—
137#3724C2311yescharacteristic
138Dic3⋊Dic3C2313yes—
139Dic3⋊Dic3C2316yes—
140Dic3⋊Dic3C2313yes—
141Dic3⋊Dic3C2313yes—
142Dic3⋊Dic3C2313yes—
143Dic3⋊Dic3C2313yes—
144Dic3⋊Dic3C2313yes—
145(C2×D3)⋊Dic3C2313yes—
146(C2×D3)⋊Dic3C2311yescharacteristic
147Dic32C2313yes—
148Dic32C2316yes—
149Dic32C2313yes—
150#3502—91noSylow
151C22×C3×Q8—31no—
152C2×D3×Q8C2×D311yescharacteristic
153C3×C4⋊Q8—33no—
154C3×#125—33no—
155C3×#125—33no—
156C3×C4×Q8—21no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×Q8—33no—
161C3×C4×Q8—33no—
162C3×C4×Q8—33no—
163C3×C4×Q8C2×D311yescharacteristic
164C3×C4×Q8C2×D311yescharacteristic
165C3×#117—33no—
166C3×#117—33no—
167#946—33no—
168Q8×Dic3—31no—
169Q8×Dic3—31no—
170Q8×Dic3—31no—
171Q8×Dic3—31no—
172Q8×Dic3—33no—
173Q8×Dic3—33no—
174Q8×Dic3—33no—
175Q8×Dic3—33no—
176Q8×Dic3—61no—
177Q8×Dic3—61no—
178Q8×Dic3C2×D311yescharacteristic
179Q8×Dic3C2×D311yescharacteristic
180Q8×Dic3C2×D311yescharacteristic
181#944—33no—
182#944—36no—
183#926—33no—
184#926—33no—
185C2×C4⋊Dic3—33no—
186C2×C4×Dic3—33no—
187#897—33no—
188#896—33no—
189#896—36no—
190#896—31no—
191#892—33no—
192#892C2×D313yes—
193D3×C4⋊C4—33no—
194#890—33no—
195#890—33no—
196#890—33no—
197#890—36no—
198#890—33no—
199#890—33no—
200#890—33no—
201#890—63no—
202#890C2×D313yes—
203#890C2×D313yes—
204#889—36no—
205#889—33no—
206#889—33no—
207#889—36no—
208#888—33no—
209#888—36no—
210#888—33no—
211#888—33no—
212#888—33no—
213#888—33no—
214#888—33no—
215#888—33no—
216#888—33no—
217#888—33no—
218#888—36no—
219#888—33no—
220#888—33no—
221#888—63no—
222#887—33no—
223#887—33no—
224#887—36no—
225#887—36no—
226#887C2×D313yes—
227#878—33no—
228#878—31no—
229#878—36no—
230#878—33no—
231#878—33no—
232#872—33no—
233#872C2×D313yes—
234C42×D3—33no—
235#870—33no—
236#870—33no—
237#870—33no—
238#870—33no—
239#870—36no—
240#870—63no—
241#869—33no—
242#869—36no—
243#869—33no—
244#869C2×D313yes—
245C4×Dic6—33no—
246C4×Dic6—33no—
247C4×Dic6—33no—
248C4×Dic6—33no—
249C4×Dic6—36no—
250C4×Dic6—36no—
251C4×Dic6—33no—
252C4×Dic6—33no—
253C4×Dic6—33no—
254C4×Dic6—33no—
255C4×Dic6—63no—
256C4×Dic6C2×D313yes—
257C4×Dic6C2×D313yes—
258C22×C3×D3C2411yescharacteristic
259C32×Q8C2×Q814yes—
260C2×C32×C4C2413yes—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2413yes—
263C2×C3⋊Dic3C2413yes—
264C2×C3⋊Dic3C2413yes—
265C2×C3⋊Dic3C2411yescharacteristic
266C2×C3⋊Dic3C2411yescharacteristic
267#634—26no—
268C2×C3×Dic3C2411yescharacteristic
269C2×C3×Dic3C2413yes—
270C2×C3×Dic3C2413yes—
271C2×C3×Dic3C2411yescharacteristic
272C2×C3×Dic3C2411yescharacteristic
273C2×C3×Dic3C2413yes—
274C2×C3×Dic3C2413yes—
275C3×C4×D3C2×Q8112yes—
276C3×Dic6—43no—
277C3×Dic6C2×Q8112yes—
278#627—22no—
279#627—43no—
280#627—46no—
281D3×Dic3—22no—
282D3×Dic3—43no—
283Q82—91no—
284Q82—93no—
285#557—31no—
286#557—93no—
287#557—91no—
288#557—93no—
289#557—93no—
290#557—91no—
291#544—93no—
292#544—93no—
293#533—93no—
294#533—93no—
295#519—31no—
296#519—91no—
297C2×C4×Q8—91no—
298C2×C3×Q8—21no—
299C2×C3×Q8—38no—
300C2×C3×Q8—33no—
301C2×C3×Q8—33no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C22×C3×C4—33no—
305C22×Dic3—31no—
306C22×Dic3—33no—
307D3×Q8Dic618yescomplemented
308C2×C4×D3—31no—
309C2×C4×D3—33no—
310C2×C4×D3C22×D313yes—
311C2×Dic6—33no—
312C2×Dic6—33no—
313C2×Dic6—31no—
314C2×Dic6—31no—
315C2×Dic6—33no—
316C2×Dic6—36no—
317C2×Dic6—33no—
318C2×Dic6—36no—
319C2×Dic6—63no—
320C2×Dic6C22×D313yes—
321C2×Dic6C22×D313yes—
322C3×C4⋊C4—23no—
323C3×C4⋊C4—33no—
324C3×C4⋊C4—33no—
325C3×C4⋊C4—36no—
326C3×C4⋊C4—33no—
327C3×C4⋊C4—33no—
328C3×C4⋊C4—33no—
329C3×C4⋊C4—33no—
330C3×C4⋊C4—33no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4C22×D313yes—
333C3×C4⋊C4C22×D313yes—
334C3×C22⋊C4—31no—
335C3×C22⋊C4—33no—
336C3×C42—23no—
337C3×C42—36no—
338C3×C42—33no—
339C3×C42—33no—
340C3×C42—33no—
341C3×C42C22×D313yes—
342C3×C42C22×D313yes—
343#217—33no—
344#217—31no—
345(C2×D3)⋊C4—31no—
346(C2×D3)⋊C4—33no—
347(C2×D3)⋊C4C22×D311yescharacteristic
348(C2×D3)⋊C4C22×D313yes—
349C4⋊Dic3—33no—
350C4⋊Dic3—33no—
351C4⋊Dic3—33no—
352C4⋊Dic3—33no—
353C4⋊Dic3—33no—
354C4⋊Dic3—33no—
355C4⋊Dic3—33no—
356C4⋊Dic3—33no—
357C4⋊Dic3—33no—
358C4⋊Dic3—33no—
359C4⋊Dic3—33no—
360C4⋊Dic3—36no—
361C4⋊Dic3—33no—
362C4⋊Dic3—63no—
363C4⋊Dic3—63no—
364C4⋊Dic3—63no—
365C4⋊Dic3C22×D316yes—
366C4⋊Dic3C22×D311yescharacteristic
367C4⋊Dic3C22×D313yes—
368C4⋊Dic3C22×D313yes—
369C4⋊Dic3C22×D313yes—
370Dic3⋊C4—31no—
371Dic3⋊C4—31no—
372Dic3⋊C4—33no—
373Dic3⋊C4—36no—
374Dic3⋊C4—33no—
375Dic3⋊C4—36no—
376Dic3⋊C4—33no—
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—33no—
380Dic3⋊C4—33no—
381Dic3⋊C4—36no—
382Dic3⋊C4—33no—
383Dic3⋊C4—33no—
384Dic3⋊C4—33no—
385Dic3⋊C4—36no—
386Dic3⋊C4—33no—
387Dic3⋊C4—36no—
388Dic3⋊C4—33no—
389Dic3⋊C4—61no—
390Dic3⋊C4—63no—
391Dic3⋊C4—66no—
392Dic3⋊C4C22×D313yes—
393Dic3⋊C4C22×D313yes—
394Dic3⋊C4C22×D313yes—
395Dic3⋊C4C22×D313yes—
396C4×Dic3—33no—
397C4×Dic3—33no—
398C4×Dic3—33no—
399C4×Dic3—33no—
400C4×Dic3—33no—
401C4×Dic3—33no—
402C4×Dic3—36no—
403C4×Dic3—33no—
404C4×Dic3—36no—
405C4×Dic3—33no—
406C4×Dic3—63no—
407C4×Dic3—63no—
408C4×Dic3C22×D313yes—
409C4×Dic3C22×D313yes—
410C4×Dic3C22×D313yes—
411C4×Dic3C22×D316yes—
412C22×C32C2511yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3C22×Q812yes—
416C32×C4—23no—
417C32×C4—21no—
418C32×C4C22×Q816yes—
419C3⋊Dic3—23no—
420C3⋊Dic3—23no—
421C3⋊Dic3—21no—
422C3⋊Dic32−1+412yes—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—23no—
427C3×Dic3—23no—
428C3×Dic3—23no—
429C3×Dic3C22×Q816yes—
430C22×Q8—31no—
431C4⋊Q8—33no—
432C4⋊Q8—93no—
433C4⋊Q8—96no—
434C4⋊Q8—93no—
435C4⋊Q8—93no—
436C4⋊Q8—93no—
437C4⋊Q8—93no—
438C4⋊Q8—93no—
439C4⋊Q8—96no—
440C4⋊Q8—93no—
441#125—33no—
442#125—33no—
443#125—93no—
444#125—96no—
445#125—93no—
446#125—93no—
447#125—93no—
448#125—96no—
449#125—93no—
450#125—93no—
451C22⋊Q8—91no—
452C22⋊Q8—93no—
453C22⋊Q8—96no—
454C22⋊Q8—93no—
455C22⋊Q8—93no—
456C4×Q8—31no—
457C4×Q8—31no—
458C4×Q8—31no—
459C4×Q8—33no—
460C4×Q8—33no—
461C4×Q8—33no—
462C4×Q8—93no—
463C4×Q8—93no—
464C4×Q8—96no—
465C4×Q8—96no—
466C4×Q8—93no—
467C4×Q8—93no—
468C4×Q8—93no—
469C4×Q8—93no—
470C4×Q8—91no—
471C4×Q8—91no—
472C4×Q8—93no—
473C4×Q8D3211yescharacteristic
474#117—33no—
475#117—33no—
476#117—93no—
477#117—93no—
478C2×C4⋊C4—93no—
479C2×C42—93no—
480C23×C3—31no—
481C22×D3C23×D311yescharacteristic
482C3×Q8—24no—
483C3×Q8—312no—
484C3×Q8—123no—
485C3×Q8C2×Dic614yes—
486C3×Q8D3×Q814yes—
487C2×C3×C4—23no—
488C2×C3×C4—21no—
489C2×C3×C4—23no—
490C2×C3×C4—33no—
491C2×C3×C4—312no—
492C2×C3×C4—31no—
493C2×C3×C4—33no—
494C2×C3×C4—33no—
495C2×C3×C4—31no—
496C2×C3×C4—33no—
497C2×C3×C4—31no—
498C2×C3×C4C23×D313yes—
499C2×C3×C4C23×D311yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501C2×C3×C4C23×D313yes—
502C2×C3×C4C23×D313yes—
503C2×C3×C4C23×D313yes—
504C2×Dic3—31no—
505C2×Dic3—31no—
506C2×Dic3—33no—
507C2×Dic3—33no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—33no—
511C2×Dic3—33no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—63no—
515C2×Dic3—63no—
516C2×Dic3—62no—
517C2×Dic3—123no—
518C2×Dic3C23×D311yescharacteristic
519C2×Dic3C23×D313yes—
520C2×Dic3C23×D313yes—
521C2×Dic3C23×D311yescharacteristic
522C2×Dic3C23×D313yes—
523C2×Dic3C23×D311yescharacteristic
524C2×Dic3C23×D313yes—
525C4×D3—62no—
526C4×D3—123no—
527C4×D3C2×Dic6112yes—
528Dic6—43no—
529Dic6—62no—
530Dic6—62no—
531Dic6—66no—
532Dic6—66no—
533Dic6—126no—
534Dic6—126no—
535Dic6—123no—
536Dic6—123no—
537Dic6—126no—
538Dic6C2×Dic6112yes—
539C2×C32C23×Q811yescharacteristic
540C2×C32C2×2−1+411yescharacteristic
541C2×C32#58511yescharacteristic
542C3×D3—22no—
543C2×Q8—38no—
544C2×Q8—33no—
545C2×Q8—33no—
546C2×Q8—91no—
547C2×Q8—96no—
548C2×Q8—93no—
549C2×Q8—93no—
550C2×Q8C2×D3211yescharacteristic
551C22×C4—33no—
552C22×C4—91no—
553C22×C4—93no—
554C4⋊C4—33no—
555C4⋊C4—33no—
556C4⋊C4—33no—
557C4⋊C4—33no—
558C4⋊C4—33no—
559C4⋊C4—31no—
560C4⋊C4—33no—
561C4⋊C4—33no—
562C4⋊C4—36no—
563C4⋊C4—96no—
564C4⋊C4—93no—
565C4⋊C4—93no—
566C4⋊C4—91no—
567C4⋊C4—93no—
568C4⋊C4—93no—
569C4⋊C4—93no—
570C4⋊C4—96no—
571C4⋊C4—93no—
572C4⋊C4—93no—
573C4⋊C4—93no—
574C4⋊C4—93no—
575C4⋊C4—91no—
576C4⋊C4—96no—
577C4⋊C4—93no—
578C4⋊C4—93no—
579C4⋊C4C2×D3213yes—
580C22⋊C4—31no—
581C22⋊C4—33no—
582C22⋊C4—91no—
583C22⋊C4—93no—
584C42—33no—
585C42—36no—
586C42—33no—
587C42—33no—
588C42—93no—
589C42—93no—
590C42—96no—
591C42—93no—
592C42—93no—
593C42C2×D3213yes—
594C22×C3—21no—
595C22×C3—32no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3C24×D311yescharacteristic
599C22×C3C24×D311yescharacteristic
600C2×D3—21no—
601C2×D3—21no—
602C2×D3C22×Dic612yes—
603C3×C4—21no—
604C3×C4—23no—
605C3×C4—23no—
606C3×C4—21no—
607C3×C4—26no—
608C3×C4—36no—
609C3×C4—43no—
610C3×C4—41no—
611C3×C4—63no—
612C3×C4—61no—
613C3×C4—61no—
614C3×C4—61no—
615C3×C4—63no—
616C3×C4—63no—
617C3×C4C22×Dic616yes—
618C3×C4C2×D3×Q816yes—
619Dic3—23no—
620Dic3—23no—
621Dic3—21no—
622Dic3—21no—
623Dic3—21no—
624Dic3—23no—
625Dic3—32no—
626Dic3—32no—
627Dic3—62no—
628Dic3—61no—
629Dic3—63no—
630Dic3—63no—
631Dic3—63no—
632Dic3—61no—
633Dic3—63no—
634Dic3—123no—
635Dic3—123no—
636Dic3—121no—
637Dic3C22×Dic616yes—
638C32#350211yescharacteristic, complemented, Sylow
639C23—31no—
640Q8—312no—
641Q8—123no—
642Q8—186no—
643Q8—182no—
644Q8—363no—
645Q8—366no—
646Q8D3×Dic614yes—
647C2×C4—33no—
648C2×C4—312no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—33no—
652C2×C4—31no—
653C2×C4—33no—
654C2×C4—33no—
655C2×C4—91no—
656C2×C4—93no—
657C2×C4—91no—
658C2×C4—93no—
659C2×C4—182no—
660C2×C4—363no—
661C2×C4C22×D3213yes—
662C2×C4C22×D3211yescharacteristic
663C2×C4C22×D3213yes—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—62no—
668C2×C3C23×Dic611yescharacteristic
669C2×C3C22×D3×Q811yescharacteristic
670C2×C3#596411yescharacteristic
671C2×C3D3×2−1+411yescharacteristic
672C2×C3D3×2−1+411yescharacteristic
673C2×C3#596811yescharacteristic
674D3—22no—
675C22—32no—
676C22—61no—
677C22—61no—
678C22C23×D3211yescharacteristic
679C4—21no—
680C4—23no—
681C4—36no—
682C4—63no—
683C4—63no—
684C4—63no—
685C4—61no—
686C4—61no—
687C4—61no—
688C4—92no—
689C4—183no—
690C4—181no—
691C4—183no—
692C4C2×D3×Dic616yes—
693C3—21no—
694C3#8587511yescharacteristic, complemented
695C3#8703211yescharacteristic, complemented
696C2—62no—
697C2C22×D3×Dic611yescharacteristic
698C2#1059668811yescharacteristic
699C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC22×C3×D3C24
hypercenterC4×Q8D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596040C2semidirect
3. C3×#5570C2semidirect
4. Q8×#627C2semidirect
6. #10595351C2semidirect
10. #10594322C2semidirect
11. #10594321C2semidirect
14. #10593856C2semidirect
15. #10593851C2semidirect
83. #5570D3semidirect
101. C3×D3×Q8Q8semidirect
307. D3×Q8Dic6semidirect
638. C32#3502semidirect
694. C3#85875semidirect
695. C3#87032semidirect

Maximal subgroups

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

subgroupindex
#105960402
C3×#55722
C3×#55702
Q8×#6272
D3×Q8×Dic32
#105953512
#105953472
#105945052
#105944772
#105943222
#105943212
#105939542
#105939262
#105938562
#105938512
#870323
#858753