Finite Group Databasebeta

← #11872591

Subgroups — #11872591

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594983C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3#10592422C211yesmaximal, characteristic, complemented
4C3×#4738C211yesmaximal, characteristic
5C3×#4720C211yesmaximal, characteristic, complemented
6#10591186C211yesmaximal, characteristic, complemented
7#10591093C211yesmaximal, characteristic
8#10590859C211yesmaximal, characteristic, complemented
9#10590859C211yesmaximal, characteristic, complemented
10#10590804C211yesmaximal, characteristic, complemented
11#10590803C211yesmaximal, characteristic, complemented
12#10590794C211yesmaximal, characteristic, complemented
13#10590793C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15Dic3×#204C211yesmaximal, characteristic, complemented
16#80032—31nomaximal
17#79394—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19#64135C2211yescharacteristic
20#64133C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25#63969—21no—
26#63959—21no—
27#63955—21no—
28#63955—21no—
29#63918C2211yescharacteristic
30#63899—21no—
31Dic3×D12C2211yescharacteristic
32#63860C2211yescharacteristic
33#63858—21no—
34#63844C2211yescharacteristic
35#63843—21no—
36#63843—21no—
37Dic3×Dic6C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63645C2211yescharacteristic
45#63644C2211yescharacteristic
46#63643C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5812—31no—
62#5603—31no—
63#5534—31no—
64#5516—31no—
65C3×#448—31no—
66C3×#433—31no—
67#5228—31no—
68#5166—31no—
69#5166—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5035—31no—
73#4851—31no—
74#4850—31no—
75#4845—31no—
76#4845—31no—
77#4793—31no—
78#4791—31no—
79#4790—31no—
80#4789—31no—
81#4739—31no—
82#4738D311yescharacteristic
83#4737—31no—
84#4723—31no—
85#4723—31no—
86#4723—61no—
87#4720D311yescharacteristic, complemented
88#4716—31no—
89#4710—31no—
90C4×Dic12—31no—
91C4×#204—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×#67—21no—
95C22×C3×Dic3—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×Dic6—21no—
98C2×C3×Dic6—22no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×D3×Dic3—21no—
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106#3757—21no—
107#3757—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111#3750—21no—
112C4×C3⋊Dic3—21no—
113C3×#217D411yescharacteristic
114C3×#217D411yescharacteristic
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3D411yescharacteristic
117C3×C4⋊Dic3D411yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C3×#204—22no—
124C3×#204—22no—
125#3724—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3719—22no—
140#3719—22no—
141#3121—91noSylow
142C22×C3×Q8—31no—
143C22×Dic6C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×#121—31no—
147C3×#117—31no—
148Q8×Dic3—31no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—61no—
153Q8×Dic3—61no—
154C2×#216—31no—
155C2×#216—31no—
156#936—31no—
157#936—61no—
158#935—61no—
159D4×Dic3—31no—
160#930C2×D311yescharacteristic
161#926—31no—
162#926—31no—
163#926—61no—
164#926—61no—
165#926—61no—
166#926C2×D311yescharacteristic
167#924—31no—
168#924—31no—
169#924—61no—
170C2×Dic12—31no—
171C2×Dic12—31no—
172C2×#204C2×D311yescharacteristic
173C2×#204C2×D311yescharacteristic
174#898—61no—
175#896—61no—
176#888—31no—
177#887—31no—
178#887—61no—
179#887—61no—
180#885—61no—
181#883—61no—
182#879—61no—
183#878—61no—
184#877—61no—
185#877—61no—
186#875—31no—
187C4×D12—31no—
188#869—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×C22⋊C8—21no—
199C3×C22⋊C8—31no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202C3×#97—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835—31no—
206#832—31no—
207#832—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#818—31no—
212#818—31no—
213#818—31no—
214#818—61no—
215#817—31no—
216#817—31no—
217#817—31no—
218#817—61no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816—61no—
227#816C2×D311yescharacteristic
228#816C2×D311yescharacteristic
229#815C2×D311yescharacteristic
230Dic3⋊C8C2×D311yescharacteristic
231Dic3⋊C8C2×D311yescharacteristic
232C8×Dic3C2×D311yescharacteristic
233#808—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245#634—21no—
246#634—21no—
247C3×#67—81no—
248C2×C3×Dic3—24no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×Dic6—24no—
259C3×Dic6—21no—
260C3×Dic6—21no—
261C3×Dic6#4112yes—
262C3×Dic6#4112yes—
263#627—81no—
264D3×Dic3—81no—
265C32×C8—21no—
266C32×C8—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—91no—
270#519—91no—
271#485—91no—
272#482—91no—
273#477—91no—
274#475—91no—
275#464—91no—
276#464—91no—
277#451—91no—
278#448—31no—
279#441—91no—
280#440—91no—
281C4×Q16—91no—
282C4×SD16—91no—
283#433—31no—
284C2×C3×Q8—31no—
285C2×C3×Q8—31no—
286C2×C3×Q8—62no—
287C2×C3×Q8—62no—
288C2×C3×Q8—61no—
289C2×C3×D4—31no—
290C2×C3×D4—61no—
291C22×C3×C4—21no—
292C22×C3×C4—61no—
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C2×#67—21no—
296C22×Dic3—21no—
297C22×Dic3—61no—
298C2×D12C22×D311yescharacteristic
299C2×C4×D3—61no—
300C2×Dic6—21no—
301C2×Dic6—22no—
302C2×Dic6—22no—
303C2×Dic6—31no—
304C2×Dic6—31no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6C22×D311yescharacteristic
309C2×Dic6C22×D311yescharacteristic
310C3×SD16—62no—
311C3×SD16—62no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8C22×D311yescharacteristic
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319C2×C3×C8C22×D311yescharacteristic
320C3×C4⋊C4—31no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C22⋊C4—31no—
324C3×C22⋊C4—31no—
325C3×C22⋊C4—61no—
326C3×C42—31no—
327C3×C42—31no—
328#217—61no—
329#217—61no—
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#217—121no—
336#217—121no—
337#217D1211yescharacteristic
338#217D1211yescharacteristic
339#216—62no—
340#216—62no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—61no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—31no—
349C4⋊Dic3—31no—
350C4⋊Dic3—31no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3D1211yescharacteristic
360C4⋊Dic3D1211yescharacteristic
361C4⋊Dic3C22×D311yescharacteristic
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—121no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—121no—
385C4×Dic3C22×D311yescharacteristic
386C4×Dic3C22×D311yescharacteristic
387C2×C3⋊C8C22×D311yescharacteristic
388C2×C3⋊C8C22×D311yescharacteristic
389Dic12—62no—
390Dic12—62no—
391#204—22no—
392#204—22no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32—21no—
396C22×C32C22×D411yescharacteristic
397C2×C3×D3—41no—
398C2×C3×D3—41no—
399C2×C3×D3—41no—
400C32×C4—21no—
401C32×C4C2×#4111yescharacteristic
402C32×C4C2×#4111yescharacteristic
403C3⋊Dic3—41no—
404C3⋊Dic3—41no—
405C3⋊Dic3—41no—
406C3⋊Dic3—41no—
407C3×Dic3—22no—
408C3×Dic3—22no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—41no—
414C22×Q8—31no—
415C2×Q16—91no—
416C2×Q16—91no—
417C2×SD16—31no—
418C2×SD16—31no—
419C4⋊Q8—91no—
420#126—181no—
421#124—91no—
422#124—181no—
423#123—181no—
424C22⋊Q8—91no—
425C22⋊Q8—181no—
426#121—31no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—181no—
433C4×Q8—181no—
434C4×D4—91no—
435#117—31no—
436#117—91no—
437#117—181no—
438#117—181no—
439#107—91no—
440#107—91no—
441#106—91no—
442#106—91no—
443C4⋊C8—31no—
444C4⋊C8—31no—
445#103—31no—
446#103—31no—
447#103—91no—
448#103—91no—
449#103—91no—
450#103—91no—
451#102—91no—
452#102—91no—
453C22⋊C8—31no—
454C22⋊C8D3211yescharacteristic
455#97—31no—
456C4×C8—31no—
457C23×C3—21no—
458C23×C3—61no—
459C23×C3C2×D1211yescharacteristic
460C23×C3D3×D411yescharacteristic
461C22×D3—21no—
462C3×Q8—32no—
463C3×Q8—32no—
464C3×Q8—64no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×D4—61no—
468C3×D4—61no—
469C3×D4—241no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—31no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—64no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4C2×D1211yescharacteristic
487C2×C3×C4D3×D411yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C23×D311yescharacteristic
490#67—81no—
491C2×Dic3—24no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—61no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—121no—
504C2×Dic3—121no—
505C2×Dic3—121no—
506C2×Dic3—121no—
507C2×Dic3—241no—
508C2×Dic3C2×D1211yescharacteristic
509C2×Dic3C2×D1211yescharacteristic
510C2×Dic3C2×D1211yescharacteristic
511C2×Dic3C2×D1211yescharacteristic
512D12—21no—
513D12—21no—
514C4×D3—241no—
515Dic6—24no—
516Dic6—21no—
517Dic6—21no—
518Dic6—61no—
519Dic6—61no—
520Dic6—61no—
521Dic6—61no—
522Dic6—121no—
523Dic6—121no—
524Dic6—241no—
525Dic6—241no—
526Dic6#23712yes—
527Dic6#23712yes—
528C3×C8—21no—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—21no—
532C3×C8—41no—
533C3×C8—41no—
534C3×C8—61no—
535C3×C8—61no—
536C3⋊C8—21no—
537C3⋊C8—21no—
538C2×C32—41no—
539C2×C32#52511yescharacteristic
540C2×C32#57711yescharacteristic
541C2×C32#57811yescharacteristic
542C3×D3—81no—
543C2×Q8—31no—
544C2×Q8—31no—
545C2×Q8—62no—
546C2×Q8—62no—
547C2×Q8—61no—
548C2×Q8—91no—
549C2×Q8—181no—
550C2×D4—31no—
551C2×D4—61no—
552C22×C4—61no—
553C22×C4—181no—
554C22×C4C2×D3211yescharacteristic
555Q16—182no—
556Q16—182no—
557SD16—62no—
558SD16—62no—
559C2×C8—31no—
560C2×C8—31no—
561C2×C8C2×D3211yescharacteristic
562C2×C8C2×D3211yescharacteristic
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—91no—
569C4⋊C4—181no—
570C4⋊C4—181no—
571C4⋊C4—181no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C22⋊C4—31no—
577C22⋊C4—31no—
578C22⋊C4—61no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C22⋊C4—181no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C42—31no—
585C42—31no—
586C42—181no—
587C42—181no—
588C42—181no—
589C42—181no—
590C42—181no—
591C42—181no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—121no—
603C22×C3—121no—
604C22×C3—121no—
605C22×C3C22×D1211yescharacteristic
606C22×C3C2×D3×D411yescharacteristic
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—41no—
615C3×C4—61no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—121no—
622C3×C4C2×#23711yescharacteristic
623C3×C4C2×#23711yescharacteristic
624C3×C4D3×#4111yescharacteristic
625C3×C4D3×#4111yescharacteristic
626Dic3—21no—
627Dic3—21no—
628Dic3—21no—
629Dic3—21no—
630Dic3—22no—
631Dic3—22no—
632Dic3—41no—
633Dic3—121no—
634Dic3—121no—
635Dic3—121no—
636Dic3—121no—
637Dic3—121no—
638Dic3—121no—
639Dic3—121no—
640Dic3—121no—
641Dic3—241no—
642Dic3—241no—
643Dic3—241no—
644Dic3—241no—
645C32#312111yescharacteristic, complemented, Sylow
646C23—61no—
647C23D3×D1211yescharacteristic
648Q8—32no—
649Q8—32no—
650Q8—64no—
651Q8—61no—
652Q8—61no—
653Q8—181no—
654Q8—181no—
655Q8—721no—
656D4—61no—
657D4—61no—
658D4—241no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—64no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—181no—
672C2×C4—181no—
673C2×C4—721no—
674C2×C4D3×D1211yescharacteristic
675C2×C4C22×D3211yescharacteristic
676C8—21no—
677C8—21no—
678C8—61no—
679C8—61no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—41no—
684C2×C3—41no—
685C2×C3—81no—
686C2×C3—241no—
687C2×C3#552411yescharacteristic
688C2×C3#558611yescharacteristic
689C2×C3#575111yescharacteristic
690C2×C3#575311yescharacteristic
691C2×C3#576211yescharacteristic
692C2×C3#577911yescharacteristic
693D3—81no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—121no—
698C22—121no—
699C22—121no—
700C22C2×D3×D1211yescharacteristic
701C4—21no—
702C4—62no—
703C4—62no—
704C4—61no—
705C4—61no—
706C4—61no—
707C4—61no—
708C4—121no—
709C4—361no—
710C4—361no—
711C4—361no—
712C4—361no—
713C4D3×#23711yescharacteristic
714C4D3×#23711yescharacteristic
715C3—21no—
716C3#7939411yescharacteristic, complemented
717C3#8003211yescharacteristic, complemented
718C2—41no—
719C2—241no—
720C2#1059407811yescharacteristic
721C2#1059467711yescharacteristic
722C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radicalC3×#930C22
hypercenterC22⋊C8D32
hypocenterC32#3121
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
3. #10592422C2semidirect
5. C3×#4720C2semidirect
6. #10591186C2semidirect
8. #10590859C2semidirect
9. #10590859C2semidirect
10. #10590804C2semidirect
11. #10590803C2semidirect
12. #10590794C2semidirect
13. #10590793C2semidirect
14. #10590766C2semidirect
15. Dic3×#204C2semidirect
87. #4720D3semidirect
645. C32#3121semidirect
716. C3#79394semidirect
717. C3#80032semidirect

Maximal subgroups

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

subgroupindex
#105949832
#105948182
#105924222
C3×#47382
C3×#47202
#105911862
#105910932
#105908592
#105908042
#105908032
#105907942
#105907932
#105907662
Dic3×#2042
#800323
#793943