Finite Group Databasebeta

← #11868760

Subgroups — #11868760

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594477C211yesmaximal, characteristic
2D3×#887C211yesmaximal, characteristic
3#10592553C211yesmaximal, characteristic, complemented
4C3×#4861C211yesmaximal, characteristic
5C3×#4857C211yesmaximal, characteristic, complemented
6#10590948C211yesmaximal, characteristic
7#10590817C211yesmaximal, characteristic, complemented
8#10590814C211yesmaximal, characteristic, complemented
9#10590663C211yesmaximal, characteristic
10#10590600C211yesmaximal, characteristic
11#10590580C211yesmaximal, characteristic
12#10590544C211yesmaximal, characteristic, complemented
13#10590497C211yesmaximal, characteristic, complemented
14#10590490C211yesmaximal, characteristic, complemented
15#10590432C211yesmaximal, characteristic, complemented
16#81230—31nomaximal
17#79245—31nomaximal
18C2×D3×Dic6C2211yescharacteristic
19#64097C2211yescharacteristic
20#64096C2211yescharacteristic
21C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
22C3×#892C2211yescharacteristic
23C3×D3×C4⋊C4C2211yescharacteristic
24C3×#890C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63919C2211yescharacteristic
27#63899—21no—
28#63896—21no—
29D3×Dic3⋊C4—21no—
30C4×D3×Dic3—21no—
31C4×D3×Dic3C2211yescharacteristic
32#63869C2211yescharacteristic
33#63844—21no—
34#63844C2211yescharacteristic
35#63843C2211yescharacteristic
36#63841C2211yescharacteristic
37#63838—21no—
38#63837—21no—
39#63837—21no—
40C2×#3711C2211yescharacteristic
41C32×#106C2211yescharacteristic
42#63643C2211yescharacteristic
43#63641C2211yescharacteristic
44#63637C2211yescharacteristic
45#63635C2211yescharacteristic
46C3×#818C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63576C2211yescharacteristic
54#63573C2211yescharacteristic
55#63572C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63565C2211yescharacteristic
61#5688—31no—
62C4×D3×Q8—31no—
63#5517—31no—
64C2×#887—31no—
65C3×#479—31no—
66C3×#428—31no—
67#5120—31no—
68#5118—31no—
69#5063—31no—
70#5022—31no—
71#5004—31no—
72#4964—31no—
73#4881—31no—
74#4877—31no—
75#4877—31no—
76#4875—31no—
77#4875—31no—
78#4875—31no—
79#4861D311yescharacteristic
80#4857—31no—
81#4857D311yescharacteristic, complemented
82#4854—31no—
83#4854—31no—
84#4854—31no—
85#4854—61no—
86#4837—31no—
87#4829—31no—
88#4802—31no—
89#4802—31no—
90#4793—31no—
91#4791—31no—
92C2×#634—21no—
93C2×#634C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×C4×D3C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#627—21no—
99C2×D3×Dic3—21no—
100C2×D3×Dic3D411yescharacteristic
101C2×D3×Dic3D411yescharacteristic
102D3×Dic6—22no—
103D3×Dic6Q814yescomplemented
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109#3750—21no—
110C4×C3⋊Dic3—21no—
111C4×C3⋊Dic3C2311yescharacteristic
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C3×ΓL(1,𝔽25)—22no—
127#3724—21no—
128#3724—21no—
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3711—22no—
139#3078—91noSylow
140C2×D3×Q8—31no—
141C22×Dic6—31no—
142C2×C3×M16—31no—
143C3×#125—31no—
144C3×C4×Q8—31no—
145C3×#117—31no—
146C2×C3×C4⋊C4—31no—
147Q8×Dic3—31no—
148#926—31no—
149C2×Dic3⋊C4—61no—
150C2×C4×Dic3—31no—
151C2×C4×Dic3—61no—
152C2×#208—31no—
153C2×ΓL(1,𝔽25)—31no—
154C2×ΓL(1,𝔽25)C2×D311yescharacteristic
155#896—61no—
156#896—61no—
157#892—31no—
158#892C2×D311yescharacteristic
159D3×C4⋊C4—61no—
160D3×C4⋊C4C2×D311yescharacteristic
161#890—31no—
162#890C2×D311yescharacteristic
163#888—31no—
164#888—31no—
165#888—31no—
166#888—31no—
167#888—61no—
168#887—31no—
169#887—31no—
170#887—31no—
171#887—31no—
172#887—61no—
173#887—61no—
174#887—61no—
175#887—61no—
176#887—61no—
177#887—61no—
178#887C2×D311yescharacteristic
179#878—61no—
180#878—61no—
181C42×D3—31no—
182C42×D3—61no—
183#870—31no—
184C4×Dic6—31no—
185C4×Dic6—61no—
186C4×Dic6—61no—
187C4×Dic6—61no—
188C3×#107—31no—
189C3×#107—31no—
190C3×#107—31no—
191C3×#106—21no—
192C3×#106—31no—
193C3×#106C2×D311yescharacteristic
194C3×#106C2×D311yescharacteristic
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198#835—31no—
199#835—31no—
200#818C2×D311yescharacteristic
201#817—31no—
202#816—31no—
203#816—31no—
204#816—31no—
205#816—31no—
206#816—31no—
207#816—61no—
208#816C2×D311yescharacteristic
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—61no—
215Dic3⋊C8C2×D311yescharacteristic
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#810C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#808C2×D311yescharacteristic
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic
231#807C2×D311yescharacteristic
232C4⋊(C3⋊C8)—31no—
233C22×C3×D3C2×D411yescharacteristic
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241#634—21no—
242#634—42no—
243#634C2×Q812yes—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×C4×D3—42no—
252C3×C4×D3C2×Q812yes—
253C3×C4×D3#4112yes—
254C3×Dic6—21no—
255C3×Dic6C2×Q812yes—
256#627—24no—
257#627—42no—
258D3×Dic3—24no—
259D3×Dic3—22no—
260D3×Dic3—41no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#533—91no—
266C2×C4×Q8—91no—
267#479—31no—
268#479—91no—
269#479—91no—
270#479—91no—
271#477—91no—
272#477—91no—
273#475—91no—
274#475—91no—
275#428—31no—
276#428—91no—
277#423—91no—
278#419—91no—
279#419—91no—
280C2×C3×Q8—31no—
281C22×C3×C4—31no—
282C22×C3×C4—61no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—61no—
286D3×Q8—34no—
287D3×Q8—62no—
288C2×C4×D3—21no—
289C2×C4×D3—31no—
290C2×C4×D3—31no—
291C2×C4×D3—61no—
292C2×C4×D3C22×D311yescharacteristic
293C2×Dic6—31no—
294C2×Dic6—31no—
295C2×Dic6—34no—
296C2×Dic6—61no—
297C2×Dic6—62no—
298C2×Dic6—61no—
299C2×Dic6—61no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6—121no—
305C2×Dic6C22×D311yescharacteristic
306C3×M16—62no—
307C2×C3×C8—21no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8C22×D311yescharacteristic
311C2×C3×C8C22×D311yescharacteristic
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—31no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C22⋊C4—61no—
326C3×C42—31no—
327C3×C42—61no—
328C3×C42—61no—
329#217—61no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—61no—
332C4⋊Dic3—21no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3C22×D311yescharacteristic
339C4⋊Dic3C22×D311yescharacteristic
340C4⋊Dic3C22×D311yescharacteristic
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344Dic3⋊C4—61no—
345Dic3⋊C4—61no—
346Dic3⋊C4—61no—
347Dic3⋊C4—61no—
348Dic3⋊C4—61no—
349Dic3⋊C4—61no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—121no—
357Dic3⋊C4—121no—
358C4×Dic3—21no—
359C4×Dic3—21no—
360C4×Dic3—31no—
361C4×Dic3—31no—
362C4×Dic3—31no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—121no—
376C4×Dic3C22×D311yescharacteristic
377#208—62no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383ΓL(1,𝔽25)—22no—
384ΓL(1,𝔽25)—62no—
385C22×C32C22×D411yescharacteristic
386C2×C3×D3—21no—
387C2×C3×D3—21no—
388C2×C3×D3C22⋊Q812yes—
389C32×C4—41no—
390C32×C4—41no—
391C32×C4C22×Q811yescharacteristic
392C32×C4C2×#4111yescharacteristic
393C3⋊Dic3—22no—
394C3⋊Dic3—21no—
395C3⋊Dic3—41no—
396C3⋊Dic3#13712yes—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3C22⋊Q812yes—
404C22×Q8—91no—
405C2×M16—31no—
406C2×M16—91no—
407C4⋊Q8—91no—
408C4⋊Q8—91no—
409#125—31no—
410#125—91no—
411C22⋊Q8—181no—
412C22⋊Q8—181no—
413C4×Q8—31no—
414C4×Q8—91no—
415C4×Q8—91no—
416C4×Q8—91no—
417C4×Q8—181no—
418C4×Q8—181no—
419C4×Q8—181no—
420C4×Q8—181no—
421#117—31no—
422#117—91no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—181no—
425C2×C42—91no—
426C2×C42—181no—
427#107—31no—
428#107—31no—
429#107—31no—
430#107—91no—
431#106—31no—
432#106—91no—
433#106—91no—
434#106D3211yescharacteristic
435C4⋊C8—31no—
436C4⋊C8—91no—
437C4⋊C8—91no—
438C4⋊C8—91no—
439#103—31no—
440#103—31no—
441#103—91no—
442#103—91no—
443#103—91no—
444#103—91no—
445#103—91no—
446#103—91no—
447C23×C3—31no—
448C22×D3D3×D411yescharacteristic
449C3×Q8—32no—
450C3×Q8—61no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—31no—
457C2×C3×C4—32no—
458C2×C3×C4—32no—
459C2×C3×C4—31no—
460C2×C3×C4—31no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—122no—
468C2×C3×C4C23×D311yescharacteristic
469C2×C3×C4C23×D311yescharacteristic
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—21no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—31no—
477C2×Dic3—31no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—62no—
481C2×Dic3—64no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—121no—
487C2×Dic3—121no—
488C2×Dic3—121no—
489C2×Dic3D3×D411yescharacteristic
490C2×Dic3D3×D411yescharacteristic
491C2×Dic3D3×D411yescharacteristic
492C4×D3—42no—
493C4×D3—62no—
494C4×D3—64no—
495C4×D3—121no—
496C4×D3#23512yes—
497C4×D3D3×Q812yes—
498Dic6—21no—
499Dic6—32no—
500Dic6—32no—
501Dic6—62no—
502Dic6—64no—
503Dic6—61no—
504Dic6—61no—
505Dic6—64no—
506Dic6—121no—
507Dic6—122no—
508Dic6—122no—
509Dic6—122no—
510Dic6—122no—
511Dic6—242no—
512Dic6D3×Q812yes—
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—41no—
516C3×C8—61no—
517C3×C8—61no—
518C3⋊C8—21no—
519C3⋊C8—21no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—121no—
523C2×C32C2×C22⋊Q811yescharacteristic
524C2×C32C2×#13711yescharacteristic
525C2×C32#57511yescharacteristic
526C3×D3—22no—
527C2×Q8—31no—
528C2×Q8—94no—
529C2×Q8—91no—
530C2×Q8—181no—
531C2×Q8—181no—
532C2×Q8—182no—
533C2×Q8—181no—
534C22×C4—31no—
535C22×C4—61no—
536C22×C4—91no—
537C22×C4—91no—
538C22×C4—181no—
539M16—62no—
540M16—182no—
541C2×C8—31no—
542C2×C8—31no—
543C2×C8—91no—
544C2×C8C2×D3211yescharacteristic
545C4⋊C4—31no—
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—91no—
553C4⋊C4—181no—
554C4⋊C4—181no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4C2×D3211yescharacteristic
561C4⋊C4C2×D3211yescharacteristic
562C22⋊C4—61no—
563C22⋊C4—181no—
564C42—31no—
565C42—61no—
566C42—61no—
567C42—91no—
568C42—91no—
569C42—91no—
570C42—181no—
571C42—181no—
572C42—181no—
573C42—181no—
574C22×C3—21no—
575C22×C3—32no—
576C22×C3—61no—
577C22×C3—61no—
578C22×C3C2×D3×D411yescharacteristic
579C22×C3C2×D3×D411yescharacteristic
580C2×D3—21no—
581C2×D3—21no—
582C2×D3#89612yes—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—32no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—41no—
589C3×C4—41no—
590C3×C4—62no—
591C3×C4—61no—
592C3×C4—61no—
593C3×C4—81no—
594C3×C4—81no—
595C3×C4—121no—
596C3×C4—121no—
597C3×C4—121no—
598C3×C4C2×#23511yescharacteristic
599C3×C4C2×D3×Q811yescharacteristic
600C3×C4C2×D3×Q811yescharacteristic
601C3×C4D3×#4111yescharacteristic
602Dic3—21no—
603Dic3—21no—
604Dic3—22no—
605Dic3—32no—
606Dic3—32no—
607Dic3—41no—
608Dic3—41no—
609Dic3—41no—
610Dic3—62no—
611Dic3—62no—
612Dic3—61no—
613Dic3—61no—
614Dic3—62no—
615Dic3—122no—
616Dic3—121no—
617Dic3—121no—
618Dic3—121no—
619Dic3—241no—
620Dic3#89612yes—
621C32#307811yescharacteristic, complemented, Sylow
622C23—31no—
623Q8—32no—
624Q8—61no—
625Q8—92no—
626Q8—184no—
627Q8—181no—
628Q8—362no—
629Q8—362no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—31no—
633C2×C4—32no—
634C2×C4—32no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—91no—
642C2×C4—91no—
643C2×C4—122no—
644C2×C4—182no—
645C2×C4—184no—
646C2×C4—181no—
647C2×C4—181no—
648C2×C4—361no—
649C2×C4C22×D3211yescharacteristic
650C8—21no—
651C8—61no—
652C8—61no—
653C8—181no—
654C2×C3—21no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—62no—
658C2×C3C2×#89611yescharacteristic
659C2×C3D3×C22⋊Q811yescharacteristic
660C2×C3#576811yescharacteristic
661C2×C3#577311yescharacteristic
662C2×C3D3×#13711yescharacteristic
663C2×C3D3×#13711yescharacteristic
664D3—22no—
665C22—32no—
666C22—61no—
667C22—61no—
668C22D32×D411yescharacteristic
669C4—32no—
670C4—41no—
671C4—41no—
672C4—62no—
673C4—61no—
674C4—61no—
675C4—92no—
676C4—121no—
677C4—121no—
678C4—121no—
679C4—182no—
680C4—181no—
681C4—361no—
682C4D3×#23511yescharacteristic
683C4D32×Q811yescharacteristic
684C3—21no—
685C3#7924511yescharacteristic, complemented
686C3#8123011yescharacteristic, complemented
687C2—62no—
688C2D3×#89611yescharacteristic
689C2#1059474211yescharacteristic
690C2#1059474511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenter#106D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10592553C2semidirect
5. C3×#4857C2semidirect
7. #10590817C2semidirect
8. #10590814C2semidirect
12. #10590544C2semidirect
13. #10590497C2semidirect
14. #10590490C2semidirect
15. #10590432C2semidirect
81. #4857D3semidirect
103. D3×Dic6Q8semidirect
621. C32#3078semidirect
685. C3#79245semidirect
686. C3#81230semidirect

Maximal subgroups

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

subgroupindex
#105944772
D3×#8872
#105925532
C3×#48612
C3×#48572
#105909482
#105908172
#105908142
#105906632
#105906002
#105905802
#105905442
#105904972
#105904902
#105904322
#812303
#792453