Finite Group Databasebeta

← #11895600

Subgroups — #11895600

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 679 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594335C211yesmaximal, characteristic
2#10594321C211yesmaximal, characteristic, complemented
3#10592556C211yesmaximal, characteristic, complemented
4C3×#4857C211yesmaximal, characteristic, complemented
5C3×#4852C211yesmaximal, characteristic
6#10590890C211yesmaximal, characteristic, complemented
7#10590859C211yesmaximal, characteristic
8#10590796C211yesmaximal, characteristic
9#10590644C211yesmaximal, characteristic, complemented
10#10590561C211yesmaximal, characteristic, complemented
11#10590555C211yesmaximal, characteristic
12#10590539C211yesmaximal, characteristic
13#10590533C211yesmaximal, characteristic
14#10590482C211yesmaximal, characteristic, complemented
15#10590476C211yesmaximal, characteristic, complemented
16#81216—31nomaximal
17#79623—31nomaximal
18#64099C2211yescharacteristic
19#64096C2211yescharacteristic
20C2×C3×#204C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#890C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25#63918—21no—
26#63918C2211yescharacteristic
27C4×#627C2211yescharacteristic
28#63866C2211yescharacteristic
29#63863C2211yescharacteristic
30#63862—21no—
31#63860C2211yescharacteristic
32#63859—21no—
33#63855—21no—
34#63851—21no—
35#63846—21no—
36#63845—21no—
37#63843C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63837—21no—
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C32×#106C2211yescharacteristic
43#63643C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#816C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5685—31no—
62#5570—31no—
63#5568—31no—
64#5542—31no—
65C3×#479—31no—
66C3×C4×SD16—31no—
67#5166—31no—
68#5166—31no—
69#5068—31no—
70#5031—31no—
71C4×#216—31no—
72#5007—31no—
73#4890—31no—
74#4873—31no—
75#4857—31no—
76#4857—31no—
77#4857—61no—
78#4857D311yescharacteristic, complemented
79#4852D311yescharacteristic
80#4845—31no—
81#4830—31no—
82#4800—31no—
83#4798—31no—
84#4795—31no—
85#4792—31no—
86#4790—31no—
87#4790—31no—
88#4768—31no—
89#4768—31no—
90#4681—31no—
91C8×Dic6—31no—
92C2×#634C2311yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#627D411yescharacteristic
99C2×C32×C8C2311yescharacteristic
100C32×C4⋊C4C2311yescharacteristic
101C32×C4⋊C4C2311yescharacteristic
102C4⋊(C3⋊Dic3)—21no—
103C4⋊(C3⋊Dic3)C2311yescharacteristic
104#3750—21no—
105#3750—21no—
106C4×C3⋊Dic3—21no—
107C4×C3⋊Dic3C2311yescharacteristic
108C2×C3⋊(C3⋊C8)C2311yescharacteristic
109C3×(C2×D3)⋊C4—21no—
110C3×C4⋊Dic3—21no—
111C3×C4⋊Dic3C2311yescharacteristic
112C3×Dic3⋊C4—21no—
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
115C3×C4×Dic3—21no—
116C3×C4×Dic3—21no—
117C3×C4×Dic3C2311yescharacteristic
118C3×C4×Dic3C2311yescharacteristic
119C2×C3×C3⋊C8C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C3×#204—22no—
122#3724D411yescharacteristic
123Dic3⋊Dic3—21no—
124Dic3⋊Dic3—21no—
125Dic3⋊Dic3—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3D411yescharacteristic
129Dic3⋊Dic3D411yescharacteristic
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3719—22no—
137#3718—22no—
138#3364—91noSylow
139C2×C3×SD16—31no—
140C3×#125—31no—
141C3×C4×Q8—31no—
142C3×C4×Q8—31no—
143C3×C4×D4—31no—
144#947—31no—
145Q8×Dic3—31no—
146Q8×Dic3—31no—
147#944—31no—
148C2×#216—31no—
149C2×#216—31no—
150C2×#216—31no—
151#936—31no—
152#936—31no—
153#926—61no—
154#924—61no—
155C2×Dic12—31no—
156C2×#204C2×D311yescharacteristic
157#898—61no—
158#896—61no—
159#893C2×D311yescharacteristic
160#890—31no—
161#890—31no—
162#890—61no—
163#890—61no—
164#890—61no—
165#890C2×D311yescharacteristic
166#889—61no—
167#889—61no—
168#888—31no—
169#888—61no—
170#887—31no—
171#887—31no—
172#887—31no—
173#887—61no—
174#887—61no—
175#887C2×D311yescharacteristic
176#887C2×D311yescharacteristic
177#879—61no—
178#879—61no—
179#876—61no—
180#875—31no—
181#872—61no—
182#869—31no—
183#869—31no—
184#869—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#107—31no—
190C3×#106—21no—
191C3×#106C2×D311yescharacteristic
192C3×#106C2×D311yescharacteristic
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#835—31no—
200#832—31no—
201#832—31no—
202#821—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—61no—
213Dic3⋊C8C2×D311yescharacteristic
214C8×Dic3—31no—
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3C2×D311yescharacteristic
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#810C2×D311yescharacteristic
223#810C2×D311yescharacteristic
224#809—31no—
225#809C2×D311yescharacteristic
226#807—31no—
227#807—31no—
228#807—61no—
229#807C2×D311yescharacteristic
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3×D3—21no—
233C2×C32×C4—21no—
234C2×C32×C4—21no—
235C2×C32×C4C2411yescharacteristic
236C2×C3⋊Dic3—21no—
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240#634—21no—
241#634—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3C2×D411yescharacteristic
246C2×C3×Dic3C2×D411yescharacteristic
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C3×D12—21no—
250C3×D12—21no—
251C3×C4×D3—42no—
252C3×Dic6—21no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6#4112yes—
256#627—22no—
257#627—42no—
258C32×C8—21no—
259C3⋊(C3⋊C8)—21no—
260C3×C3⋊C8—21no—
261C3×C3⋊C8—21no—
262#557—91no—
263#556—91no—
264#488—91no—
265#488—91no—
266#487—91no—
267#479—31no—
268#479—91no—
269#474—91no—
270#464—91no—
271#464—91no—
272#462—91no—
273C8×Q8—91no—
274C4×Q16—91no—
275C4×Q16—91no—
276C4×SD16—31no—
277C2×C3×Q8—31no—
278C2×C3×Q8—31no—
279C2×C3×D4—31no—
280C22×C3×C4—61no—
281C2×D12C22×D311yescharacteristic
282C2×C4×D3—21no—
283C2×Dic6—31no—
284C2×Dic6—31no—
285C2×Dic6—31no—
286C2×Dic6—31no—
287C2×Dic6—61no—
288C2×Dic6—61no—
289C2×Dic6—61no—
290C2×Dic6C22×D311yescharacteristic
291C2×Dic6C22×D311yescharacteristic
292C3×SD16—62no—
293C2×C3×C8—21no—
294C2×C3×C8—31no—
295C2×C3×C8—31no—
296C2×C3×C8C22×D311yescharacteristic
297C2×C3×C8C22×D311yescharacteristic
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—31no—
301C3×C4⋊C4—61no—
302C3×C4⋊C4—61no—
303C3×C4⋊C4—61no—
304C3×C4⋊C4—61no—
305C3×C4⋊C4C22×D311yescharacteristic
306C3×C4⋊C4C22×D311yescharacteristic
307C3×C4⋊C4C22×D311yescharacteristic
308C3×C4⋊C4C22×D311yescharacteristic
309C3×C22⋊C4—61no—
310C3×C42—31no—
311C3×C42—31no—
312C3×C42—61no—
313C3×C42—61no—
314#217—61no—
315#217—61no—
316#217—61no—
317#217—61no—
318#216—62no—
319#216—62no—
320#216—62no—
321(C2×D3)⋊C4—21no—
322(C2×D3)⋊C4—61no—
323(C2×D3)⋊C4—61no—
324(C2×D3)⋊C4—61no—
325(C2×D3)⋊C4—61no—
326C4⋊Dic3—21no—
327C4⋊Dic3—31no—
328C4⋊Dic3—31no—
329C4⋊Dic3—31no—
330C4⋊Dic3—31no—
331C4⋊Dic3—61no—
332C4⋊Dic3—61no—
333C4⋊Dic3—61no—
334C4⋊Dic3—61no—
335C4⋊Dic3—61no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—121no—
340C4⋊Dic3C22×D311yescharacteristic
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343Dic3⋊C4—21no—
344Dic3⋊C4—31no—
345Dic3⋊C4—31no—
346Dic3⋊C4—31no—
347Dic3⋊C4—31no—
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—61no—
357Dic3⋊C4—121no—
358Dic3⋊C4—121no—
359C4×Dic3—21no—
360C4×Dic3—21no—
361C4×Dic3—31no—
362C4×Dic3—31no—
363C4×Dic3—61no—
364C4×Dic3—61no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—121no—
371C4×Dic3C22×D311yescharacteristic
372C4×Dic3C22×D311yescharacteristic
373C2×C3⋊C8—31no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—61no—
376C2×C3⋊C8C22×D311yescharacteristic
377C2×C3⋊C8C22×D311yescharacteristic
378Dic12—62no—
379#204—22no—
380C22×C32C22×D411yescharacteristic
381C2×C3×D3—41no—
382C2×C3×D3—41no—
383C2×C3×D3—41no—
384C32×C4—41no—
385C32×C4—41no—
386C32×C4C2×#4111yescharacteristic
387C32×C42−1+411yescharacteristic
388C3⋊Dic3—21no—
389C3⋊Dic3—21no—
390C3⋊Dic3—41no—
391C3⋊Dic3—41no—
392C3×Dic3—22no—
393C3×Dic3—21no—
394C3×Dic3—21no—
395C3×Dic3—21no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C3×Dic3#13512yes—
399C2×Q16—91no—
400C2×Q16—91no—
401C2×SD16—31no—
402C4⋊Q8—91no—
403C4⋊Q8—91no—
404C4⋊Q8—181no—
405#126—181no—
406#126—181no—
407#125—31no—
408#125—91no—
409#125—181no—
410#125—181no—
411#124—91no—
412#124—91no—
413C22⋊Q8—181no—
414C4×Q8—31no—
415C4×Q8—31no—
416C4×Q8—91no—
417C4×Q8—91no—
418C4×Q8—91no—
419C4×Q8—91no—
420C4×Q8—181no—
421C4×D4—31no—
422#117—181no—
423#107—31no—
424#107—91no—
425#106D3211yescharacteristic
426C4⋊C8—31no—
427C4⋊C8—91no—
428C4⋊C8—91no—
429#103—31no—
430#103—31no—
431#103—31no—
432#103—91no—
433#103—91no—
434#103—91no—
435#103—91no—
436#102—31no—
437#102—91no—
438#102—91no—
439C4×C8—31no—
440C4×C8—91no—
441C4×C8—91no—
442C23×C3—61no—
443C22×D3—21no—
444C3×Q8—32no—
445C3×Q8—61no—
446C3×Q8—61no—
447C3×Q8—61no—
448C3×D4—61no—
449C3×D4—61no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—31no—
456C2×C3×C4—31no—
457C2×C3×C4—31no—
458C2×C3×C4—31no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—122no—
465C2×C3×C4C23×D311yescharacteristic
466C2×C3×C4C23×D311yescharacteristic
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—31no—
471C2×Dic3—31no—
472C2×Dic3—31no—
473C2×Dic3—31no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—121no—
481C2×Dic3—121no—
482C2×Dic3D3×D411yescharacteristic
483C2×Dic3D3×D411yescharacteristic
484C2×Dic3D3×D411yescharacteristic
485C2×Dic3D3×D411yescharacteristic
486D12—21no—
487D12—21no—
488C4×D3—42no—
489Dic6—21no—
490Dic6—21no—
491Dic6—21no—
492Dic6—62no—
493Dic6—62no—
494Dic6—62no—
495Dic6—61no—
496Dic6—61no—
497Dic6—61no—
498Dic6—61no—
499Dic6—121no—
500Dic6—122no—
501Dic6—122no—
502Dic6#23512yes—
503C3×C8—21no—
504C3×C8—21no—
505C3×C8—41no—
506C3×C8—61no—
507C3×C8—61no—
508C3⋊C8—21no—
509C3⋊C8—21no—
510C3⋊C8—61no—
511C3⋊C8—61no—
512C3⋊C8—121no—
513C2×C32#54811yescharacteristic
514C2×C32C2×#13511yescharacteristic
515C2×C32#57811yescharacteristic
516C3×D3—81no—
517C2×Q8—31no—
518C2×Q8—31no—
519C2×Q8—91no—
520C2×Q8—91no—
521C2×Q8—181no—
522C2×D4—31no—
523C22×C4—61no—
524Q16—182no—
525Q16—182no—
526SD16—62no—
527C2×C8—31no—
528C2×C8—31no—
529C2×C8—91no—
530C2×C8C2×D3211yescharacteristic
531C4⋊C4—31no—
532C4⋊C4—61no—
533C4⋊C4—61no—
534C4⋊C4—61no—
535C4⋊C4—61no—
536C4⋊C4—91no—
537C4⋊C4—91no—
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4—181no—
541C4⋊C4—181no—
542C4⋊C4—181no—
543C4⋊C4—181no—
544C4⋊C4—181no—
545C4⋊C4—181no—
546C4⋊C4—181no—
547C4⋊C4—181no—
548C4⋊C4C2×D3211yescharacteristic
549C4⋊C4C2×D3211yescharacteristic
550C22⋊C4—61no—
551C22⋊C4—181no—
552C22⋊C4—181no—
553C22⋊C4—181no—
554C22⋊C4—181no—
555C42—31no—
556C42—31no—
557C42—61no—
558C42—61no—
559C42—91no—
560C42—181no—
561C42—181no—
562C42—181no—
563C22×C3—21no—
564C22×C3—121no—
565C22×C3—121no—
566C22×C3—121no—
567C22×C3C2×D3×D411yescharacteristic
568C22×C3C2×D3×D411yescharacteristic
569C2×D3—41no—
570C2×D3—41no—
571C2×D3—41no—
572C3×C4—21no—
573C3×C4—21no—
574C3×C4—32no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—41no—
578C3×C4—41no—
579C3×C4—62no—
580C3×C4—61no—
581C3×C4—61no—
582C3×C4—61no—
583C3×C4—81no—
584C3×C4—81no—
585C3×C4—121no—
586C3×C4—121no—
587C3×C4C2×#23511yescharacteristic
588C3×C4#100711yescharacteristic
589C3×C4D3×#4111yescharacteristic
590C3×C4#101011yescharacteristic
591Dic3—21no—
592Dic3—21no—
593Dic3—21no—
594Dic3—22no—
595Dic3—41no—
596Dic3—41no—
597Dic3—61no—
598Dic3—61no—
599Dic3—61no—
600Dic3—61no—
601Dic3—121no—
602Dic3—121no—
603Dic3—122no—
604Dic3—121no—
605Dic3—121no—
606Dic3—121no—
607Dic3—121no—
608Dic3—241no—
609Dic3#91612yes—
610C32#336411yescharacteristic, complemented, Sylow
611C23—61no—
612Q8—32no—
613Q8—61no—
614Q8—61no—
615Q8—61no—
616Q8—182no—
617Q8—181no—
618Q8—181no—
619Q8—362no—
620D4—61no—
621D4—61no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—91no—
632C2×C4—91no—
633C2×C4—122no—
634C2×C4—181no—
635C2×C4—181no—
636C2×C4C22×D3211yescharacteristic
637C8—21no—
638C8—61no—
639C8—61no—
640C8—181no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—241no—
645C2×C3#555211yescharacteristic
646C2×C3#563311yescharacteristic
647C2×C3C2×#91611yescharacteristic
648C2×C3D3×#13511yescharacteristic
649C2×C3#577111yescharacteristic
650C2×C3#577911yescharacteristic
651D3—81no—
652C22—121no—
653C22—121no—
654C22—121no—
655C22D32×D411yescharacteristic
656C4—32no—
657C4—41no—
658C4—41no—
659C4—62no—
660C4—61no—
661C4—61no—
662C4—61no—
663C4—121no—
664C4—121no—
665C4—181no—
666C4—181no—
667C4—361no—
668C4—361no—
669C4D3×#23511yescharacteristic
670C4#6431511yescharacteristic
671C3—21no—
672C3#7962311yescharacteristic, complemented
673C3#8121611yescharacteristic, complemented
674C2—241no—
675C2#1059437511yescharacteristic
676C2D3×#91611yescharacteristic
677C2#1059475611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×C3×D12C23
hypercenter#106D32
hypocenterC32#3364
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
2. #10594321C2semidirect
3. #10592556C2semidirect
4. C3×#4857C2semidirect
6. #10590890C2semidirect
9. #10590644C2semidirect
10. #10590561C2semidirect
14. #10590482C2semidirect
15. #10590476C2semidirect
78. #4857D3semidirect
610. C32#3364semidirect
672. C3#79623semidirect
673. C3#81216semidirect

Maximal subgroups

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

subgroupindex
#105943352
#105943212
#105925562
C3×#48572
C3×#48522
#105908902
#105908592
#105907962
#105906442
#105905612
#105905552
#105905392
#105905332
#105904822
#105904762
#812163
#796233