Finite Group Databasebeta

← #11895277

Subgroups — #11895277

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 703 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594460C211yesmaximal, characteristic, complemented
2#10594335C211yesmaximal, characteristic, complemented
3#10592556C211yesmaximal, characteristic, complemented
4C3×#4870C211yesmaximal, characteristic, complemented
5C3×#4852C211yesmaximal, characteristic, complemented
6#10590863C211yesmaximal, characteristic, complemented
7#10590752C211yesmaximal, characteristic, complemented
8#10590750C211yesmaximal, characteristic
9#10590644C211yesmaximal, characteristic, complemented
10#10590560C211yesmaximal, characteristic, complemented
11#10590543C211yesmaximal, characteristic, complemented
12#10590539C211yesmaximal, characteristic, complemented
13#10590530C211yesmaximal, characteristic
14#10590460C211yesmaximal, characteristic, complemented
15#10590452C211yesmaximal, characteristic
16#81087—31nomaximal
17#79620—31nomaximal
18#64099C2211yescharacteristic
19#64096C2211yescharacteristic
20C2×C3×#204C2211yescharacteristic
21C3×#893C2211yescharacteristic
22C3×#893C2211yescharacteristic
23C3×#888C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C4×#627C2211yescharacteristic
26#63898C2211yescharacteristic
27#63893—21no—
28Dic3×D12C2211yescharacteristic
29#63887—21no—
30D3×Dic3⋊C4—21no—
31#63869C2211yescharacteristic
32#63866C2211yescharacteristic
33#63863C2211yescharacteristic
34#63862—21no—
35#63860C2211yescharacteristic
36#63859—21no—
37#63856—21no—
38#63855—21no—
39#63851—21no—
40C2×#3716C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C32×#106C2211yescharacteristic
43#63643C2211yescharacteristic
44#63641C2211yescharacteristic
45#63637C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#821C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×C8×Dic3C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63563C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5730—31no—
62#5568—31no—
63#5542—31no—
64#5539—31no—
65C3×#476—31no—
66C3×C4×SD16—31no—
67#5165—31no—
68#5162—31no—
69#5093—31no—
70#5022—31no—
71#5016—31no—
72C4×#213—31no—
73#4870D311yescharacteristic, complemented
74#4857—31no—
75#4857—31no—
76#4857—31no—
77#4857—61no—
78#4852—31no—
79#4852D311yescharacteristic, complemented
80#4841—31no—
81#4830—31no—
82#4800—31no—
83#4792—31no—
84#4787—31no—
85#4787—31no—
86#4768—31no—
87#4768—31no—
88#4758—31no—
89#4756—31no—
90#4697—31no—
91C8×Dic6—31no—
92C2×#634C2311yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×C4×D3—21no—
97C2×C3×Dic6—21no—
98C2×C3×Dic6C2311yescharacteristic
99C2×#627D411yescharacteristic
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108#3750—21no—
109C4×C3⋊Dic3—21no—
110C4×C3⋊Dic3C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3C2311yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C2×C3×C3⋊C8C2311yescharacteristic
121C2×C3×C3⋊C8C2311yescharacteristic
122C3×#204—22no—
123#3724—21no—
124#3724D411yescharacteristic
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—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136#3716—22no—
137#3713—22no—
138#3360—91noSylow
139C2×C3×SD16—31no—
140C3×C4⋊Q8—31no—
141C3×C4×Q8—31no—
142C3×C4×D4—31no—
143C3×C4×D4—31no—
144#947—31no—
145#946—61no—
146#946—61no—
147#944—31no—
148#936—31no—
149#936—31no—
150D4×Dic3—31no—
151D4×Dic3—31no—
152C2×#214—31no—
153C2×#213—31no—
154C2×#213—31no—
155#926—61no—
156#924—61no—
157#924—61no—
158C2×Dic3⋊C4—61no—
159C2×#204—31no—
160C2×#204C2×D311yescharacteristic
161#898—61no—
162#897—61no—
163#896—61no—
164#893—31no—
165#893C2×D311yescharacteristic
166#893C2×D311yescharacteristic
167D3×C4⋊C4—61no—
168#890—31no—
169#890—31no—
170#890—31no—
171#890—61no—
172#888C2×D311yescharacteristic
173#887—31no—
174#887—31no—
175#887—61no—
176#887C2×D311yescharacteristic
177#879—61no—
178#879—61no—
179#878—61no—
180#878—61no—
181#876—61no—
182#875—31no—
183C4×D12—31no—
184#872—61no—
185#870—31no—
186#869—31no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C3×#106—21no—
190C3×#106—31no—
191C3×#106C2×D311yescharacteristic
192C3×#106C2×D311yescharacteristic
193C3×C4⋊C8—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#821—31no—
203#821C2×D311yescharacteristic
204#816—31no—
205#816—31no—
206#816—31no—
207#816—31no—
208#816—61no—
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—31no—
222#810—61no—
223#810C2×D311yescharacteristic
224#809C2×D311yescharacteristic
225#809C2×D311yescharacteristic
226#808C2×D311yescharacteristic
227#807—31no—
228#807—31no—
229#807—61no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
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—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×D12—21no—
252C3×D12#4112yes—
253C3×C4×D3—42no—
254C3×C4×D3—81no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—81no—
258#627—22no—
259D3×Dic3—42no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#556—91no—
266#554—91no—
267#488—91no—
268#488—91no—
269#487—91no—
270#479—91no—
271#479—91no—
272#476—31no—
273#463—91no—
274#463—91no—
275#461—91no—
276C8×Q8—91no—
277C4×SD16—31no—
278C4×SD16—91no—
279C4×D8—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×D4—31no—
283C2×C3×D4—31no—
284C22×C3×C4—61no—
285C22×C3×C4—61no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C2×D12C22×D311yescharacteristic
289C2×D12C22×D311yescharacteristic
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×Dic6—21no—
295C2×Dic6—31no—
296C2×Dic6—31no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—61no—
300C2×Dic6C22×D311yescharacteristic
301C3×SD16—62no—
302C2×C3×C8—21no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4C22×D311yescharacteristic
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C4⋊C4C22×D311yescharacteristic
316C3×C22⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C42—31no—
319C3×C42—31no—
320C3×C42—61no—
321#217—61no—
322#217—61no—
323#217—61no—
324#217—61no—
325#217—61no—
326#217—61no—
327#214—62no—
328#213—62no—
329#213—62no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—121no—
349C4⋊Dic3C22×D311yescharacteristic
350Dic3⋊C4—21no—
351Dic3⋊C4—21no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—121no—
366Dic3⋊C4—121no—
367C4×Dic3—21no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—121no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381#204—22no—
382#204—62no—
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—22no—
385C2×C3×D3—41no—
386C2×C3×D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—41no—
391C32×C4—41no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3⋊Dic3—21no—
395C3⋊Dic3—21no—
396C3⋊Dic3—41no—
397C3⋊Dic3—41no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3#13512yes—
404C2×SD16—31no—
405C2×SD16—91no—
406C2×D8—91no—
407C4⋊Q8—31no—
408C4⋊Q8—91no—
409#126—181no—
410#126—181no—
411#125—91no—
412#125—91no—
413#124—91no—
414#124—91no—
415C22⋊Q8—181no—
416C22⋊Q8—181no—
417C22⋊Q8—181no—
418C22⋊Q8—181no—
419C4×Q8—31no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×D4—31no—
423C4×D4—31no—
424C4×D4—91no—
425C4×D4—91no—
426#117—181no—
427C2×C4⋊C4—181no—
428#107—91no—
429#106—31no—
430#106D3211yescharacteristic
431C4⋊C8—31no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#103—91no—
439#103—91no—
440#102—31no—
441#102—31no—
442#102—31no—
443#102—91no—
444C4×C8—31no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—61no—
448C23×C3—61no—
449C22×D3—21no—
450C22×D3—21no—
451C3×Q8—61no—
452C3×Q8—61no—
453C3×Q8—241no—
454C3×D4—32no—
455C3×D4—61no—
456C3×D4—61no—
457C3×D4—61no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—122no—
472C2×C3×C4—241no—
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—31no—
480C2×Dic3—31no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—121no—
488C2×Dic3—121no—
489C2×Dic3—122no—
490C2×Dic3—241no—
491C2×Dic3D3×D411yescharacteristic
492C2×Dic3D3×D411yescharacteristic
493C2×Dic3D3×D411yescharacteristic
494C2×Dic3D3×D411yescharacteristic
495D12—21no—
496D12—21no—
497D12—21no—
498D12#23512yes—
499C4×D3—42no—
500C4×D3—81no—
501C4×D3—122no—
502C4×D3—241no—
503Dic6—21no—
504Dic6—21no—
505Dic6—62no—
506Dic6—62no—
507Dic6—62no—
508Dic6—61no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—81no—
513Dic6—121no—
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—41no—
517C3×C8—61no—
518C3×C8—61no—
519C3⋊C8—21no—
520C3⋊C8—21no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—121no—
524C2×C32#54811yescharacteristic
525C2×C32C2×#13511yescharacteristic
526C2×C32#57711yescharacteristic
527C3×D3—42no—
528C3×D3—81no—
529C2×Q8—31no—
530C2×Q8—61no—
531C2×Q8—91no—
532C2×Q8—91no—
533C2×D4—31no—
534C2×D4—31no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—181no—
538C22×C4—181no—
539SD16—62no—
540SD16—182no—
541D8—182no—
542C2×C8—31no—
543C2×C8—31no—
544C2×C8—91no—
545C2×C8C2×D3211yescharacteristic
546C4⋊C4—31no—
547C4⋊C4—61no—
548C4⋊C4—61no—
549C4⋊C4—91no—
550C4⋊C4—91no—
551C4⋊C4—91no—
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—61no—
564C22⋊C4—181no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C42—31no—
571C42—31no—
572C42—61no—
573C42—91no—
574C42—181no—
575C22×C3—21no—
576C22×C3—62no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3—121no—
582C22×C3C2×D3×D411yescharacteristic
583C22×C3C2×D3×D411yescharacteristic
584C2×D3—22no—
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—32no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—61no—
598C3×C4—61no—
599C3×C4—61no—
600C3×C4—81no—
601C3×C4—81no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4C2×#23511yescharacteristic
605C3×C4#100711yescharacteristic
606C3×C4D3×#4111yescharacteristic
607C3×C4#101011yescharacteristic
608Dic3—21no—
609Dic3—21no—
610Dic3—21no—
611Dic3—41no—
612Dic3—41no—
613Dic3—61no—
614Dic3—61no—
615Dic3—61no—
616Dic3—61no—
617Dic3—121no—
618Dic3—121no—
619Dic3—122no—
620Dic3—121no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—241no—
625Dic3#91612yes—
626C32#336011yescharacteristic, complemented, Sylow
627C23—61no—
628C23—61no—
629Q8—61no—
630Q8—61no—
631Q8—182no—
632Q8—181no—
633Q8—181no—
634Q8—241no—
635D4—32no—
636D4—61no—
637D4—61no—
638D4—61no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—91no—
648C2×C4—91no—
649C2×C4—122no—
650C2×C4—181no—
651C2×C4—181no—
652C2×C4—241no—
653C2×C4—362no—
654C2×C4—721no—
655C2×C4C22×D3211yescharacteristic
656C8—21no—
657C8—61no—
658C8—61no—
659C8—181no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—122no—
664C2×C3—241no—
665C2×C3#555211yescharacteristic
666C2×C3#563311yescharacteristic
667C2×C3C2×#91611yescharacteristic
668C2×C3#576211yescharacteristic
669C2×C3D3×#13511yescharacteristic
670C2×C3#577511yescharacteristic
671D3—42no—
672D3—81no—
673C22—62no—
674C22—121no—
675C22—121no—
676C22—121no—
677C22—121no—
678C22—121no—
679C22D32×D411yescharacteristic
680C4—32no—
681C4—41no—
682C4—41no—
683C4—61no—
684C4—61no—
685C4—61no—
686C4—121no—
687C4—121no—
688C4—181no—
689C4—181no—
690C4—361no—
691C4—361no—
692C4D3×#23511yescharacteristic
693C4#6431511yescharacteristic
694C3—21no—
695C3#7962011yescharacteristic, complemented
696C3#8108711yescharacteristic, complemented
697C2—122no—
698C2—241no—
699C2#1059437511yescharacteristic
700C2D3×#91611yescharacteristic
701C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenter#106D32
hypocenterC32#3360
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
1. #10594460C2semidirect
2. #10594335C2semidirect
3. #10592556C2semidirect
4. C3×#4870C2semidirect
5. C3×#4852C2semidirect
6. #10590863C2semidirect
7. #10590752C2semidirect
9. #10590644C2semidirect
10. #10590560C2semidirect
11. #10590543C2semidirect
12. #10590539C2semidirect
14. #10590460C2semidirect
73. #4870D3semidirect
79. #4852D3semidirect
626. C32#3360semidirect
695. C3#79620semidirect
696. C3#81087semidirect

Maximal subgroups

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

subgroupindex
#105944602
#105943352
#105925562
C3×#48702
C3×#48522
#105908632
#105907522
#105907502
#105906442
#105905602
#105905432
#105905392
#105905302
#105904602
#105904522
#810873
#796203