Finite Group Databasebeta

← #11895236

Subgroups — #11895236

Order 1152.

751 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593942C211yesmaximal, characteristic, complemented
2#10593941C211yesmaximal, characteristic, complemented
3C8×#634C211yesmaximal, characteristic, complemented
4C3×#4697C211yesmaximal, characteristic, complemented
5C3×C4×#204C211yesmaximal, characteristic, complemented
6#10590901C211yesmaximal, characteristic, complemented
7#10590868C211yesmaximal, characteristic, complemented
8#10590820C211yesmaximal, characteristic, complemented
9#10590776C211yesmaximal, characteristic, complemented
10#10590750C211yesmaximal, characteristic
11#10590748C211yesmaximal, characteristic, complemented
12#10590742C211yesmaximal, characteristic, complemented
13#10590740C211yesmaximal, characteristic
14#10590348C211yesmaximal, characteristic
15#10590286C211yesmaximal, characteristic, complemented
16#81632—31nomaximal
17#79620—31nomaximal
18C4×#634C2211yescharacteristic
19C2×C3×#204C2211yescharacteristic
20C3×#875C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×#870C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63919C2211yescharacteristic
25#63898C2211yescharacteristic
26#63898C2211yescharacteristic
27#63898C2211yescharacteristic
28#63896—21no—
29#63896—21no—
30#63893—21no—
31#63877—21no—
32D3×Dic3⋊C4—21no—
33#63873C2211yescharacteristic
34#63872C2211yescharacteristic
35#63863C2211yescharacteristic
36#63861—21no—
37#63859—21no—
38#63851—21no—
39#63843C2211yescharacteristic
40C2×#3715C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C32×C4×C8C2211yescharacteristic
43#63641C2211yescharacteristic
44#63641C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46C8×C3⋊Dic3C2211yescharacteristic
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55#63576C2211yescharacteristic
56#63574C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61#5690—31no—
62#5671—31no—
63#5568—31no—
64#5539—31no—
65C3×#488—31no—
66C3×C4×SD16—31no—
67#5165—31no—
68#5162—31no—
69#5063—31no—
70#5057—31no—
71#5022—31no—
72#5016—31no—
73#4870—31no—
74#4857—31no—
75#4818—31no—
76#4800—31no—
77#4799—31no—
78#4792—31no—
79#4792—31no—
80#4788—31no—
81#4787—31no—
82#4768—31no—
83#4761—31no—
84#4758—31no—
85#4756—31no—
86#4756—31no—
87#4697D311yescharacteristic, complemented
88C4×#204D311yescharacteristic, complemented
89C8×Dic6—31no—
90C8×Dic6—31no—
91C8×Dic6—61no—
92C2×#634D411yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×D3×Dic3—21no—
100C2×D3×Dic3—21no—
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C42C2311yescharacteristic
105C4⋊(C3⋊Dic3)D411yescharacteristic
106#3750D411yescharacteristic
107#3750D411yescharacteristic
108C4×C3⋊Dic3C2311yescharacteristic
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×(C2×D3)⋊C4—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×#204—22no—
124#3724—21no—
125#3724—21no—
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
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—
135Dic32—21no—
136#3715—22no—
137#3713—22no—
138#3360—91noSylow
139C2×C3×SD16—31no—
140C3×#125—31no—
141C3×#124—31no—
142C3×C4×Q8—31no—
143C3×C4×D4—31no—
144#947—31no—
145Q8×Dic3—31no—
146#944—31no—
147#944—31no—
148C2×#215—31no—
149#936—31no—
150D4×Dic3—31no—
151D4×Dic3—31no—
152D4×Dic3—31no—
153C2×#214—31no—
154C2×#213—31no—
155C2×#213—31no—
156#924—61no—
157C2×Dic3⋊C4—61no—
158C2×#204C2×D311yescharacteristic
159#898—61no—
160#897—61no—
161#896—61no—
162#896—61no—
163#896—61no—
164#893—31no—
165#893—31no—
166#893—31no—
167D3×C4⋊C4—61no—
168#890—31no—
169#890—31no—
170#888—31no—
171#888—31no—
172#887—31no—
173#879—61no—
174#879—61no—
175#878—61no—
176#878—61no—
177#878—61no—
178#877—61no—
179#876—61no—
180#875C2×D311yescharacteristic
181C4×D12C2×D311yescharacteristic
182#872—61no—
183#870C2×D311yescharacteristic
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C3×#106—31no—
189C3×#103—31no—
190C3×#103—31no—
191C3×#103—31no—
192C3×#102—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×C4×C8—21no—
196C3×C4×C8C2×D311yescharacteristic
197C3×C4×C8C2×D311yescharacteristic
198#835—31no—
199#835—31no—
200#835—31no—
201#832—31no—
202#821C2×D311yescharacteristic
203#821C2×D311yescharacteristic
204#821C2×D311yescharacteristic
205#817C2×D311yescharacteristic
206#816C2×D311yescharacteristic
207#816C2×D311yescharacteristic
208#816C2×D311yescharacteristic
209Dic3⋊C8—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—61no—
214Dic3⋊C8—61no—
215C8×Dic3—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3—31no—
219C8×Dic3—61no—
220C8×Dic3—61no—
221#810—31no—
222#810—31no—
223#810—31no—
224#809—31no—
225#808—31no—
226#808—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C2×C32×C4C2×D411yescharacteristic
235C2×C32×C4C2×D411yescharacteristic
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3C2×D411yescharacteristic
238C2×C3⋊Dic3C2×D411yescharacteristic
239C2×C3⋊Dic3C2×D411yescharacteristic
240C2×C3⋊Dic3C2×D411yescharacteristic
241#634—22no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C3×D12—21no—
249C3×D12—21no—
250C3×D12—21no—
251C3×D12#4112yes—
252C3×C4×D3—81no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257#627—81no—
258D3×Dic3—42no—
259D3×Dic3—42no—
260D3×Dic3—81no—
261C32×C8—21no—
262C32×C8—21no—
263C3⋊(C3⋊C8)—21no—
264C3⋊(C3⋊C8)—21no—
265#556—91no—
266#554—91no—
267#488—31no—
268#488—91no—
269#487—91no—
270#479—91no—
271#479—91no—
272#476—91no—
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—31no—
282C2×C3×D4—31no—
283C2×C3×D4—31no—
284C22×C3×C4—61no—
285C22×Dic3—61no—
286C22×Dic3—61no—
287C22×Dic3—61no—
288C2×D12C22×D311yescharacteristic
289C2×D12C22×D311yescharacteristic
290C2×C4×D3—21no—
291C2×C4×D3—61no—
292C2×C4×D3—61no—
293C2×C4×D3—61no—
294C2×Dic6—31no—
295C2×Dic6—31no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C2×Dic6C22×D311yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C3×SD16—62no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8C22×D311yescharacteristic
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C22⋊C4—61no—
316C3×C22⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C42—21no—
319C3×C42—61no—
320C3×C42C22×D311yescharacteristic
321C3×C42C22×D311yescharacteristic
322#217—61no—
323#217—61no—
324#217—61no—
325#217—61no—
326#217—61no—
327#215—62no—
328#214—62no—
329#213—62no—
330#213—62no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—21no—
333(C2×D3)⋊C4—21no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336(C2×D3)⋊C4—61no—
337(C2×D3)⋊C4—61no—
338(C2×D3)⋊C4—61no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3C22×D311yescharacteristic
346C4⋊Dic3C22×D311yescharacteristic
347C4⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349Dic3⋊C4—21no—
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—61no—
366Dic3⋊C4—61no—
367C4×Dic3—21no—
368C4×Dic3—31no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—31no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—31no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8—61no—
382#204—22no—
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—21no—
391C32×C4—21no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3⋊Dic3—21no—
395C3⋊Dic3—21no—
396C3⋊Dic3—21no—
397C3⋊Dic3#13512yes—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C2×SD16—31no—
405C2×SD16—91no—
406C2×D8—91no—
407C4⋊Q8—91no—
408C4⋊Q8—91no—
409#126—181no—
410#126—181no—
411#125—31no—
412#125—91no—
413#124—31no—
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—91no—
424C4×D4—91no—
425C4×D4—91no—
426#117—181no—
427C2×C4⋊C4—181no—
428#107—91no—
429#106—31no—
430#106—91no—
431C4⋊C8—91no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—31no—
435#103—31no—
436#103—31no—
437#103—91no—
438#103—91no—
439#103—91no—
440#102—31no—
441#102—31no—
442#102—31no—
443#102—91no—
444C4×C8—91no—
445C4×C8—91no—
446C4×C8D3211yescharacteristic
447C23×C3—61no—
448C23×C3—61no—
449C22×D3—21no—
450C22×D3—21no—
451C3×Q8—61no—
452C3×Q8—61no—
453C3×Q8—61no—
454C3×Q8—61no—
455C3×D4—32no—
456C3×D4—61no—
457C3×D4—61no—
458C3×D4—61no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—241no—
469C2×C3×C4D3×D411yescharacteristic
470C2×C3×C4D3×D411yescharacteristic
471C2×C3×C4D3×D411yescharacteristic
472C2×C3×C4D3×D411yescharacteristic
473C2×C3×C4C23×D311yescharacteristic
474C2×C3×C4C23×D311yescharacteristic
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—21no—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—31no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—122no—
494C2×Dic3—122no—
495C2×Dic3—241no—
496D12—21no—
497D12—21no—
498D12—21no—
499D12#23512yes—
500C4×D3—81no—
501C4×D3—122no—
502C4×D3—122no—
503C4×D3—241no—
504Dic6—21no—
505Dic6—21no—
506Dic6—21no—
507Dic6—21no—
508Dic6—62no—
509Dic6—62no—
510Dic6—64no—
511Dic6—241no—
512Dic6—241no—
513C3×C8—22no—
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—41no—
519C3⋊C8—61no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—121no—
524C3⋊C8—121no—
525C2×C32#54811yescharacteristic
526C2×C32C2×#13511yescharacteristic
527C2×C32#57711yescharacteristic
528C3×D3—42no—
529C3×D3—81no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—91no—
533C2×Q8—181no—
534C2×D4—31no—
535C2×D4—31no—
536C22×C4—61no—
537C22×C4—181no—
538C22×C4—181no—
539C22×C4—181no—
540SD16—62no—
541SD16—182no—
542D8—182no—
543C2×C8—91no—
544C2×C8—91no—
545C2×C8C2×D3211yescharacteristic
546C2×C8C2×D3211yescharacteristic
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C22⋊C4—61no—
564C22⋊C4—61no—
565C22⋊C4—61no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C42—61no—
572C42—91no—
573C42—91no—
574C42—181no—
575C42C2×D3211yescharacteristic
576C22×C3—21no—
577C22×C3—62no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3C2×D3×D411yescharacteristic
584C22×C3C2×D3×D411yescharacteristic
585C2×D3—22no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C3×C4—22no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—41no—
599C3×C4—121no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×#23511yescharacteristic
606C3×C4D3×#4111yescharacteristic
607C3×C4#101011yescharacteristic
608C3×C4#101011yescharacteristic
609Dic3—32no—
610Dic3—32no—
611Dic3—41no—
612Dic3—41no—
613Dic3—41no—
614Dic3—41no—
615Dic3—41no—
616Dic3—41no—
617Dic3—62no—
618Dic3—62no—
619Dic3—61no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—61no—
624Dic3—61no—
625Dic3—121no—
626Dic3—121no—
627C32#336011yescharacteristic, complemented, Sylow
628C23—61no—
629C23—61no—
630Q8—61no—
631Q8—61no—
632Q8—61no—
633Q8—61no—
634Q8—182no—
635Q8—721no—
636D4—32no—
637D4—61no—
638D4—61no—
639D4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—91no—
647C2×C4—91no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—241no—
651C2×C4—362no—
652C2×C4—362no—
653C2×C4—721no—
654C2×C4#380211yescharacteristic
655C2×C4#380211yescharacteristic
656C2×C4C22×D3211yescharacteristic
657C8—21no—
658C8—21no—
659C8—181no—
660C8—181no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—122no—
665C2×C3—241no—
666C2×C3#555211yescharacteristic
667C2×C3#567711yescharacteristic
668C2×C3#576211yescharacteristic
669C2×C3D3×#13511yescharacteristic
670C2×C3D3×#13511yescharacteristic
671C2×C3#577011yescharacteristic
672D3—42no—
673D3—81no—
674C22—62no—
675C22—121no—
676C22—121no—
677C22—121no—
678C22—121no—
679C22—121no—
680C22C2×#380211yescharacteristic
681C4—21no—
682C4—21no—
683C4—92no—
684C4—121no—
685C4—121no—
686C4—121no—
687C4—121no—
688C4—121no—
689C4—121no—
690C4—181no—
691C4—181no—
692C4—181no—
693C4#6429811yescharacteristic
694C4D3×#23511yescharacteristic
695C3—21no—
696C3#7962011yescharacteristic, complemented
697C3#8163211yescharacteristic, complemented
698C2—122no—
699C2—241no—
700C2#1059390511yescharacteristic
701C2#1059468411yescharacteristic
702C2#1059468611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3713C22
hypercenterC4×C8D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593942C2semidirect
2. #10593941C2semidirect
3. C8×#634C2semidirect
4. C3×#4697C2semidirect
5. C3×C4×#204C2semidirect
6. #10590901C2semidirect
7. #10590868C2semidirect
8. #10590820C2semidirect
9. #10590776C2semidirect
11. #10590748C2semidirect
12. #10590742C2semidirect
15. #10590286C2semidirect
87. #4697D3semidirect
88. C4×#204D3semidirect
627. C32#3360semidirect
696. C3#79620semidirect
697. C3#81632semidirect

Maximal subgroups

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

subgroupindex
#105939422
#105939412
C8×#6342
C3×#46972
C3×C4×#2042
#105909012
#105908682
#105908202
#105907762
#105907502
#105907482
#105907422
#105907402
#105903482
#105902862
#816323
#796203