Finite Group Databasebeta

← #11895244

Subgroups — #11895244

Order 1152.

760 conjugacy classes of subgroups.

The subgroup lattice has 713 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595389C211yesmaximal, characteristic, complemented
2#10595274C211yesmaximal, characteristic, complemented
3#10592861C211yesmaximal, characteristic, complemented
4C3×#5165C211yesmaximal, characteristic
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591614C211yesmaximal, characteristic, complemented
7#10591547C211yesmaximal, characteristic, complemented
8#10591538C211yesmaximal, characteristic, complemented
9#10591468C211yesmaximal, characteristic
10#10591435C211yesmaximal, characteristic
11#10591401C211yesmaximal, characteristic, complemented
12#10590863C211yesmaximal, characteristic, complemented
13#10590809C211yesmaximal, characteristic, complemented
14#10590776C211yesmaximal, characteristic, complemented
15#10590644C211yesmaximal, characteristic, complemented
16#80516—31nomaximal
17#79620—31nomaximal
18C2×C32×SD16C2211yescharacteristic
19#64153C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27#63982—21no—
28C2×#3724—21no—
29#63964—21no—
30#63964—21no—
31#63919C2211yescharacteristic
32C4×#627C2211yescharacteristic
33#63899—21no—
34#63898C2211yescharacteristic
35#63877—21no—
36#63869C2211yescharacteristic
37#63869C2211yescharacteristic
38#63860C2211yescharacteristic
39#63859—21no—
40#63858—21no—
41#63844C2211yescharacteristic
42#63662C2211yescharacteristic
43#63643C2211yescharacteristic
44#63641C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52#63575C2211yescharacteristic
53#63574C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5671—31no—
62#5568—31no—
63#5539—31no—
64#5539—31no—
65C3×#463—31no—
66C3×C4×SD16—31no—
67#5165D311yescharacteristic
68#5162—31no—
69#5162—31no—
70#5162—61no—
71Dic3×SD16D311yescharacteristic, complemented
72#5153—31no—
73Dic3×D8—31no—
74#5056—31no—
75#5022—31no—
76C4×#214—31no—
77#5016—31no—
78#4870—31no—
79#4857—31no—
80#4830—31no—
81#4829—31no—
82#4800—31no—
83#4796—31no—
84#4792—31no—
85#4792—31no—
86#4768—31no—
87#4761—31no—
88#4758—31no—
89#4756—31no—
90#4697—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C2×C3×D12C2311yescharacteristic
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×D3×Dic3—21no—
102C32×SD16—22no—
103C2×C32×C8C2311yescharacteristic
104#3757—21no—
105#3754—22no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108#3750—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×#213—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724—21no—
127#3724—21no—
128#3724—21no—
129#3724D411yescharacteristic
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138#3360—91noSylow
139C2×C3×SD16—21no—
140C2×C3×SD16C2×D311yescharacteristic
141C2×C3×SD16C2×D311yescharacteristic
142C2×C3×D8—31no—
143C3×#124—31no—
144C3×C4×Q8—31no—
145C3×C4×D4—31no—
146C3×C4×D4—31no—
147#947C2×D311yescharacteristic
148Q8×Dic3C2×D311yescharacteristic
149#944—31no—
150#944—31no—
151#944—61no—
152#936—31no—
153D4×Dic3—31no—
154D4×Dic3—31no—
155D4×Dic3—31no—
156D4×Dic3—61no—
157D4×Dic3C2×D311yescharacteristic
158D4×Dic3C2×D311yescharacteristic
159C2×#214—31no—
160C2×#214—31no—
161C2×#214—61no—
162C2×#213C2×D311yescharacteristic
163#924—61no—
164#924—61no—
165C2×Dic3⋊C4—61no—
166C2×Dic3⋊C4—61no—
167#898—61no—
168#896—61no—
169#893—31no—
170#890—31no—
171#890—31no—
172#888—31no—
173#888—31no—
174#887—31no—
175#879—61no—
176#879—61no—
177#878—61no—
178#878—61no—
179#878—61no—
180#878—61no—
181#878—61no—
182#877—61no—
183#876—61no—
184#875—31no—
185#872—61no—
186#870—31no—
187#870—31no—
188C4×Dic6—31no—
189C4×Dic6—31no—
190C4×Dic6—31no—
191C3×#106—31no—
192C3×C4⋊C8—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×C4×C8—31no—
198#835—31no—
199#835—31no—
200#835—61no—
201#835C2×D311yescharacteristic
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#832C2×D311yescharacteristic
206#821—31no—
207#821C2×D311yescharacteristic
208#818—31no—
209#817C2×D311yescharacteristic
210#816—31no—
211#816—31no—
212#816—31no—
213#816—31no—
214#816—61no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—61no—
219Dic3⋊C8C2×D311yescharacteristic
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3C2×D311yescharacteristic
224#810—31no—
225#810—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×D4—21no—
237C32×D4#4112yes—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—42no—
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3⋊Dic3C2×D411yescharacteristic
245#634—21no—
246#634—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—81no—
251C2×C3×Dic3—81no—
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258#627—22no—
259#627—81no—
260D3×Dic3—42no—
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—91no—
273#463—31no—
274#463—91no—
275#461—91no—
276C8×Q8—91no—
277C4×SD16—31no—
278C4×SD16—91no—
279C4×D8—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8C22×D311yescharacteristic
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×D4—21no—
284C2×C3×D4—31no—
285C2×C3×D4C22×D311yescharacteristic
286C2×C3×D4C22×D311yescharacteristic
287C22×C3×C4—61no—
288C22×C3×C4—61no—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—61no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—121no—
295C2×D12C22×D311yescharacteristic
296C2×C4×D3—61no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C3×SD16—22no—
305C3×SD16—22no—
306C3×SD16—42no—
307C3×D8—62no—
308C2×C3×C8—21no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8C22×D311yescharacteristic
312C2×C3×C8C22×D311yescharacteristic
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—31no—
316C3×C4⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C22⋊C4—61no—
321C3×C42—31no—
322C3×C42—31no—
323C3×C42—61no—
324#217—21no—
325#217—21no—
326#217—61no—
327#217—61no—
328#217—61no—
329#217—61no—
330#217—61no—
331#217—121no—
332#214—62no—
333#214—62no—
334#214—122no—
335#213—22no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—21no—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—61no—
340(C2×D3)⋊C4—61no—
341C4⋊Dic3—21no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3C22×D311yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351C4⋊Dic3C22×D311yescharacteristic
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—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—121no—
371Dic3⋊C4—121no—
372C4×Dic3—21no—
373C4×Dic3—31no—
374C4×Dic3—31no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3C22×D311yescharacteristic
379C4×Dic3C22×D311yescharacteristic
380C2×C3⋊C8—31no—
381C2×C3⋊C8—31no—
382C2×C3⋊C8—61no—
383C2×C3⋊C8C22×D311yescharacteristic
384C2×C3⋊C8C22×D311yescharacteristic
385C22×C32—22no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32C22×D411yescharacteristic
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C32×C4—41no—
393C32×C4C2×#4111yescharacteristic
394C32×C42−1+411yescharacteristic
395C3⋊Dic3—21no—
396C3⋊Dic3—41no—
397C3⋊Dic3—41no—
398C3⋊Dic3#13512yes—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—21no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C2×SD16—91no—
407C2×SD16D3211yescharacteristic
408C2×D8—31no—
409C4⋊Q8—91no—
410C4⋊Q8—91no—
411#126—181no—
412#126—181no—
413#125—91no—
414#125—91no—
415#124—31no—
416#124—91no—
417C22⋊Q8—181no—
418C22⋊Q8—181no—
419C22⋊Q8—181no—
420C22⋊Q8—181no—
421C4×Q8—31no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×D4—31no—
425C4×D4—31no—
426C4×D4—91no—
427C4×D4—91no—
428#117—181no—
429C2×C4⋊C4—181no—
430#107—91no—
431#106—31no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#103—31no—
437#103—31no—
438#103—91no—
439#103—91no—
440#103—91no—
441#103—91no—
442#102—31no—
443#102—31no—
444#102—91no—
445#102—91no—
446C4×C8—31no—
447C4×C8—91no—
448C4×C8—91no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—41no—
452C23×C3—61no—
453C22×D3—21no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—22no—
463C3×D4—41no—
464C3×D4—61no—
465C3×D4—61no—
466C3×D4#23512yes—
467C3×D4#23712yes—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—31no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—41no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—241no—
480C2×C3×C4—241no—
481C2×C3×C4C23×D311yescharacteristic
482C2×C3×C4C23×D311yescharacteristic
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—31no—
489C2×Dic3—31no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—81no—
497C2×Dic3—81no—
498C2×Dic3—121no—
499C2×Dic3—121no—
500C2×Dic3—122no—
501C2×Dic3—122no—
502C2×Dic3—122no—
503C2×Dic3—242no—
504C2×Dic3D3×D411yescharacteristic
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508D12—21no—
509D12—21no—
510C4×D3—122no—
511Dic6—62no—
512Dic6—62no—
513Dic6—61no—
514Dic6—61no—
515Dic6—61no—
516Dic6—61no—
517Dic6—121no—
518Dic6—121no—
519Dic6—241no—
520Dic6—241no—
521C3×C8—21no—
522C3×C8—21no—
523C3×C8—41no—
524C3×C8—61no—
525C3×C8—61no—
526C3⋊C8—21no—
527C3⋊C8—21no—
528C3⋊C8—61no—
529C3⋊C8—61no—
530C3⋊C8—121no—
531C2×C32—42no—
532C2×C32#54811yescharacteristic
533C2×C32C2×#13511yescharacteristic
534C2×C32#57711yescharacteristic
535C3×D3—81no—
536C2×Q8—91no—
537C2×Q8—91no—
538C2×Q8—181no—
539C2×Q8C2×D3211yescharacteristic
540C2×D4—31no—
541C2×D4C2×D3211yescharacteristic
542C22×C4—61no—
543C22×C4—61no—
544C22×C4—181no—
545C22×C4—181no—
546SD16—22no—
547SD16—182no—
548D8—62no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8—91no—
552C2×C8C2×D3211yescharacteristic
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—61no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C4⋊C4—181no—
569C22⋊C4—61no—
570C22⋊C4—61no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—181no—
574C22⋊C4—181no—
575C22⋊C4—181no—
576C22⋊C4—181no—
577C42—31no—
578C42—31no—
579C42—61no—
580C42—91no—
581C42—181no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—21no—
585C22×C3—42no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3—121no—
593C22×C3—121no—
594C22×C3—121no—
595C22×C3C2×D3×D411yescharacteristic
596C22×C3C2×D3×D411yescharacteristic
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—41no—
600C3×C4—21no—
601C3×C4—21no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—81no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4C2×#23511yescharacteristic
613C3×C4C2×#23711yescharacteristic
614C3×C4#101011yescharacteristic
615C3×C4#101011yescharacteristic
616Dic3—21no—
617Dic3—21no—
618Dic3—21no—
619Dic3—21no—
620Dic3—32no—
621Dic3—32no—
622Dic3—41no—
623Dic3—41no—
624Dic3—41no—
625Dic3—62no—
626Dic3—61no—
627Dic3—61no—
628Dic3—121no—
629Dic3—121no—
630Dic3—121no—
631Dic3—121no—
632Dic3—121no—
633Dic3—241no—
634Dic3—241no—
635C32#336011yescharacteristic, complemented, Sylow
636C23—21no—
637C23—61no—
638Q8—21no—
639Q8—21no—
640Q8—182no—
641Q8—181no—
642Q8—181no—
643Q8—721no—
644D4—21no—
645D4—61no—
646D4—61no—
647D4#380412yes—
648C2×C4—21no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—91no—
657C2×C4—91no—
658C2×C4—181no—
659C2×C4—181no—
660C2×C4—241no—
661C2×C4—241no—
662C2×C4—362no—
663C2×C4—362no—
664C2×C4C22×D3211yescharacteristic
665C8—21no—
666C8—61no—
667C8—61no—
668C8—181no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—42no—
673C2×C3—42no—
674C2×C3—82no—
675C2×C3—241no—
676C2×C3#555211yescharacteristic
677C2×C3#559811yescharacteristic
678C2×C3#576211yescharacteristic
679C2×C3D3×#13511yescharacteristic
680C2×C3D3×#13511yescharacteristic
681C2×C3#577511yescharacteristic
682D3—81no—
683C22—22no—
684C22—41no—
685C22—41no—
686C22—121no—
687C22—121no—
688C22—121no—
689C22D32×D411yescharacteristic
690C4—41no—
691C4—61no—
692C4—61no—
693C4—61no—
694C4—61no—
695C4—92no—
696C4—121no—
697C4—121no—
698C4—121no—
699C4—181no—
700C4—361no—
701C4—361no—
702C4#6430911yescharacteristic
703C4C2×#380411yescharacteristic
704C3—21no—
705C3#7962011yescharacteristic, complemented
706C3#8051611yescharacteristic, complemented
707C2—42no—
708C2—241no—
709C2#1059474711yescharacteristic
710C2#1059474911yescharacteristic
711C2#1059514111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC2×SD16D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595389C2semidirect
2. #10595274C2semidirect
3. #10592861C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591614C2semidirect
7. #10591547C2semidirect
8. #10591538C2semidirect
11. #10591401C2semidirect
12. #10590863C2semidirect
13. #10590809C2semidirect
14. #10590776C2semidirect
15. #10590644C2semidirect
71. Dic3×SD16D3semidirect
635. C32#3360semidirect
705. C3#79620semidirect
706. C3#80516semidirect

Maximal subgroups

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

subgroupindex
#105953892
#105952742
#105928612
C3×#51652
C3×Dic3×SD162
#105916142
#105915472
#105915382
#105914682
#105914352
#105914012
#105908632
#105908092
#105907762
#105906442
#805163
#796203