Finite Group Databasebeta

← #11895650

Subgroups — #11895650

Order 1152.

752 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595422C211yesmaximal, characteristic, complemented
2#10595388C211yesmaximal, characteristic
3#10592884C211yesmaximal, characteristic, complemented
4C3×#5185C211yesmaximal, characteristic, complemented
5C3×Dic3×Q16C211yesmaximal, characteristic, complemented
6#10591617C211yesmaximal, characteristic
7#10591614C211yesmaximal, characteristic, complemented
8#10591571C211yesmaximal, characteristic, complemented
9#10591544C211yesmaximal, characteristic, complemented
10#10591539C211yesmaximal, characteristic, complemented
11#10591536C211yesmaximal, characteristic, complemented
12#10590878C211yesmaximal, characteristic
13#10590780C211yesmaximal, characteristic, complemented
14#10590774C211yesmaximal, characteristic, complemented
15#10590644C211yesmaximal, characteristic, complemented
16#80581—31nomaximal
17#79701—31nomaximal
18C2×C32×Q16C2211yescharacteristic
19#64156C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21C2×#3755C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic
27#63918—21no—
28#63918C2211yescharacteristic
29C4×#627—21no—
30C4×#627C2211yescharacteristic
31#63911C2211yescharacteristic
32#63898C2211yescharacteristic
33#63894C2211yescharacteristic
34#63890—21no—
35#63880—21no—
36#63872—21no—
37#63872C2211yescharacteristic
38#63869—21no—
39#63869C2211yescharacteristic
40#63854—21no—
41#63852—21no—
42#63662C2211yescharacteristic
43#63648C2211yescharacteristic
44#63641C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52#63574C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63553C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5681—31no—
62#5585—31no—
63#5570—31no—
64#5569—31no—
65C3×#464—31no—
66C3×C4×Q16—31no—
67#5185—31no—
68#5185—31no—
69#5185—61no—
70#5185D311yescharacteristic, complemented
71Dic3×Q16D311yescharacteristic, complemented
72#5163—31no—
73Dic3×SD16—31no—
74#5056—31no—
75#5027—31no—
76C4×#215—31no—
77#5020—31no—
78#4891—31no—
79#4891—31no—
80#4847—31no—
81#4830—31no—
82#4800—31no—
83#4800—31no—
84#4800—31no—
85#4791—31no—
86#4788—31no—
87#4788—31no—
88#4766—31no—
89#4760—31no—
90#4694—31no—
91C8×Dic6—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C3×D12C2311yescharacteristic
96C2×#627—21no—
97C2×#627D411yescharacteristic
98C2×#626—21no—
99C2×#626—21no—
100C2×#624—21no—
101C2×D3×Dic3—21no—
102C32×Q16—22no—
103C2×C32×C8C2311yescharacteristic
104#3755—22no—
105#3752—21no—
106#3752—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4×C3⋊Dic3—21no—
110C4×C3⋊Dic3C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×#215—22no—
113C3×(C2×D3)⋊C4—21no—
114C3×(C2×D3)⋊C4—21no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724—21no—
129#3724D411yescharacteristic
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138#3365—91noSylow
139C2×C3×Q16—21no—
140C2×C3×Q16C2×D311yescharacteristic
141C2×C3×Q16C2×D311yescharacteristic
142C2×C3×SD16—31no—
143C3×#124—31no—
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147#947—31no—
148#947—31no—
149#947—61no—
150#947C2×D311yescharacteristic
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153Q8×Dic3—61no—
154Q8×Dic3C2×D311yescharacteristic
155Q8×Dic3C2×D311yescharacteristic
156Q8×Dic3C2×D311yescharacteristic
157C2×#215—31no—
158C2×#215—31no—
159C2×#215—61no—
160C2×#215C2×D311yescharacteristic
161#940—31no—
162D4×Dic3—31no—
163#894—61no—
164#894—61no—
165#893—31no—
166#893—31no—
167#890—31no—
168#890—31no—
169#890—31no—
170#890—61no—
171#890—61no—
172#890—61no—
173#888—31no—
174#888—61no—
175#886—61no—
176#885—61no—
177#883—61no—
178#67⋊C4—61no—
179#875—61no—
180#874—31no—
181C4×D12—31no—
182C4×D12—61no—
183#870—31no—
184#870—61no—
185#869—31no—
186#869—61no—
187C4×Dic6—31no—
188C4×Dic6—31no—
189C4×Dic6—61no—
190C4×Dic6—61no—
191C3×#107—31no—
192C3×C4⋊C8—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#102—31no—
197C3×C4×C8—31no—
198#835—31no—
199#835—31no—
200#835—61no—
201#835C2×D311yescharacteristic
202#835C2×D311yescharacteristic
203#835C2×D311yescharacteristic
204#832—31no—
205#832—31no—
206#821—31no—
207#821—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—61no—
212#821C2×D311yescharacteristic
213#818C2×D311yescharacteristic
214#817—31no—
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#809—31no—
225#809—31no—
226#809—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C32×Q8—21no—
235C32×Q8—21no—
236C32×Q8—21no—
237C32×Q8#4112yes—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3C2×D411yescharacteristic
243C2×C3⋊Dic3C2×D411yescharacteristic
244C4⋊(C3⋊D3)—21no—
245C4⋊(C3⋊D3)—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C3×D12—21no—
254C3×D12—21no—
255#627—22no—
256#627—42no—
257#626—42no—
258#626—81no—
259#624—81no—
260D3×Dic3—81no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—91no—
266#557—91no—
267#488—91no—
268#488—91no—
269#486—91no—
270#478—91no—
271#478—91no—
272#475—91no—
273#464—31no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—31no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8—21no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×Q8C22×D311yescharacteristic
285C2×C3×Q8C22×D311yescharacteristic
286C2×C3×D4—31no—
287C2×#67—61no—
288C2×#67—61no—
289C22×Dic3—61no—
290C2×D12—31no—
291C2×D12—31no—
292C2×D12—61no—
293C2×D12—61no—
294C2×D12—61no—
295C2×D12C22×D311yescharacteristic
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×Dic6—31no—
300C2×Dic6—31no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C3×Q16—22no—
304C3×Q16—22no—
305C3×Q16—42no—
306C3×SD16—62no—
307C2×C3×C8—21no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8C22×D311yescharacteristic
311C2×C3×C8C22×D311yescharacteristic
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C42—31no—
321C3×C42—31no—
322C3×C42—61no—
323C3×C42—61no—
324C3×C42—61no—
325#217—61no—
326#215—22no—
327#215—62no—
328#215—62no—
329#215—122no—
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—
338(C2×D3)⋊C4—61no—
339(C2×D3)⋊C4—121no—
340(C2×D3)⋊C4—121no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346C4⋊Dic3—31no—
347C4⋊Dic3—31no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—121no—
356C4⋊Dic3C22×D311yescharacteristic
357C4⋊Dic3C22×D311yescharacteristic
358C4⋊Dic3C22×D311yescharacteristic
359Dic3⋊C4—31no—
360Dic3⋊C4—31no—
361Dic3⋊C4—31no—
362Dic3⋊C4—31no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369C4×Dic3—21no—
370C4×Dic3—21no—
371C4×Dic3—21no—
372C4×Dic3—31no—
373C4×Dic3—31no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—121no—
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×C32C22×D411yescharacteristic
386C2×C3⋊D3—41no—
387C2×C3⋊D3—41no—
388C2×C3⋊D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C2×C3×D3—41no—
392C32×C4—22no—
393C32×C4—41no—
394C32×C4C2×#4111yescharacteristic
395C32×C42−1+411yescharacteristic
396C3⋊Dic3—21no—
397C3⋊Dic3—21no—
398C3⋊Dic3—41no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3—41no—
405C3×Dic3#13512yes—
406C2×Q16D3211yescharacteristic
407C2×SD16—31no—
408C2×SD16—91no—
409C4⋊Q8—91no—
410C4⋊Q8—181no—
411#127—91no—
412#125—91no—
413#125—91no—
414#125—181no—
415#125—181no—
416#124—31no—
417#124—91no—
418#124—181no—
419#123—181no—
420#123—181no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—31no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—181no—
427C4×D4—91no—
428C4×D4—91no—
429C4×D4—181no—
430#107—31no—
431#106—91no—
432#106—91no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435C4⋊C8—91no—
436#103—31no—
437#103—31no—
438#103—31no—
439#103—91no—
440#102—31no—
441#102—91no—
442#102—91no—
443#102—91no—
444#102—91no—
445#102—91no—
446C4×C8—31no—
447C4×C8—91no—
448C4×C8—91no—
449C23×C3—61no—
450C22×D3—21no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—121no—
454C3×Q8—21no—
455C3×Q8—21no—
456C3×Q8—21no—
457C3×Q8—21no—
458C3×Q8—21no—
459C3×Q8—21no—
460C3×Q8—22no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—41no—
464C3×Q8#23512yes—
465C3×Q8#23712yes—
466C3×D4—61no—
467C3×D4—61no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4C23×D311yescharacteristic
483C2×C3×C4C23×D311yescharacteristic
484#67—122no—
485#67—241no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—31no—
490C2×Dic3—31no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—121no—
498C2×Dic3—241no—
499C2×Dic3D3×D411yescharacteristic
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502C2×Dic3D3×D411yescharacteristic
503D12—21no—
504D12—21no—
505D12—61no—
506D12—61no—
507D12—61no—
508D12—61no—
509D12—121no—
510D12—121no—
511D12—122no—
512D12—241no—
513C4×D3—241no—
514C4×D3—241no—
515C4×D3—241no—
516Dic6—62no—
517Dic6—62no—
518Dic6—122no—
519Dic6—122no—
520C3×C8—21no—
521C3×C8—21no—
522C3×C8—41no—
523C3×C8—61no—
524C3×C8—61no—
525C3⋊C8—21no—
526C3⋊C8—21no—
527C3⋊C8—61no—
528C3⋊C8—61no—
529C3⋊C8—121no—
530C2×C32#54811yescharacteristic
531C2×C32C2×#13511yescharacteristic
532C2×C32#57711yescharacteristic
533C3⋊D3—81no—
534C3×D3—81no—
535C2×Q8—91no—
536C2×Q8—181no—
537C2×Q8C2×D3211yescharacteristic
538C2×Q8C2×D3211yescharacteristic
539C2×D4—31no—
540C2×D4—91no—
541C2×D4—181no—
542C2×D4—181no—
543C22×C4—181no—
544C22×C4—181no—
545Q16—22no—
546SD16—62no—
547SD16—182no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—91no—
551C2×C8C2×D3211yescharacteristic
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—91no—
559C4⋊C4—91no—
560C4⋊C4—91no—
561C4⋊C4—91no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C4⋊C4—181no—
567C4⋊C4—181no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C22⋊C4—181no—
573C22⋊C4—181no—
574C42—31no—
575C42—31no—
576C42—61no—
577C42—61no—
578C42—61no—
579C42—91no—
580C42—181no—
581C22×C3—21no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3—121no—
585C22×C3C2×D3×D411yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C2×D3—41no—
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C2×D3—121no—
596C2×D3—241no—
597C2×D3—241no—
598C2×D3—241no—
599C3×C4—22no—
600C3×C4—22no—
601C3×C4—21no—
602C3×C4—21no—
603C3×C4—32no—
604C3×C4—42no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—61no—
608C3×C4—61no—
609C3×C4—61no—
610C3×C4—81no—
611C3×C4—121no—
612C3×C4—121no—
613C3×C4—121no—
614C3×C4C2×#23511yescharacteristic
615C3×C4C2×#23711yescharacteristic
616C3×C4#101011yescharacteristic
617C3×C4#101011yescharacteristic
618Dic3—21no—
619Dic3—21no—
620Dic3—21no—
621Dic3—41no—
622Dic3—41no—
623Dic3—41no—
624Dic3—61no—
625Dic3—61no—
626Dic3—61no—
627Dic3—61no—
628Dic3—121no—
629Dic3—121no—
630Dic3—121no—
631Dic3—121no—
632Dic3—241no—
633Dic3#91912yes—
634C32#336511yescharacteristic, complemented, Sylow
635C23—61no—
636C23—181no—
637Q8—21no—
638Q8—21no—
639Q8—21no—
640Q8—182no—
641Q8—362no—
642Q8#380412yes—
643D4—61no—
644D4—61no—
645D4—181no—
646D4—181no—
647D4—362no—
648D4—721no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—91no—
659C2×C4—91no—
660C2×C4—181no—
661C2×C4—721no—
662C2×C4—721no—
663C2×C4C22×D3211yescharacteristic
664C8—21no—
665C8—61no—
666C8—61no—
667C8—181no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—241no—
672C2×C3#555211yescharacteristic
673C2×C3#559811yescharacteristic
674C2×C3C2×#91911yescharacteristic
675C2×C3D3×#13511yescharacteristic
676C2×C3#577011yescharacteristic
677C2×C3#577811yescharacteristic
678D3—81no—
679D3—241no—
680D3—241no—
681D3—481no—
682C22—121no—
683C22—121no—
684C22—121no—
685C22—361no—
686C22—361no—
687C22—361no—
688C22D32×D411yescharacteristic
689C4—22no—
690C4—32no—
691C4—41no—
692C4—61no—
693C4—61no—
694C4—61no—
695C4—121no—
696C4—121no—
697C4—121no—
698C4—181no—
699C4—181no—
700C4—361no—
701C4#6430911yescharacteristic
702C4C2×#380411yescharacteristic
703C3—21no—
704C3#7970111yescharacteristic, complemented
705C3#8058111yescharacteristic, complemented
706C2—241no—
707C2—721no—
708C2D3×#91911yescharacteristic
709C2#1059477011yescharacteristic
710C2#1059514111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenterC2×Q16D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #10595422C2semidirect
3. #10592884C2semidirect
4. C3×#5185C2semidirect
5. C3×Dic3×Q16C2semidirect
7. #10591614C2semidirect
8. #10591571C2semidirect
9. #10591544C2semidirect
10. #10591539C2semidirect
11. #10591536C2semidirect
13. #10590780C2semidirect
14. #10590774C2semidirect
15. #10590644C2semidirect
70. #5185D3semidirect
71. Dic3×Q16D3semidirect
634. C32#3365semidirect
704. C3#79701semidirect
705. C3#80581semidirect

Maximal subgroups

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

subgroupindex
#105954222
#105953882
#105928842
C3×#51852
C3×Dic3×Q162
#105916172
#105916142
#105915712
#105915442
#105915392
#105915362
#105908782
#105907802
#105907742
#105906442
#805813
#797013