Finite Group Databasebeta

← #11895642

Subgroups — #11895642

Order 1152.

747 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#10593981C211yesmaximal, characteristic
2#10593853C211yesmaximal, characteristic, complemented
3#10592529C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4845C211yesmaximal, characteristic, complemented
6#10590885C211yesmaximal, characteristic
7#10590876C211yesmaximal, characteristic
8#10590868C211yesmaximal, characteristic, complemented
9#10590818C211yesmaximal, characteristic, complemented
10#10590816C211yesmaximal, characteristic, complemented
11#10590797C211yesmaximal, characteristic, complemented
12#10590780C211yesmaximal, characteristic, complemented
13#10590775C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15#10590278C211yesmaximal, characteristic, complemented
16#81151—31nomaximal
17#80581—31nomaximal
18C4×#634C2211yescharacteristic
19C2×C3×Dic12C2211yescharacteristic
20C2×C3×#204C2211yescharacteristic
21C3×#875C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#870C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63919C2211yescharacteristic
26#63914C2211yescharacteristic
27#63913—21no—
28#63905—21no—
29#63898C2211yescharacteristic
30#63891—21no—
31#63879—21no—
32#63872C2211yescharacteristic
33#63867—21no—
34#63863C2211yescharacteristic
35#63845—21no—
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63843C2211yescharacteristic
39#63840—21no—
40#63837—21no—
41C2×#3715C2211yescharacteristic
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×#818C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54#63574C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5685—31no—
62#5681—31no—
63#5569—31no—
64#5559—31no—
65C3×#478—31no—
66C3×#464—31no—
67#5185—31no—
68Dic3×Q16—31no—
69#5163—31no—
70Dic3×SD16—31no—
71#5068—31no—
72#5056—31no—
73C4×#215—31no—
74C4×#214—31no—
75#4891—31no—
76#4873—31no—
77#4854—31no—
78#4852—31no—
79#4847D311yescharacteristic, complemented
80#4845D311yescharacteristic, complemented
81#4830—31no—
82#4830—31no—
83#4830—61no—
84#4800—31no—
85#4791—31no—
86#4768—31no—
87#4767—31no—
88#4766—31no—
89#4762—31no—
90#4760—31no—
91#4760—31no—
92C2×#634D411yescharacteristic
93C2×C3×D12C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×#627—21no—
99C2×#625—21no—
100C2×#625—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×Dic12—22no—
124C3×#204—22no—
125#3724—21no—
126Dic3⋊Dic3—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32—21no—
137#3715—22no—
138#3365—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—31no—
141C3×#125—31no—
142C3×#124—31no—
143C3×C4×Q8—31no—
144C3×C4×D4—31no—
145#947—31no—
146Q8×Dic3—31no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149C2×#215—31no—
150#940—31no—
151#940—31no—
152#936—31no—
153D4×Dic3—31no—
154C2×#214—31no—
155#929—61no—
156C4×#67—61no—
157C2×Dic12C2×D311yescharacteristic
158C2×#204C2×D311yescharacteristic
159#893—31no—
160#890—31no—
161#890—31no—
162#890—61no—
163#889—61no—
164#889—61no—
165#888—31no—
166#888—31no—
167#888—61no—
168#888—61no—
169#887—31no—
170#887—31no—
171#887—31no—
172#887—61no—
173#886—61no—
174#885—61no—
175#885—61no—
176#883—61no—
177#883—61no—
178#67⋊C4—61no—
179#875C2×D311yescharacteristic
180C4×D12C2×D311yescharacteristic
181#870—61no—
182#870C2×D311yescharacteristic
183C4×Dic6—31no—
184C4×Dic6—31no—
185C4×Dic6—61no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C3×#107—31no—
189C3×#106—31no—
190C3×C4⋊C8—21no—
191C3×C4⋊C8C2×D311yescharacteristic
192C3×C4⋊C8C2×D311yescharacteristic
193C3×#103—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×#102—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#821C2×D311yescharacteristic
204#821C2×D311yescharacteristic
205#821C2×D311yescharacteristic
206#818C2×D311yescharacteristic
207#817C2×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#809—31no—
226#809—31no—
227#808—31no—
228#808—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—21no—
252C3×C4×D3—81no—
253C3×Dic6—21no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6#4112yes—
257#627—42no—
258#625—42no—
259#625—81no—
260D3×Dic3—81no—
261C32×C8—21no—
262C32×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—31no—
271#478—91no—
272#475—91no—
273#464—31no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×D4—31no—
283C2×C3×D4—31no—
284C22×C3×C4—61no—
285C2×#67—61no—
286C2×#67—61no—
287C2×#67—61no—
288C2×#67—61no—
289C22×Dic3—61no—
290C2×D12C22×D311yescharacteristic
291C2×D12C22×D311yescharacteristic
292C2×C4×D3—21no—
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×Q16—62no—
302C3×SD16—62no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8C22×D311yescharacteristic
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C2×C3×C8C22×D311yescharacteristic
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—61no—
314C3×C4⋊C4—61no—
315C3×C4⋊C4—61no—
316C3×C22⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C42—21no—
320C3×C42—61no—
321C3×C42C22×D311yescharacteristic
322C3×C42C22×D311yescharacteristic
323#217—61no—
324#217—61no—
325#217—61no—
326#215—62no—
327#214—62no—
328(C2×D3)⋊C4—21no—
329(C2×D3)⋊C4—21no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—61no—
333(C2×D3)⋊C4—61no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—61no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3C22×D311yescharacteristic
343C4⋊Dic3C22×D311yescharacteristic
344C4⋊Dic3C22×D311yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362C4×Dic3—21no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—31no—
366C4×Dic3—31no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8—61no—
381Dic12—22no—
382#204—22no—
383C22×C32C22×D411yescharacteristic
384C2×C3×D3—41no—
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—22no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C2×Q16—31no—
405C2×SD16—31no—
406C2×SD16—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409#127—91no—
410#125—31no—
411#125—91no—
412#125—181no—
413#125—181no—
414#124—31no—
415#124—91no—
416#124—181no—
417#123—181no—
418#123—181no—
419C4×Q8—31no—
420C4×Q8—91no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—181no—
425C4×D4—31no—
426C4×D4—91no—
427C4×D4—181no—
428#107—31no—
429#106—31no—
430#106—91no—
431C4⋊C8—91no—
432C4⋊C8—91no—
433C4⋊C8D3211yescharacteristic
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—31no—
440#102—31no—
441#102—91no—
442#102—91no—
443#102—91no—
444C4×C8—91no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—61no—
448C23×C3—61no—
449C22×D3—21no—
450C22×D3—21no—
451C3×Q8—32no—
452C3×Q8—61no—
453C3×Q8—61no—
454C3×Q8—61no—
455C3×D4—61no—
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
475#67—122no—
476#67—122no—
477#67—241no—
478#67—241no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—31no—
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—241no—
498D12—21no—
499D12—21no—
500D12—21no—
501D12—21no—
502C4×D3—81no—
503C4×D3—241no—
504Dic6—21no—
505Dic6—21no—
506Dic6—21no—
507Dic6—62no—
508Dic6—62no—
509Dic6—64no—
510Dic6—122no—
511Dic6—122no—
512Dic6#23712yes—
513C3×C8—21no—
514C3×C8—21no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—41no—
518C3×C8—41no—
519C3⋊C8—62no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C2×C32#54811yescharacteristic
526C2×C32C2×#13511yescharacteristic
527C2×C32#57711yescharacteristic
528C3×D3—81no—
529C3×D3—81no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—91no—
533C2×Q8—181no—
534C2×D4—31no—
535C2×D4—31no—
536C2×D4—181no—
537C2×D4—181no—
538C22×C4—61no—
539C22×C4—181no—
540Q16—62no—
541SD16—62no—
542SD16—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—
569C42—61no—
570C42—91no—
571C42—91no—
572C42—181no—
573C42—181no—
574C42—181no—
575C42C2×D3211yescharacteristic
576C22×C3—21no—
577C22×C3—121no—
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—41no—
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—62no—
600C3×C4—121no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4—121no—
604C3×C4—121no—
605C3×C4C2×#23711yescharacteristic
606C3×C4#100711yescharacteristic
607C3×C4D3×#4111yescharacteristic
608C3×C4#101011yescharacteristic
609Dic3—22no—
610Dic3—32no—
611Dic3—32no—
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#336511yescharacteristic, complemented, Sylow
628C23—61no—
629C23—61no—
630Q8—32no—
631Q8—61no—
632Q8—61no—
633Q8—61no—
634Q8—182no—
635Q8—362no—
636D4—61no—
637D4—61no—
638D4—61no—
639D4—61no—
640D4—362no—
641D4—721no—
642C2×C4—61no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—91no—
651C2×C4—91no—
652C2×C4—241no—
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—241no—
665C2×C3—241no—
666C2×C3#559811yescharacteristic
667C2×C3#563311yescharacteristic
668C2×C3D3×#13511yescharacteristic
669C2×C3D3×#13511yescharacteristic
670C2×C3#577511yescharacteristic
671C2×C3#577811yescharacteristic
672D3—81no—
673D3—81no—
674C22—121no—
675C22—121no—
676C22—121no—
677C22—121no—
678C22—121no—
679C22—121no—
680C22C2×#380211yescharacteristic
681C4—21no—
682C4—21no—
683C4—62no—
684C4—92no—
685C4—121no—
686C4—121no—
687C4—121no—
688C4—121no—
689C4—121no—
690C4—181no—
691C4—181no—
692C4—181no—
693C4D3×#23711yescharacteristic
694C4#6431511yescharacteristic
695C3—21no—
696C3#8058111yescharacteristic, complemented
697C3#8115111yescharacteristic, complemented
698C2—241no—
699C2—241no—
700C2#1059452511yescharacteristic
701C2#1059468411yescharacteristic
702C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#63914C22
hypercenterC4⋊C8D32
hypocenterC32#3365
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
2. #10593853C2semidirect
3. #10592529C2semidirect
4. C3×#4847C2semidirect
5. C3×#4845C2semidirect
8. #10590868C2semidirect
9. #10590818C2semidirect
10. #10590816C2semidirect
11. #10590797C2semidirect
12. #10590780C2semidirect
13. #10590775C2semidirect
14. C4×#3715C2semidirect
15. #10590278C2semidirect
79. #4847D3semidirect
80. #4845D3semidirect
627. C32#3365semidirect
696. C3#80581semidirect
697. C3#81151semidirect

Maximal subgroups

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

subgroupindex
#105939812
#105938532
#105925292
C3×#48472
C3×#48452
#105908852
#105908762
#105908682
#105908182
#105908162
#105907972
#105907802
#105907752
C4×#37152
#105902782
#811513
#805813