Finite Group Databasebeta

← #11895692

Subgroups — #11895692

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595198C211yesmaximal, characteristic
2#10594317C211yesmaximal, characteristic, complemented
3#10592467C211yesmaximal, characteristic, complemented
4C3×#4760C211yesmaximal, characteristic
5C3×#4758C211yesmaximal, characteristic, complemented
6#10591443C211yesmaximal, characteristic, complemented
7#10591438C211yesmaximal, characteristic
8#10591411C211yesmaximal, characteristic, complemented
9#10590863C211yesmaximal, characteristic, complemented
10#10590793C211yesmaximal, characteristic, complemented
11C8×#627C211yesmaximal, characteristic, complemented
12#10590742C211yesmaximal, characteristic, complemented
13#10590532C211yesmaximal, characteristic, complemented
14#10590487C211yesmaximal, characteristic, complemented
15#10590474C211yesmaximal, characteristic, complemented
16#81589—31nomaximal
17#79624—31nomaximal
18#64145C2211yescharacteristic
19#64099C2211yescharacteristic
20C3×#940C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#888C2211yescharacteristic
24C3×#887C2211yescharacteristic
25Dic3×#67—21no—
26#63969—21no—
27#63961—21no—
28#63959—21no—
29C4×#627C2211yescharacteristic
30#63898C2211yescharacteristic
31#63869C2211yescharacteristic
32#63867—21no—
33#63860C2211yescharacteristic
34#63845—21no—
35#63844C2211yescharacteristic
36#63843C2211yescharacteristic
37Dic3×Dic6—21no—
38Dic3×Dic6C2211yescharacteristic
39#63839—21no—
40C2×#3719C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C32×#102C2211yescharacteristic
43#63659C2211yescharacteristic
44#63643C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63575C2211yescharacteristic
55#63574C2211yescharacteristic
56#63572C2211yescharacteristic
57Dic3⋊(C3⋊C8)C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63567C2211yescharacteristic
60#63563C2211yescharacteristic
61#5721—31no—
62#5713—31no—
63#5569—31no—
64#5559—31no—
65C3×#486—31no—
66C3×C4×SD16—31no—
67#5166—31no—
68#5163—31no—
69#5094—31no—
70#5075—31no—
71#5028—31no—
72#5009—31no—
73#4871—31no—
74#4854—31no—
75#4790—31no—
76#4788—31no—
77#4768—31no—
78#4768—31no—
79#4768—31no—
80#4768—61no—
81#4767—31no—
82#4767—31no—
83#4766—31no—
84#4766—31no—
85#4760D311yescharacteristic
86#4758—31no—
87#4758D311yescharacteristic, complemented
88C4×Dic12—31no—
89#4697—31no—
90C8×Dic6—31no—
91C8×Dic6—31no—
92C2×C32×D4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×Dic6—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×#627D411yescharacteristic
101C2×D3×Dic3—21no—
102C2×C32×C8C2311yescharacteristic
103C32×C4⋊C4C2311yescharacteristic
104#3757—21no—
105#3757—21no—
106C4⋊(C3⋊Dic3)—21no—
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108#3750—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#214—22no—
113C3×C4⋊Dic3C2311yescharacteristic
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
122#3724—21no—
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—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136#3719—22no—
137#3715—22no—
138#3365—91noSylow
139C2×C3×SD16—31no—
140C3×C4⋊Q8—31no—
141C3×#127—31no—
142C3×C4×Q8—31no—
143C3×C4×D4—31no—
144Q8×Dic3—31no—
145Q8×Dic3—31no—
146Q8×Dic3—61no—
147#944—61no—
148C2×#216—31no—
149C2×#215—31no—
150#940C2×D311yescharacteristic
151#936—31no—
152#936—31no—
153#936—31no—
154#936—61no—
155#936—61no—
156#935—61no—
157#935—61no—
158D4×Dic3—31no—
159D4×Dic3—61no—
160D4×Dic3C2×D311yescharacteristic
161C2×#214—31no—
162C2×#214C2×D311yescharacteristic
163#929—61no—
164C4×#67—61no—
165C2×Dic12—31no—
166#893—31no—
167#890—31no—
168#890—31no—
169#890—31no—
170#890—61no—
171#890—61no—
172#889—61no—
173#889—61no—
174#888—61no—
175#888C2×D311yescharacteristic
176#887—31no—
177#887—31no—
178#887C2×D311yescharacteristic
179#885—61no—
180#883—61no—
181#875—31no—
182#870—31no—
183#870—61no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C3×#106—31no—
190C3×#103—31no—
191C3×#102—21no—
192C3×#102—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#102C2×D311yescharacteristic
196C3×#102C2×D311yescharacteristic
197C3×C4×C8—31no—
198C3×C4×C8—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—61no—
203#832C2×D311yescharacteristic
204#821—31no—
205#821C2×D311yescharacteristic
206#818—31no—
207#816—31no—
208#816—31no—
209#816—31no—
210#816—61no—
211#816C2×D311yescharacteristic
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216C8×Dic3—31no—
217C8×Dic3—31no—
218C8×Dic3—61no—
219C8×Dic3C2×D311yescharacteristic
220C8×Dic3C2×D311yescharacteristic
221#810—31no—
222#810—31no—
223#810—31no—
224#810—61no—
225#809C2×D311yescharacteristic
226#808—31no—
227#808—31no—
228#808C2×D311yescharacteristic
229#807—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—31no—
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×D4—21no—
235C32×D4—21no—
236C2×C32×C4—21no—
237C2×C32×C4C2411yescharacteristic
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3—21no—
240C2×C3⋊Dic3C2×D411yescharacteristic
241C2×C3⋊Dic3C2×D411yescharacteristic
242#634—21no—
243#634—21no—
244C3×#67—42no—
245C3×#67—81no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—81no—
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C3×D12—21no—
255C3×D12—21no—
256C3×Dic6—21no—
257C3×Dic6—42no—
258C3×Dic6#4112yes—
259#627—22no—
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—31no—
270#478—91no—
271#478—91no—
272#475—91no—
273#464—91no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—31no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—61no—
282C2×C3×D4—21no—
283C2×C3×D4—31no—
284C2×C3×D4—61no—
285C2×C3×D4—61no—
286C2×C3×D4C22×D311yescharacteristic
287C2×C3×D4C22×D311yescharacteristic
288C22×C3×C4—61no—
289C2×#67—21no—
290C2×#67—21no—
291C22×Dic3—21no—
292C22×Dic3—61no—
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—61no—
295C2×Dic6—21no—
296C2×Dic6—31no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6C22×D311yescharacteristic
302C3×SD16—62no—
303C2×C3×C8—21no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8C22×D311yescharacteristic
307C2×C3×C8C22×D311yescharacteristic
308C3×C4⋊C4—21no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4—61no—
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C4⋊C4C22×D311yescharacteristic
315C3×C22⋊C4—61no—
316C3×C42—31no—
317C3×C42—31no—
318C3×C42—61no—
319#217—21no—
320#217—61no—
321#217—61no—
322#217—61no—
323#217—61no—
324#217—61no—
325#217—61no—
326#217—61no—
327#217—121no—
328#217—121no—
329#216—62no—
330#215—62no—
331#214—22no—
332#214—62no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—121no—
347C4⋊Dic3C22×D311yescharacteristic
348C4⋊Dic3C22×D311yescharacteristic
349Dic3⋊C4—21no—
350Dic3⋊C4—21no—
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—61no—
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—121no—
365C4×Dic3—21no—
366C4×Dic3—31no—
367C4×Dic3—31no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3C22×D311yescharacteristic
376C4×Dic3C22×D311yescharacteristic
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8C22×D311yescharacteristic
381C2×C3⋊C8C22×D311yescharacteristic
382Dic12—62no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32C22×D411yescharacteristic
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—41no—
391C32×C4C2×#4111yescharacteristic
392C32×C42−1+411yescharacteristic
393C3⋊Dic3—21no—
394C3⋊Dic3—21no—
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3#13512yes—
404C2×Q16—91no—
405C2×SD16—31no—
406C2×SD16—91no—
407C4⋊Q8—31no—
408C4⋊Q8—181no—
409#127—31no—
410#125—91no—
411#125—91no—
412#125—181no—
413#125—181no—
414#124—91no—
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—91no—
429#106—31no—
430#106—91no—
431C4⋊C8—91no—
432C4⋊C8—91no—
433C4⋊C8—91no—
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#102D3211yescharacteristic
444C4×C8—31no—
445C4×C8—31no—
446C4×C8—91no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—41no—
450C23×C3—61no—
451C22×D3—21no—
452C3×Q8—32no—
453C3×Q8—61no—
454C3×Q8—122no—
455C3×D4—21no—
456C3×D4—21no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—41no—
460C3×D4—41no—
461C3×D4—61no—
462C3×D4—61no—
463C3×D4—122no—
464C3×D4—241no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—31no—
469C2×C3×C4—31no—
470C2×C3×C4—31no—
471C2×C3×C4—31no—
472C2×C3×C4—41no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—241no—
477C2×C3×C4C23×D311yescharacteristic
478C2×C3×C4C23×D311yescharacteristic
479#67—42no—
480#67—81no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—31no—
487C2×Dic3—31no—
488C2×Dic3—61no—
489C2×Dic3—61no—
490C2×Dic3—61no—
491C2×Dic3—61no—
492C2×Dic3—61no—
493C2×Dic3—61no—
494C2×Dic3—81no—
495C2×Dic3—121no—
496C2×Dic3—121no—
497C2×Dic3—241no—
498C2×Dic3D3×D411yescharacteristic
499C2×Dic3D3×D411yescharacteristic
500C2×Dic3D3×D411yescharacteristic
501C2×Dic3D3×D411yescharacteristic
502D12—21no—
503D12—21no—
504C4×D3—241no—
505Dic6—21no—
506Dic6—42no—
507Dic6—62no—
508Dic6—62no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—121no—
514Dic6—121no—
515Dic6#23512yes—
516C3×C8—21no—
517C3×C8—21no—
518C3×C8—41no—
519C3×C8—61no—
520C3×C8—61no—
521C3⋊C8—21no—
522C3⋊C8—21no—
523C3⋊C8—61no—
524C3⋊C8—61no—
525C3⋊C8—121no—
526C2×C32—81no—
527C2×C32#54811yescharacteristic
528C2×C32C2×#13511yescharacteristic
529C2×C32#57711yescharacteristic
530C3×D3—81no—
531C2×Q8—31no—
532C2×Q8—61no—
533C2×Q8—91no—
534C2×Q8—91no—
535C2×D4—31no—
536C2×D4—61no—
537C2×D4—61no—
538C2×D4C2×D3211yescharacteristic
539C22×C4—61no—
540C22×C4—181no—
541Q16—182no—
542SD16—62no—
543SD16—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8C2×D3211yescharacteristic
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—91no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4C2×D3211yescharacteristic
564C22⋊C4—61no—
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—
575C42—181no—
576C42—181no—
577C22×C3—21no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3—121no—
590C22×C3C2×D3×D411yescharacteristic
591C22×C3C2×D3×D411yescharacteristic
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—41no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—32no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—62no—
601C3×C4—61no—
602C3×C4—61no—
603C3×C4—61no—
604C3×C4—81no—
605C3×C4—121no—
606C3×C4—121no—
607C3×C4C2×#23511yescharacteristic
608C3×C4D3×#4111yescharacteristic
609C3×C4#101011yescharacteristic
610C3×C4#101011yescharacteristic
611Dic3—21no—
612Dic3—21no—
613Dic3—21no—
614Dic3—22no—
615Dic3—41no—
616Dic3—41no—
617Dic3—61no—
618Dic3—61no—
619Dic3—61no—
620Dic3—61no—
621Dic3—121no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—241no—
628Dic3—241no—
629Dic3#91212yes—
630C32#336511yescharacteristic, complemented, Sylow
631C23—21no—
632C23—61no—
633Q8—32no—
634Q8—61no—
635Q8—122no—
636Q8—182no—
637Q8—181no—
638Q8—181no—
639D4—21no—
640D4—21no—
641D4—61no—
642D4—61no—
643D4—122no—
644D4—241no—
645C2×C4—21no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—91no—
654C2×C4—91no—
655C2×C4—181no—
656C2×C4—181no—
657C2×C4—241no—
658C2×C4—721no—
659C2×C4C22×D3211yescharacteristic
660C8—21no—
661C8—61no—
662C8—61no—
663C8—181no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—81no—
668C2×C3—81no—
669C2×C3—161no—
670C2×C3—241no—
671C2×C3#555211yescharacteristic
672C2×C3#567711yescharacteristic
673C2×C3C2×#91211yescharacteristic
674C2×C3#576211yescharacteristic
675C2×C3#576211yescharacteristic
676C2×C3D3×#13511yescharacteristic
677D3—81no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—121no—
682C22—121no—
683C22—121no—
684C22D32×D411yescharacteristic
685C4—32no—
686C4—41no—
687C4—62no—
688C4—61no—
689C4—61no—
690C4—61no—
691C4—121no—
692C4—121no—
693C4—181no—
694C4—181no—
695C4—361no—
696C4—361no—
697C4D3×#23511yescharacteristic
698C4#6430911yescharacteristic
699C3—21no—
700C3#7962411yescharacteristic, complemented
701C3#8158911yescharacteristic, complemented
702C2—81no—
703C2—241no—
704C2#1059407311yescharacteristic
705C2D3×#91211yescharacteristic
706C2#1059474811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenter#102D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594317C2semidirect
3. #10592467C2semidirect
5. C3×#4758C2semidirect
6. #10591443C2semidirect
8. #10591411C2semidirect
9. #10590863C2semidirect
10. #10590793C2semidirect
11. C8×#627C2semidirect
12. #10590742C2semidirect
13. #10590532C2semidirect
14. #10590487C2semidirect
15. #10590474C2semidirect
87. #4758D3semidirect
630. C32#3365semidirect
700. C3#79624semidirect
701. C3#81589semidirect

Maximal subgroups

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

subgroupindex
#105951982
#105943172
#105924672
C3×#47602
C3×#47582
#105914432
#105914382
#105914112
#105908632
#105907932
C8×#6272
#105907422
#105905322
#105904872
#105904742
#815893
#796243