Finite Group Databasebeta

← #11895657

Subgroups — #11895657

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595422C211yesmaximal, characteristic, complemented
2#10595199C211yesmaximal, characteristic
3SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#5166C211yesmaximal, characteristic, complemented
5C3×#5163C211yesmaximal, characteristic
6#10591612C211yesmaximal, characteristic, complemented
7Dic3×#216C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10591487C211yesmaximal, characteristic
10#10591479C211yesmaximal, characteristic, complemented
11#10591478C211yesmaximal, characteristic, complemented
12#10590868C211yesmaximal, characteristic, complemented
13#10590803C211yesmaximal, characteristic, complemented
14#10590772C211yesmaximal, characteristic, complemented
15#10590645C211yesmaximal, characteristic, complemented
16#80581—31nomaximal
17#80370—31nomaximal
18C2×C32×SD16C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C3×Q8×Dic3C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#940C2211yescharacteristic
26C3×#936C2211yescharacteristic
27#67⋊Dic3—21no—
28#63969—21no—
29#63962—21no—
30#63959—21no—
31#63918—21no—
32#63918C2211yescharacteristic
33C4×#627—21no—
34C4×#627C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63872—21no—
37#63872C2211yescharacteristic
38#63869—21no—
39#63869C2211yescharacteristic
40#63863C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63662C2211yescharacteristic
43#63659C2211yescharacteristic
44#63644C2211yescharacteristic
45C8×C3⋊Dic3C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52#63575C2211yescharacteristic
53#63573C2211yescharacteristic
54#63572C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5713—31no—
62#5681—31no—
63#5570—31no—
64#5569—31no—
65C3×#464—31no—
66C3×#460—31no—
67#5185—31no—
68Dic3×Q16—31no—
69#5166—31no—
70#5166D311yescharacteristic, complemented
71#5163D311yescharacteristic
72Dic3×SD16—31no—
73Dic3×SD16—31no—
74Dic3×SD16—31no—
75Dic3×SD16—61no—
76#5070—31no—
77#5056—31no—
78C4×#216—31no—
79C4×#215—31no—
80#4851—31no—
81#4847—31no—
82#4830—31no—
83#4830—31no—
84#4800—31no—
85#4791—31no—
86#4768—31no—
87#4768—31no—
88#4766—31no—
89#4763—31no—
90#4763—31no—
91#4760—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#627D411yescharacteristic
101C2×D3×Dic3—21no—
102C32×SD16—22no—
103C2×C32×C8C2311yescharacteristic
104#3757—21no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107C4⋊(C3⋊Dic3)C2311yescharacteristic
108C4×C3⋊Dic3—21no—
109C4×C3⋊Dic3C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×#216—22no—
114C3×#215—22no—
115C3×C4⋊Dic3—21no—
116C3×C4⋊Dic3—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4×Dic3—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125#3724—21no—
126#3724D411yescharacteristic
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
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#3365—91noSylow
139C2×C3×Q16—31no—
140C2×C3×SD16—21no—
141C2×C3×SD16—31no—
142C2×C3×SD16C2×D311yescharacteristic
143C2×C3×SD16C2×D311yescharacteristic
144C3×#127—31no—
145C3×#124—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148#947—31no—
149Q8×Dic3—31no—
150Q8×Dic3—31no—
151Q8×Dic3—31no—
152Q8×Dic3—61no—
153Q8×Dic3C2×D311yescharacteristic
154Q8×Dic3C2×D311yescharacteristic
155C2×#216C2×D311yescharacteristic
156C2×#215C2×D311yescharacteristic
157#940C2×D311yescharacteristic
158#936—31no—
159#936—61no—
160#936C2×D311yescharacteristic
161#935—61no—
162#935—61no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168#890—31no—
169#890—31no—
170#890—31no—
171#890—61no—
172#890—61no—
173#890—61no—
174#888—31no—
175#888—61no—
176#886—61no—
177#885—61no—
178#883—61no—
179#67⋊C4—61no—
180C4×D12—31no—
181#870—31no—
182#870—61no—
183#869—31no—
184#869—61no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—31no—
188C4×Dic6—61no—
189C4×Dic6—61no—
190C3×C4⋊C8—31no—
191C3×C4⋊C8—31no—
192C3×#103—31no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#102—31no—
196#835—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—61no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832C2×D311yescharacteristic
207#832C2×D311yescharacteristic
208#821—31no—
209#821C2×D311yescharacteristic
210#818—31no—
211#817—31no—
212#817—31no—
213#817—31no—
214#817—61no—
215#816—31no—
216#816C2×D311yescharacteristic
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8C2×D311yescharacteristic
220Dic3⋊C8C2×D311yescharacteristic
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—61no—
226#810—31no—
227#809—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#4112yes—
236C32×D4—21no—
237C32×D4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—81no—
243C2×C3⋊Dic3C2×D411yescharacteristic
244C2×C3⋊Dic3C2×D411yescharacteristic
245C3×#67—42no—
246C3×#67—81no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
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—21no—
258#627—22no—
259#627—42no—
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—31no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—21no—
281C2×C3×Q8—31no—
282C2×C3×Q8C22×D311yescharacteristic
283C2×C3×Q8C22×D311yescharacteristic
284C2×C3×D4—21no—
285C2×C3×D4—31no—
286C2×C3×D4—61no—
287C2×C3×D4—61no—
288C2×C3×D4C22×D311yescharacteristic
289C2×C3×D4C22×D311yescharacteristic
290C2×#67—21no—
291C2×#67—21no—
292C22×Dic3—61no—
293C22×Dic3—61no—
294C22×Dic3—61no—
295C22×Dic3—121no—
296C2×D12C22×D311yescharacteristic
297C2×C4×D3—61no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6C22×D311yescharacteristic
303C3×Q16—62no—
304C3×SD16—24no—
305C3×SD16—22no—
306C3×SD16—22no—
307C3×SD16—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—61no—
316C3×C4⋊C4—61no—
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C42—31no—
320C3×C42—31no—
321C3×C42—61no—
322C3×C42—61no—
323#217—21no—
324#217—21no—
325#217—61no—
326#217—61no—
327#217—61no—
328#217—61no—
329#217—61no—
330#217—121no—
331#216—22no—
332#215—22no—
333(C2×D3)⋊C4—61no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—31no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3—61no—
350C4⋊Dic3—61no—
351C4⋊Dic3—61no—
352C4⋊Dic3—61no—
353C4⋊Dic3—121no—
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—31no—
357Dic3⋊C4—31no—
358Dic3⋊C4—31no—
359Dic3⋊C4—31no—
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—21no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—61no—
374C4×Dic3—61no—
375C4×Dic3—61no—
376C4×Dic3—121no—
377C4×Dic3C22×D311yescharacteristic
378C4×Dic3C22×D311yescharacteristic
379C2×C3⋊C8—31no—
380C2×C3⋊C8—31no—
381C2×C3⋊C8—61no—
382C2×C3⋊C8C22×D311yescharacteristic
383C2×C3⋊C8C22×D311yescharacteristic
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32C22×D411yescharacteristic
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C2×C3×D3—41no—
391C32×C4—22no—
392C32×C4C2×#4111yescharacteristic
393C32×C42−1+411yescharacteristic
394C3⋊Dic3—21no—
395C3⋊Dic3—21no—
396C3⋊Dic3—41no—
397C3⋊Dic3—41no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3#13512yes—
405C2×Q16—31no—
406C2×SD16—31no—
407C2×SD16D3211yescharacteristic
408C4⋊Q8—91no—
409C4⋊Q8—181no—
410#127—31no—
411#125—91no—
412#125—91no—
413#125—181no—
414#125—181no—
415#124—31no—
416#124—91no—
417#124—181no—
418#123—181no—
419#123—181no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—91no—
425C4×Q8—181no—
426C4×D4—91no—
427C4×D4—91no—
428C4×D4—181no—
429#107—91no—
430#106—91no—
431#106—91no—
432C4⋊C8—31no—
433C4⋊C8—31no—
434C4⋊C8—91no—
435#103—31no—
436#103—91no—
437#103—91no—
438#103—91no—
439#102—31no—
440#102—31no—
441#102—31no—
442#102—91no—
443#102—91no—
444#102—91no—
445C4×C8—91no—
446C4×C8—91no—
447C4×C8—91no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—41no—
451C23×C3—61no—
452C22×D3—21no—
453C3×Q8—21no—
454C3×Q8—21no—
455C3×Q8—22no—
456C3×Q8—41no—
457C3×Q8—61no—
458C3×Q8—61no—
459C3×Q8#23712yes—
460C3×Q8#23712yes—
461C3×D4—22no—
462C3×D4—21no—
463C3×D4—21no—
464C3×D4—21no—
465C3×D4—21no—
466C3×D4—41no—
467C3×D4—61no—
468C3×D4—61no—
469C3×D4—122no—
470C3×D4—241no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
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—42no—
485#67—81no—
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—61no—
498C2×Dic3—61no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3—241no—
502C2×Dic3—241no—
503C2×Dic3—241no—
504C2×Dic3—242no—
505C2×Dic3D3×D411yescharacteristic
506C2×Dic3D3×D411yescharacteristic
507C2×Dic3D3×D411yescharacteristic
508C2×Dic3D3×D411yescharacteristic
509D12—21no—
510D12—21no—
511C4×D3—241no—
512Dic6—21no—
513Dic6—21no—
514Dic6—62no—
515Dic6—62no—
516Dic6—122no—
517Dic6—122no—
518C3×C8—22no—
519C3×C8—21no—
520C3×C8—21no—
521C3×C8—61no—
522C3×C8—61no—
523C3⋊C8—21no—
524C3⋊C8—21no—
525C3⋊C8—61no—
526C3⋊C8—61no—
527C3⋊C8—121no—
528C2×C32—81no—
529C2×C32#54811yescharacteristic
530C2×C32C2×#13511yescharacteristic
531C2×C32#57711yescharacteristic
532C3×D3—81no—
533C2×Q8—31no—
534C2×Q8—91no—
535C2×Q8—181no—
536C2×Q8C2×D3211yescharacteristic
537C2×D4—31no—
538C2×D4—61no—
539C2×D4—61no—
540C2×D4C2×D3211yescharacteristic
541C22×C4—181no—
542C22×C4—181no—
543Q16—62no—
544SD16—22no—
545SD16—62no—
546C2×C8—31no—
547C2×C8—31no—
548C2×C8—91no—
549C2×C8C2×D3211yescharacteristic
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—91no—
555C4⋊C4—91no—
556C4⋊C4—91no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C4⋊C4—181no—
564C4⋊C4—181no—
565C4⋊C4—181no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C22⋊C4—181no—
571C22⋊C4—181no—
572C42—31no—
573C42—31no—
574C42—61no—
575C42—61no—
576C42—91no—
577C42—181no—
578C42—181no—
579C22×C3—21no—
580C22×C3—42no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—81no—
588C22×C3—81no—
589C22×C3—121no—
590C22×C3—121no—
591C22×C3—121no—
592C22×C3C2×D3×D411yescharacteristic
593C22×C3C2×D3×D411yescharacteristic
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C3×C4—22no—
598C3×C4—22no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—32no—
602C3×C4—42no—
603C3×C4—61no—
604C3×C4—61no—
605C3×C4—61no—
606C3×C4—121no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4C2×#23711yescharacteristic
610C3×C4C2×#23711yescharacteristic
611C3×C4#101011yescharacteristic
612C3×C4#101011yescharacteristic
613Dic3—21no—
614Dic3—21no—
615Dic3—21no—
616Dic3—41no—
617Dic3—41no—
618Dic3—41no—
619Dic3—62no—
620Dic3—61no—
621Dic3—61no—
622Dic3—61no—
623Dic3—61no—
624Dic3—121no—
625Dic3—121no—
626Dic3—121no—
627Dic3—121no—
628Dic3—121no—
629Dic3—241no—
630Dic3—241no—
631Dic3#91612yes—
632C32#336511yescharacteristic, complemented, Sylow
633C23—21no—
634C23—61no—
635Q8—21no—
636Q8—61no—
637Q8—61no—
638Q8—182no—
639Q8—362no—
640Q8#380512yes—
641D4—21no—
642D4—21no—
643D4—61no—
644D4—61no—
645D4—122no—
646D4—241no—
647C2×C4—21no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—31no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—91no—
656C2×C4—91no—
657C2×C4—181no—
658C2×C4—181no—
659C2×C4—721no—
660C2×C4—721no—
661C2×C4C22×D3211yescharacteristic
662C8—21no—
663C8—61no—
664C8—61no—
665C8—181no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—82no—
670C2×C3—81no—
671C2×C3—81no—
672C2×C3—241no—
673C2×C3#559811yescharacteristic
674C2×C3#559811yescharacteristic
675C2×C3C2×#91611yescharacteristic
676C2×C3D3×#13511yescharacteristic
677C2×C3#577511yescharacteristic
678C2×C3#577811yescharacteristic
679D3—81no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—121no—
684C22—121no—
685C22—121no—
686C22D32×D411yescharacteristic
687C4—22no—
688C4—32no—
689C4—61no—
690C4—61no—
691C4—61no—
692C4—121no—
693C4—121no—
694C4—121no—
695C4—181no—
696C4—181no—
697C4—361no—
698C4—361no—
699C4#6430911yescharacteristic
700C4C2×#380511yescharacteristic
701C3—21no—
702C3#8037011yescharacteristic, complemented
703C3#8058111yescharacteristic, complemented
704C2—81no—
705C2—241no—
706C2D3×#91611yescharacteristic
707C2#1059475411yescharacteristic
708C2#1059514211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenterC2×SD16D32
hypocenterC32#3365
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. #10595422C2semidirect
3. SD16×C3⋊Dic3C2semidirect
4. C3×#5166C2semidirect
6. #10591612C2semidirect
7. Dic3×#216C2semidirect
8. Dic3×#215C2semidirect
10. #10591479C2semidirect
11. #10591478C2semidirect
12. #10590868C2semidirect
13. #10590803C2semidirect
14. #10590772C2semidirect
15. #10590645C2semidirect
70. #5166D3semidirect
632. C32#3365semidirect
702. C3#80370semidirect
703. C3#80581semidirect

Maximal subgroups

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

subgroupindex
#105954222
#105951992
SD16×C3⋊Dic32
C3×#51662
C3×#51632
#105916122
Dic3×#2162
Dic3×#2152
#105914872
#105914792
#105914782
#105908682
#105908032
#105907722
#105906452
#805813
#803703