Finite Group Databasebeta

← #11864517

Subgroups — #11864517

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic
2C22×#3756C211yesmaximal, characteristic, complemented
3#10594856C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6#10591599C214yesmaximal, complemented
7#10591595C214yesmaximal, complemented
8#10591083C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#84117—31nomaximal
11#78961—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C3×#1007—24no—
15C3×#1007—24no—
16C2×C3×#239—21no—
17C2×C3×#239C2212yes—
18C2×C3×D3×Q8—21no—
19C2×C3×D3×Q8C2212yes—
20C2×C3×#235—22no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C2×#3756—24no—
24C2×#3756C2214yes—
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28#63962—22no—
29#63866—21no—
30#63860—21no—
31#63857C2214yes—
32C2×#3719C2212yes—
33#63831—24no—
34C2×#3716C2212yes—
35C3×#835C2214yes—
36#63565C2212yes—
37#63562C2212yes—
38(C2×D3)⋊(C3⋊C8)C2214yes—
39C2×C3×2−1+4—31no—
40C2×#1007D311yescharacteristic
41#5825—31no—
42C2×#951—31no—
43C22×#216—31no—
44C22×#216—31no—
45C22×#216—61no—
46C2×#909—31no—
47#5526—31no—
48C3×#419—31no—
49#5239—34no—
50#5234—31no—
51#5233—31no—
52#5228—34no—
53#5225D311yescharacteristic, complemented
54#5129—31no—
55#5002—31no—
56#4809—34no—
57#4808—34no—
58C2×C32×Q8—21no—
59C2×C32×Q8—22no—
60C2×C32×Q8D414yes—
61C2×C32×Q8C2312yes—
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3—21no—
65C2×#634—22no—
66C2×#634—22no—
67C2×#634—21no—
68C2×#634C2312yes—
69C2×C3×#67—21no—
70C2×C3×#67D412yes—
71C3×#239—28no—
72C3×#239—24no—
73C3×#239—24no—
74C3×D3×Q8—28no—
75C3×D3×Q8—24no—
76C3×D3×Q8—24no—
77C3×#235—216no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235D414yes—
82C2×C3×D12—22no—
83C2×C3×D12D411yescharacteristic
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3—21no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3C2312yes—
89C2×C3×Dic6—22no—
90C2×C3×Dic6D411yescharacteristic
91C2×C3×Dic6C2311yescharacteristic
92#3756—28no—
93C2×C3⋊(C3⋊C8)—22no—
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4×Dic3—21no—
98C3×#208—22no—
99C2×C3×C3⋊C8C2312yes—
100Dic3⋊Dic3—24no—
101(C2×D3)⋊Dic3—24no—
102#3719—24no—
103#3716—24no—
104#3011—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C22×C3×Q8—21no—
113C22×C3×Q8—32no—
114C22×C3×Q8—61no—
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×Q8C2×D311yescharacteristic
117#1007—24no—
118#1007—24no—
119C2×#239—21no—
120C2×#239C2×D312yes—
121C2×D3×Q8—21no—
122C2×D3×Q8C2×D312yes—
123C2×#235—22no—
124C2×#235C2×D311yescharacteristic
125C2×#235C2×D311yescharacteristic
126C22×Dic6—31no—
127C22×Dic6—31no—
128C22×Dic6—61no—
129C2×C3×M16—31no—
130C3×#117—31no—
131#951—64no—
132#944—61no—
133C2×#216—34no—
134C2×#216—34no—
135C2×#216—32no—
136C2×#216—64no—
137C2×#216—68no—
138C2×#216—64no—
139C2×#216—64no—
140#936—61no—
141#935—62no—
142C2×#214—32no—
143#926C2×D311yescharacteristic
144#924—34no—
145C2×#208C2×D311yescharacteristic
146C22×C3⋊C8—31no—
147C22×C3⋊C8—31no—
148C22×C3⋊C8—61no—
149#909—64no—
150C2×Dic12—32no—
151C2×#204—32no—
152#897—34no—
153#886—62no—
154#875—61no—
155#869—61no—
156C3×#103—34no—
157#835—32no—
158#835C2×D314yes—
159#832—32no—
160#830—34no—
161(C2×D3)⋊C8—34no—
162#810—32no—
163#809—32no—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—21no—
166C22×C3×D3C2×D412yes—
167C32×Q8—24no—
168C32×Q8—22no—
169C32×Q8C2×D414yes—
170C2×C32×C4—24no—
171C2×C32×C4—22no—
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—42no—
178#634—22no—
179#634—22no—
180#634—42no—
181C3×#67—24no—
182C3×#67—24no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—28no—
187C3×D12—22no—
188C3×D12—21no—
189C3×D12C2×D412yes—
190C3×C4×D3—28no—
191C3×C4×D3—28no—
192C3×C4×D3—24no—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6—28no—
196C3×Dic6—22no—
197C3×Dic6—21no—
198C3×Dic6C2×D412yes—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—22no—
201C2×2−1+4—31no—
202C2×#137—91no—
203C22×Q16—91no—
204#536—91no—
205#452—94no—
206#451—94no—
207#419—31no—
208#416—91no—
209#408—91no—
210C3×#41—34no—
211C3×#41—616no—
212C3×#41—64no—
213C3×#41—68no—
214C3×#41—64no—
215C3×#41—62no—
216C3×#41—62no—
217C3×#41—62no—
218C2×C3×Q8—21no—
219C2×C3×Q8—22no—
220C2×C3×Q8—21no—
221C2×C3×Q8—22no—
222C2×C3×Q8—24no—
223C2×C3×Q8—22no—
224C2×C3×Q8—31no—
225C2×C3×Q8—31no—
226C2×C3×Q8—41no—
227C2×C3×Q8—42no—
228C2×C3×Q8—62no—
229C2×C3×Q8—64no—
230C2×C3×Q8—68no—
231C2×C3×Q8—64no—
232C2×C3×Q8D1214yes—
233C2×C3×Q8#6714yes—
234C2×C3×Q8C22×D312yes—
235C2×C3×Q8C22×D312yes—
236C2×C3×D4—32no—
237C2×C3×D4—31no—
238C2×C3×D4—31no—
239C2×C3×D4—62no—
240C2×C3×D4—61no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—32no—
245C22×C3×C4—41no—
246C22×C3×C4—62no—
247C22×C3×C4—62no—
248C22×C3×C4—61no—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C2×#67—21no—
252C2×#67#6712yes—
253C22×Dic3—61no—
254C22×Dic3—61no—
255C22×Dic3—121no—
256#239—28no—
257#239—24no—
258#239—24no—
259D3×Q8—28no—
260D3×Q8—24no—
261D3×Q8—24no—
262#235—216no—
263#235—22no—
264#235—22no—
265#235—22no—
266#235#6714yes—
267C2×D12—22no—
268C2×D12#6711yescharacteristic
269C2×D12C22×D311yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—21no—
272C2×C4×D3—22no—
273C2×C4×D3C22×D312yes—
274C2×Dic6—22no—
275C2×Dic6—32no—
276C2×Dic6—32no—
277C2×Dic6—62no—
278C2×Dic6—64no—
279C2×Dic6—62no—
280C2×Dic6—62no—
281C2×Dic6—62no—
282C2×Dic6—62no—
283C2×Dic6—61no—
284C2×Dic6—61no—
285C2×Dic6—121no—
286C2×Dic6—122no—
287C2×Dic6#6711yescharacteristic
288C2×Dic6C22×D311yescharacteristic
289C3×M16—62no—
290C2×C3×C8—32no—
291C3×C4⋊C4—32no—
292C3×C22⋊C4—61no—
293C3×C42—61no—
294#217—21no—
295#217—64no—
296#216—64no—
297#216—616no—
298#216—68no—
299#216—68no—
300#214—64no—
301(C2×D3)⋊C4—64no—
302C4⋊Dic3—64no—
303C4⋊Dic3C22×D312yes—
304Dic3⋊C4—64no—
305C4×Dic3—21no—
306#208—22no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—62no—
310C2×C3⋊C8—64no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8C22×D312yes—
314Dic12—64no—
315#204—64no—
316C22×C32—22no—
317C22×C32#12012yes—
318C22×C32C22×D411yescharacteristic
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3—24no—
322C2×C3×D3—42no—
323C32×C4—24no—
324C32×C4#12012yes—
325C32×C4C22×D411yescharacteristic
326C32×C4C22×D411yescharacteristic
327C3⋊Dic3—42no—
328C3×Dic3—22no—
329C3×Dic3—22no—
330C3×Dic3—42no—
3312−1+4—64no—
3322−1+4—64no—
333C2×#41—31no—
334C2×#41—32no—
335C2×#41—31no—
336C2×#41—62no—
337C2×#41—61no—
338C22×Q8—32no—
339C22×Q8—61no—
340C22×Q8—91no—
341C22×Q8D3211yescharacteristic
342#137—184no—
343C2×Q16—92no—
344C2×Q16—94no—
345C2×Q16—184no—
346C2×SD16—92no—
347C2×M16—31no—
348C22×C8—91no—
349C4⋊Q8—181no—
350#124—181no—
351#123—182no—
352C22⋊Q8—94no—
353#117—31no—
354#103—34no—
355#103—92no—
356#102—92no—
357C22⋊C8—94no—
358C23×C3—21no—
359C23×C3—32no—
360C23×C3—61no—
361C23×C3D3×D411yescharacteristic
362C23×C3C2×#6711yescharacteristic
363C22×D3—21no—
364C22×D3C2×#6712yes—
365C3×Q8—24no—
366C3×Q8—24no—
367C3×Q8—22no—
368C3×Q8—22no—
369C3×Q8—24no—
370C3×Q8—32no—
371C3×Q8—42no—
372C3×Q8—44no—
373C3×Q8—68no—
374C3×Q8—62no—
375C3×Q8—61no—
376C3×Q8C2×D1214yes—
377C3×Q8C2×#6714yes—
378C3×D4—32no—
379C3×D4—68no—
380C3×D4—64no—
381C3×D4—64no—
382C3×D4—62no—
383C3×D4—61no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—32no—
393C2×C3×C4—42no—
394C2×C3×C4—44no—
395C2×C3×C4—68no—
396C2×C3×C4—68no—
397C2×C3×C4—61no—
398C2×C3×C4—64no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4C2×D1212yes—
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D412yes—
405C2×C3×C4C2×#6712yes—
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C2×#6712yes—
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—24no—
411#67—24no—
412C2×Dic3—21no—
413C2×Dic3—22no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—122no—
417C2×Dic3—124no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3C2×#6712yes—
421D12—28no—
422D12—22no—
423D12—21no—
424D12C2×#6712yes—
425C4×D3—28no—
426C4×D3—28no—
427C4×D3—24no—
428C4×D3—22no—
429C4×D3—22no—
430Dic6—28no—
431Dic6—22no—
432Dic6—21no—
433Dic6—64no—
434Dic6—62no—
435Dic6—62no—
436Dic6—62no—
437Dic6—62no—
438Dic6—122no—
439Dic6—124no—
440Dic6—122no—
441Dic6—122no—
442Dic6C2×#6712yes—
443C3×C8—62no—
444C3⋊C8—22no—
445C3⋊C8—64no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C2×C32—22no—
449C2×C32C2×#12011yescharacteristic
450C2×C32#57812yes—
451C3×D3—42no—
452C3×D3—42no—
453#41—34no—
454#41—616no—
455#41—64no—
456#41—68no—
457#41—64no—
458#41—62no—
459#41—62no—
460#41—62no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—31no—
464C2×Q8—31no—
465C2×Q8—62no—
466C2×Q8—64no—
467C2×Q8—68no—
468C2×Q8—64no—
469C2×Q8—92no—
470C2×Q8—181no—
471C2×Q8—182no—
472C2×Q8—182no—
473C2×Q8#62614yes—
474C2×Q8C2×D3212yes—
475C2×D4—32no—
476C2×D4—31no—
477C2×D4—31no—
478C2×D4—62no—
479C2×D4—61no—
480C22×C4—21no—
481C22×C4—32no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—61no—
485C22×C4—181no—
486C22×C4C2×D3211yescharacteristic
487Q16—184no—
488Q16—188no—
489SD16—184no—
490M16—62no—
491C2×C8—32no—
492C2×C8—92no—
493C2×C8—182no—
494C4⋊C4—32no—
495C4⋊C4—184no—
496C22⋊C4—61no—
497C22⋊C4—184no—
498C42—61no—
499C22×C3—24no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—62no—
505C22×C3—62no—
506C22×C3—64no—
507C22×C3—122no—
508C22×C3#88212yes—
509C22×C3#95312yes—
510C22×C3C2×D3×D411yescharacteristic
511C22×C3C22×#6711yescharacteristic
512C2×D3—24no—
513C2×D3—22no—
514C2×D3—22no—
515C2×D3—42no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—22no—
521C3×C4—44no—
522C3×C4—62no—
523C3×C4—62no—
524C3×C4—122no—
525C3×C4#88212yes—
526C3×C4#95312yes—
527C3×C4C22×D1211yescharacteristic
528C3×C4C2×D3×D411yescharacteristic
529C3×C4C22×#6711yescharacteristic
530C3×C4C22×#6711yescharacteristic
531Dic3—22no—
532Dic3—22no—
533Dic3—42no—
534Dic3—124no—
535Dic3—122no—
536Dic3—122no—
537C32#301111yescharacteristic, complemented, Sylow
538C23—32no—
539C23—61no—
540C23D3×#6711yescharacteristic
541Q8—22no—
542Q8—24no—
543Q8—32no—
544Q8—68no—
545Q8—61no—
546Q8—62no—
547Q8—182no—
548Q8—182no—
549Q8—362no—
550Q8C2×#62614yes—
551D4—32no—
552D4—68no—
553D4—64no—
554D4—64no—
555D4—61no—
556D4—62no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—32no—
560C2×C4—68no—
561C2×C4—68no—
562C2×C4—61no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—64no—
566C2×C4—62no—
567C2×C4—182no—
568C2×C4—362no—
569C2×C4C2×#62612yes—
570C2×C4D3×#6712yes—
571C2×C4D3×#6711yescharacteristic
572C2×C4C22×D3211yescharacteristic
573C8—62no—
574C8—182no—
575C2×C3—24no—
576C2×C3—22no—
577C2×C3—22no—
578C2×C3—22no—
579C2×C3—21no—
580C2×C3—122no—
581C2×C3—122no—
582C2×C3C2×#88211yescharacteristic
583C2×C3#577912yes—
584C2×C3#583812yes—
585C2×C3C2×#95311yescharacteristic
586D3—42no—
587D3—42no—
588C22—22no—
589C22—64no—
590C22—62no—
591C22—62no—
592C22—122no—
593C22#6397712yes—
594C22C2×D3×#6711yescharacteristic
595C4—24no—
596C4—62no—
597C4—62no—
598C4—122no—
599C4—362no—
600C4#6397712yes—
601C4C22×#62611yescharacteristic
602C4C2×D3×#6711yescharacteristic
603C3—21no—
604C3#7896111yescharacteristic, complemented
605C3#8411711yescharacteristic, complemented
606C2—22no—
607C2—122no—
608C2—122no—
609C2#1059532812yes—
610C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#1007C2
hypercenterC22×Q8D32
hypocenterC32#3011
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#3756C2semidirect
3. #10594856C2semidirect
4. C2×#63831C2semidirect
5. C3×#5225C2semidirect
6. #10591599C2semidirect
7. #10591595C2semidirect
8. #10591083C2semidirect
9. #10591071C2semidirect
53. #5225D3semidirect
537. C32#3011semidirect
604. C3#78961semidirect
605. C3#84117semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×#37562
#105948562
C2×#638312
C3×#52252
#105915992
#105915952
#105910832
#105910712
#841173
#789613