Finite Group Databasebeta

← #11864514

Subgroups — #11864514

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×#64298C211yesmaximal, characteristic
2C22×#3756C211yesmaximal, characteristic, complemented
3C3×#5816C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5#10591655C214yesmaximal, complemented
6#10591653C214yesmaximal, complemented
7#10591107C211yesmaximal, characteristic, complemented
8#10591083C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#83983—31nomaximal
11#83411—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×#3805—22no—
17#64298—24no—
18#64298—24no—
19C2×#3795—21no—
20C2×#3795C2212yes—
21C2×D3×Dic6—21no—
22C2×D3×Dic6C2212yes—
23C2×#3756—24no—
24C2×#3756C2214yes—
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×#947—21no—
27C3×#946C2214yes—
28C3×#944—21no—
29C2×C3×#216C2212yes—
30C3×#942—24no—
31C2×C3×#215C2212yes—
32C3×#929—22no—
33C3×#926C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35#63567C2214yes—
36#63565C2212yes—
37#63562C2212yes—
38(C2×D3)⋊(C3⋊C8)C2214yes—
39C2×#1010—31no—
40C2×#1010—31no—
41C2×C3×#137—31no—
42C3×#536—31no—
43#5816D311yescharacteristic, complemented
44C22×#216—31no—
45C22×#216—31no—
46C22×#216—61no—
47C2×#942D311yescharacteristic, complemented
48#5234—31no—
49#5233—31no—
50#5186—34no—
51#5173—34no—
52#5129—31no—
53#5120—31no—
54#5050—34no—
55#5047—34no—
56#5004—31no—
57#5002—31no—
58C2×C32×Q8—21no—
59C2×C32×Q8—22no—
60C2×C32×Q8—22no—
61C2×C32×Q8C2312yes—
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3—21no—
65C2×#634—21no—
66C2×#634—22no—
67C2×#634D414yes—
68C2×#634C2312yes—
69C2×C3×#67—21no—
70C2×C3×#67D412yes—
71C3×#235—22no—
72C3×#235—22no—
73C3×#235—22no—
74C3×#235D414yes—
75C2×C3×D12D411yescharacteristic
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3C2312yes—
79C2×C3×Dic6D411yescharacteristic
80C2×C3×Dic6C2311yescharacteristic
81C2×#627—22no—
82C2×#625—22no—
83#3805—216no—
84C2×D3×Dic3—22no—
85C2×D3×Dic3—22no—
86#3795—28no—
87#3795—24no—
88#3795—24no—
89D3×Dic6—28no—
90D3×Dic6—24no—
91D3×Dic6—24no—
92#3756—28no—
93C2×C3⋊(C3⋊C8)—22no—
94C2×C3⋊(C3⋊C8)C2312yes—
95C3×#217—21no—
96C3×#216—24no—
97C3×#215—24no—
98C3×(C2×D3)⋊C4—24no—
99C3×C4⋊Dic3C2312yes—
100C3×Dic3⋊C4—24no—
101C3×C4×Dic3—21no—
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104#3011—91noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×Q8—21no—
108C22×C3×Q8C2×D311yescharacteristic
109C22×C3×Q8C2×D311yescharacteristic
110#1010—64no—
111#1010—64no—
112#1010—64no—
113#1010—64no—
114C2×D3×Q8—32no—
115C2×D3×Q8—61no—
116C2×#237—32no—
117C2×#237—61no—
118C2×#237—62no—
119C2×#237—62no—
120C2×#235—32no—
121C2×#235—61no—
122C2×#235C2×D311yescharacteristic
123C2×#235C2×D311yescharacteristic
124C22×Dic6—31no—
125C22×Dic6—31no—
126C22×Dic6—32no—
127C22×Dic6—61no—
128C22×Dic6—61no—
129C3×#137—64no—
130C2×C3×Q16—32no—
131C2×C3×SD16—32no—
132C2×C3×M16—31no—
133C3×C4⋊Q8—61no—
134C3×#124—61no—
135C3×#123—62no—
136C3×C22⋊Q8—34no—
137C3×#117—31no—
138#947—21no—
139#946C2×D314yes—
140#944—21no—
141C2×#216—34no—
142C2×#216—34no—
143C2×#216—64no—
144C2×#216—64no—
145C2×#216—64no—
146C2×#216—68no—
147C2×#216C2×D312yes—
148#942—24no—
149C2×#215C2×D312yes—
150#929—22no—
151#926C2×D311yescharacteristic
152C2×#208C2×D311yescharacteristic
153C22×C3⋊C8—31no—
154C22×C3⋊C8—31no—
155C22×C3⋊C8—61no—
156#835—32no—
157#832—32no—
158#830—34no—
159(C2×D3)⋊C8—34no—
160#816—34no—
161#810—32no—
162#810—34no—
163#809—32no—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—21no—
166C22×C3×D3C2×D412yes—
167C32×Q8—22no—
168C32×Q8—22no—
169C32×Q8—42no—
170C2×C32×C4—22no—
171C2×C32×C4—42no—
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—24no—
177C2×C3⋊Dic3—22no—
178#634—24no—
179#634—22no—
180#634C2×D414yes—
181C3×#67—24no—
182C3×#67—24no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—22no—
187C3×D12—21no—
188C3×D12C2×D412yes—
189C3×C4×D3—24no—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×Dic6—22no—
193C3×Dic6—21no—
194C3×Dic6C2×D412yes—
195#627—28no—
196#625—28no—
197D3×Dic3—28no—
198D3×Dic3—28no—
199C3⋊(C3⋊C8)—22no—
200C3×C3⋊C8—22no—
201C2×2−1+4—91no—
202C2×#137—31no—
203C22×Q16—91no—
204#536—31no—
205#452—94no—
206#451—94no—
207#419—91no—
208#416—91no—
209#408—91no—
210C3×#41—34no—
211C3×#41—62no—
212C3×#41—62no—
213C3×#41—62no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—24no—
217C2×C3×Q8—22no—
218C2×C3×Q8—22no—
219C2×C3×Q8—22no—
220C2×C3×Q8—22no—
221C2×C3×Q8—22no—
222C2×C3×Q8—31no—
223C2×C3×Q8—31no—
224C2×C3×Q8—41no—
225C2×C3×Q8—42no—
226C2×C3×Q8C22×D312yes—
227C2×C3×Q8C22×D312yes—
228C2×C3×D4—32no—
229C2×C3×D4—31no—
230C2×C3×D4—31no—
231C2×C3×D4—61no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—32no—
236C22×C3×C4—41no—
237C22×C3×C4—61no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—21no—
241C2×#67—62no—
242C2×#67—62no—
243C2×#67#6712yes—
244C22×Dic3—62no—
245C22×Dic3—61no—
246C22×Dic3—61no—
247C22×Dic3—62no—
248C22×Dic3—121no—
249D3×Q8—64no—
250D3×Q8—64no—
251D3×Q8—68no—
252#237—64no—
253#237—64no—
254#237—68no—
255#237—616no—
256#237—616no—
257#235—22no—
258#235—22no—
259#235—22no—
260#235—64no—
261#235—68no—
262#235—64no—
263#235#6714yes—
264C2×D12#6711yescharacteristic
265C2×D12C22×D311yescharacteristic
266C2×C4×D3—21no—
267C2×C4×D3—62no—
268C2×C4×D3—62no—
269C2×C4×D3C22×D312yes—
270C2×Dic6—34no—
271C2×Dic6—34no—
272C2×Dic6—32no—
273C2×Dic6—32no—
274C2×Dic6—64no—
275C2×Dic6—62no—
276C2×Dic6—64no—
277C2×Dic6—68no—
278C2×Dic6—62no—
279C2×Dic6—61no—
280C2×Dic6—62no—
281C2×Dic6—61no—
282C2×Dic6—62no—
283C2×Dic6—62no—
284C2×Dic6—64no—
285C2×Dic6—121no—
286C2×Dic6—122no—
287C2×Dic6#6711yescharacteristic
288C2×Dic6C22×D311yescharacteristic
289C3×Q16—64no—
290C3×SD16—64no—
291C3×M16—62no—
292C2×C3×C8—32no—
293C3×C4⋊C4—32no—
294C3×C4⋊C4—64no—
295C3×C22⋊C4—64no—
296C3×C22⋊C4—61no—
297C3×C42—61no—
298#217—21no—
299#216—24no—
300#216—68no—
301#216—68no—
302#216—616no—
303#215—24no—
304(C2×D3)⋊C4—24no—
305C4⋊Dic3C22×D312yes—
306Dic3⋊C4—24no—
307C4×Dic3—21no—
308#208—22no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—64no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—62no—
315C2×C3⋊C8C22×D312yes—
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—42no—
324C32×C4#12012yes—
325C32×C4C22×D411yescharacteristic
326C32×C4C22×D411yescharacteristic
327C3⋊Dic3—24no—
328C3×Dic3—22no—
329C3×Dic3—22no—
330C3×Dic3—42no—
3312−1+4—184no—
3322−1+4—184no—
333C2×#41—31no—
334C2×#41—31no—
335C2×#41—92no—
336C2×#41—181no—
337C2×#41—182no—
338C22×Q8—92no—
339C22×Q8—91no—
340C22×Q8—181no—
341C22×Q8D3211yescharacteristic
342#137—64no—
343C2×Q16—32no—
344C2×Q16—94no—
345C2×Q16—184no—
346C2×SD16—32no—
347C2×M16—31no—
348C22×C8—91no—
349C4⋊Q8—61no—
350#124—61no—
351#123—62no—
352C22⋊Q8—34no—
353#117—31no—
354#103—94no—
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—22no—
367C3×Q8—22no—
368C3×Q8—22no—
369C3×Q8—22no—
370C3×Q8—32no—
371C3×Q8—42no—
372C3×Q8—44no—
373C3×Q8—42no—
374C3×Q8—42no—
375C3×Q8—62no—
376C3×Q8—61no—
377C3×D4—32no—
378C3×D4—64no—
379C3×D4—64no—
380C3×D4—62no—
381C3×D4—61no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—32no—
389C2×C3×C4—42no—
390C2×C3×C4—44no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—61no—
394C2×C3×C4—64no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D412yes—
400C2×C3×C4D3×D412yes—
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6712yes—
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—24no—
407#67—24no—
408#67—68no—
409#67—68no—
410C2×Dic3—21no—
411C2×Dic3—22no—
412C2×Dic3—68no—
413C2×Dic3—68no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—122no—
419C2×Dic3—124no—
420C2×Dic3C2×#6712yes—
421D12—22no—
422D12—21no—
423D12C2×#6712yes—
424C4×D3—24no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—68no—
428C4×D3—68no—
429Dic6—22no—
430Dic6—21no—
431Dic6—34no—
432Dic6—34no—
433Dic6—64no—
434Dic6—68no—
435Dic6—68no—
436Dic6—64no—
437Dic6—64no—
438Dic6—62no—
439Dic6—62no—
440Dic6—122no—
441Dic6—124no—
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—62no—
455#41—62no—
456#41—62no—
457#41—184no—
458#41—184no—
459#41—188no—
460#41—1816no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—31no—
465C2×Q8—31no—
466C2×Q8—92no—
467C2×Q8—94no—
468C2×Q8—182no—
469C2×Q8—184no—
470C2×Q8—184no—
471C2×Q8—188no—
472C2×Q8—181no—
473C2×Q8—182no—
474C2×Q8C2×D3212yes—
475C2×D4—32no—
476C2×D4—31no—
477C2×D4—31no—
478C2×D4—61no—
479C2×D4—182no—
480C22×C4—21no—
481C22×C4—32no—
482C22×C4—61no—
483C22×C4—182no—
484C22×C4—182no—
485C22×C4—181no—
486C22×C4C2×D3211yescharacteristic
487Q16—64no—
488Q16—188no—
489SD16—64no—
490M16—62no—
491C2×C8—32no—
492C2×C8—92no—
493C2×C8—182no—
494C4⋊C4—32no—
495C4⋊C4—64no—
496C22⋊C4—64no—
497C22⋊C4—61no—
498C42—61no—
499C22×C3—24no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—64no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—122no—
508C22×C3#93712yes—
509C22×C3#93712yes—
510C22×C3C2×D3×D411yescharacteristic
511C22×C3C22×#6711yescharacteristic
512C2×D3—22no—
513C2×D3—22no—
514C2×D3—24no—
515C2×D3—42no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—22no—
519C3×C4—44no—
520C3×C4—42no—
521C3×C4—42no—
522C3×C4—62no—
523C3×C4—62no—
524C3×C4—122no—
525C3×C4#93712yes—
526C3×C4#93712yes—
527C3×C4C2×D3×D411yescharacteristic
528C3×C4C2×D3×D411yescharacteristic
529C3×C4C2×D3×D411yescharacteristic
530C3×C4C22×#6711yescharacteristic
531Dic3—22no—
532Dic3—22no—
533Dic3—42no—
534Dic3—64no—
535Dic3—64no—
536Dic3—124no—
537C32#301111yescharacteristic, complemented, Sylow
538C23—32no—
539C23—61no—
540C23D3×#6711yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—32no—
544Q8—42no—
545Q8—61no—
546Q8—62no—
547Q8—94no—
548Q8—188no—
549Q8—182no—
550Q8—184no—
551D4—32no—
552D4—64no—
553D4—64no—
554D4—61no—
555D4—62no—
556D4—188no—
557C2×C4—22no—
558C2×C4—32no—
559C2×C4—42no—
560C2×C4—61no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—64no—
564C2×C4—62no—
565C2×C4—188no—
566C2×C4—188no—
567C2×C4—182no—
568C2×C4—184no—
569C2×C4D3×#6712yes—
570C2×C4D3×#6711yescharacteristic
571C2×C4#381112yes—
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×C3#577912yes—
583C2×C3C2×#93711yescharacteristic
584C2×C3C2×#93711yescharacteristic
585C2×C3#583812yes—
586D3—42no—
587D3—42no—
588C22—22no—
589C22—64no—
590C22—62no—
591C22—62no—
592C22—122no—
593C22#6398312yes—
594C22C2×D3×#6711yescharacteristic
595C4—42no—
596C4—62no—
597C4—62no—
598C4—122no—
599C4—184no—
600C4#6398312yes—
601C4C2×D3×#6711yescharacteristic
602C4C2×#381111yescharacteristic
603C3—21no—
604C3#8341111yescharacteristic, complemented
605C3#8398311yescharacteristic, complemented
606C2—22no—
607C2—122no—
608C2—122no—
609C2#1059532812yes—
610C2C2×#6398311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×#64298C2
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. C3×#5816C2semidirect
4. C2×C3×#942C2semidirect
5. #10591655C2semidirect
6. #10591653C2semidirect
7. #10591107C2semidirect
8. #10591083C2semidirect
9. #10591071C2semidirect
43. #5816D3semidirect
47. C2×#942D3semidirect
537. C32#3011semidirect
604. C3#83411semidirect
605. C3#83983semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C22×#37562
C3×#58162
C2×C3×#9422
#105916552
#105916532
#105911072
#105910832
#105910712
#839833
#834113