Finite Group Databasebeta

← #11864520

Subgroups — #11864520

Order 1152.

1535 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic
2#10596296C211yesmaximal, characteristic, complemented
3C22×#3719C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5C3×#5234C211yesmaximal, characteristic, complemented
6#10591186C214yesmaximal, complemented
7#10591173C214yesmaximal, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#84117—31nomaximal
11#78679—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C3×#1010—24no—
15C3×#1010—24no—
16C2×C3×D3×Q8—21no—
17C2×C3×#237—22no—
18C2×C3×#237—21no—
19C2×C3×#235C2212yes—
20C2×C3×#235C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C22×C3×Dic6C2211yescharacteristic
23#64153—21no—
24#64145—21no—
25#64144—22no—
26#64135C2211yescharacteristic
27#64133C2214yes—
28C2×C3×#208C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C2×#3719—24no—
31C2×#3719C2214yes—
32C2×#3719C2212yes—
33#63831—24no—
34C2×#3716C2212yes—
35C3×#830C2214yes—
36#63566C2212yes—
37#63566C2214yes—
38#63563C2212yes—
39C2×C3×2−1+4—31no—
40C2×#1010D311yescharacteristic
41#5825—31no—
42#5825—31no—
43#5825—61no—
44C2×#951—31no—
45C22×#216—31no—
46C2×#909—31no—
47C22×Dic12—31no—
48C3×#408—31no—
49#5239—34no—
50#5234D311yescharacteristic, complemented
51#5233—31no—
52#5228—34no—
53#5225—31no—
54#5120—31no—
55#5113—31no—
56#4739—34no—
57#4733—34no—
58C32×#41—22no—
59C32×#41—22no—
60C2×C32×Q8D411yescharacteristic
61C2×C32×D4D412yes—
62C2×C32×D4D411yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3—21no—
66C2×#634—22no—
67C2×#634—22no—
68C2×#634—21no—
69C2×#634C2312yes—
70C2×C3×#67—22no—
71C2×C3×#67—21no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—21no—
74C3×D3×Q8—28no—
75C3×#237—216no—
76C3×#237—28no—
77C3×#235—22no—
78C3×#235—24no—
79C3×#235—24no—
80C3×#235D414yes—
81C2×C3×D12C2311yescharacteristic
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3—21no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—24no—
88C2×C3×Dic6—24no—
89C2×C3×Dic6D414yes—
90C2×C3×Dic6C2311yescharacteristic
91C2×C3×Dic6C2312yes—
92#3757—24no—
93#3757—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95#3750—24no—
96C4×C3⋊Dic3—21no—
97C3×#208—22no—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2312yes—
101#3719—24no—
102#3719—28no—
103#3716—24no—
104#3011—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116C22×C3×Q8—61no—
117#1010—24no—
118#1010—24no—
119C2×D3×Q8—21no—
120C2×#237—22no—
121C2×#237—21no—
122C2×#235C2×D312yes—
123C2×#235C2×D311yescharacteristic
124C22×Dic6—31no—
125C22×Dic6—31no—
126C22×Dic6—61no—
127C22×Dic6C2×D312yes—
128C22×Dic6C2×D311yescharacteristic
129C2×C3×M16—31no—
130C22×C3×C8—31no—
131#951—64no—
132#944—62no—
133#944—61no—
134#944—61no—
135C2×#216—32no—
136C2×#216—34no—
137C2×#216—64no—
138#936—62no—
139#936—61no—
140#936—61no—
141#935—64no—
142#935—62no—
143#935—62no—
144C2×#214—32no—
145#926—31no—
146#926—31no—
147#926—61no—
148#924—34no—
149#924—34no—
150#924—64no—
151C2×#208C2×D311yescharacteristic
152C22×C3⋊C8C2×D311yescharacteristic
153#909—64no—
154C2×Dic12—34no—
155C2×Dic12—32no—
156C2×Dic12—64no—
157C2×#204—32no—
158C3×C22⋊C8—34no—
159#835—34no—
160#835—32no—
161#832—32no—
162#830C2×D314yes—
163#821—32no—
164#816—34no—
165#816—32no—
166C23×C32C2×D412yes—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—21no—
169C32×Q8—22no—
170C32×D4—24no—
171C32×D4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—42no—
182#634—22no—
183#634—22no—
184#634—42no—
185C3×#67—28no—
186C3×#67—24no—
187C2×C3×Dic3—28no—
188C2×C3×Dic3—24no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C3×D12—21no—
192C3×D12C2×D412yes—
193C3×C4×D3—28no—
194C3×C4×D3—24no—
195C3×Dic6—28no—
196C3×Dic6—24no—
197C3×Dic6—22no—
198C3×Dic6—21no—
199C3×Dic6C2×D412yes—
200C3×Dic6C2×D414yes—
201C3×C3⋊C8—22no—
202C3×C3⋊C8—22no—
203C2×2−1+4—31no—
204C2×#137—91no—
205C22×Q16—91no—
206#536—91no—
207#452—94no—
208#451—94no—
209#419—91no—
210#416—91no—
211#408—31no—
212C3×#41—22no—
213C3×#41—22no—
214C3×#41—22no—
215C3×#41—22no—
216C3×#41—34no—
217C3×#41—42no—
218C3×#41—42no—
219C3×#41—64no—
220C3×#41—64no—
221C3×#41—616no—
222C3×#41—68no—
223C3×#41—62no—
224C2×C3×Q8—21no—
225C2×C3×Q8—34no—
226C2×C3×Q8—32no—
227C2×C3×Q8—31no—
228C2×C3×Q8—64no—
229C2×C3×Q8—64no—
230C2×C3×Q8—68no—
231C2×C3×Q8—62no—
232C2×C3×Q8—61no—
233C2×C3×Q8—62no—
234C2×C3×Q8D1211yescharacteristic
235C2×C3×Q8#6711yescharacteristic
236C2×C3×D4—22no—
237C2×C3×D4—21no—
238C2×C3×D4—31no—
239C2×C3×D4—62no—
240C2×C3×D4—61no—
241C2×C3×D4D1212yes—
242C2×C3×D4D1211yescharacteristic
243C2×C3×D4#6712yes—
244C2×C3×D4#6711yescharacteristic
245C22×C3×C4—21no—
246C22×C3×C4—22no—
247C22×C3×C4—62no—
248C22×C3×C4—61no—
249C22×C3×C4—62no—
250C22×C3×C4—61no—
251C22×C3×C4C22×D312yes—
252C22×C3×C4C22×D312yes—
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C2×#67—22no—
256C2×#67—21no—
257C22×Dic3—22no—
258C22×Dic3—21no—
259C22×Dic3—62no—
260C22×Dic3—61no—
261C22×Dic3—61no—
262D3×Q8—28no—
263#237—216no—
264#237—28no—
265#235—22no—
266#235—24no—
267#235—24no—
268#235#6714yes—
269C2×D12C22×D311yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—21no—
272C2×Dic6—22no—
273C2×Dic6—21no—
274C2×Dic6—22no—
275C2×Dic6—24no—
276C2×Dic6—24no—
277C2×Dic6—32no—
278C2×Dic6—32no—
279C2×Dic6—62no—
280C2×Dic6—62no—
281C2×Dic6—62no—
282C2×Dic6—62no—
283C2×Dic6—62no—
284C2×Dic6—62no—
285C2×Dic6—61no—
286C2×Dic6—61no—
287C2×Dic6—122no—
288C2×Dic6—122no—
289C2×Dic6#6714yes—
290C2×Dic6C22×D311yescharacteristic
291C2×Dic6C22×D312yes—
292C3×M16—62no—
293C2×C3×C8—32no—
294C2×C3×C8—32no—
295C2×C3×C8—62no—
296#217—68no—
297#217—62no—
298#217—64no—
299#217—61no—
300#217—64no—
301#217—61no—
302#216—68no—
303#216—64no—
304#214—64no—
305C4⋊Dic3—32no—
306C4⋊Dic3—32no—
307C4⋊Dic3—62no—
308Dic3⋊C4—68no—
309Dic3⋊C4—64no—
310Dic3⋊C4—64no—
311C4×Dic3—62no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314#208—22no—
315C2×C3⋊C8—22no—
316C2×C3⋊C8C22×D312yes—
317C2×C3⋊C8C22×D312yes—
318Dic12—68no—
319Dic12—64no—
320#204—64no—
321C22×C32—22no—
322C22×C32—22no—
323C22×C32—24no—
324C22×C32#12012yes—
325C22×C32C22×D411yescharacteristic
326C2×C3×D3—22no—
327C2×C3×D3—42no—
328C32×C4—22no—
329C32×C4#12012yes—
330C32×C4C22×D411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3⋊Dic3—42no—
333C3⋊Dic3—42no—
334C3×Dic3—22no—
335C3×Dic3—24no—
3362−1+4—64no—
3372−1+4—64no—
338C2×#41—31no—
339C2×#41—32no—
340C2×#41—62no—
341C2×#41—61no—
342C2×#41D3211yescharacteristic
343C22×Q8—31no—
344C22×Q8—32no—
345C22×Q8—61no—
346C22×Q8—91no—
347#137—184no—
348C2×Q16—94no—
349C2×Q16—92no—
350C2×Q16—184no—
351C2×SD16—92no—
352C2×M16—31no—
353C22×C8—31no—
354C4⋊Q8—181no—
355#124—181no—
356#123—182no—
357C22⋊Q8—94no—
358#117—91no—
359#103—92no—
360#103—94no—
361#102—92no—
362C22⋊C8—34no—
363C23×C3—21no—
364C23×C3—22no—
365C23×C3—61no—
366C23×C3C2×D1212yes—
367C23×C3C2×D1211yescharacteristic
368C23×C3C2×#6712yes—
369C23×C3C2×#6711yescharacteristic
370C22×D3—21no—
371C3×Q8—22no—
372C3×Q8—22no—
373C3×Q8—34no—
374C3×Q8—32no—
375C3×Q8—42no—
376C3×Q8—68no—
377C3×Q8—64no—
378C3×Q8—62no—
379C3×Q8—61no—
380C3×D4—24no—
381C3×D4—24no—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—32no—
385C3×D4—42no—
386C3×D4—44no—
387C3×D4—68no—
388C3×D4—64no—
389C3×D4—61no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—68no—
402C2×C3×C4—68no—
403C2×C3×C4—64no—
404C2×C3×C4—62no—
405C2×C3×C4—61no—
406C2×C3×C4—64no—
407C2×C3×C4C2×D1212yes—
408C2×C3×C4C2×D1211yescharacteristic
409C2×C3×C4D3×D412yes—
410C2×C3×C4D3×D412yes—
411C2×C3×C4C2×#6712yes—
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C2×#6712yes—
414C2×C3×C4C2×#6712yes—
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—28no—
418#67—24no—
419C2×Dic3—28no—
420C2×Dic3—24no—
421C2×Dic3—21no—
422C2×Dic3—22no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—124no—
430C2×Dic3—122no—
431C2×Dic3—122no—
432D12—21no—
433D12C2×#6712yes—
434C4×D3—28no—
435C4×D3—24no—
436Dic6—28no—
437Dic6—24no—
438Dic6—22no—
439Dic6—21no—
440Dic6—62no—
441Dic6—62no—
442Dic6—62no—
443Dic6—62no—
444Dic6—122no—
445Dic6—122no—
446Dic6—124no—
447Dic6—122no—
448Dic6—122no—
449Dic6C2×#6712yes—
450Dic6C2×#6714yes—
451C3×C8—62no—
452C3×C8—62no—
453C3⋊C8—22no—
454C3⋊C8—22no—
455C2×C32—22no—
456C2×C32—42no—
457C2×C32C2×#12011yescharacteristic
458C2×C32#57812yes—
459C3×D3—42no—
460#41—22no—
461#41—22no—
462#41—34no—
463#41—64no—
464#41—64no—
465#41—616no—
466#41—68no—
467#41—62no—
468C2×Q8—32no—
469C2×Q8—31no—
470C2×Q8—34no—
471C2×Q8—64no—
472C2×Q8—64no—
473C2×Q8—68no—
474C2×Q8—62no—
475C2×Q8—61no—
476C2×Q8—62no—
477C2×Q8—92no—
478C2×Q8—181no—
479C2×Q8—182no—
480C2×Q8—182no—
481C2×Q8#62611yescharacteristic
482C2×D4—31no—
483C2×D4—62no—
484C2×D4—61no—
485C2×D4#62612yes—
486C2×D4#62611yescharacteristic
487C22×C4—62no—
488C22×C4—61no—
489C22×C4—62no—
490C22×C4—61no—
491C22×C4—181no—
492C22×C4C2×D3212yes—
493C22×C4C2×D3211yescharacteristic
494Q16—188no—
495Q16—184no—
496SD16—184no—
497M16—62no—
498C2×C8—32no—
499C2×C8—32no—
500C2×C8—62no—
501C4⋊C4—92no—
502C4⋊C4—184no—
503C22⋊C4—181no—
504C22⋊C4—184no—
505C42—181no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—24no—
510C22×C3—24no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—42no—
515C22×C3—42no—
516C22×C3—44no—
517C22×C3—62no—
518C22×C3—122no—
519C22×C3#88212yes—
520C22×C3#95312yes—
521C22×C3C22×D1211yescharacteristic
522C22×C3C22×#6711yescharacteristic
523C2×D3—22no—
524C2×D3—42no—
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—22no—
530C3×C4—42no—
531C3×C4—64no—
532C3×C4—62no—
533C3×C4#88212yes—
534C3×C4#95312yes—
535C3×C4C2×D3×D411yescharacteristic
536C3×C4C2×D3×D411yescharacteristic
537C3×C4C22×#6711yescharacteristic
538C3×C4C22×#6711yescharacteristic
539Dic3—22no—
540Dic3—24no—
541Dic3—124no—
542Dic3—124no—
543Dic3—122no—
544Dic3—122no—
545Dic3—122no—
546Dic3—122no—
547C32#301111yescharacteristic, complemented, Sylow
548C23—61no—
549C23C2×#62612yes—
550C23C2×#62611yescharacteristic
551Q8—22no—
552Q8—34no—
553Q8—32no—
554Q8—68no—
555Q8—62no—
556Q8—61no—
557Q8—64no—
558Q8—182no—
559Q8—182no—
560Q8—362no—
561D4—24no—
562D4—22no—
563D4—32no—
564D4—68no—
565D4—64no—
566D4—61no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—68no—
570C2×C4—68no—
571C2×C4—62no—
572C2×C4—61no—
573C2×C4—64no—
574C2×C4—64no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4—362no—
578C2×C4C2×#62612yes—
579C2×C4C2×#62611yescharacteristic
580C2×C4D3×#6712yes—
581C2×C4D3×#6712yes—
582C2×C4C22×D3211yescharacteristic
583C8—62no—
584C8—62no—
585C2×C3—22no—
586C2×C3—22no—
587C2×C3—22no—
588C2×C3—21no—
589C2×C3—42no—
590C2×C3—42no—
591C2×C3—42no—
592C2×C3—82no—
593C2×C3—122no—
594C2×C3C2×#88211yescharacteristic
595C2×C3#575312yes—
596C2×C3#583812yes—
597C2×C3C2×#95311yescharacteristic
598D3—42no—
599C22—22no—
600C22—24no—
601C22—22no—
602C22—62no—
603C22—122no—
604C22#6397712yes—
605C22C22×#62611yescharacteristic
606C4—22no—
607C4—64no—
608C4—62no—
609C4—362no—
610C4—362no—
611C4#6397712yes—
612C4C2×D3×#6711yescharacteristic
613C4C2×D3×#6711yescharacteristic
614C3—21no—
615C3#7867911yescharacteristic, complemented
616C3#8411711yescharacteristic, complemented
617C2—22no—
618C2—42no—
619C2—122no—
620C2#1059545012yes—
621C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#1010C2
hypercenterC2×#41D32
hypocenterC32#3011
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10596296C2semidirect
3. C22×#3719C2semidirect
4. C2×#63831C2semidirect
5. C3×#5234C2semidirect
6. #10591186C2semidirect
7. #10591173C2semidirect
8. #10591100C2semidirect
9. #10591084C2semidirect
50. #5234D3semidirect
547. C32#3011semidirect
615. C3#78679semidirect
616. C3#84117semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
#105962962
C22×#37192
C2×#638312
C3×#52342
#105911862
#105911732
#105911002
#105910842
#841173
#786793