Finite Group Databasebeta

← #11808731

Subgroups — #11808731

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63878C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3#10592348C211yesmaximal, characteristic, complemented
4C3×#4677C211yesmaximal, characteristic
5C3×#4656C211yesmaximal, characteristic, complemented
6#10591368C212yesmaximal
7#10591358C212yesmaximal, complemented
8#10591308C212yesmaximal
9#10591304C211yesmaximal, characteristic
10#10591274C212yesmaximal, complemented
11#10591225C211yesmaximal, characteristic, complemented
12#78018—31nomaximal
13#77170—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C22×D3×Dic3C2211yescharacteristic
16C2×#3750C2212yes—
17C2×C4×C3⋊Dic3C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2211yescharacteristic
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2211yescharacteristic
31#63878—24no—
32#63843—24no—
33C32×#95C2211yescharacteristic
34#63658C2211yescharacteristic
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×Q8×Dic3—31no—
40C2×#892—31no—
41C2×#887—31no—
42C2×#877—31no—
43C3×#399—31no—
44C3×#395—31no—
45#5231—31no—
46#4994—32no—
47#4986—31no—
48#4985—31no—
49#4983—32no—
50Dic3×C4⋊C4—32no—
51Dic3×C4⋊C4—32no—
52#4948—32no—
53#4947—31no—
54Dic3×C22⋊C4—32no—
55#4677D311yescharacteristic
56#4666—32no—
57#4661—32no—
58#4656D311yescharacteristic, complemented
59#4649—31no—
60#4649—31no—
61#4649—61no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2312yes—
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C2×C3×Dic6—22no—
74C2×C3×Dic6—24no—
75C2×D3×Dic3—22no—
76C2×D3×Dic3—22no—
77C2×D3×Dic3Q814yescomplemented
78#3750—24no—
79C4×C3⋊Dic3—24no—
80C4×C3⋊Dic3D414yes—
81C3×(C2×D3)⋊C4—22no—
82C3×(C2×D3)⋊C4—24no—
83C3×C4⋊Dic3—22no—
84C3×C4⋊Dic3—24no—
85C3×C4⋊Dic3—24no—
86C3×Dic3⋊C4—22no—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—22no—
89(C2×D3)⋊Dic3—22no—
90(C2×D3)⋊Dic3—24no—
91Dic32—24no—
92Dic32—22no—
93#2396—91noSylow
94C22×C3×Q8—31no—
95C23×Dic3—31no—
96C22×C4×D3—31no—
97C22×Dic6C2×D311yescharacteristic
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—31no—
104C2×#217—32no—
105C2×#217—31no—
106Q8×Dic3—64no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4C2×D312yes—
110C2×(C2×D3)⋊C4C2×D311yescharacteristic
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3C2×D312yes—
114C2×C4⋊Dic3C2×D312yes—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—62no—
121C2×Dic3⋊C4C2×D311yescharacteristic
122C2×C4×Dic3—31no—
123C2×C4×Dic3—31no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—61no—
131C2×C4×Dic3—62no—
132#892—64no—
133#887—64no—
134#877—64no—
135C3×#95—21no—
136C3×#95—32no—
137C3×#95C2×D311yescharacteristic
138C3×#95C2×D311yescharacteristic
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—61no—
148C3⋊#95C2×D312yes—
149C23×C32C2411yescharacteristic
150C22×C3×D3—21no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3C2×Q812yes—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4C2×D412yes—
159C2×C32×C4#4114yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3C2×D412yes—
165C2×C3⋊Dic3C2×D412yes—
166C2×C3⋊Dic3C2×Q812yes—
167C2×C3⋊Dic3#4112yes—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×Q812yes—
180C2×C3×Dic3#4114yes—
181C3×Dic6—28no—
182D3×Dic3—28no—
183C2×C4×Q8—91no—
184C2×#117—91no—
185#400—91no—
186#399—31no—
187#398—92no—
188#396—92no—
189#395—31no—
190#393—91no—
191C4×C4⋊C4—92no—
192C4×C4⋊C4—91no—
193C4×C22⋊C4—92no—
194C24×C3—31no—
195C23×D3C22×D311yescharacteristic
196C2×C3×Q8—64no—
197C2×C3×Q8—62no—
198C22×C3×C4—21no—
199C22×C3×C4—22no—
200C22×C3×C4—31no—
201C22×C3×C4—32no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D312yes—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—34no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D311yescharacteristic
226C2×C4×D3—34no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×Dic6—22no—
230C2×Dic6—24no—
231C3×C4⋊C4—64no—
232C3×C4⋊C4—62no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—64no—
235C3×C22⋊C4—62no—
236C3×C22⋊C4—64no—
237#217—62no—
238#217—64no—
239(C2×D3)⋊C4—22no—
240(C2×D3)⋊C4—24no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—64no—
243C4⋊Dic3—22no—
244C4⋊Dic3—24no—
245C4⋊Dic3—24no—
246C4⋊Dic3—62no—
247C4⋊Dic3—64no—
248Dic3⋊C4—22no—
249Dic3⋊C4—62no—
250Dic3⋊C4—64no—
251Dic3⋊C4—68no—
252Dic3⋊C4—64no—
253Dic3⋊C4—64no—
254C4×Dic3—34no—
255C4×Dic3—34no—
256C4×Dic3—64no—
257C4×Dic3—62no—
258C4×Dic3—64no—
259C4×Dic3—62no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—124no—
264C22×C32C22×D411yescharacteristic
265C22×C32C22×Q811yescharacteristic
266C22×C32C2×#4112yes—
267C22×C32C2×#4112yes—
268C22×C32C2×#4111yescharacteristic
269C2×C3×D3—22no—
270C2×C3×D3—24no—
271C2×C3×D3—41no—
272C2×C3×D3—42no—
273C2×C3×D3—41no—
274C32×C4—22no—
275C32×C4—24no—
276C3⋊Dic3—22no—
277C3⋊Dic3—42no—
278C3⋊Dic3C22⋊Q814yes—
279C3×Dic3—22no—
280C3×Dic3—24no—
281C3×Dic3—41no—
282C3×Dic3—42no—
283C3×Dic3—41no—
284C22×Q8—31no—
285C23×C4—91no—
286C4×Q8—184no—
287#117—184no—
288C2×C4⋊C4—31no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—32no—
297C2×C22⋊C4—91no—
298C2×C22⋊C4—92no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—92no—
302C2×C42—92no—
303#95—32no—
304#95—92no—
305#95—92no—
306#95—92no—
307#95—91no—
308#95D3211yescharacteristic
309C23×C3—21no—
310C23×C3—32no—
311C23×C3—61no—
312C23×C3—62no—
313C23×C3—62no—
314C23×C3—61no—
315C23×C3C23×D311yescharacteristic
316C23×C3C23×D311yescharacteristic
317C22×D3—21no—
318C22×D3—22no—
319C22×D3—22no—
320C22×D3—21no—
321C22×D3D3×Q812yes—
322C3×Q8—68no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—32no—
332C2×C3×C4—34no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—62no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4D3×D412yes—
348C2×C3×C4D3×D412yes—
349C2×C3×C4#23714yes—
350C2×C3×C4#23914yes—
351C2×Dic3—22no—
352C2×Dic3—21no—
353C2×Dic3—22no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—21no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—68no—
375C2×Dic3—64no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—64no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3#23714yes—
388C2×Dic3D3×Q812yes—
389C4×D3—68no—
390Dic6—28no—
391C2×C32C2×C22⋊Q811yescharacteristic
392C2×C32#52511yescharacteristic
393C2×C32#52912yes—
394C2×C32#53211yescharacteristic
395C2×C32#53312yes—
396C3×D3—42no—
397C24—31no—
398C2×Q8—64no—
399C2×Q8—62no—
400C22×C4—31no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—94no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—92no—
409C22×C4—182no—
410C22×C4—182no—
411C22×C4C2×D3212yes—
412C22×C4C2×D3211yescharacteristic
413C4⋊C4—64no—
414C4⋊C4—64no—
415C4⋊C4—62no—
416C4⋊C4—62no—
417C4⋊C4—182no—
418C4⋊C4—184no—
419C4⋊C4—184no—
420C22⋊C4—64no—
421C22⋊C4—62no—
422C22⋊C4—184no—
423C22⋊C4—182no—
424C42—94no—
425C42—184no—
426C42—182no—
427C42—184no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—64no—
434C22×C3—62no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3—122no—
438C22×C3C2×D3×D411yescharacteristic
439C22×C3C2×D3×D411yescharacteristic
440C22×C3C2×#23712yes—
441C22×C3C2×#23712yes—
442C22×C3C2×D3×Q811yescharacteristic
443C22×C3C2×D3×Q811yescharacteristic
444C22×C3C2×#23912yes—
445C22×C3D3×#4112yes—
446C22×C3D3×#4111yescharacteristic
447C22×C3D3×#4111yescharacteristic
448C2×D3—24no—
449C2×D3—22no—
450C2×D3—42no—
451C2×D3—41no—
452C2×D3—41no—
453C3×C4—24no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—24no—
457C3×C4—42no—
458C3×C4—44no—
459C3×C4—64no—
460C3×C4—62no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4—122no—
464Dic3—24no—
465Dic3—22no—
466Dic3—34no—
467Dic3—34no—
468Dic3—42no—
469Dic3—41no—
470Dic3—41no—
471Dic3—64no—
472Dic3—64no—
473Dic3—62no—
474Dic3—62no—
475Dic3—124no—
476Dic3—122no—
477Dic3—122no—
478C32#239611yescharacteristic, complemented, Sylow
479C23—32no—
480C23—62no—
481C23—61no—
482C23—62no—
483C23—61no—
484C23C22×D3211yescharacteristic
485Q8—68no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—34no—
490C2×C4—32no—
491C2×C4—62no—
492C2×C4—61no—
493C2×C4—62no—
494C2×C4—61no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—92no—
505C2×C4—92no—
506C2×C4—188no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—182no—
511C2×C4#379614yes—
512C2×C4#380212yes—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—22no—
516C2×C3—22no—
517C2×C3—21no—
518C2×C3—122no—
519C2×C3#558611yescharacteristic
520C2×C3#562212yes—
521C2×C3#562412yes—
522C2×C3D3×C22⋊Q811yescharacteristic
523C2×C3D3×C22⋊Q811yescharacteristic
524C2×C3#564912yes—
525C2×C3#565611yescharacteristic
526C2×C3#571611yescharacteristic
527C2×C3#572511yescharacteristic
528C2×C3#572812yes—
529D3—42no—
530C22—62no—
531C22—64no—
532C22—121no—
533C22—122no—
534C22—121no—
535C22C2×#379612yes—
536C22C2×#380211yescharacteristic
537C22D3×#23712yes—
538C22#6431211yescharacteristic
539C22D32×Q811yescharacteristic
540C4—22no—
541C4—24no—
542C4—64no—
543C4—62no—
544C4—94no—
545C4—121no—
546C4—122no—
547C4—121no—
548C4—182no—
549C4—362no—
550C3—21no—
551C3#7717011yescharacteristic, complemented
552C3#7801811yescharacteristic, complemented
553C2—122no—
554C2#1059390711yescharacteristic
555C2#1059408211yescharacteristic
556C2#1059414412yes—
557C2#1059438712yes—
558C2#1059463111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63843C2semidirect
3. #10592348C2semidirect
5. C3×#4656C2semidirect
7. #10591358C2semidirect
10. #10591274C2semidirect
11. #10591225C2semidirect
58. #4656D3semidirect
77. C2×D3×Dic3Q8semidirect
478. C32#2396semidirect
551. C3#77170semidirect
552. C3#78018semidirect

Maximal subgroups

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

subgroupindex
C2×#638782
C2×#638432
#105923482
C3×#46772
C3×#46562
#105913682
#105913582
#105913082
#105913042
#105912742
#105912252
#780183
#771703