Finite Group Databasebeta

← #11801966

Subgroups — #11801966

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C4×#3757C211yesmaximal, characteristic
3C3×C4×#217C211yesmaximal, characteristic
4#10591702C212yesmaximal
5#10591701C212yesmaximal
6C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8#10591270C212yesmaximal, complemented
9#10591269C212yesmaximal, complemented
10C4×Dic32C211yesmaximal, characteristic, complemented
11#10591222C211yesmaximal, characteristic, complemented
12#82229—31nomaximal
13#73440—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C2×#3757C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×#217C2212yes—
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C3×#926C418yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63658C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×#117—31no—
39C2×#926D311yescharacteristic
40C3×C4×C22⋊C4—31no—
41C4×#217—31no—
42C4×#217—31no—
43C4×#217—61no—
44C4×#217D311yescharacteristic
45#4980—32no—
46#4980—32no—
47#4951—32no—
48#4951—32no—
49#4945—32no—
50#4944—32no—
51C4×C4⋊Dic3—31no—
52C4×C4⋊Dic3—31no—
53#4932—31no—
54#4932—31no—
55C4×Dic3⋊C4—31no—
56C4×Dic3⋊C4—31no—
57C42×Dic3—31no—
58C42×Dic3—31no—
59#4654—32no—
60#4653—32no—
61C24×C32C2311yescharacteristic
62C22×C32×C4—22no—
63C22×C32×C4—22no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75#3757—24no—
76C4×C3⋊Dic3—22no—
77C4×C3⋊Dic3—22no—
78C3×#217—24no—
79C3×#217C2×C414yes—
80C3×#217C2×C414yes—
81C3×C4⋊Dic3C2×C414yes—
82C3×C4⋊Dic3C2×C414yes—
83C3×C4×Dic3—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3C2×C414yes—
86C3×C4×Dic3C2×C414yes—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—24no—
89Dic32—24no—
90Dic32—24no—
91#2298—91noSylow
92C23×C3×C4—21no—
93C23×C3×C4C2×D311yescharacteristic
94C23×C3×C4C2×D311yescharacteristic
95C3×#117—38no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4—31no—
100C2×C3×C22⋊C4—32no—
101C2×C3×C42—31no—
102C2×C3×C42—31no—
103C2×C3×C42—31no—
104C2×C3×C42—31no—
105C2×#217—32no—
106C2×#217—32no—
107C2×#217—62no—
108C2×#217C2×D312yes—
109C2×#217C2×D311yescharacteristic
110C2×#217C2×D311yescharacteristic
111#926Dic318yescomplemented
112C2×C4⋊Dic3—32no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—61no—
127C2×C4×Dic3—61no—
128C2×C4×Dic3C2×D311yescharacteristic
129C2×C4×Dic3C2×D311yescharacteristic
130C2×C4×Dic3C2×D311yescharacteristic
131C2×C4×Dic3C2×D311yescharacteristic
132C3×#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—62no—
144C3⋊#95C2×D312yes—
145C23×C32—22no—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32C22×C412yes—
150C23×C32C2411yescharacteristic
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—28no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C22×C412yes—
156C2×C32×C4#4112yes—
157C2×C32×C4#4112yes—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3#4114yes—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3#4114yes—
178C2×#117—31no—
179#388—92no—
180#388—92no—
181#387—92no—
182#387—92no—
183C4×C4⋊C4—91no—
184C4×C4⋊C4—91no—
185C4×C22⋊C4—31no—
186C4×C22⋊C4—91no—
187#376—91no—
188C43—91no—
189C24×C3—21no—
190C24×C3C22×D311yescharacteristic
191C24×C3C22×D311yescharacteristic
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—22no—
195C22×C3×C4—22no—
196C22×C3×C4—24no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—32no—
205C22×C3×C4—42no—
206C22×C3×C4—42no—
207C22×C3×C4C4×D314yes—
208C22×C3×C4C2×Dic314yes—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—62no—
218C22×Dic3—62no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D311yescharacteristic
225C3×C4⋊C4—34no—
226C3×C4⋊C4—34no—
227C3×C22⋊C4—34no—
228C3×C22⋊C4—34no—
229C3×C22⋊C4—64no—
230C3×C42—34no—
231C3×C42—34no—
232C3×C42—62no—
233C3×C42—62no—
234#217—24no—
235#217—64no—
236#217—64no—
237#217—68no—
238#217C2×Dic314yes—
239#217C2×Dic314yes—
240C4⋊Dic3—64no—
241C4⋊Dic3—64no—
242C4⋊Dic3C2×Dic314yes—
243C4⋊Dic3C2×Dic314yes—
244Dic3⋊C4—64no—
245Dic3⋊C4—64no—
246C4×Dic3—22no—
247C4×Dic3—22no—
248C4×Dic3—64no—
249C4×Dic3—64no—
250C4×Dic3—64no—
251C4×Dic3—62no—
252C4×Dic3—62no—
253C4×Dic3—62no—
254C4×Dic3—62no—
255C4×Dic3—64no—
256C4×Dic3—122no—
257C4×Dic3—122no—
258C4×Dic3C2×Dic314yes—
259C4×Dic3C2×Dic314yes—
260C22×C32—22no—
261C22×C32—22no—
262C22×C32—22no—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32C23×C411yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32C2×#4111yescharacteristic
268C22×C32C2×#4112yes—
269C22×C32C2×#4112yes—
270C32×C4—22no—
271C32×C4#11714yes—
272C3⋊Dic3—24no—
273C3⋊Dic3—42no—
274C3×Dic3—22no—
275C3×Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—24no—
279C3×Dic3—42no—
280C23×C4D3211yescharacteristic
281#117—38no—
282C2×C4⋊C4—31no—
283C2×C4⋊C4—31no—
284C2×C4⋊C4—92no—
285C2×C4⋊C4—92no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—31no—
288C2×C22⋊C4—32no—
289C2×C22⋊C4—92no—
290C2×C42—31no—
291C2×C42—31no—
292C2×C42—31no—
293C2×C42—31no—
294C2×C42—92no—
295C2×C42—92no—
296C2×C42—91no—
297C2×C42—91no—
298#95—32no—
299#95—92no—
300#95—92no—
301#95—92no—
302#95—92no—
303#95—92no—
304C23×C3—24no—
305C23×C3—22no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—22no—
313C23×C3—21no—
314C23×C3—22no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—42no—
318C23×C3C2×C4×D312yes—
319C23×C3C22×Dic312yes—
320C23×C3C23×D311yescharacteristic
321C23×C3C23×D311yescharacteristic
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—28no—
327C2×C3×C4—28no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—34no—
337C2×C3×C4—48no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4C2×C4×D312yes—
350C2×C3×C4C2×C4×D312yes—
351C2×C3×C4#23512yes—
352C2×C3×C4#23512yes—
353C2×C3×C4#23712yes—
354C2×C3×C4#23712yes—
355C2×C3×C4C22×Dic312yes—
356C2×C3×C4C22×Dic312yes—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—34no—
367C2×Dic3—34no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—64no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—122no—
381C2×Dic3—122no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3#23514yes—
385C2×Dic3C22×Dic312yes—
386C2×Dic3C22×Dic312yes—
387C2×Dic3C22×Dic312yes—
388C2×Dic3C22×Dic312yes—
389C2×C32—42no—
390C2×C32C2×#11711yescharacteristic
391C2×C32C4×#4111yescharacteristic
392C2×C32C4×#4111yescharacteristic
393C2×C32#52912yes—
394C2×C32#52912yes—
395C24C2×D3211yescharacteristic
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—32no—
399C22×C4—31no—
400C22×C4—31no—
401C22×C4—31no—
402C22×C4—31no—
403C22×C4—32no—
404C22×C4—92no—
405C22×C4—92no—
406C22×C4D3×Dic314yes—
407C22×C4C2×D3211yescharacteristic
408C22×C4C2×D3211yescharacteristic
409C4⋊C4—34no—
410C4⋊C4—34no—
411C4⋊C4—184no—
412C4⋊C4—184no—
413C22⋊C4—34no—
414C22⋊C4—34no—
415C22⋊C4—64no—
416C22⋊C4—184no—
417C42—34no—
418C42—34no—
419C42—62no—
420C42—62no—
421C42—184no—
422C42—184no—
423C42—182no—
424C42—182no—
425C22×C3—24no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3C22×C4×D311yescharacteristic
446C22×C3C2×#23512yes—
447C22×C3C2×#23511yescharacteristic
448C22×C3C2×#23511yescharacteristic
449C22×C3C2×#23711yescharacteristic
450C22×C3C2×#23711yescharacteristic
451C22×C3D3×#4112yes—
452C22×C3D3×#4112yes—
453C22×C3D3×#4112yes—
454C22×C3C23×Dic311yescharacteristic
455C3×C4—22no—
456C3×C4—22no—
457C3×C4—24no—
458C3×C4—42no—
459C3×C4—62no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—62no—
463C3×C4—64no—
464C3×C4—122no—
465C3×C4#87714yes—
466C3×C4#92614yes—
467Dic3—24no—
468Dic3—22no—
469Dic3—22no—
470Dic3—22no—
471Dic3—22no—
472Dic3—42no—
473Dic3—64no—
474Dic3—64no—
475Dic3—124no—
476Dic3—124no—
477Dic3—122no—
478Dic3—122no—
479C32#229811yescharacteristic, complemented, Sylow
480C23—22no—
481C23—22no—
482C23—21no—
483C23—21no—
484C23C2×D3×Dic312yes—
485C23C22×D3211yescharacteristic
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—28no—
489C2×C4—34no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—94no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4C2×D3×Dic312yes—
510C2×C4C2×D3×Dic312yes—
511C2×C4#380412yes—
512C2×C4#380412yes—
513C2×C3—22no—
514C2×C3—22no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—44no—
519C2×C3—42no—
520C2×C3—42no—
521C2×C3C4×#23511yescharacteristic
522C2×C3C2×#87711yescharacteristic
523C2×C3#552211yescharacteristic
524C2×C3#552812yes—
525C2×C3#552812yes—
526C2×C3#553812yes—
527C2×C3#555712yes—
528C2×C3C2×#92611yescharacteristic
529C2×C3Dic3×#4111yescharacteristic
530C2×C3Dic3×#4111yescharacteristic
531C22—22no—
532C22—22no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22D3×#23512yes—
537C22#6430612yes—
538C22C22×D3×Dic311yescharacteristic
539C22C2×#380411yescharacteristic
540C22C2×#380411yescharacteristic
541C4—22no—
542C4—64no—
543C4—62no—
544C4—62no—
545C4—62no—
546C4—62no—
547C4—122no—
548C4—184no—
549C4—362no—
550C4#6395514yes—
551C3—21no—
552C3#7344011yescharacteristic, complemented
553C3#8222911yescharacteristic, complemented
554C2—42no—
555C2#1059483612yes—
556C2#1059493312yes—
557C2Dic3×#23511yescharacteristic
558C2#1059495811yescharacteristic
559C2C2×#6395511yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. C4×Dic3⋊Dic3C2semidirect
7. C4×Dic3⋊Dic3C2semidirect
8. #10591270C2semidirect
9. #10591269C2semidirect
10. C4×Dic32C2semidirect
11. #10591222C2semidirect
21. C3×#926C4semidirect
111. #926Dic3semidirect
479. C32#2298semidirect
552. C3#73440semidirect
553. C3#82229semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C4×#37572
C3×C4×#2172
#105917022
#105917012
C4×Dic3⋊Dic32
#105912702
#105912692
C4×Dic322
#105912222
#822293
#734403