Finite Group Databasebeta

← #11808718

Subgroups — #11808718

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic
2C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
3#10592685C211yesmaximal, characteristic, complemented
4C3×#4979C211yesmaximal, characteristic, complemented
5#10591348C212yesmaximal, complemented
6#10591317C211yesmaximal, characteristic
7#10591306C212yesmaximal
8#10591304C211yesmaximal, characteristic
9#10591242C211yesmaximal, characteristic, complemented
10Dic3×Dic3⋊C4C212yesmaximal, complemented
11#10591237C212yesmaximal
12#82245—31nomaximal
13#77170—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×Dic3⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#892—24no—
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32Dic3×Dic6—24no—
33#63658C2212yes—
34#63658C2212yes—
35#63658C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39C2×C3×#117—31no—
40C2×Q8×Dic3—31no—
41C2×#892D311yescharacteristic
42C2×C4×Dic6—31no—
43C3×#395—31no—
44#5231—31no—
45C4×#217—32no—
46#4994—32no—
47#4986—31no—
48#4986—31no—
49#4986—61no—
50#4982—32no—
51#4979D311yescharacteristic, complemented
52Dic3×C4⋊C4—32no—
53#4949—31no—
54#4948—32no—
55#4947—31no—
56C4×C4⋊Dic3—31no—
57C4×Dic3⋊C4—32no—
58#4677—31no—
59#4666—32no—
60#4661—32no—
61#4649—31no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3Q814yescomplemented
76C2×C3×Dic6—22no—
77C2×C3×Dic6—24no—
78C32×C4⋊C4—22no—
79C4⋊(C3⋊Dic3)—22no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—22no—
82C3×C4⋊Dic3—22no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3D414yes—
86Dic3⋊Dic3—24no—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—24no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91Dic32—24no—
92Dic32—24no—
93#2396—91noSylow
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C22×C4×D3C2×D311yescharacteristic
97C22×Dic6C2×D311yescharacteristic
98C3×#117—64no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4C2×D311yescharacteristic
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—31no—
106C2×C3×C42—31no—
107C2×C3×C42—31no—
108C2×#217—32no—
109C2×#217—32no—
110Q8×Dic3—64no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4C2×D311yescharacteristic
114C2×(C2×D3)⋊C4C2×D311yescharacteristic
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—61no—
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4C2×D312yes—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×C4×Dic3C2×D311yescharacteristic
132#892—24no—
133C4×Dic6—64no—
134C3×#95—31no—
135C3×#95—32no—
136C3⋊#95—31no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—62no—
145C3⋊#95—61no—
146C3⋊#95—62no—
147C3⋊#95C2×D311yescharacteristic
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—21no—
156C2×C32×C4—22no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×Q812yes—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
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×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×Q812yes—
178C2×C3×Dic3#4112yes—
179C2×C3×Dic3#4114yes—
180C2×C3×Dic3#4114yes—
181C3×C4×D3—28no—
182C3×Dic6—28no—
183C2×C4×Q8—91no—
184C2×#117—31no—
185#400—91no—
186#399—91no—
187#398—92no—
188#396—92no—
189#395—31no—
190#393—91no—
191C4×C4⋊C4—91no—
192C4×C4⋊C4—92no—
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—21no—
200C22×C3×C4—21no—
201C22×C3×C4—31no—
202C22×C3×C4—32no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
205C22×C3×C4—34no—
206C22×C3×C4—31no—
207C22×C3×C4—62no—
208C22×C3×C4—62no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—62no—
220C22×Dic3—62no—
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D311yescharacteristic
225C22×Dic3C22×D311yescharacteristic
226C2×C4×D3—22no—
227C2×C4×D3—22no—
228C2×C4×D3Dic614yescomplemented
229C2×Dic6—22no—
230C2×Dic6—24no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—42no—
234C3×C4⋊C4—64no—
235C3×C4⋊C4—62no—
236C3×C22⋊C4—62no—
237C3×C22⋊C4—62no—
238C3×C42—34no—
239C3×C42—62no—
240#217—64no—
241#217—64no—
242(C2×D3)⋊C4—22no—
243(C2×D3)⋊C4—22no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—22no—
247C4⋊Dic3—64no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—64no—
251C4⋊Dic3—64no—
252C4⋊Dic3—122no—
253Dic3⋊C4—24no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257C4×Dic3—22no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C4×Dic3—64no—
261C4×Dic3—64no—
262C4×Dic3#6714yes—
263C22×C32C22×D411yescharacteristic
264C22×C32C22×Q811yescharacteristic
265C22×C32C2×#4111yescharacteristic
266C22×C32C2×#4112yes—
267C22×C32C2×#4112yes—
268C2×C3×D3—22no—
269C2×C3×D3—24no—
270C2×C3×D3—41no—
271C2×C3×D3—42no—
272C2×C3×D3—41no—
273C32×C4—22no—
274C32×C4—22no—
275C32×C4—41no—
276C3⋊Dic3—42no—
277C3⋊Dic3—42no—
278C3×Dic3—24no—
279C3×Dic3—24no—
280C3×Dic3—22no—
281C3×Dic3—41no—
282C3×Dic3C22⋊Q814yes—
283C22×Q8—31no—
284C23×C4—31no—
285C4×Q8—184no—
286#117—64no—
287C2×C4⋊C4—31no—
288C2×C4⋊C4—32no—
289C2×C4⋊C4—92no—
290C2×C4⋊C4—92no—
291C2×C4⋊C4—92no—
292C2×C4⋊C4—91no—
293C2×C4⋊C4D3211yescharacteristic
294C2×C22⋊C4—31no—
295C2×C22⋊C4—31no—
296C2×C22⋊C4—92no—
297C2×C22⋊C4—92no—
298C2×C42—31no—
299C2×C42—31no—
300C2×C42—92no—
301C2×C42—92no—
302#95—32no—
303#95—31no—
304#95—92no—
305#95—92no—
306#95—91no—
307#95—92no—
308C23×C3—21no—
309C23×C3—32no—
310C23×C3—61no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3—61no—
314C23×C3C23×D311yescharacteristic
315C23×C3C23×D311yescharacteristic
316C22×D3—21no—
317C22×D3—22no—
318C22×D3—22no—
319C22×D3—21no—
320C22×D3C2×Dic612yes—
321C3×Q8—68no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—34no—
339C2×C3×C4—34no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—42no—
345C2×C3×C4—68no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4C2×Dic612yes—
354C2×C3×C4D3×D412yes—
355C2×C3×C4D3×Q812yes—
356C2×C3×C4C2×#6712yes—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380C2×Dic3—122no—
381C2×Dic3—122no—
382C2×Dic3C2×Dic612yes—
383C2×Dic3#23512yes—
384C2×Dic3#23714yes—
385C2×Dic3#23914yes—
386C2×Dic3C2×#6712yes—
387C2×Dic3C2×#6712yes—
388C4×D3—28no—
389Dic6—28no—
390C2×C32C2×C22⋊Q811yescharacteristic
391C2×C32#52511yescharacteristic
392C2×C32#52912yes—
393C2×C32#53211yescharacteristic
394C2×C32#53312yes—
395C3×D3—42no—
396C24—31no—
397C2×Q8—64no—
398C2×Q8—62no—
399C22×C4—31no—
400C22×C4—32no—
401C22×C4—32no—
402C22×C4—31no—
403C22×C4—34no—
404C22×C4—31no—
405C22×C4—62no—
406C22×C4—62no—
407C22×C4—92no—
408C22×C4—92no—
409C22×C4C2×D3211yescharacteristic
410C22×C4C2×D3211yescharacteristic
411C22×C4C2×D3211yescharacteristic
412C4⋊C4—22no—
413C4⋊C4—62no—
414C4⋊C4—64no—
415C4⋊C4—184no—
416C4⋊C4—184no—
417C4⋊C4—184no—
418C4⋊C4—182no—
419C22⋊C4—62no—
420C22⋊C4—62no—
421C22⋊C4—184no—
422C22⋊C4—184no—
423C42—34no—
424C42—62no—
425C42—184no—
426C42—184no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—64no—
433C22×C3—62no—
434C22×C3—121no—
435C22×C3—121no—
436C22×C3—122no—
437C22×C3C22×Dic611yescharacteristic
438C22×C3C2×#23511yescharacteristic
439C22×C3C2×D3×D411yescharacteristic
440C22×C3C2×#23712yes—
441C22×C3C2×D3×Q811yescharacteristic
442C22×C3C2×#23912yes—
443C22×C3D3×#4111yescharacteristic
444C22×C3D3×#4112yes—
445C22×C3D3×#4112yes—
446C22×C3C22×#6711yescharacteristic
447C2×D3—24no—
448C2×D3—22no—
449C2×D3—42no—
450C2×D3—41no—
451C2×D3—41no—
452C3×C4—22no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—34no—
457C3×C4—42no—
458C3×C4—42no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—62no—
462C3×C4—64no—
463C3×C4—64no—
464C3×C4—81no—
465C3×C4—121no—
466Dic3—22no—
467Dic3—24no—
468Dic3—24no—
469Dic3—41no—
470Dic3—122no—
471Dic3—122no—
472Dic3—122no—
473Dic3—122no—
474Dic3—242no—
475Dic3—242no—
476Dic3#92414yes—
477C32#239611yescharacteristic, complemented, Sylow
478C23—32no—
479C23—61no—
480C23—62no—
481C23—62no—
482C23—61no—
483C23C22×D3211yescharacteristic
484Q8—68no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—21no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—34no—
494C2×C4—34no—
495C2×C4—32no—
496C2×C4—68no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—62no—
503C2×C4—61no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4D3×Dic612yes—
511C2×C4D3×#6712yes—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—22no—
516C2×C3—22no—
517C2×C3—122no—
518C2×C3#551712yes—
519C2×C3#552812yes—
520C2×C3#558611yescharacteristic
521C2×C3#562412yes—
522C2×C3D3×C22⋊Q811yescharacteristic
523C2×C3#572511yescharacteristic
524C2×C3#572812yes—
525C2×C3C2×#92411yescharacteristic
526C2×C3#582811yescharacteristic
527C2×C3#583211yescharacteristic
528D3—42no—
529C22—62no—
530C22—64no—
531C22—121no—
532C22—121no—
533C22—122no—
534C22C2×D3×Dic611yescharacteristic
535C22D3×#23511yescharacteristic
536C22D3×#23712yes—
537C22D3×#23912yes—
538C22C2×D3×#6711yescharacteristic
539C4—22no—
540C4—22no—
541C4—34no—
542C4—41no—
543C4—62no—
544C4—64no—
545C4—64no—
546C4—121no—
547C4—362no—
548C4—362no—
549C3—21no—
550C3#7717011yescharacteristic, complemented
551C3#8224511yescharacteristic, complemented
552C2—122no—
553C2#1059440212yes—
554C2#1059444512yes—
555C2D3×#92411yescharacteristic
556C2#1059515411yescharacteristic
557C2#1059536011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Dic6C2semidirect
3. #10592685C2semidirect
4. C3×#4979C2semidirect
5. #10591348C2semidirect
9. #10591242C2semidirect
10. Dic3×Dic3⋊C4C2semidirect
51. #4979D3semidirect
75. C2×C3×C4×D3Q8semidirect
228. C2×C4×D3Dic6semidirect
477. C32#2396semidirect
550. C3#77170semidirect
551. C3#82245semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×Dic3×Dic62
#105926852
C3×#49792
#105913482
#105913172
#105913062
#105913042
#105912422
Dic3×Dic3⋊C42
#105912372
#822453
#771703