Finite Group Databasebeta

← #11808681

Subgroups — #11808681

Order 1152.

1147 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C2×#63877C211yesmaximal, characteristic
3#10592929C211yesmaximal, characteristic, complemented
4C3×#5231C211yesmaximal, characteristic
5Dic3×(C2×D3)⋊C4C212yesmaximal
6#10591345C212yesmaximal, complemented
7#10591324C211yesmaximal, characteristic
8#10591308C212yesmaximal
9#10591243C212yesmaximal, complemented
10#10591242C211yesmaximal, characteristic, complemented
11#10591227C211yesmaximal, characteristic, complemented
12#82491—31nomaximal
13#76778—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C22×D3×Dic3C2211yescharacteristic
16C2×#3750C2212yes—
17C2×#3750C2211yescharacteristic
18C3×Q8×Dic3—24no—
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×#3724C2212yes—
26C2×#3724C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2211yescharacteristic
32#63877—24no—
33#63658C2211yescharacteristic
34#63658C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×Q8—31no—
40C2×Q8×Dic3D311yescharacteristic, complemented
41C2×#877—31no—
42C2×#872—31no—
43C3×#393—31no—
44#5231D311yescharacteristic
45#5230—31no—
46#5230—31no—
47#5230—61no—
48#4994—32no—
49#4993—31no—
50#4985—31no—
51#4982—32no—
52#4949—31no—
53#4948—32no—
54Dic3×C22⋊C4—32no—
55C4×(C2×D3)⋊C4—32no—
56C4×C4⋊Dic3—31no—
57C4×Dic3⋊C4—32no—
58#4659—31no—
59#4657—32no—
60#4649—31no—
61#4649—32no—
62C23×C3×D3C2311yescharacteristic
63C2×C32×Q8—22no—
64C2×C32×Q8—24no—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×D3×Dic3—22no—
76C2×D3×Dic3—22no—
77C2×D3×Dic3Q814yescomplemented
78#3750—22no—
79#3750—24no—
80C3×(C2×D3)⋊C4—22no—
81C3×(C2×D3)⋊C4—24no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3—24no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3D414yes—
86#3724—24no—
87#3724—22no—
88Dic3⋊Dic3—24no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—22no—
91Dic32—22no—
92Dic32—24no—
93#2396—91noSylow
94C22×C3×Q8—21no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C23×Dic3—31no—
98C22×C4×D3—31no—
99C3×C4×Q8—64no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C42—31no—
105C2×C3×C42—32no—
106C2×#217—32no—
107C2×#217—31no—
108Q8×Dic3—24no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4C2×D312yes—
112C2×(C2×D3)⋊C4C2×D311yescharacteristic
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3C2×D312yes—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—31no—
125C2×Dic3⋊C4—61no—
126C2×Dic3⋊C4—62no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3C2×D312yes—
132C2×C4×Dic3C2×D311yescharacteristic
133#877—64no—
134#872—64no—
135C3×#95—32no—
136C3×#95—31no—
137C3⋊#95—31no—
138C3⋊#95—32no—
139C3⋊#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—62no—
146C3⋊#95—61no—
147C3⋊#95C2×D312yes—
148C3⋊#95C2×D311yescharacteristic
149C23×C32C2411yescharacteristic
150C22×C3×D3—21no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—21no—
154C22×C3×D3C2×Q812yes—
155C32×Q8—28no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4#4114yes—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C2×Q812yes—
168C2×C3⋊Dic3#4114yes—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×Q812yes—
181C2×C3×Dic3#4112yes—
182D3×Dic3—28no—
183C2×C4×Q8—31no—
184C2×#117—91no—
185#400—91no—
186#399—91no—
187#398—92no—
188#396—92no—
189#395—91no—
190#393—31no—
191C4×C4⋊C4—92no—
192C4×C4⋊C4—91no—
193C4×C22⋊C4—92no—
194C24×C3—31no—
195C23×D3C22×D311yescharacteristic
196C2×C3×Q8—24no—
197C2×C3×Q8—22no—
198C2×C3×Q8—24no—
199C2×C3×Q8—22no—
200C2×C3×Q8—44no—
201C2×C3×Q8—42no—
202C22×C3×C4—22no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—31no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—34no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—61no—
221C22×Dic3—62no—
222C22×Dic3—61no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D311yescharacteristic
229C22×Dic3C22×D311yescharacteristic
230C2×C4×D3—34no—
231C2×C4×D3—62no—
232C2×C4×D3—62no—
233C3×C4⋊C4—64no—
234C3×C4⋊C4—62no—
235C3×C22⋊C4—64no—
236C3×C22⋊C4—62no—
237C3×C42—34no—
238C3×C42—64no—
239#217—64no—
240#217—62no—
241(C2×D3)⋊C4—22no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—62no—
245C4⋊Dic3—22no—
246C4⋊Dic3—24no—
247C4⋊Dic3—64no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—62no—
252Dic3⋊C4—64no—
253Dic3⋊C4—62no—
254Dic3⋊C4—64no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257Dic3⋊C4—124no—
258Dic3⋊C4—122no—
259C4×Dic3—24no—
260C4×Dic3—62no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—62no—
264C4×Dic3#6714yes—
265C22×C32C22×D411yescharacteristic
266C22×C32C22×Q811yescharacteristic
267C22×C32C2×#4112yes—
268C22×C32C2×#4111yescharacteristic
269C22×C32C2×#4112yes—
270C2×C3×D3—22no—
271C2×C3×D3—24no—
272C2×C3×D3—41no—
273C2×C3×D3—42no—
274C2×C3×D3—41no—
275C32×C4—22no—
276C32×C4—24no—
277C3⋊Dic3—22no—
278C3⋊Dic3—24no—
279C3⋊Dic3—41no—
280C3×Dic3—22no—
281C3×Dic3—42no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C3×Dic3C22⋊Q814yes—
285C22×Q8D3211yescharacteristic
286C23×C4—91no—
287C4×Q8—64no—
288#117—184no—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—92no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—92no—
296C2×C22⋊C4—31no—
297C2×C22⋊C4—32no—
298C2×C22⋊C4—91no—
299C2×C22⋊C4—92no—
300C2×C42—31no—
301C2×C42—32no—
302C2×C42—91no—
303C2×C42—92no—
304#95—32no—
305#95—31no—
306#95—92no—
307#95—92no—
308#95—92no—
309#95—91no—
310C23×C3—21no—
311C23×C3—32no—
312C23×C3—62no—
313C23×C3—61no—
314C23×C3—62no—
315C23×C3—61no—
316C23×C3C23×D311yescharacteristic
317C23×C3C23×D311yescharacteristic
318C22×D3—21no—
319C22×D3—22no—
320C22×D3—22no—
321C22×D3—21no—
322C22×D3D3×Q812yes—
323C3×Q8—28no—
324C3×Q8—28no—
325C3×Q8—48no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—24no—
333C2×C3×C4—22no—
334C2×C3×C4—32no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
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×C4—61no—
350C2×C3×C4#23514yes—
351C2×C3×C4D3×D412yes—
352C2×C3×C4#23714yes—
353C2×C3×C4C2×#6712yes—
354C2×Dic3—22no—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—34no—
366C2×Dic3—34no—
367C2×Dic3—62no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—61no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—68no—
378C2×Dic3—62no—
379C2×Dic3—61no—
380C2×Dic3—62no—
381C2×Dic3—61no—
382C2×Dic3—122no—
383C2×Dic3—121no—
384C2×Dic3—122no—
385C2×Dic3—121no—
386C2×Dic3—122no—
387C2×Dic3—121no—
388C2×Dic3D3×Q812yes—
389C2×Dic3#23912yes—
390C2×Dic3C2×#6712yes—
391C2×Dic3C2×#6712yes—
392C4×D3—68no—
393C2×C32C2×C22⋊Q811yescharacteristic
394C2×C32#52511yescharacteristic
395C2×C32#52912yes—
396C2×C32#53211yescharacteristic
397C2×C32#53312yes—
398C3×D3—42no—
399C24—31no—
400C2×Q8—24no—
401C2×Q8—22no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—32no—
405C22×C4—31no—
406C22×C4—32no—
407C22×C4—94no—
408C22×C4—91no—
409C22×C4—92no—
410C22×C4—91no—
411C22×C4—182no—
412C22×C4—182no—
413C22×C4C2×D3212yes—
414C22×C4C2×D3211yescharacteristic
415C4⋊C4—64no—
416C4⋊C4—62no—
417C4⋊C4—182no—
418C4⋊C4—184no—
419C4⋊C4—184no—
420C4⋊C4—184no—
421C4⋊C4—182no—
422C22⋊C4—64no—
423C22⋊C4—62no—
424C22⋊C4—182no—
425C22⋊C4—184no—
426C42—34no—
427C42—64no—
428C42—182no—
429C42—184no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—21no—
435C22×C3—62no—
436C22×C3—64no—
437C22×C3—121no—
438C22×C3—121no—
439C22×C3—122no—
440C22×C3C2×#23512yes—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C2×#23712yes—
443C22×C3C2×D3×Q811yescharacteristic
444C22×C3C2×D3×Q811yescharacteristic
445C22×C3C2×#23911yescharacteristic
446C22×C3D3×#4111yescharacteristic
447C22×C3D3×#4112yes—
448C22×C3D3×#4112yes—
449C22×C3C22×#6711yescharacteristic
450C2×D3—24no—
451C2×D3—22no—
452C2×D3—41no—
453C2×D3—42no—
454C2×D3—41no—
455C3×C4—24no—
456C3×C4—22no—
457C3×C4—22no—
458C3×C4—24no—
459C3×C4—34no—
460C3×C4—44no—
461C3×C4—42no—
462C3×C4—62no—
463C3×C4—122no—
464C3×C4—121no—
465C3×C4—122no—
466Dic3—22no—
467Dic3—41no—
468Dic3—42no—
469Dic3—42no—
470Dic3—64no—
471Dic3—62no—
472Dic3—64no—
473Dic3—62no—
474Dic3—124no—
475Dic3—122no—
476Dic3—121no—
477Dic3—121no—
478Dic3—241no—
479Dic3#94614yes—
480C32#239611yescharacteristic, complemented, Sylow
481C23—32no—
482C23—61no—
483C23—62no—
484C23—62no—
485C23—61no—
486C23C22×D3211yescharacteristic
487Q8—28no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—32no—
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—61no—
504C2×C4—92no—
505C2×C4—94no—
506C2×C4—188no—
507C2×C4—182no—
508C2×C4—181no—
509C2×C4—182no—
510C2×C4—181no—
511C2×C4—182no—
512C2×C4—181no—
513C2×C4#380414yes—
514C2×C4D3×#6712yes—
515C2×C3—21no—
516C2×C3—22no—
517C2×C3—22no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—122no—
521C2×C3#557812yes—
522C2×C3#558012yes—
523C2×C3#558611yescharacteristic
524C2×C3#562212yes—
525C2×C3D3×C22⋊Q811yescharacteristic
526C2×C3#566811yescharacteristic
527C2×C3#568012yes—
528C2×C3#579111yescharacteristic
529C2×C3C2×#94611yescharacteristic
530C2×C3#583211yescharacteristic
531D3—42no—
532C22—64no—
533C22—62no—
534C22—121no—
535C22—122no—
536C22—121no—
537C22D32×Q811yescharacteristic
538C22D3×#23911yescharacteristic
539C22#6431912yes—
540C22C2×#380412yes—
541C22C2×D3×#6711yescharacteristic
542C4—24no—
543C4—22no—
544C4—34no—
545C4—62no—
546C4—122no—
547C4—121no—
548C4—122no—
549C4—184no—
550C4—182no—
551C4—361no—
552C3—21no—
553C3#7677811yescharacteristic, complemented
554C3#8249111yescharacteristic, complemented
555C2—122no—
556C2#1059535911yescharacteristic
557C2#1059536712yes—
558C2#1059538212yes—
559C2D3×#94611yescharacteristic
560C2#1059549811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×Q8C22
prime radicalC23×C3×D3C23
hypercenterC22×Q8D32
hypocenterC32#2396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
3. #10592929C2semidirect
6. #10591345C2semidirect
9. #10591243C2semidirect
10. #10591242C2semidirect
11. #10591227C2semidirect
40. C2×Q8×Dic3D3semidirect
77. C2×D3×Dic3Q8semidirect
480. C32#2396semidirect
553. C3#76778semidirect
554. C3#82491semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
C2×#638772
#105929292
C3×#52312
Dic3×(C2×D3)⋊C42
#105913452
#105913242
#105913082
#105912432
#105912422
#105912272
#824913
#767783