Finite Group Databasebeta

← #11808724

Subgroups — #11808724

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2C2×#63836C211yesmaximal, characteristic
3#10592692C211yesmaximal, characteristic
4C3×#4985C211yesmaximal, characteristic, complemented
5#10591347C212yesmaximal
6#10591344C211yesmaximal, characteristic, complemented
7#10591340C212yesmaximal, complemented
8#10591310C211yesmaximal, characteristic
9#10591243C212yesmaximal, complemented
10#10591242C211yesmaximal, characteristic, complemented
11#10591233C212yesmaximal
12#82491—31nomaximal
13#78130—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C22×#624C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752C2212yes—
18C2×#3752C2211yescharacteristic
19C2×#3750C2212yes—
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2211yescharacteristic
22C2×C3×C4×Dic3C2212yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#887—24no—
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2211yescharacteristic
28C2×#3722C2212yes—
29C2×#3722C2211yescharacteristic
30C2×Dic32C2212yes—
31C2×Dic32C2211yescharacteristic
32#63836—24no—
33#63658C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4×Q8—31no—
40C2×#892—31no—
41C2×#887D311yescharacteristic, complemented
42C2×#872—31no—
43C3×#400—31no—
44#5231—31no—
45#5230—31no—
46#4994—32no—
47#4993—31no—
48#4993—31no—
49#4993—61no—
50#4985D311yescharacteristic, complemented
51#4982—32no—
52#4979—31no—
53C4×(C2×D3)⋊C4—32no—
54C4×C4⋊Dic3—31no—
55C4×Dic3⋊C4—32no—
56#4676—32no—
57#4673—31no—
58#4666—32no—
59#4657—32no—
60#4649—31no—
61#4649—32no—
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3×Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×Dic6—22no—
74C2×C3×Dic6—24no—
75C2×#624—22no—
76C2×#624—22no—
77C2×#624Q814yescomplemented
78C32×C4⋊C4—22no—
79#3752—22no—
80#3752—24no—
81#3750—24no—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—24no—
84C3×C4×Dic3—24no—
85C3×C4×Dic3D414yes—
86#3724—24no—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—22no—
89#3722—22no—
90#3722—24no—
91Dic32—22no—
92Dic32—24no—
93#2396—91noSylow
94C22×C3×Q8—31no—
95C22×C4×D3—31no—
96C22×C4×D3—31no—
97C22×Dic6C2×D311yescharacteristic
98C3×C4×Q8—64no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4C2×D311yescharacteristic
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C42—31no—
105C2×C3×C42—32no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—62no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—62no—
125C2×Dic3⋊C4C2×D312yes—
126C2×Dic3⋊C4C2×D311yescharacteristic
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#892—64no—
134#887—24no—
135#872—64no—
136C3×#95—31no—
137C3×#95—32no—
138C3×#95—32no—
139C3⋊#95—31no—
140C3⋊#95—31no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—61no—
146C3⋊#95C2×D312yes—
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—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4—22no—
159C2×C32×C4C2×D412yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3#4114yes—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×Q812yes—
178C2×C3×Dic3C2×Q812yes—
179C2×C3×Dic3#4114yes—
180C2×C3×Dic3#4112yes—
181C3×Dic6—28no—
182#624—28no—
183C2×C4×Q8—31no—
184C2×#117—91no—
185#400—31no—
186#399—91no—
187#398—92no—
188#396—92no—
189#395—91no—
190#393—91no—
191C4×C4⋊C4—92no—
192C4×C4⋊C4—91no—
193C4×C22⋊C4—92no—
194C23×D3—31no—
195C23×D3—31no—
196C23×D3—61no—
197C2×C3×Q8—64no—
198C2×C3×Q8—62no—
199C22×C3×C4—21no—
200C22×C3×C4—22no—
201C22×C3×C4—31no—
202C22×C3×C4—31no—
203C22×C3×C4—32no—
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—31no—
207C22×C3×C4C22×D312yes—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×Dic3—32no—
212C22×Dic3—32no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—62no—
216C22×Dic3—61no—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D311yescharacteristic
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D311yescharacteristic
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D311yescharacteristic
223C2×C4×D3—34no—
224C2×C4×D3—34no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
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×C42—34no—
237C3×C42—64no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—124no—
247(C2×D3)⋊C4—122no—
248C4⋊Dic3—64no—
249C4⋊Dic3—62no—
250Dic3⋊C4—22no—
251Dic3⋊C4—24no—
252Dic3⋊C4—64no—
253Dic3⋊C4—62no—
254Dic3⋊C4—64no—
255Dic3⋊C4—64no—
256Dic3⋊C4—64no—
257Dic3⋊C4—64no—
258Dic3⋊C4—124no—
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—42no—
277C3⋊Dic3—24no—
278C3⋊Dic3—41no—
279C3×Dic3—22no—
280C3×Dic3—24no—
281C3×Dic3—22no—
282C3×Dic3—41no—
283C3×Dic3—42no—
284C3×Dic3C22⋊Q814yes—
285C22×Q8—31no—
286C23×C4—91no—
287C4×Q8—64no—
288#117—184no—
289C2×C4⋊C4—31no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—92no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4D3211yescharacteristic
296C2×C22⋊C4—91no—
297C2×C22⋊C4—92no—
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—32no—
307#95—92no—
308#95—92no—
309#95—91no—
310C23×C3—21no—
311C23×C3C23×D311yescharacteristic
312C23×C3C23×D311yescharacteristic
313C22×D3—32no—
314C22×D3—32no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—61no—
318C22×D3—61no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—61no—
323C22×D3—61no—
324C22×D3—122no—
325C22×D3—121no—
326C22×D3—122no—
327C22×D3—121no—
328C3×Q8—68no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—34no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—61no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4D3×D412yes—
359C2×C3×C4C2×#6712yes—
360C2×Dic3—22no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—22no—
365C2×Dic3—21no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—61no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—61no—
381C2×Dic3—122no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—121no—
385C2×Dic3#23514yes—
386C2×Dic3D3×Q812yes—
387C2×Dic3D3×Q812yes—
388C2×Dic3#23912yes—
389C2×Dic3C2×#6712yes—
390C2×Dic3C2×#6712yes—
391C4×D3—68no—
392C4×D3—68no—
393Dic6—28no—
394C2×C32C2×C22⋊Q811yescharacteristic
395C2×C32#52511yescharacteristic
396C2×C32#52912yes—
397C2×C32#53211yescharacteristic
398C2×C32#53312yes—
399C3⋊D3—42no—
400C24—91no—
401C2×Q8—64no—
402C2×Q8—62no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—32no—
406C22×C4—31no—
407C22×C4—32no—
408C22×C4—31no—
409C22×C4—94no—
410C22×C4—92no—
411C22×C4—91no—
412C22×C4—182no—
413C22×C4—182no—
414C22×C4C2×D3212yes—
415C22×C4C2×D3211yescharacteristic
416C4⋊C4—22no—
417C4⋊C4—64no—
418C4⋊C4—62no—
419C4⋊C4—184no—
420C4⋊C4—182no—
421C4⋊C4—184no—
422C4⋊C4—184no—
423C22⋊C4—184no—
424C22⋊C4—182no—
425C22⋊C4—184no—
426C22⋊C4—182no—
427C42—34no—
428C42—64no—
429C42—182no—
430C42—184no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3C2×#23512yes—
437C22×C3C2×D3×D411yescharacteristic
438C22×C3C2×D3×Q811yescharacteristic
439C22×C3C2×D3×Q811yescharacteristic
440C22×C3C2×#23911yescharacteristic
441C22×C3D3×#4112yes—
442C22×C3D3×#4112yes—
443C22×C3D3×#4112yes—
444C22×C3D3×#4111yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—64no—
447C2×D3—62no—
448C2×D3—64no—
449C2×D3—62no—
450C2×D3—124no—
451C2×D3—122no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—122no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—122no—
458C2×D3—241no—
459C2×D3—241no—
460C2×D3—242no—
461C3×C4—22no—
462C3×C4—22no—
463C3×C4—34no—
464C3×C4—42no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—64no—
468C3×C4—62no—
469C3×C4—62no—
470C3×C4—82no—
471C3×C4—121no—
472C3×C4—122no—
473Dic3—24no—
474Dic3—22no—
475Dic3—22no—
476Dic3—41no—
477Dic3—42no—
478Dic3—64no—
479Dic3—64no—
480Dic3—124no—
481Dic3—121no—
482Dic3—121no—
483Dic3—241no—
484Dic3#94614yes—
485C32#239611yescharacteristic, complemented, Sylow
486C23—92no—
487C23—182no—
488C23—182no—
489C23—181no—
490C23—181no—
491C23C22×D3211yescharacteristic
492Q8—68no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—32no—
498C2×C4—32no—
499C2×C4—32no—
500C2×C4—34no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—61no—
506C2×C4—62no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—61no—
513C2×C4—94no—
514C2×C4—188no—
515C2×C4—182no—
516C2×C4—182no—
517C2×C4—182no—
518C2×C4—181no—
519C2×C4D3×#6712yes—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3—21no—
524C2×C3—22no—
525C2×C3#557812yes—
526C2×C3#558012yes—
527C2×C3D3×C22⋊Q811yescharacteristic
528C2×C3#565611yescharacteristic
529C2×C3#566811yescharacteristic
530C2×C3#568812yes—
531C2×C3#570612yes—
532C2×C3#579111yescharacteristic
533C2×C3C2×#94611yescharacteristic
534C2×C3#583211yescharacteristic
535D3—122no—
536D3—122no—
537D3—242no—
538C22—184no—
539C22—182no—
540C22—361no—
541C22—361no—
542C22—362no—
543C22D3×#23512yes—
544C22#6431212yes—
545C22D32×Q811yescharacteristic
546C22D3×#23911yescharacteristic
547C22C2×D3×#6711yescharacteristic
548C4—22no—
549C4—34no—
550C4—42no—
551C4—64no—
552C4—62no—
553C4—62no—
554C4—121no—
555C4—122no—
556C4—184no—
557C4—361no—
558C3—21no—
559C3#7813011yescharacteristic, complemented
560C3#8249111yescharacteristic, complemented
561C2—362no—
562C2#1059439812yes—
563C2#1059442312yes—
564C2#1059489611yescharacteristic
565C2#1059515311yescharacteristic
566C2D3×#94611yescharacteristic
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
1. C2×C3×#887C2semidirect
4. C3×#4985C2semidirect
6. #10591344C2semidirect
7. #10591340C2semidirect
9. #10591243C2semidirect
10. #10591242C2semidirect
41. C2×#887D3semidirect
50. #4985D3semidirect
77. C2×#624Q8semidirect
485. C32#2396semidirect
559. C3#78130semidirect
560. C3#82491semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
C2×#638362
#105926922
C3×#49852
#105913472
#105913442
#105913402
#105913102
#105912432
#105912422
#105912332
#824913
#781303