Finite Group Databasebeta

← #11860622

Subgroups — #11860622

Order 1152.

999 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C2×#63827C211yesmaximal, characteristic
4#10592663C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6#10591084C211yesmaximal, characteristic
7#10591055C211yesmaximal, characteristic, complemented
8#10590478C212yesmaximal, complemented
9#10590477C212yesmaximal, complemented
10#10590476C212yesmaximal, complemented
11#10590475C212yesmaximal, complemented
12#82571—31nomaximal
13#78774—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C3×C4×#67—22no—
20C3×#926C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#893C2212yes—
23C3×#892—21no—
24C3×D3×C4⋊C4—21no—
25C3×#887C2212yes—
26#63955—22no—
27#63843—21no—
28#63843—21no—
29Dic3×Dic6C2212yes—
30Dic3×Dic6C2212yes—
31C2×#3718C2212yes—
32#63827C418yescomplemented
33C2×#3715C2212yes—
34#63635C2212yes—
35#63634C2212yes—
36C3×#810C2212yes—
37C3×#810C2212yes—
38#63566C2211yescharacteristic
39#63566C2211yescharacteristic
40#63563C2211yescharacteristic
41#63563C2211yescharacteristic
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C3×#520—31no—
45C2×#951—31no—
46#5812—31no—
47C2×#942—31no—
48#5516—31no—
49#5504D311yescharacteristic
50C2×C3×#103—31no—
51#5233—31no—
52#5113—31no—
53#5101—31no—
54#5030—32no—
55C4×#216—32no—
56#5018—32no—
57C4×#214—32no—
58#4997—31no—
59C2×#810D311yescharacteristic, complemented
60#4964—31no—
61#4964—31no—
62#4964—61no—
63#4817—32no—
64#4790—32no—
65#4789—32no—
66#4788—32no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67—21no—
70C22×C3×Dic3—21no—
71C3×#235—22no—
72C3×#235C2×C414yes—
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6C2×C414yescomplemented
79C2×C3×Dic6C2311yescharacteristic
80C2×C3×Dic6C2312yes—
81C32×C4⋊C4—21no—
82C32×C4⋊C4C2312yes—
83#3757—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4⋊(C3⋊Dic3)C2311yescharacteristic
86C4×C3⋊Dic3—21no—
87#3748C2×C414yescomplemented
88C2×C3⋊(C3⋊C8)C2312yes—
89C3×#217D412yes—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3D411yescharacteristic
92C3×C4⋊Dic3D411yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—22no—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8—22no—
97C2×C3×C3⋊C8C2311yescharacteristic
98C2×C3×C3⋊C8C2311yescharacteristic
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—22no—
101Dic32—22no—
102Dic32—22no—
103#3718C2×C418yescomplemented
104#3715C2×C418yescomplemented
105#2947—91noSylow
106C2×C3×#41—31no—
107C22×C3×Q8—31no—
108C2×#235C2×D311yescharacteristic
109C22×Dic6C2×D311yescharacteristic
110C22×C3×C8—31no—
111C3×C4×Q8—32no—
112C3×C4×D4—32no—
113C3×C4×D4—62no—
114C3×#117—31no—
115C3×#117—61no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—61no—
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C4⋊C4C2×D311yescharacteristic
120#951—38no—
121Q8×Dic3—32no—
122Q8×Dic3—32no—
123Q8×Dic3—61no—
124Q8×Dic3—61no—
125C2×#216—32no—
126C2×#216—32no—
127#942—38no—
128C2×#215—32no—
129C2×#214—32no—
130C4×#67—22no—
131#926—31no—
132#926—31no—
133#926—61no—
134#926—62no—
135#926C2×D311yescharacteristic
136C2×#208—31no—
137C2×#208—31no—
138C2×#208—61no—
139C22×C3⋊C8C2×D311yescharacteristic
140#893C2×D312yes—
141#892—21no—
142D3×C4⋊C4—21no—
143#887—61no—
144#887—61no—
145#887C2×D312yes—
146#877—62no—
147C4×Dic6—32no—
148C4×Dic6—32no—
149C3×#103—32no—
150C3×#103—32no—
151#835—31no—
152#835—31no—
153#832—31no—
154#832—31no—
155#821—31no—
156#821—31no—
157#816—31no—
158#816—31no—
159#815—32no—
160C8×Dic3—32no—
161#810C2×D312yes—
162#810C2×D312yes—
163#808—32no—
164#808—32no—
165#808—62no—
166#807—32no—
167#807—32no—
168#807—62no—
169#803—32no—
170C4×C3⋊C8—32no—
171C23×C32C2×D411yescharacteristic
172C22×C3×D3—21no—
173C2×C32×C4—22no—
174C2×C32×C4—81no—
175C2×C32×C4C22×C412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4#4112yes—
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3—21no—
180C2×C3⋊Dic3—21no—
181C3×#67—24no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C3×D12—21no—
188C3×D12C22×C412yes—
189C3×C4×D3—24no—
190C3×C4×D3—82no—
191C3×Dic6—24no—
192C3×Dic6—22no—
193C3×Dic6—21no—
194C3×Dic6C22×C414yes—
195C3×Dic6C22×C412yes—
196C3⋊(C3⋊C8)C22×C414yes—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199C2×#137—91no—
200#520—31no—
201#519—91no—
202#441—92no—
203#440—92no—
204C4×Q16—92no—
205C4×SD16—92no—
206#428—91no—
207#416—91no—
208C2×#103—31no—
209#405—91no—
210C3×#41—34no—
211C3×#41—62no—
212C2×C3×Q8—34no—
213C2×C3×Q8—31no—
214C2×C3×Q8—32no—
215C2×C3×Q8—62no—
216C2×C3×Q8—61no—
217C2×C3×D4—31no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—41no—
223C22×C3×C4—62no—
224C22×C3×C4—61no—
225C22×C3×C4—61no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C2×#67—21no—
229C22×Dic3—21no—
230#235—22no—
231#235C4×D314yes—
232C2×D12C22×D311yescharacteristic
233C2×C4×D3—21no—
234C2×C4×D3—22no—
235C2×Dic6—21no—
236C2×Dic6—22no—
237C2×Dic6C4×D314yescomplemented
238C2×Dic6C22×D312yes—
239C2×Dic6C22×D311yescharacteristic
240C2×C3×C8—31no—
241C2×C3×C8—31no—
242C2×C3×C8—62no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—22no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4—41no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4C22×D312yes—
251C3×C4⋊C4C22×D312yes—
252C3×C22⋊C4—32no—
253C3×C22⋊C4—62no—
254C3×C42—32no—
255C3×C42—62no—
256#217—61no—
257#217—61no—
258#217—121no—
259#217#6712yes—
260#216—38no—
261#216—38no—
262#215—38no—
263#214—38no—
264(C2×D3)⋊C4—22no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3#6711yescharacteristic
274C4⋊Dic3#6711yescharacteristic
275Dic3⋊C4—22no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278C4×Dic3—22no—
279C4×Dic3—62no—
280C4×Dic3—62no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283C4×Dic3—62no—
284C4×Dic3—62no—
285C4×Dic3—121no—
286C4×Dic3C22×D312yes—
287#208—34no—
288#208—34no—
289#208—64no—
290C2×C3⋊C8—22no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—32no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8C22×D311yescharacteristic
295C2×C3⋊C8C22×D311yescharacteristic
296C22×C32—21no—
297C22×C32—21no—
298C22×C32C4×D412yes—
299C22×C32C22×D411yescharacteristic
300C2×C3×D3—22no—
301C2×C3×D3—41no—
302C2×C3×D3—41no—
303C32×C4—42no—
304C32×C4C4×D412yes—
305C32×C4C23×C411yescharacteristic
306C32×C4C2×#4111yescharacteristic
307C3⋊Dic3—41no—
308C3⋊Dic3—41no—
309C3×Dic3—24no—
310C3×Dic3—22no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C2×#41—31no—
314C22×Q8—31no—
315#137—98no—
316C2×Q16—92no—
317C2×SD16—92no—
318C2×M16—91no—
319C22×C8—31no—
320C4×Q8—32no—
321C4×Q8—92no—
322C4×Q8—92no—
323C4×Q8—181no—
324C4×Q8—181no—
325C4×D4—32no—
326C4×D4—62no—
327#117—31no—
328#117—61no—
329#117—91no—
330#117—182no—
331C2×C4⋊C4—61no—
332C2×C4⋊C4D3211yescharacteristic
333#107—92no—
334#106—92no—
335#103—32no—
336#103—32no—
337#103—91no—
338#103—91no—
339#102—91no—
340#102—91no—
341#97—92no—
342C4×C8—92no—
343C23×C3—21no—
344C23×C3—61no—
345C23×C3D3×D411yescharacteristic
346C23×C3C2×#6711yescharacteristic
347C22×D3—21no—
348C3×Q8—34no—
349C3×Q8—32no—
350C3×Q8—64no—
351C3×Q8—62no—
352C3×Q8—61no—
353C3×D4—32no—
354C3×D4—64no—
355C3×D4—61no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—42no—
365C2×C3×C4—64no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—64no—
369C2×C3×C4—81no—
370C2×C3×C4—81no—
371C2×C3×C4—82no—
372C2×C3×C4—242no—
373C2×C3×C4C2×C4×D312yes—
374C2×C3×C4C2×C4×D312yes—
375C2×C3×C4#23512yes—
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4#23712yes—
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381#67—24no—
382C2×Dic3—24no—
383C2×Dic3—22no—
384C2×Dic3—21no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3C2×#6712yes—
392C2×Dic3C2×#6712yes—
393D12—21no—
394D12C2×C4×D312yes—
395C4×D3—24no—
396C4×D3—82no—
397Dic6—24no—
398Dic6—21no—
399Dic6—22no—
400Dic6C2×C4×D314yes—
401Dic6C2×C4×D312yes—
402C3×C8—61no—
403C3×C8—61no—
404C3⋊C8—21no—
405C3⋊C8—21no—
406C3⋊C8—34no—
407C3⋊C8—34no—
408C3⋊C8—64no—
409C2×C32—22no—
410C2×C32C2×C4×D411yescharacteristic
411C2×C32#57711yescharacteristic
412C2×C32#57811yescharacteristic
413C3×D3—42no—
414#41—34no—
415#41—62no—
416C2×Q8—32no—
417C2×Q8—31no—
418C2×Q8—34no—
419C2×Q8—62no—
420C2×Q8—61no—
421C2×D4—31no—
422C2×D4—61no—
423C22×C4—21no—
424C22×C4—62no—
425C22×C4—61no—
426C22×C4—61no—
427C22×C4C2×D3211yescharacteristic
428Q16—98no—
429SD16—98no—
430M16—94no—
431C2×C8—31no—
432C2×C8—31no—
433C2×C8—62no—
434C2×C8—92no—
435C4⋊C4—21no—
436C4⋊C4—31no—
437C4⋊C4—31no—
438C4⋊C4—62no—
439C4⋊C4—91no—
440C4⋊C4—91no—
441C4⋊C4—182no—
442C4⋊C4—182no—
443C4⋊C4C2×D3212yes—
444C22⋊C4—32no—
445C22⋊C4—62no—
446C22⋊C4—181no—
447C42—32no—
448C42—62no—
449C42—182no—
450C42—182no—
451C42—181no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—22no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—121no—
462C22×C3—121no—
463C22×C3#67⋊C412yes—
464C22×C3C4×#6712yes—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C22×#6711yescharacteristic
467C2×D3—22no—
468C2×D3—41no—
469C2×D3—41no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—62no—
476C3×C4—62no—
477C3×C4—62no—
478C3×C4—64no—
479C3×C4—82no—
480C3×C4#67⋊C412yes—
481C3×C4C4×#6712yes—
482C3×C4C22×C4×D311yescharacteristic
483C3×C4C22×C4×D311yescharacteristic
484C3×C4C2×#23511yescharacteristic
485C3×C4C2×#23711yescharacteristic
486Dic3—24no—
487Dic3—22no—
488Dic3—22no—
489Dic3—22no—
490Dic3—121no—
491Dic3—121no—
492Dic3—121no—
493Dic3—121no—
494Dic3—241no—
495Dic3—241no—
496C32#294711yescharacteristic, complemented, Sylow
497C23—61no—
498C23D3×#6711yescharacteristic
499Q8—34no—
500Q8—32no—
501Q8—62no—
502Q8—61no—
503Q8—64no—
504D4—32no—
505D4—64no—
506D4—61no—
507C2×C4—22no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—61no—
511C2×C4—62no—
512C2×C4—64no—
513C2×C4—64no—
514C2×C4—81no—
515C2×C4—181no—
516C2×C4—181no—
517C2×C4—242no—
518C2×C4#379512yes—
519C2×C4C4×D3212yes—
520C2×C4D3×#6711yescharacteristic
521C2×C4C22×D3211yescharacteristic
522C8—61no—
523C8—61no—
524C8—94no—
525C2×C3—22no—
526C2×C3—22no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—42no—
531C2×C3—122no—
532C2×C3C2×#67⋊C411yescharacteristic
533C2×C3#576211yescharacteristic
534C2×C3#576611yescharacteristic
535C2×C3C2×C4×#6711yescharacteristic
536C2×C3#583611yescharacteristic
537C2×C3#583811yescharacteristic
538D3—42no—
539C22—21no—
540C22—21no—
541C22—62no—
542C22—121no—
543C22—121no—
544C22#6387912yes—
545C22C2×D3×#6711yescharacteristic
546C4—42no—
547C4—62no—
548C4—62no—
549C4—64no—
550C4—62no—
551C4—361no—
552C4—361no—
553C4#6387912yes—
554C4C2×#379511yescharacteristic
555C4C2×C4×D3211yescharacteristic
556C3—21no—
557C3#7877411yescharacteristic, complemented
558C3#8257111yescharacteristic, complemented
559C2—22no—
560C2—122no—
561C2C2×#6387911yescharacteristic
562C2#1059510511yescharacteristic
563C2#1059532711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
4. #10592663C2semidirect
5. C2×C3×#810C2semidirect
7. #10591055C2semidirect
8. #10590478C2semidirect
9. #10590477C2semidirect
10. #10590476C2semidirect
11. #10590475C2semidirect
32. #63827C4semidirect
59. C2×#810D3semidirect
78. C2×C3×Dic6C2×C4semidirect
87. #3748C2×C4semidirect
103. #3718C2×C4semidirect
104. #3715C2×C4semidirect
237. C2×Dic6C4×D3semidirect
496. C32#2947semidirect
557. C3#78774semidirect
558. C3#82571semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
#105948182
C2×#638272
#105926632
C2×C3×#8102
#105910842
#105910552
#105904782
#105904772
#105904762
#105904752
#825713
#787743