Finite Group Databasebeta

← #11869688

Subgroups — #11869688

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic, complemented
4#10591127C212yesmaximal, complemented
5#10591126C211yesmaximal, characteristic, complemented
6#10591122C212yesmaximal, complemented
7#10591103C211yesmaximal, characteristic, complemented
8#10591094C211yesmaximal, characteristic, complemented
9#10591093C212yesmaximal, complemented
10#10591092C211yesmaximal, characteristic, complemented
11#10591084C212yesmaximal, complemented
12#82913—31nomaximal
13#78591—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×#3757—21no—
17#64135—21no—
18#64135—21no—
19#64135C2212yes—
20#64135C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3—21no—
24C3×#953—21no—
25C3×#930C2211yescharacteristic
26C3×#930C2211yescharacteristic
27C3×#929—21no—
28C3×C4×#67—21no—
29C3×C4×#67—21no—
30C3×#926C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C22×C3×C3⋊C8C2212yes—
34C3×#830C2211yescharacteristic
35C3×#830C2212yes—
36C3×#830C2211yescharacteristic
37#63575C2212yescomplemented
38#63575C2212yescomplemented
39#63573C2212yescomplemented
40#63573C2212yescomplemented
41#63566C2212yescomplemented
42#63566C2212yescomplemented
43#63563C2212yescomplemented
44#63563C2212yescomplemented
45C3×#525—31no—
46#5791D311yescharacteristic
47C2×#926—31no—
48C2×#926—31no—
49C2×#926—61no—
50C2×C3×C22⋊C8—31no—
51#5233—32no—
52C2×#830D311yescharacteristic, complemented
53#5113—32no—
54#5106—32no—
55#5045—32no—
56#5044—31no—
57#5043—31no—
58#5035—32no—
59#5034—31no—
60#5033—31no—
61#4998—32no—
62#4737—32no—
63#4736—31no—
64#4735—31no—
65#4723—32no—
66#4722—31no—
67#4721—31no—
68C24×C32D411yescharacteristic
69C22×C32×C4—24no—
70C22×C32×C4D411yescharacteristic
71C22×C32×C4D411yescharacteristic
72C22×C32×C4D411yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C3⋊Dic3—21no—
77C22×C3⋊Dic3—21no—
78C2×C3×#67—21no—
79C2×C3×#67—21no—
80C2×C3×#67—21no—
81C3×#235—24no—
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—21no—
84C2×C3×Dic6C2311yescharacteristic
85#3757—22no—
86#3757—22no—
87C4⋊(C3⋊Dic3)—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C4⋊(C3⋊Dic3)C2312yes—
91C4×C3⋊Dic3—22no—
92C4×C3⋊Dic3—22no—
93C3×#217—21no—
94C3×#217—21no—
95C3×#217—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×(C2×D3)⋊C4—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2311yescharacteristic
100C3×Dic3⋊C4—21no—
101C3×Dic3⋊C4—21no—
102C3×C4×Dic3—21no—
103C2×C3×C3⋊C8—24no—
104C2×C3×C3⋊C8C2312yes—
105C2×C3×C3⋊C8C2312yes—
106#3091—91noSylow
107C2×C3×#41—31no—
108C23×C3×C4—21no—
109C23×C3×C4C2×D311yescharacteristic
110C23×C3×C4C2×D311yescharacteristic
111C2×#235C2×D311yescharacteristic
112C22×C3×C8—32no—
113C3×#123—61no—
114C3×C22⋊Q8—31no—
115C3×C22⋊Q8—31no—
116C3×#121—31no—
117C3×#121—31no—
118C3×#120—61no—
119C3×C4×D4—61no—
120C3×C4×D4—61no—
121C3×#117—31no—
122#953—21no—
123C2×#217—62no—
124C2×#217—61no—
125C2×#217—61no—
126#930C2×D311yescharacteristic
127#930C2×D311yescharacteristic
128#929—21no—
129C4×#67—21no—
130C4×#67—21no—
131#926—32no—
132#926—32no—
133#926—32no—
134#926—32no—
135#926—62no—
136#926—62no—
137#926—62no—
138#926—62no—
139#926—61no—
140#926—61no—
141#926—61no—
142#926—61no—
143#926C2×D311yescharacteristic
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—61no—
149C2×C4⋊Dic3—61no—
150#924C2×D311yescharacteristic
151#924C2×D311yescharacteristic
152C2×C4×Dic3—62no—
153C2×C4×Dic3—61no—
154C2×C4×Dic3—61no—
155C22×C3⋊C8C2×D312yes—
156C3×C22⋊C8—31no—
157C3×C22⋊C8—31no—
158C3×C22⋊C8—32no—
159#835—32no—
160#835—32no—
161#832—32no—
162#832—32no—
163#830C2×D311yescharacteristic
164#830C2×D311yescharacteristic
165#830C2×D312yes—
166#821—32no—
167#821—32no—
168#818—32no—
169#818—32no—
170#817—32no—
171#817—32no—
172#816—32no—
173#816—32no—
174#808—32no—
175#808—32no—
176#807—32no—
177#807—32no—
178C23×C32—22no—
179C23×C32—22no—
180C23×C32—41no—
181C23×C32C2×D411yescharacteristic
182C23×C32C2×D411yescharacteristic
183C23×C32C2×D411yescharacteristic
184C22×C3×D3—21no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4#4114yes—
194C2×C32×C4C2411yescharacteristic
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3—22no—
197C2×C3⋊Dic3—42no—
198C2×C3⋊Dic3—42no—
199C3×#67—42no—
200C3×#67—42no—
201C3×#67—42no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C3×D12—22no—
206C3×C4×D3—42no—
207C3×Dic6—22no—
208C3×C3⋊C8—22no—
209C3×C3⋊C8—22no—
210#525—31no—
211C2×#117—91no—
212#485—92no—
213#484—91no—
214#483—91no—
215#482—92no—
216#481—91no—
217#480—91no—
218#427—92no—
219#416—92no—
220C2×C22⋊C8—31no—
221C24×C3—21no—
222C24×C3D1211yescharacteristic
223C24×C3#6711yescharacteristic
224C3×#41—64no—
225C2×C3×Q8—31no—
226C2×C3×D4—31no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C22×C3×C4—28no—
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—61no—
240C22×C3×C4D1211yescharacteristic
241C22×C3×C4D1211yescharacteristic
242C22×C3×C4D1211yescharacteristic
243C22×C3×C4#6711yescharacteristic
244C22×C3×C4#6711yescharacteristic
245C22×C3×C4#6711yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—21no—
253C2×#67—21no—
254C2×#67—21no—
255C22×Dic3—62no—
256C22×Dic3—62no—
257C22×Dic3—61no—
258C22×Dic3—61no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261#235—24no—
262C2×D12C22×D311yescharacteristic
263C2×C4×D3—21no—
264C2×Dic6C22×D311yescharacteristic
265C2×C3×C8—32no—
266C2×C3×C8—32no—
267C2×C3×C8—64no—
268C3×C4⋊C4—31no—
269C3×C4⋊C4—31no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C22⋊C4—61no—
274C3×C22⋊C4—61no—
275C3×C22⋊C4—61no—
276C3×C22⋊C4—61no—
277C3×C42—61no—
278#217—21no—
279#217—21no—
280#217—21no—
281#217—64no—
282#217—64no—
283#217—62no—
284#217—62no—
285#217—62no—
286#217—62no—
287(C2×D3)⋊C4—21no—
288(C2×D3)⋊C4—21no—
289C4⋊Dic3—32no—
290C4⋊Dic3—32no—
291C4⋊Dic3—32no—
292C4⋊Dic3—32no—
293C4⋊Dic3—62no—
294C4⋊Dic3—62no—
295C4⋊Dic3—62no—
296C4⋊Dic3—62no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3—61no—
300C4⋊Dic3—61no—
301C4⋊Dic3C22×D311yescharacteristic
302C4⋊Dic3C22×D311yescharacteristic
303Dic3⋊C4—21no—
304Dic3⋊C4—21no—
305C4×Dic3—21no—
306C4×Dic3—64no—
307C4×Dic3—64no—
308C4×Dic3—62no—
309C4×Dic3—62no—
310C4×Dic3—62no—
311C4×Dic3—62no—
312C2×C3⋊C8—24no—
313C2×C3⋊C8C22×D312yes—
314C2×C3⋊C8C22×D312yes—
315C22×C32—21no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—21no—
322C22×C32—44no—
323C22×C32#12312yes—
324C22×C32#13512yes—
325C22×C32C22×D411yescharacteristic
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C32×C4—21no—
330C32×C4—21no—
331C32×C4#12312yes—
332C32×C4C2×#4112yes—
333C3⋊Dic3—42no—
334C3⋊Dic3—42no—
335C3×Dic3—41no—
336C3×Dic3—41no—
337C3×Dic3—41no—
338C2×#41—31no—
339C23×C4D3211yescharacteristic
340C22×C8—32no—
341#123—61no—
342C22⋊Q8—31no—
343C22⋊Q8—31no—
344#121—31no—
345#121—31no—
346#120—61no—
347C4×D4—61no—
348C4×D4—61no—
349#117—31no—
350#117—92no—
351#117—92no—
352#117—181no—
353#117—181no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—91no—
356C2×C22⋊C4—181no—
357C2×C42—181no—
358#107—92no—
359#107—92no—
360#106—92no—
361#106—92no—
362#103—92no—
363#103—92no—
364#102—92no—
365#102—92no—
366C22⋊C8—31no—
367C22⋊C8—31no—
368C22⋊C8—32no—
369C23×C3—24no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—42no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—42no—
381C23×C3—61no—
382C23×C3C2×D1211yescharacteristic
383C23×C3C2×D1211yescharacteristic
384C23×C3C2×D1211yescharacteristic
385C23×C3C2×#6711yescharacteristic
386C23×C3C2×#6711yescharacteristic
387C23×C3C2×#6711yescharacteristic
388C22×D3—21no—
389C3×Q8—62no—
390C3×D4—62no—
391C3×D4—122no—
392C3×D4—122no—
393C3×D4—122no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—24no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—122no—
418C2×C3×C4C2×D1211yescharacteristic
419C2×C3×C4C2×D1211yescharacteristic
420C2×C3×C4C2×D1211yescharacteristic
421C2×C3×C4#23714yes—
422C2×C3×C4#23714yes—
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C2×#6711yescharacteristic
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427C2×C3×C4C23×D311yescharacteristic
428#67—42no—
429#67—42no—
430#67—42no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—64no—
435C2×Dic3—64no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—124no—
441C2×Dic3—122no—
442C2×Dic3—122no—
443C2×Dic3—124no—
444C2×Dic3—122no—
445C2×Dic3—122no—
446D12—22no—
447C4×D3—42no—
448Dic6—22no—
449C3×C8—62no—
450C3×C8—62no—
451C3⋊C8—22no—
452C3⋊C8—22no—
453C2×C32—22no—
454C2×C32—22no—
455C2×C32—41no—
456C2×C32C2×#12311yescharacteristic
457C2×C32C2×#13511yescharacteristic
458C2×C32#57511yescharacteristic
459C3×D3—81no—
460C24#62611yescharacteristic
461#41—64no—
462C2×Q8—31no—
463C2×D4—31no—
464C2×D4—61no—
465C2×D4—61no—
466C2×D4—61no—
467C22×C4—24no—
468C22×C4—61no—
469C22×C4—181no—
470C22×C4—181no—
471C22×C4#62611yescharacteristic
472C22×C4#62611yescharacteristic
473C22×C4#62611yescharacteristic
474C22×C4C2×D3211yescharacteristic
475C22×C4C2×D3211yescharacteristic
476C22×C4C2×D3211yescharacteristic
477C2×C8—32no—
478C2×C8—32no—
479C2×C8—64no—
480C4⋊C4—31no—
481C4⋊C4—31no—
482C4⋊C4—61no—
483C4⋊C4—61no—
484C4⋊C4—92no—
485C4⋊C4—92no—
486C4⋊C4—181no—
487C4⋊C4—181no—
488C22⋊C4—61no—
489C22⋊C4—61no—
490C22⋊C4—61no—
491C22⋊C4—61no—
492C22⋊C4—61no—
493C22⋊C4—182no—
494C22⋊C4—182no—
495C42—61no—
496C42—182no—
497C42—182no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—44no—
523C22×C3—44no—
524C22×C3—48no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—121no—
528C22×C3#88612yes—
529C22×C3#90412yes—
530C22×C3#93512yes—
531C22×C3#95012yes—
532C22×C3C22×D1211yescharacteristic
533C22×C3C22×#6711yescharacteristic
534C2×D3—41no—
535C2×D3—41no—
536C2×D3—41no—
537C3×C4—22no—
538C3×C4—22no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—22no—
544C3×C4—22no—
545C3×C4—121no—
546C3×C4—121no—
547C3×C4—121no—
548C3×C4#88612yes—
549C3×C4#93512yes—
550C3×C4C2×#23712yes—
551C3×C4C2×#23712yes—
552Dic3—41no—
553Dic3—41no—
554Dic3—41no—
555Dic3—124no—
556Dic3—124no—
557Dic3—122no—
558Dic3—122no—
559Dic3—122no—
560Dic3—122no—
561C32#309111yescharacteristic, complemented, Sylow
562C23—22no—
563C23—22no—
564C23—41no—
565C23—61no—
566C23C2×#62611yescharacteristic
567C23C2×#62611yescharacteristic
568C23C2×#62611yescharacteristic
569Q8—62no—
570D4—62no—
571D4—122no—
572D4—122no—
573D4—122no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—61no—
580C2×C4—61no—
581C2×C4—61no—
582C2×C4—122no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—362no—
586C2×C4—362no—
587C2×C4#380514yes—
588C2×C4C2×#62611yescharacteristic
589C2×C4C2×#62611yescharacteristic
590C2×C4C2×#62611yescharacteristic
591C2×C4C22×D3211yescharacteristic
592C8—62no—
593C8—62no—
594C2×C3—24no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—22no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—42no—
603C2×C3—42no—
604C2×C3—41no—
605C2×C3—41no—
606C2×C3—241no—
607C2×C3C2×#88611yescharacteristic
608C2×C3C2×#90411yescharacteristic
609C2×C3#574811yescharacteristic
610C2×C3C2×#93511yescharacteristic
611C2×C3C2×#95011yescharacteristic
612C2×C3#582211yescharacteristic
613D3—81no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—44no—
622C22—121no—
623C22—121no—
624C22—121no—
625C22#6382912yes—
626C22#6396212yes—
627C22C22×#62611yescharacteristic
628C4—21no—
629C4—21no—
630C4—121no—
631C4—121no—
632C4—121no—
633C4—362no—
634C4—362no—
635C4#6396212yes—
636C4C2×#380512yes—
637C3—21no—
638C3#7859111yescharacteristic, complemented
639C3#8291311yescharacteristic, complemented
640C2—22no—
641C2—22no—
642C2—41no—
643C2—241no—
644C2C2×#6382911yescharacteristic
645C2#1059479511yescharacteristic
646C2C2×#6396211yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
prime radicalC3×#5791C2
hypercenterC23×C4D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64135C2semidirect
3. C2×C3×#830C2semidirect
4. #10591127C2semidirect
5. #10591126C2semidirect
6. #10591122C2semidirect
7. #10591103C2semidirect
8. #10591094C2semidirect
9. #10591093C2semidirect
10. #10591092C2semidirect
11. #10591084C2semidirect
37. #63575C22semidirect
38. #63575C22semidirect
39. #63573C22semidirect
40. #63573C22semidirect
41. #63566C22semidirect
42. #63566C22semidirect
43. #63563C22semidirect
44. #63563C22semidirect
52. C2×#830D3semidirect
561. C32#3091semidirect
638. C3#78591semidirect
639. C3#82913semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C3×#57912
C2×C3×#8302
#105911272
#105911262
#105911222
#105911032
#105910942
#105910932
#105910922
#105910842
#829133
#785913