Finite Group Databasebeta

← #11860422

Subgroups — #11860422

Order 1152.

1027 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#887C211yesmaximal, characteristic, complemented
2Dic3×#235C211yesmaximal, characteristic
3C2×#63827C211yesmaximal, characteristic
4#10592663C211yesmaximal, characteristic, complemented
5C3×#4966C211yesmaximal, characteristic
6#10591100C211yesmaximal, characteristic, complemented
7Dic3×#208C211yesmaximal, characteristic, complemented
8#10590477C212yesmaximal, complemented
9#10590476C212yesmaximal, complemented
10#10590454C212yesmaximal, complemented
11#10590453C212yesmaximal, complemented
12C4×#942—31nomaximal
13#78867—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×#3748C2211yescharacteristic
19C2×C3×Dic3⋊C4—21no—
20C2×C3×C4×Dic3—21no—
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C3×#887—21no—
24C3×#887—21no—
25C3×#887C2212yes—
26C3×#887C2212yes—
27Dic3×#67—21no—
28Dic3×#67—21no—
29Dic3×D12C2211yescharacteristic
30Dic3×D12C2211yescharacteristic
31C4×D3×Dic3—21no—
32#63855—21no—
33Dic3×Dic6C2211yescharacteristic
34Dic3×Dic6C2211yescharacteristic
35C2×#3718C2212yes—
36#63827C418yescomplemented
37C2×#3715C2212yes—
38#63635C2212yes—
39#63634C2212yes—
40C3×#810C2212yes—
41C3×#809C2212yes—
42#63566C2212yes—
43#63566C2212yes—
44#63554C2212yes—
45Dic3×C3⋊C8C2212yes—
46C2×C3×C4×Q8—31no—
47Dic3×#41—31no—
48C2×#951—31no—
49C2×#942—31no—
50C2×#887D311yescharacteristic, complemented
51C4×#235—31no—
52C3×#417—31no—
53#5225—31no—
54#5120—31no—
55Dic3×M16—31no—
56#5030—32no—
57C4×#216—32no—
58#5026—32no—
59C4×#215—32no—
60#4966D311yescharacteristic
61#4964—31no—
62#4964—31no—
63#4964—61no—
64C4×#208—31no—
65#4790—32no—
66#4789—32no—
67#4758—32no—
68#4757—32no—
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C2×C3×#67—21no—
72C22×C3×Dic3—21no—
73C22×C3×Dic3D411yescharacteristic
74C22×C3×Dic3D411yescharacteristic
75C3×#235—22no—
76C3×#235C2×C414yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×Dic6—21no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6C2×C414yescomplemented
82C2×C3×Dic6C2312yes—
83C2×C3×Dic6C2311yescharacteristic
84C2×D3×Dic3—21no—
85C2×D3×Dic3—21no—
86C32×C4⋊C4—21no—
87C32×C4⋊C4C2312yes—
88#3757—21no—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C4×C3⋊Dic3—21no—
92#3748C2×C414yescomplemented
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×Dic3⋊C4—22no—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—22no—
97C3×C4×Dic3—22no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C3×#208—22no—
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—21no—
105Dic3⋊Dic3—21no—
106(C2×D3)⋊Dic3—21no—
107(C2×D3)⋊Dic3—21no—
108Dic32—21no—
109Dic32—21no—
110#3718C2×C418yescomplemented
111#3715C2×C418yescomplemented
112C4×#137—91noSylow
113C2×C3×#41—31no—
114C22×C3×Q8—31no—
115C2×#235C2×D311yescharacteristic
116C22×Dic6C2×D311yescharacteristic
117C2×C3×M16—31no—
118C3×C4×Q8—32no—
119C3×C4×Q8—32no—
120C3×C4×Q8—61no—
121C3×C4×Q8—61no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—61no—
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C4⋊C4C2×D311yescharacteristic
126C2×C3×C42—31no—
127C2×C3×C42—61no—
128#951—38no—
129Q8×Dic3—31no—
130Q8×Dic3—31no—
131C2×#216—32no—
132C2×#216—32no—
133#942—38no—
134C2×#215—32no—
135D4×Dic3—31no—
136D4×Dic3—31no—
137D4×Dic3—61no—
138D4×Dic3—61no—
139C2×#214—32no—
140C4×#67—61no—
141C4×#67—61no—
142#926—31no—
143#926—31no—
144#926—61no—
145#926—61no—
146C2×Dic3⋊C4—21no—
147C2×C4×Dic3—21no—
148C2×C4×Dic3—61no—
149C2×C4×Dic3C2×D311yescharacteristic
150C2×#208—31no—
151C2×#208—31no—
152C2×#208—61no—
153C2×#208C2×D311yescharacteristic
154#887—21no—
155#887—21no—
156#887C2×D312yes—
157#887C2×D312yes—
158C4×D12—31no—
159C4×D12—31no—
160#872—61no—
161C42×D3—61no—
162C4×Dic6—31no—
163C4×Dic6—31no—
164C3×#103—32no—
165C3×#102—32no—
166#835—32no—
167#835—32no—
168#816—32no—
169#816—32no—
170#815—32no—
171C8×Dic3—32no—
172#810C2×D312yes—
173#809C2×D312yes—
174#808—32no—
175#808—32no—
176#808—62no—
177#807—32no—
178#807—32no—
179#807—62no—
180#803—32no—
181C4×C3⋊C8—32no—
182C23×C32C2×D411yescharacteristic
183C22×C3×D3—21no—
184C2×C32×C4—22no—
185C2×C32×C4—42no—
186C2×C32×C4C22×C412yes—
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C3×#67—24no—
193C2×C3×Dic3—24no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—41no—
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—21no—
203C3×D12C22×C412yes—
204C3×C4×D3—24no—
205C3×Dic6—24no—
206C3×Dic6—22no—
207C3×Dic6—21no—
208C3×Dic6C22×C414yes—
209C3×Dic6C22×C412yes—
210D3×Dic3—42no—
211D3×Dic3—42no—
212C3⋊(C3⋊C8)C22×C414yes—
213C3×C3⋊C8—22no—
214C2×#137—91no—
215C4×#41—91no—
216C2×C4×Q8—31no—
217#441—92no—
218#440—92no—
219C4×Q16—92no—
220C4×SD16—92no—
221#428—91no—
222#419—91no—
223#417—31no—
224C4×M16—91no—
225C3×#41—34no—
226C3×#41—62no—
227C2×C3×Q8—34no—
228C2×C3×Q8—32no—
229C2×C3×Q8—31no—
230C2×C3×Q8—61no—
231C2×C3×Q8—62no—
232C2×C3×D4—31no—
233C2×C3×D4—61no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—41no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C2×#67—21no—
245C22×Dic3—21no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3#6711yescharacteristic
249C22×Dic3#6711yescharacteristic
250#235—22no—
251#235C4×D314yes—
252C2×D12C22×D311yescharacteristic
253C2×C4×D3—21no—
254C2×C4×D3—61no—
255C2×C4×D3—61no—
256C2×Dic6—22no—
257C2×Dic6—21no—
258C2×Dic6C4×D314yescomplemented
259C2×Dic6C22×D311yescharacteristic
260C2×Dic6C22×D312yes—
261C3×M16—62no—
262C2×C3×C8—32no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—41no—
267C3×C4⋊C4—62no—
268C3×C4⋊C4—62no—
269C3×C4⋊C4C22×D312yes—
270C3×C4⋊C4C22×D312yes—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—31no—
274C3×C42—31no—
275C3×C42—62no—
276C3×C42—62no—
277#217—61no—
278#217—61no—
279#217—61no—
280#217—61no—
281#217—121no—
282#216—38no—
283#216—38no—
284#215—38no—
285#214—38no—
286(C2×D3)⋊C4—61no—
287(C2×D3)⋊C4—61no—
288C4⋊Dic3—31no—
289C4⋊Dic3—31no—
290C4⋊Dic3—31no—
291C4⋊Dic3—31no—
292C4⋊Dic3—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—61no—
296Dic3⋊C4—22no—
297Dic3⋊C4—22no—
298Dic3⋊C4—61no—
299Dic3⋊C4—61no—
300C4×Dic3—22no—
301C4×Dic3—22no—
302C4×Dic3—61no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—61no—
306C4×Dic3—61no—
307C4×Dic3—61no—
308C4×Dic3—121no—
309C4×Dic3#6711yescharacteristic
310C4×Dic3#6711yescharacteristic
311C4×Dic3C22×D311yescharacteristic
312C4×Dic3C22×D311yescharacteristic
313#208—22no—
314#208—34no—
315#208—34no—
316#208—64no—
317C2×C3⋊C8—32no—
318C2×C3⋊C8—32no—
319C2×C3⋊C8—62no—
320C2×C3⋊C8C22×D312yes—
321C22×C32—21no—
322C22×C32—21no—
323C22×C32C4×D412yes—
324C22×C32C22×D411yescharacteristic
325C2×C3×D3—22no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4—42no—
329C32×C4C4×D412yes—
330C32×C4C23×C411yescharacteristic
331C32×C4C2×#4111yescharacteristic
332C3⋊Dic3—41no—
333C3⋊Dic3—41no—
334C3×Dic3—24no—
335C3×Dic3—22no—
336C3×Dic3—21no—
337C3×Dic3—21no—
338C3×Dic3—21no—
339C3×Dic3#13712yescomplemented
340C2×#41—31no—
341C22×Q8—31no—
342#137—98no—
343C2×Q16—92no—
344C2×SD16—92no—
345C2×M16—31no—
346C2×M16—91no—
347C4×Q8—32no—
348C4×Q8—32no—
349C4×Q8—61no—
350C4×Q8—61no—
351C4×Q8—91no—
352C4×Q8—91no—
353C4×D4—91no—
354C4×D4—91no—
355C4×D4—181no—
356C4×D4—181no—
357#117—91no—
358#117—181no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4D3211yescharacteristic
361C2×C42—31no—
362C2×C42—61no—
363C2×C42—181no—
364#107—92no—
365#106—92no—
366#103—32no—
367#103—92no—
368#103—92no—
369#102—32no—
370#97—92no—
371C4×C8—92no—
372C23×C3—21no—
373C23×C3—61no—
374C23×C3D3×D411yescharacteristic
375C23×C3C2×#6711yescharacteristic
376C22×D3—21no—
377C3×Q8—34no—
378C3×Q8—32no—
379C3×Q8—64no—
380C3×Q8—61no—
381C3×Q8—62no—
382C3×D4—32no—
383C3×D4—64no—
384C3×D4—61no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—31no—
392C2×C3×C4—31no—
393C2×C3×C4—31no—
394C2×C3×C4—31no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—62no—
399C2×C3×C4—64no—
400C2×C3×C4—62no—
401C2×C3×C4—61no—
402C2×C3×C4—64no—
403C2×C3×C4—82no—
404C2×C3×C4—121no—
405C2×C3×C4C2×C4×D312yes—
406C2×C3×C4C2×C4×D312yes—
407C2×C3×C4#23512yes—
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4#23712yes—
410C2×C3×C4C2×#6711yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413#67—24no—
414C2×Dic3—24no—
415C2×Dic3—21no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—41no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—121no—
424C2×Dic3—121no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3C2×#6711yescharacteristic
428C2×Dic3C2×#6711yescharacteristic
429C2×Dic3C2×#6711yescharacteristic
430C2×Dic3C2×#6711yescharacteristic
431D12—21no—
432D12C2×C4×D312yes—
433C4×D3—24no—
434C4×D3—122no—
435C4×D3—122no—
436Dic6—24no—
437Dic6—22no—
438Dic6—21no—
439Dic6C2×C4×D314yes—
440Dic6C2×C4×D312yes—
441C3×C8—62no—
442C3⋊C8—22no—
443C3⋊C8—34no—
444C3⋊C8—34no—
445C3⋊C8—64no—
446C2×C32—22no—
447C2×C32C2×C4×D411yescharacteristic
448C2×C32C2×#13711yescharacteristic
449C2×C32#57511yescharacteristic
450C3×D3—42no—
451#41—34no—
452#41—62no—
453C2×Q8—31no—
454C2×Q8—32no—
455C2×Q8—34no—
456C2×Q8—62no—
457C2×Q8—61no—
458C2×D4—31no—
459C2×D4—61no—
460C22×C4—21no—
461C22×C4—31no—
462C22×C4—31no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—181no—
466C22×C4—181no—
467C22×C4C2×D3211yescharacteristic
468Q16—98no—
469SD16—98no—
470M16—62no—
471M16—94no—
472C2×C8—32no—
473C2×C8—92no—
474C4⋊C4—21no—
475C4⋊C4—62no—
476C4⋊C4—62no—
477C4⋊C4—91no—
478C4⋊C4—91no—
479C4⋊C4—181no—
480C4⋊C4—181no—
481C4⋊C4C2×D3212yes—
482C22⋊C4—181no—
483C22⋊C4—181no—
484C22⋊C4—181no—
485C42—31no—
486C42—31no—
487C42—31no—
488C42—31no—
489C42—62no—
490C42—62no—
491C42—181no—
492C42—181no—
493C42—181no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—22no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—62no—
503C22×C3—121no—
504C22×C3—121no—
505C22×C3#67⋊C412yes—
506C22×C3C4×#6712yes—
507C22×C3C2×D3×D411yescharacteristic
508C22×C3C22×#6711yescharacteristic
509C2×D3—22no—
510C2×D3—41no—
511C2×D3—41no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—32no—
516C3×C4—42no—
517C3×C4—42no—
518C3×C4—64no—
519C3×C4—61no—
520C3×C4—61no—
521C3×C4—61no—
522C3×C4—62no—
523C3×C4—82no—
524C3×C4#67⋊C412yes—
525C3×C4C4×#6712yes—
526C3×C4C22×C4×D311yescharacteristic
527C3×C4C22×C4×D311yescharacteristic
528C3×C4C2×#23511yescharacteristic
529C3×C4C2×#23711yescharacteristic
530Dic3—22no—
531Dic3—24no—
532Dic3—21no—
533Dic3—21no—
534Dic3—21no—
535Dic3—121no—
536Dic3—121no—
537Dic3—121no—
538Dic3—121no—
539Dic3—241no—
540Dic3—241no—
541Dic3#94212yescomplemented
542C32C4×#13711yescharacteristic, complemented, Sylow
543C23—61no—
544C23D3×#6711yescharacteristic
545Q8—34no—
546Q8—32no—
547Q8—62no—
548Q8—61no—
549Q8—64no—
550D4—32no—
551D4—64no—
552D4—61no—
553C2×C4—22no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—31no—
558C2×C4—42no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—61no—
562C2×C4—64no—
563C2×C4—64no—
564C2×C4—121no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—362no—
568C2×C4—362no—
569C2×C4#379512yes—
570C2×C4C4×D3212yes—
571C2×C4D3×#6711yescharacteristic
572C2×C4C22×D3211yescharacteristic
573C8—62no—
574C8—94no—
575C2×C3—22no—
576C2×C3—22no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—42no—
581C2×C3—122no—
582C2×C3C2×#67⋊C411yescharacteristic
583C2×C3#577311yescharacteristic
584C2×C3D3×#13711yescharacteristic
585C2×C3C2×C4×#6711yescharacteristic
586C2×C3C2×#94211yescharacteristic
587C2×C3#582211yescharacteristic
588D3—42no—
589C22—21no—
590C22—21no—
591C22—62no—
592C22—121no—
593C22—121no—
594C22#6387912yes—
595C22C2×D3×#6711yescharacteristic
596C4—32no—
597C4—42no—
598C4—61no—
599C4—61no—
600C4—62no—
601C4—64no—
602C4—61no—
603C4—361no—
604C4—361no—
605C4#6387912yes—
606C4C2×#379511yescharacteristic
607C4C2×C4×D3211yescharacteristic
608C3—21no—
609C3#7886711yescharacteristic, complemented
610C3C4×#94211yescharacteristic, complemented
611C2—22no—
612C2—122no—
613C2C2×#6387911yescharacteristic
614C2#1059509511yescharacteristic
615C2D3×#94211yescharacteristic
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
hypocenterC32C4×#137
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
1. C2×C3×#887C2semidirect
4. #10592663C2semidirect
6. #10591100C2semidirect
7. Dic3×#208C2semidirect
8. #10590477C2semidirect
9. #10590476C2semidirect
10. #10590454C2semidirect
11. #10590453C2semidirect
36. #63827C4semidirect
50. C2×#887D3semidirect
81. C2×C3×Dic6C2×C4semidirect
92. #3748C2×C4semidirect
110. #3718C2×C4semidirect
111. #3715C2×C4semidirect
258. C2×Dic6C4×D3semidirect
339. C3×Dic3#137semidirect
541. Dic3#942semidirect
542. C32C4×#137semidirect
609. C3#78867semidirect
610. C3C4×#942semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8872
Dic3×#2352
C2×#638272
#105926632
C3×#49662
#105911002
Dic3×#2082
#105904772
#105904762
#105904542
#105904532
C4×#9423
#788673