Finite Group Databasebeta

← #11860889

Subgroups — #11860889

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5827C211yesmaximal, characteristic, complemented
2C2×C3×#950C211yesmaximal, characteristic
3#10594992C211yesmaximal, characteristic, complemented
4#10592931C211yesmaximal, characteristic, complemented
5Dic3×#216C212yesmaximal, complemented
6#10591566C212yesmaximal, complemented
7#10591440C212yesmaximal, complemented
8Dic3×#213C212yesmaximal, complemented
9C2×#63575C211yesmaximal, characteristic, complemented
10#10591087C211yesmaximal, characteristic, complemented
11#10591055C211yesmaximal, characteristic, complemented
12#83898—31nomaximal
13#82557—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#950C418yescomplemented
19C3×Q8×Dic3C2212yes—
20C2×C3×#216C2211yescharacteristic
21C2×C3×#215C2211yescharacteristic
22C3×D4×Dic3—22no—
23C3×D4×Dic3C2212yes—
24C2×C3×#214C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#926—21no—
27C3×#926C2211yescharacteristic
28C2×C3×C4⋊Dic3—21no—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31#67⋊Dic3—22no—
32Dic3×D12C2212yes—
33D3×C4⋊Dic3—21no—
34Dic3×Dic6C2212yes—
35#63841—21no—
36#63662C2212yes—
37#63659C2212yes—
38#63575C2212yes—
39#63575C2212yes—
40#63565C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43Dic3×C3⋊C8C2212yes—
44C2×C3×#135—31no—
45C3×#520—31no—
46#5827—31no—
47#5827D311yescharacteristic, complemented
48C2×#950D311yescharacteristic
49#5523—31no—
50#5232—31no—
51#5232—31no—
52#5232—31no—
53#5232—61no—
54Dic3×Q16—32no—
55#5164—32no—
56#5164—32no—
57Dic3×D8—32no—
58C2×#818—31no—
59#5101—31no—
60C4×#216—32no—
61#5026—32no—
62#5018—32no—
63C4×#213—32no—
64#4997—31no—
65#4966—31no—
66C2×#807—31no—
67C32×#41—22no—
68C32×#41C2×C414yescomplemented
69C2×C32×Q8C2311yescharacteristic
70C2×C32×D4—21no—
71C2×C32×D4C2311yescharacteristic
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3—21no—
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—22no—
78C3×#235—22no—
79C3×#235C2×C414yescomplemented
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×Dic6C2311yescharacteristic
83C2×D3×Dic3—22no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86#3748—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—22no—
89C3×#217D412yes—
90C3×#216C2×C414yescomplemented
91C3×#215C2×C414yescomplemented
92C3×#214C2×C414yescomplemented
93C3×#213C2×C414yescomplemented
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3D411yescharacteristic
97C3×C4⋊Dic3D411yescharacteristic
98C3×C4⋊Dic3C2312yes—
99C3×C4×Dic3—22no—
100C3×C4×Dic3C2312yes—
101C2×C3×C3⋊C8C2×C414yescomplemented
102C2×C3×C3⋊C8C2311yescharacteristic
103C2×C3×C3⋊C8C2311yescharacteristic
104Dic3⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106Dic32—22no—
107#2951—91noSylow
108C2×C3×#41—21no—
109C2×C3×#41—31no—
110C2×C3×#41C2×D311yescharacteristic
111C2×C3×#41C2×D311yescharacteristic
112C2×#235C2×D311yescharacteristic
113C3×#135—38no—
114C2×C3×Q16—31no—
115C2×C3×SD16—31no—
116C2×C3×SD16—31no—
117C2×C3×D8—31no—
118C22×C3×C8—31no—
119C3×C4×Q8—32no—
120C3×C4×D4—32no—
121C3×C4×D4—62no—
122C3×#117—31no—
123C3×#117—61no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C4⋊C4—61no—
126#950Dic318yescomplemented
127Q8×Dic3—32no—
128Q8×Dic3C2×D312yes—
129C2×#216C2×D311yescharacteristic
130C2×#215C2×D311yescharacteristic
131D4×Dic3—22no—
132D4×Dic3—32no—
133D4×Dic3—62no—
134D4×Dic3C2×D312yes—
135C2×#214C2×D311yescharacteristic
136C2×#213C2×D311yescharacteristic
137#926—21no—
138#926—61no—
139#926C2×D311yescharacteristic
140C2×C4⋊Dic3—21no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—61no—
144C2×C4⋊Dic3—61no—
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×#208—31no—
147C2×#208—31no—
148C2×#208—61no—
149C22×C3⋊C8C2×D311yescharacteristic
150#892—61no—
151D3×C4⋊C4—61no—
152#67⋊C4—62no—
153C4×D12—32no—
154C4×Dic6—32no—
155#835—32no—
156#835—32no—
157#835—32no—
158#835—62no—
159#832—32no—
160#832—32no—
161#832—32no—
162#832—62no—
163#818—32no—
164#818—32no—
165#815—32no—
166C8×Dic3—32no—
167#810—32no—
168#809—32no—
169#807—32no—
170#807—32no—
171#803—32no—
172C4×C3⋊C8—32no—
173C23×C32—21no—
174C23×C32C2×D411yescharacteristic
175C22×C3×D3—21no—
176C32×Q8—21no—
177C32×Q8C22×C412yes—
178C32×D4—24no—
179C32×D4—21no—
180C32×D4C22×C412yes—
181C2×C32×C4—21no—
182C2×C32×C4—24no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4#4112yes—
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—81no—
189C3×#67—24no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—82no—
193C2×C3×Dic3—81no—
194C2×C3×Dic3C2×D412yes—
195C2×C3×Dic3C2×D412yes—
196C3×D12—21no—
197C3×D12C22×C412yes—
198C3×C4×D3—24no—
199C3×Dic6—21no—
200C3×Dic6C22×C412yes—
201D3×Dic3—82no—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8C22×C412yes—
204C3×C3⋊C8C22×C412yes—
205C2×#135—31no—
206#520—31no—
207#520—91no—
208#440—92no—
209#440—92no—
210C4×Q16—92no—
211C4×D8—92no—
212C2×#107—91no—
213#417—91no—
214#417—91no—
215#405—91no—
216C3×#41—22no—
217C3×#41—22no—
218C3×#41—24no—
219C3×#41—34no—
220C3×#41—42no—
221C3×#41—62no—
222C3×#41C4×D314yescomplemented
223C3×#41C2×Dic314yescomplemented
224C2×C3×Q8—21no—
225C2×C3×Q8—31no—
226C2×C3×Q8C22×D311yescharacteristic
227C2×C3×Q8C22×D311yescharacteristic
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—31no—
232C2×C3×D4—41no—
233C2×C3×D4—61no—
234C2×C3×D4C22×D311yescharacteristic
235C2×C3×D4C22×D311yescharacteristic
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—41no—
240C22×C3×C4—62no—
241C22×C3×C4—61no—
242C22×C3×C4—61no—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—21no—
246C22×Dic3—21no—
247C22×Dic3—22no—
248C22×Dic3—61no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251C22×Dic3—121no—
252#235—22no—
253#235C2×Dic314yescomplemented
254C2×D12C22×D311yescharacteristic
255C2×C4×D3—21no—
256C2×C4×D3—62no—
257C2×Dic6C22×D311yescharacteristic
258C3×Q16—34no—
259C3×SD16—34no—
260C3×SD16—34no—
261C3×D8—34no—
262C2×C3×C8—34no—
263C2×C3×C8—31no—
264C2×C3×C8—31no—
265C3×C4⋊C4—31no—
266C3×C4⋊C4—31no—
267C3×C4⋊C4—32no—
268C3×C4⋊C4—62no—
269C3×C4⋊C4—61no—
270C3×C22⋊C4—32no—
271C3×C22⋊C4—62no—
272C3×C42—32no—
273C3×C42—62no—
274#217—22no—
275#217—62no—
276#217#6712yes—
277#216C2×Dic314yescomplemented
278#215C2×Dic314yescomplemented
279#214C2×Dic314yescomplemented
280#213C2×Dic314yescomplemented
281(C2×D3)⋊C4—62no—
282C4⋊Dic3—21no—
283C4⋊Dic3—22no—
284C4⋊Dic3—32no—
285C4⋊Dic3—32no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3—61no—
289C4⋊Dic3—62no—
290C4⋊Dic3—121no—
291C4⋊Dic3#6711yescharacteristic
292C4⋊Dic3#6711yescharacteristic
293C4⋊Dic3C22×D312yes—
294Dic3⋊C4—62no—
295C4×Dic3—22no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C4×Dic3C22×D312yes—
299#208—62no—
300#208—62no—
301#208—122no—
302C2×C3⋊C8—32no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—62no—
305C2×C3⋊C8C2×Dic314yescomplemented
306C2×C3⋊C8C22×D311yescharacteristic
307C2×C3⋊C8C22×D311yescharacteristic
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—22no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32C4×D412yes—
314C22×C32C22×D411yescharacteristic
315C2×C3×D3—22no—
316C2×C3×D3—41no—
317C2×C3×D3—41no—
318C32×C4—22no—
319C32×C4C4×D412yes—
320C32×C4C23×C411yescharacteristic
321C32×C4C2×#4111yescharacteristic
322C3⋊Dic3—42no—
323C3×Dic3—22no—
324C3×Dic3—22no—
325C3×Dic3—22no—
326C3×Dic3—42no—
327C2×#41—31no—
328C2×#41D3211yescharacteristic
329#135—38no—
330C2×Q16—31no—
331C2×SD16—31no—
332C2×SD16—31no—
333C2×D8—31no—
334C2×M16—91no—
335C22×C8—31no—
336C4×Q8—32no—
337C4×Q8—92no—
338C4×D4—32no—
339C4×D4—62no—
340C4×D4—92no—
341C4×D4—182no—
342#117—31no—
343#117—61no—
344#117—181no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—61no—
347C2×C4⋊C4—91no—
348C2×C4⋊C4—181no—
349#107—92no—
350#107—92no—
351#103—92no—
352#103—92no—
353#102—92no—
354#102—92no—
355#97—92no—
356C4×C8—92no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—41no—
361C23×C3—61no—
362C23×C3D3×D411yescharacteristic
363C23×C3C2×#6711yescharacteristic
364C22×D3—21no—
365C3×Q8—21no—
366C3×Q8—21no—
367C3×Q8—22no—
368C3×Q8—32no—
369C3×Q8—41no—
370C3×Q8—61no—
371C3×Q8C2×C4×D312yes—
372C3×Q8C22×Dic312yes—
373C3×D4—24no—
374C3×D4—24no—
375C3×D4—21no—
376C3×D4—21no—
377C3×D4—22no—
378C3×D4—32no—
379C3×D4—41no—
380C3×D4—44no—
381C3×D4—64no—
382C3×D4—61no—
383C3×D4C2×C4×D312yes—
384C3×D4C22×Dic312yes—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—32no—
394C2×C3×C4—32no—
395C2×C3×C4—44no—
396C2×C3×C4—41no—
397C2×C3×C4—61no—
398C2×C3×C4—64no—
399C2×C3×C4—62no—
400C2×C3×C4—242no—
401C2×C3×C4—241no—
402C2×C3×C4C2×C4×D312yes—
403C2×C3×C4#23512yes—
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4#23712yes—
406C2×C3×C4C22×Dic312yes—
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410#67—24no—
411C2×Dic3—21no—
412C2×Dic3—22no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—82no—
416C2×Dic3—81no—
417C2×Dic3—122no—
418C2×Dic3—242no—
419C2×Dic3—241no—
420C2×Dic3—241no—
421C2×Dic3—242no—
422C2×Dic3C2×#6712yes—
423C2×Dic3C2×#6712yes—
424D12—21no—
425D12C22×Dic312yes—
426C4×D3—24no—
427C4×D3—242no—
428Dic6—21no—
429Dic6C22×Dic312yes—
430C3×C8—32no—
431C3×C8—32no—
432C3⋊C8—62no—
433C3⋊C8—62no—
434C3⋊C8—122no—
435C3⋊C8C22×Dic312yes—
436C3⋊C8C22×Dic312yes—
437C2×C32—22no—
438C2×C32—42no—
439C2×C32C2×C4×D411yescharacteristic
440C2×C32#57611yescharacteristic
441C2×C32#57811yescharacteristic
442C3×D3—42no—
443#41—22no—
444#41—34no—
445#41—62no—
446#41D3×Dic314yescomplemented
447C2×Q8—31no—
448C2×Q8C2×D3211yescharacteristic
449C2×D4—21no—
450C2×D4—31no—
451C2×D4—61no—
452C2×D4C2×D3211yescharacteristic
453C22×C4—21no—
454C22×C4—62no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—182no—
458C22×C4—181no—
459C22×C4C2×D3211yescharacteristic
460Q16—34no—
461SD16—34no—
462SD16—34no—
463D8—34no—
464M16—182no—
465C2×C8—31no—
466C2×C8—31no—
467C2×C8—34no—
468C2×C8—92no—
469C4⋊C4—31no—
470C4⋊C4—31no—
471C4⋊C4—32no—
472C4⋊C4—62no—
473C4⋊C4—61no—
474C4⋊C4—92no—
475C4⋊C4—182no—
476C4⋊C4—181no—
477C22⋊C4—32no—
478C22⋊C4—62no—
479C22⋊C4—182no—
480C42—32no—
481C42—62no—
482C42—182no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—21no—
490C22×C3—22no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—42no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—62no—
499C22×C3—81no—
500C22×C3—81no—
501C22×C3—121no—
502C22×C3—121no—
503C22×C3C4×#6712yes—
504C22×C3D4×Dic312yes—
505C22×C3C2×D3×D411yescharacteristic
506C22×C3C22×#6711yescharacteristic
507C2×D3—22no—
508C2×D3—41no—
509C2×D3—41no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—42no—
516C3×C4—62no—
517C3×C4—62no—
518C3×C4—62no—
519C3×C4—122no—
520C3×C4C4×#6712yes—
521C3×C4D4×Dic312yes—
522C3×C4C22×C4×D311yescharacteristic
523C3×C4C2×#23511yescharacteristic
524C3×C4C2×#23711yescharacteristic
525C3×C4C23×Dic311yescharacteristic
526Dic3—22no—
527Dic3—22no—
528Dic3—22no—
529Dic3—42no—
530Dic3—122no—
531Dic3—122no—
532Dic3—242no—
533C32#295111yescharacteristic, complemented, Sylow
534C23—21no—
535C23—61no—
536C23D3×#6711yescharacteristic
537Q8—21no—
538Q8—32no—
539Q8—61no—
540Q8C2×D3×Dic312yes—
541D4—24no—
542D4—21no—
543D4—32no—
544D4—64no—
545D4—61no—
546D4C2×D3×Dic312yes—
547C2×C4—21no—
548C2×C4—24no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—61no—
552C2×C4—64no—
553C2×C4—62no—
554C2×C4—182no—
555C2×C4—242no—
556C2×C4—241no—
557C2×C4—722no—
558C2×C4—721no—
559C2×C4C2×D3×Dic312yes—
560C2×C4#380412yes—
561C2×C4D3×#6711yescharacteristic
562C2×C4C22×D3211yescharacteristic
563C8—32no—
564C8—32no—
565C8—182no—
566C2×C3—22no—
567C2×C3—22no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—42no—
572C2×C3—42no—
573C2×C3—42no—
574C2×C3—82no—
575C2×C3—122no—
576C2×C3#576911yescharacteristic
577C2×C3#577111yescharacteristic
578C2×C3C2×C4×#6711yescharacteristic
579C2×C3C2×D4×Dic311yescharacteristic
580C2×C3#583511yescharacteristic
581C2×C3#583811yescharacteristic
582D3—42no—
583C22—21no—
584C22—21no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—62no—
589C22—121no—
590C22—121no—
591C22Dic3×#6712yes—
592C22C2×D3×#6711yescharacteristic
593C4—22no—
594C4—62no—
595C4—62no—
596C4—62no—
597C4—122no—
598C4—362no—
599C4Dic3×#6712yes—
600C4C22×D3×Dic311yescharacteristic
601C4C2×#380411yescharacteristic
602C3—21no—
603C3#8255711yescharacteristic, complemented
604C3#8389811yescharacteristic, complemented
605C2—22no—
606C2—42no—
607C2—122no—
608C2#1059545611yescharacteristic
609C2#1059546711yescharacteristic
610C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#950C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5827C2semidirect
3. #10594992C2semidirect
4. #10592931C2semidirect
5. Dic3×#216C2semidirect
6. #10591566C2semidirect
7. #10591440C2semidirect
8. Dic3×#213C2semidirect
9. C2×#63575C2semidirect
10. #10591087C2semidirect
11. #10591055C2semidirect
18. C3×#950C4semidirect
47. #5827D3semidirect
68. C32×#41C2×C4semidirect
79. C3×#235C2×C4semidirect
90. C3×#216C2×C4semidirect
91. C3×#215C2×C4semidirect
92. C3×#214C2×C4semidirect
93. C3×#213C2×C4semidirect
101. C2×C3×C3⋊C8C2×C4semidirect
126. #950Dic3semidirect
222. C3×#41C4×D3semidirect
223. C3×#41C2×Dic3semidirect
253. #235C2×Dic3semidirect
277. #216C2×Dic3semidirect
278. #215C2×Dic3semidirect
279. #214C2×Dic3semidirect
280. #213C2×Dic3semidirect
305. C2×C3⋊C8C2×Dic3semidirect
446. #41D3×Dic3semidirect
533. C32#2951semidirect
603. C3#82557semidirect
604. C3#83898semidirect

Maximal subgroups

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

subgroupindex
C3×#58272
C2×C3×#9502
#105949922
#105929312
Dic3×#2162
#105915662
#105914402
Dic3×#2132
C2×#635752
#105910872
#105910552
#838983
#825573