Finite Group Databasebeta

← #11878724

Subgroups — #11878724

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic
2C2×#63866C211yesmaximal, characteristic, complemented
3#10592739C211yesmaximal, characteristic, complemented
4C3×#5040C211yesmaximal, characteristic, complemented
5#10591490C212yesmaximal, complemented
6#10591489C212yesmaximal, complemented
7#10591181C211yesmaximal, characteristic, complemented
8#10591171C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590560C212yesmaximal, complemented
11#10590559C212yesmaximal, complemented
12#83317—31nomaximal
13#80034—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#237—21no—
16C22×C3×Dic6C2211yescharacteristic
17C32×#121C2211yescharacteristic
18C2×#3754C2212yes—
19C3×#940C2211yescharacteristic
20C3×#939—21no—
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2212yes—
23C3×#930C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×#893C2211yescharacteristic
26C3×#888C2211yescharacteristic
27C3×#885—21no—
28C3×#67⋊C4—21no—
29C2×Dic3⋊Dic3—21no—
30C2×Dic3⋊Dic3—21no—
31#63866—21no—
32#63866—21no—
33#63866C2212yes—
34#63866C2212yes—
35C2×#3716C2212yes—
36C2×#3715C2212yes—
37#63657C2211yescharacteristic
38#63637C2212yes—
39C3×#830C2211yescharacteristic
40C3×#810C2212yes—
41Dic3⋊(C3⋊C8)C2212yes—
42#63567C2212yes—
43#63565C2212yes—
44Dic3×C3⋊C8C2212yes—
45C3×#532—31no—
46C2×#944—31no—
47#5596D311yescharacteristic
48C2×#869—31no—
49C3×#448—31no—
50#5227—31no—
51#5175—32no—
52#5162—32no—
53#5093—32no—
54#5076—32no—
55#5040—31no—
56#5040—31no—
57#5040—31no—
58#5040—31no—
59#5040—61no—
60#5040D311yescharacteristic, complemented
61#5019—32no—
62#5019—32no—
63#4925—31no—
64#4818—32no—
65#4792—32no—
66#4738—31no—
67#4718—31no—
68C2×C32×D4—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C2×#634—21no—
73C2×#634—42no—
74C2×#634C2312yes—
75C2×C3×#67—21no—
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3D411yescharacteristic
81C22×C3×Dic3D411yescharacteristic
82C3×#237—44no—
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6—21no—
87C2×C3×Dic6—42no—
88C2×C3×Dic6C2312yes—
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91#3754—42no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×#214—42no—
95C3×(C2×D3)⋊C4—21no—
96C3×(C2×D3)⋊C4—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×Dic3⋊C4—21no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—22no—
105Dic3⋊Dic3—22no—
106Dic3⋊Dic3—22no—
107Dic3⋊Dic3—22no—
108#3716—42no—
109#3715—42no—
110#3206—91noSylow
111C2×C3×#41—61no—
112C22×C3×Q8—31no—
113C2×#237—21no—
114C22×Dic6—31no—
115C22×Dic6—31no—
116C22×Dic6—61no—
117C22×Dic6C2×D311yescharacteristic
118C2×C3×SD16—32no—
119C3×C4⋊Q8—31no—
120C3×#127—31no—
121C3×#124—61no—
122C3×#121—21no—
123C3×#121—31no—
124C3×#121—61no—
125C3×#121C2×D311yescharacteristic
126C3×#121C2×D311yescharacteristic
127C3×C4×D4—31no—
128C3×C4×D4—31no—
129C3×C4×D4—61no—
130C2×C3×C42—31no—
131#944—32no—
132#944—32no—
133#944—61no—
134#944—61no—
135C2×#215—32no—
136#940C2×D311yescharacteristic
137#939—21no—
138D4×Dic3C2×D311yescharacteristic
139C2×#214—32no—
140C2×#214—32no—
141C2×#214—32no—
142C2×#214—32no—
143C2×#214—62no—
144C2×#214C2×D312yes—
145#930C2×D311yescharacteristic
146C2×C4⋊Dic3—61no—
147C2×C4⋊Dic3—61no—
148C2×Dic3⋊C4—61no—
149C2×Dic3⋊C4—61no—
150C2×C4×Dic3C2×D311yescharacteristic
151C2×#204—32no—
152#893C2×D311yescharacteristic
153#888C2×D311yescharacteristic
154#885—21no—
155#67⋊C4—21no—
156#869—32no—
157#869—32no—
158#869—61no—
159#869—61no—
160C3×#103—32no—
161C3×C22⋊C8—31no—
162#835—32no—
163#830—31no—
164#830—31no—
165#830—61no—
166#830C2×D311yescharacteristic
167#816—32no—
168Dic3⋊C8—32no—
169C8×Dic3—32no—
170#810—32no—
171#810—32no—
172#810—32no—
173#810—32no—
174#810—62no—
175#810C2×D312yes—
176C4⋊(C3⋊C8)—32no—
177C4×C3⋊C8—32no—
178C23×C32—21no—
179C23×C32C2×D411yescharacteristic
180C22×C3×D3—21no—
181C32×D4—22no—
182C32×D4—42no—
183C2×C32×C4—22no—
184C2×C32×C4—21no—
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—42no—
189#634—22no—
190#634—22no—
191#634—42no—
192C3×#67—42no—
193C3×#67—42no—
194C3×#67—42no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—42no—
199C2×C3×Dic3—42no—
200C2×C3×Dic3SD1614yescomplemented
201C2×C3×Dic3C2×D411yescharacteristic
202C2×C3×Dic3C2×D411yescharacteristic
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C3×D12—22no—
206C3×C4×D3—42no—
207C3×Dic6—22no—
208C3×Dic6—22no—
209C3×Dic6—42no—
210C3×Dic6—42no—
211C3⋊(C3⋊C8)—22no—
212C3×C3⋊C8—22no—
213#532—31no—
214C2×C4⋊Q8—91no—
215#492—92no—
216#487—92no—
217#461—92no—
218#461—92no—
219#448—31no—
220#448—91no—
221#448—91no—
222#448—91no—
223#431—91no—
224C3×#41—124no—
225C2×C3×Q8—32no—
226C2×C3×Q8—61no—
227C2×C3×Q8—61no—
228C2×C3×Q8—122no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—31no—
233C2×C3×D4—41no—
234C2×C3×D4—61no—
235C2×C3×D4—61no—
236C2×C3×D4—61no—
237C2×C3×D4C22×D311yescharacteristic
238C2×C3×D4C22×D311yescharacteristic
239C22×C3×C4—21no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—61no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C2×#67—21no—
248C2×#67—21no—
249C2×#67—21no—
250C22×Dic3—21no—
251C22×Dic3—21no—
252C22×Dic3—61no—
253C22×Dic3—61no—
254C22×Dic3—121no—
255C22×Dic3#6711yescharacteristic
256C22×Dic3#6711yescharacteristic
257#237—44no—
258C2×D12C22×D311yescharacteristic
259C2×C4×D3—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—32no—
263C2×Dic6—32no—
264C2×Dic6—42no—
265C2×Dic6—62no—
266C2×Dic6—61no—
267C2×Dic6—61no—
268C2×Dic6—121no—
269C2×Dic6—122no—
270C2×Dic6—122no—
271C2×Dic6—124no—
272C2×Dic6C22×D312yes—
273C3×SD16—122no—
274C2×C3×C8—32no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—31no—
277C3×C4⋊C4—61no—
278C3×C4⋊C4C22×D311yescharacteristic
279C3×C4⋊C4C22×D311yescharacteristic
280C3×C22⋊C4—21no—
281C3×C22⋊C4—21no—
282C3×C22⋊C4—41no—
283C3×C22⋊C4—61no—
284C3×C22⋊C4—61no—
285C3×C22⋊C4—61no—
286C3×C42—31no—
287C3×C42—31no—
288C3×C42—31no—
289C3×C42—31no—
290#217—21no—
291#215—122no—
292#214—42no—
293#214—122no—
294#214—122no—
295#214—122no—
296#214—122no—
297#214—124no—
298(C2×D3)⋊C4—21no—
299(C2×D3)⋊C4—21no—
300C4⋊Dic3—62no—
301C4⋊Dic3—62no—
302C4⋊Dic3—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3C22×D311yescharacteristic
305Dic3⋊C4—21no—
306Dic3⋊C4—62no—
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309Dic3⋊C4—62no—
310C4×Dic3#6711yescharacteristic
311C4×Dic3#6711yescharacteristic
312C4×Dic3C22×D311yescharacteristic
313C4×Dic3C22×D311yescharacteristic
314C2×C3⋊C8—32no—
315C2×C3⋊C8—32no—
316C2×C3⋊C8—62no—
317C2×C3⋊C8C22×D312yes—
318#204—122no—
319C22×C32—21no—
320C22×C32—21no—
321C22×C32—41no—
322C22×C32—41no—
323C22×C32—41no—
324C22×C32C2×SD1612yes—
325C22×C32C22×D411yescharacteristic
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C2×C3×D3—41no—
329C32×C4—21no—
330C32×C4—41no—
331C32×C4H(5,𝔽2)12yes—
332C3⋊Dic3—42no—
333C3×Dic3—21no—
334C3×Dic3—42no—
335C3×Dic3—41no—
336C3×Dic3C2×SD1612yes—
337C3×Dic3C2×SD1612yes—
338C3×Dic3#13712yes—
339C2×#41—61no—
340C22×Q8—31no—
341C22×Q8—91no—
342C2×SD16—32no—
343C2×SD16—92no—
344C2×SD16—92no—
345C2×SD16—92no—
346C4⋊Q8—31no—
347C4⋊Q8—92no—
348C4⋊Q8—92no—
349C4⋊Q8—181no—
350C4⋊Q8—181no—
351#127—31no—
352#124—61no—
353#121—31no—
354#121—61no—
355#121D3211yescharacteristic
356C4×D4—31no—
357C4×D4—31no—
358C4×D4—61no—
359C2×C4⋊C4—181no—
360C2×C4⋊C4—181no—
361C2×C42—31no—
362C4⋊C8—92no—
363#103—32no—
364#103—92no—
365#103—92no—
366#103—92no—
367C22⋊C8—31no—
368C22⋊C8—91no—
369C4×C8—92no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—41no—
374C23×C3—61no—
375C23×C3D3×D411yescharacteristic
376C23×C3C2×#6711yescharacteristic
377C22×D3—21no—
378C3×Q8—62no—
379C3×Q8—62no—
380C3×Q8—122no—
381C3×Q8—122no—
382C3×D4—22no—
383C3×D4—22no—
384C3×D4—42no—
385C3×D4—42no—
386C3×D4—42no—
387C3×D4—62no—
388C3×D4—82no—
389C3×D4—122no—
390C3×D4—122no—
391C3×D4—122no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—34no—
399C2×C3×C4—31no—
400C2×C3×C4—31no—
401C2×C3×C4—31no—
402C2×C3×C4—31no—
403C2×C3×C4—42no—
404C2×C3×C4—41no—
405C2×C3×C4—62no—
406C2×C3×C4—61no—
407C2×C3×C4—62no—
408C2×C3×C4—122no—
409C2×C3×C4—122no—
410C2×C3×C4—122no—
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—42no—
416#67—42no—
417#67—42no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—21no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3—124no—
429C2×Dic3#21414yescomplemented
430C2×Dic3C2×#6711yescharacteristic
431C2×Dic3C2×#6711yescharacteristic
432C2×Dic3C2×#6711yescharacteristic
433C2×Dic3C2×#6711yescharacteristic
434D12—22no—
435C4×D3—42no—
436Dic6—22no—
437Dic6—22no—
438Dic6—42no—
439Dic6—42no—
440Dic6—64no—
441Dic6—62no—
442Dic6—62no—
443Dic6—62no—
444Dic6—62no—
445Dic6—122no—
446Dic6—122no—
447Dic6—122no—
448Dic6—124no—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—62no—
452C3⋊C8—62no—
453C3⋊C8—122no—
454C2×C32—22no—
455C2×C32—81no—
456C2×C32#53511yescharacteristic
457C2×C32C22×SD1611yescharacteristic
458C2×C32C2×#13711yescharacteristic
459C3×D3—81no—
460#41—124no—
461C2×Q8—32no—
462C2×Q8—61no—
463C2×Q8—61no—
464C2×Q8—92no—
465C2×Q8—122no—
466C2×Q8—181no—
467C2×Q8—362no—
468C2×D4—21no—
469C2×D4—31no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—61no—
473C2×D4C2×D3211yescharacteristic
474C22×C4—31no—
475C22×C4—31no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—181no—
480C22×C4C2×D3211yescharacteristic
481SD16—122no—
482SD16—362no—
483SD16—362no—
484SD16—362no—
485C2×C8—32no—
486C2×C8—92no—
487C4⋊C4—31no—
488C4⋊C4—61no—
489C4⋊C4—182no—
490C4⋊C4—182no—
491C4⋊C4—182no—
492C4⋊C4—182no—
493C4⋊C4C2×D3211yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—61no—
496C22⋊C4—61no—
497C22⋊C4—61no—
498C42—31no—
499C42—31no—
500C42—31no—
501C42—31no—
502C22×C3—21no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—22no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—81no—
517C22×C3—81no—
518C22×C3—81no—
519C22×C3—121no—
520C22×C3—121no—
521C22×C3—121no—
522C22×C3D3×SD1612yes—
523C22×C3C2×#21412yes—
524C22×C3C2×D3×D411yescharacteristic
525C22×C3C22×#6711yescharacteristic
526C2×D3—41no—
527C2×D3—41no—
528C2×D3—41no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—32no—
533C3×C4—32no—
534C3×C4—32no—
535C3×C4—41no—
536C3×C4—41no—
537C3×C4—41no—
538C3×C4—61no—
539C3×C4—81no—
540C3×C4—121no—
541C3×C4—122no—
542C3×C4#100412yes—
543C3×C4#100912yes—
544Dic3—21no—
545Dic3—41no—
546Dic3—42no—
547Dic3—124no—
548Dic3—122no—
549Dic3—122no—
550Dic3C2×#21412yes—
551Dic3C2×#21412yes—
552Dic3#95112yes—
553C32#320611yescharacteristic, complemented, Sylow
554C23—21no—
555C23—61no—
556C23D3×#6711yescharacteristic
557Q8—62no—
558Q8—62no—
559Q8—122no—
560Q8—122no—
561Q8—182no—
562Q8—182no—
563Q8—362no—
564D4—22no—
565D4—42no—
566D4—62no—
567D4—122no—
568D4—122no—
569D4—122no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—31no—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—34no—
576C2×C4—31no—
577C2×C4—62no—
578C2×C4—61no—
579C2×C4—62no—
580C2×C4—122no—
581C2×C4—122no—
582C2×C4—122no—
583C2×C4—182no—
584C2×C4—362no—
585C2×C4D3×#6711yescharacteristic
586C2×C4C22×D3211yescharacteristic
587C8—62no—
588C8—182no—
589C2×C3—22no—
590C2×C3—22no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—42no—
595C2×C3—81no—
596C2×C3—81no—
597C2×C3—161no—
598C2×C3—241no—
599C2×C3#559211yescharacteristic
600C2×C3C2×D3×SD1611yescharacteristic
601C2×C3D3×#13711yescharacteristic
602C2×C3C22×#21411yescharacteristic
603C2×C3C2×#95111yescharacteristic
604C2×C3#583011yescharacteristic
605D3—81no—
606C22—21no—
607C22—21no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—121no—
612C22—121no—
613C22—121no—
614C22D3×#21412yes—
615C22C2×D3×#6711yescharacteristic
616C4—21no—
617C4—32no—
618C4—32no—
619C4—32no—
620C4—41no—
621C4—61no—
622C4—121no—
623C4—122no—
624C4—362no—
625C4#6431412yes—
626C3—21no—
627C3#8003411yescharacteristic, complemented
628C3#8331711yescharacteristic, complemented
629C2—22no—
630C2—81no—
631C2—241no—
632C2C2×D3×#21411yescharacteristic
633C2#1059523811yescharacteristic
634C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5596C2
hypercenter#121D32
hypocenterC32#3206
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×#63866C2semidirect
3. #10592739C2semidirect
4. C3×#5040C2semidirect
5. #10591490C2semidirect
6. #10591489C2semidirect
7. #10591181C2semidirect
8. #10591171C2semidirect
9. #10591053C2semidirect
10. #10590560C2semidirect
11. #10590559C2semidirect
60. #5040D3semidirect
200. C2×C3×Dic3SD16semidirect
429. C2×Dic3#214semidirect
553. C32#3206semidirect
627. C3#80034semidirect
628. C3#83317semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
C2×#638662
#105927392
C3×#50402
#105914902
#105914892
#105911812
#105911712
#105910532
#105905602
#105905592
#833173
#800343