Finite Group Databasebeta

← #11819073

Subgroups — #11819073

Order 1152.

1145 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic, complemented
3C4×#3757C211yesmaximal, characteristic
4C3×#5212C211yesmaximal, characteristic
5#10591703C212yesmaximal
6#10591692C212yesmaximal
7#10591274C211yesmaximal, characteristic, complemented
8#10591235C212yesmaximal, complemented
9#10591221C211yesmaximal, characteristic, complemented
10#10591221C211yesmaximal, characteristic, complemented
11#10591199C212yesmaximal, complemented
12#82773—31nomaximal
13#73916—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#627C2212yes—
17C2×#3757C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×#217C2212yes—
22C2×C3×#217C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C3×#924—24no—
27C2×C3×Dic3⋊C4C2212yes—
28C2×#3724C2212yes—
29C2×Dic32C2212yes—
30#63919—24no—
31#63658C2211yescharacteristic
32#63658C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C22⋊Q8—31no—
40C2×#924D311yescharacteristic
41C2×#888—31no—
42C2×#888—31no—
43C3×#380—31no—
44#5229—31no—
45#5229—31no—
46#5212D311yescharacteristic
47C4×#217—31no—
48C4×#217—31no—
49C4×#217—61no—
50#4985—32no—
51Dic3×C4⋊C4—31no—
52Dic3×C4⋊C4—31no—
53#4973—31no—
54#4973—31no—
55#4973—32no—
56#4947—32no—
57#4947—32no—
58#4945—32no—
59#4944—32no—
60#4658—32no—
61#4646—32no—
62C24×C32C2311yescharacteristic
63C22×C32×C4—22no—
64C22×C32×C4—22no—
65C22×C32×C4—22no—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×#627—24no—
80C2×#627—24no—
81C2×#627—42no—
82#3757—22no—
83#3757Q814yescomplemented
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3—22no—
86C3×#217—24no—
87C3×#217—42no—
88C3×C4⋊Dic3—22no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D414yes—
91C3×Dic3⋊C4—24no—
92#3724—24no—
93Dic32—42no—
94#2492—91noSylow
95C22×C3×Q8—31no—
96C23×C3×C4—21no—
97C23×C3×C4C2×D311yescharacteristic
98C23×C3×C4C2×D311yescharacteristic
99C22×Dic6—32no—
100C22×Dic6—32no—
101C22×Dic6C2×D311yescharacteristic
102C3×C22⋊Q8—64no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C22⋊C4—32no—
108C2×C3×C22⋊C4—32no—
109C2×#217—31no—
110C2×#217—31no—
111C2×#217—31no—
112C2×#217—31no—
113C2×#217—61no—
114C2×#217—61no—
115C2×#217C2×D312yes—
116C2×#217C2×D312yes—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×C4⋊Dic3C2×D311yescharacteristic
120#924—24no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4C2×D312yes—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—61no—
131C2×C4×Dic3—61no—
132#888—64no—
133#888—64no—
134C3×#95—32no—
135C3⋊#95—31no—
136C3⋊#95—31no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—61no—
150C3⋊#95—61no—
151C3⋊#95C2×D312yes—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32—21no—
157C23×C32—21no—
158C23×C32C2×Q812yes—
159C23×C32C2411yescharacteristic
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—44no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4#4112yes—
166C2×C32×C4#4112yes—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3C2×Q812yes—
177C2×C3⋊Dic3C2×Q812yes—
178C2×C3⋊Dic3#4112yes—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D414yes—
191C3×Dic6—44no—
192#627—48no—
193C2×C4⋊Q8—91no—
194C2×C22⋊Q8—31no—
195#400—92no—
196#393—92no—
197#391—92no—
198#391—91no—
199#391—91no—
200#388—92no—
201#380—31no—
202C4×C4⋊C4—91no—
203C4×C22⋊C4—91no—
204C24×C3—21no—
205C24×C3C22×D311yescharacteristic
206C24×C3C22×D311yescharacteristic
207C2×C3×Q8—62no—
208C2×C3×Q8—62no—
209C2×C3×Q8—62no—
210C22×C3×C4—24no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—42no—
224C22×C3×C4—42no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—61no—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D312yes—
245C2×Dic6—22no—
246C2×Dic6—22no—
247C2×Dic6—22no—
248C2×Dic6—64no—
249C2×Dic6—64no—
250C2×Dic6—64no—
251C2×Dic6—64no—
252C2×Dic6—122no—
253C2×Dic6—122no—
254C3×C4⋊C4—34no—
255C3×C4⋊C4—64no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—62no—
258C3×C22⋊C4—64no—
259C3×C22⋊C4—122no—
260#217—24no—
261#217—34no—
262#217—34no—
263#217—42no—
264#217—64no—
265#217—62no—
266#217—62no—
267#217—64no—
268C4⋊Dic3—22no—
269C4⋊Dic3—22no—
270C4⋊Dic3#6714yes—
271Dic3⋊C4—24no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3—122no—
279C4×Dic3—122no—
280C4×Dic3—122no—
281C4×Dic3—122no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—22no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32—41no—
289C22×C32C22×D411yescharacteristic
290C22×C32C22×Q811yescharacteristic
291C22×C32C2×#4111yescharacteristic
292C22×C32C2×#4111yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C22×C32H(5,𝔽2)11yescharacteristic
295C22×C322−1+411yescharacteristic
296C32×C4—41no—
297C32×C4#12414yes—
298C3⋊Dic3—22no—
299C3⋊Dic3—22no—
300C3⋊Dic3—22no—
301C3⋊Dic3—41no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C3×Dic3—42no—
305C3×Dic3—42no—
306C22×Q8—31no—
307C22×Q8—92no—
308C23×C4D3211yescharacteristic
309C4⋊Q8—184no—
310C22⋊Q8—64no—
311C2×C4⋊C4—31no—
312C2×C4⋊C4—32no—
313C2×C4⋊C4—31no—
314C2×C4⋊C4—31no—
315C2×C4⋊C4—92no—
316C2×C22⋊C4—32no—
317C2×C22⋊C4—32no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C42—91no—
321C2×C42—91no—
322C2×C42—92no—
323#95—32no—
324#95—92no—
325#95—92no—
326#95—92no—
327#95—92no—
328#95—92no—
329#95—91no—
330#95—91no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—22no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3D3×Q812yes—
352C23×C3D3×Q812yes—
353C23×C3C23×D311yescharacteristic
354C23×C3C23×D311yescharacteristic
355C3×Q8—124no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—34no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—48no—
370C2×C3×C4—44no—
371C2×C3×C4—44no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4#23512yes—
384C2×C3×C4D3×D412yes—
385C2×C3×C4#23712yes—
386C2×C3×C4#23712yes—
387C2×C3×C4#23712yes—
388C2×C3×C4C2×#6712yes—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—62no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—121no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3—121no—
434C2×Dic3—121no—
435C2×Dic3—121no—
436C2×Dic3C2×#6714yes—
437Dic6—44no—
438Dic6—128no—
439Dic6—128no—
440C2×C32—42no—
441C2×C32C2×#12411yescharacteristic
442C2×C32#53311yescharacteristic
443C2×C32#54211yescharacteristic
444C2×C32#54611yescharacteristic
445C2×C32D4×Q811yescharacteristic
446C2×C32#55411yescharacteristic
447C2×C32#55611yescharacteristic
448C24C2×D3211yescharacteristic
449C2×Q8—62no—
450C2×Q8—62no—
451C2×Q8—62no—
452C2×Q8—184no—
453C2×Q8—184no—
454C2×Q8—362no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4C2×D3211yescharacteristic
467C22×C4C2×D3211yescharacteristic
468C4⋊C4—34no—
469C4⋊C4—64no—
470C4⋊C4—62no—
471C4⋊C4—62no—
472C4⋊C4—184no—
473C22⋊C4—64no—
474C22⋊C4—94no—
475C22⋊C4—122no—
476C22⋊C4—182no—
477C42—182no—
478C42—182no—
479C42—362no—
480C22×C3—24no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3C2×#23511yescharacteristic
509C22×C3C2×D3×D411yescharacteristic
510C22×C3C2×#23711yescharacteristic
511C22×C3C2×#23711yescharacteristic
512C22×C3C2×#23711yescharacteristic
513C22×C3#100411yescharacteristic
514C22×C3C2×D3×Q811yescharacteristic
515C22×C3C2×D3×Q811yescharacteristic
516C22×C3#100711yescharacteristic
517C22×C3D3×#4111yescharacteristic
518C22×C3D3×#4111yescharacteristic
519C22×C3#100911yescharacteristic
520C22×C3#101011yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C3×C4—24no—
523C3×C4—42no—
524C3×C4—41no—
525C3×C4—41no—
526C3×C4—64no—
527C3×C4—122no—
528C3×C4—122no—
529C3×C4—122no—
530C3×C4#88514yes—
531C3×C4#93614yes—
532Dic3—24no—
533Dic3—42no—
534Dic3—42no—
535Dic3—42no—
536Dic3—62no—
537Dic3—62no—
538Dic3—62no—
539Dic3—62no—
540Dic3—62no—
541Dic3—62no—
542Dic3—122no—
543Dic3—122no—
544Dic3—122no—
545Dic3—122no—
546Dic3—121no—
547Dic3—121no—
548C32#249211yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23#379712yes—
556C23C22×D3211yescharacteristic
557Q8—124no—
558Q8—368no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—34no—
563C2×C4—44no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—92no—
576C2×C4—92no—
577C2×C4—92no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4#380412yes—
588C2×C4#380512yes—
589C2×C4D3×#6712yes—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—44no—
598C2×C3—42no—
599C2×C3—42no—
600C2×C3C2×#88511yescharacteristic
601C2×C3#551111yescharacteristic
602C2×C3#553311yescharacteristic
603C2×C3#560311yescharacteristic
604C2×C3#561211yescharacteristic
605C2×C3#562211yescharacteristic
606C2×C3#562211yescharacteristic
607C2×C3#563211yescharacteristic
608C2×C3#563511yescharacteristic
609C2×C3#564111yescharacteristic
610C2×C3#564311yescharacteristic
611C2×C3C2×#93611yescharacteristic
612C2×C3Q8×#6711yescharacteristic
613C2×C3#582911yescharacteristic
614C22—22no—
615C22—22no—
616C22—22no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22#6429711yescharacteristic
622C22C2×#379711yescharacteristic
623C22#6430611yescharacteristic
624C22#6430711yescharacteristic
625C22C2×#380411yescharacteristic
626C22C2×#380511yescharacteristic
627C22C2×D3×#6711yescharacteristic
628C4—41no—
629C4—64no—
630C4—122no—
631C4—122no—
632C4—122no—
633C4—182no—
634C4—182no—
635C4—182no—
636C4—361no—
637C4#6395914yes—
638C3—21no—
639C3#7391611yescharacteristic, complemented
640C3#8277311yescharacteristic, complemented
641C2—42no—
642C2#1059480311yescharacteristic
643C2#1059480911yescharacteristic
644C2#1059481011yescharacteristic
645C2#1059498411yescharacteristic
646C2#1059499111yescharacteristic
647C2#1059507011yescharacteristic
648C2C2×#6395911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#63919C2semidirect
7. #10591274C2semidirect
8. #10591235C2semidirect
9. #10591221C2semidirect
10. #10591221C2semidirect
11. #10591199C2semidirect
83. #3757Q8semidirect
548. C32#2492semidirect
639. C3#73916semidirect
640. C3#82773semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
C2×#639192
C4×#37572
C3×#52122
#105917032
#105916922
#105912742
#105912352
#105912212
#105911992
#827733
#739163