Finite Group Databasebeta

← #11819072

Subgroups — #11819072

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 637 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2C2×#63918C211yesmaximal, characteristic, complemented
3#10592911C211yesmaximal, characteristic
4C3×C4×#217C211yesmaximal, characteristic
5#10591702C212yesmaximal
6#10591692C212yesmaximal
7Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
8#10591235C212yesmaximal, complemented
9#10591220C211yesmaximal, characteristic, complemented
10#10591220C211yesmaximal, characteristic, complemented
11#10591196C212yesmaximal, complemented
12#82773—31nomaximal
13#73508—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#627C2212yes—
17C2×#3757C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#217C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×#924—24no—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30#63918—24no—
31#63658C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C22⋊Q8—31no—
40C2×#924D311yescharacteristic
41C2×#888—31no—
42C2×#869—31no—
43C3×C4×C22⋊C4—31no—
44#5229—31no—
45#5229—31no—
46#5212—31no—
47#5212—31no—
48#5212—61no—
49C4×#217D311yescharacteristic
50#4985—32no—
51Dic3×C4⋊C4—31no—
52#4973—32no—
53#4951—32no—
54#4947—32no—
55#4947—32no—
56#4945—32no—
57C4×C4⋊Dic3—31no—
58#4929—31no—
59#4929—31no—
60#4660—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⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×#627—24no—
80C2×#627—24no—
81C2×#627—42no—
82#3757—42no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)—22no—
85C3×#217—24no—
86C3×#217—22no—
87C3×#217Q814yescomplemented
88C3×C4⋊Dic3D414yes—
89C3×Dic3⋊C4—24no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3—22no—
92Dic3⋊Dic3—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×C22⋊C4—31no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C42—31no—
109C2×C3×C42—31no—
110C2×#217—32no—
111C2×#217—32no—
112C2×#217—62no—
113C2×#217C2×D311yescharacteristic
114C2×#217C2×D312yes—
115C2×#217C2×D311yescharacteristic
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3—61no—
123C2×C4⋊Dic3C2×D311yescharacteristic
124#924—24no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4C2×D312yes—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3C2×D311yescharacteristic
130C2×C4×Dic3C2×D311yescharacteristic
131#888—64no—
132#869—64no—
133C3×#95—31no—
134C3×#95—31no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
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—62no—
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D311yescharacteristic
150C23×C32—21no—
151C23×C32—21no—
152C23×C32—21no—
153C23×C32—21no—
154C23×C32—21no—
155C23×C32—21no—
156C23×C32C2×Q812yes—
157C23×C32C2411yescharacteristic
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—44no—
162C2×C32×C4C2×D412yes—
163C2×C32×C4#4112yes—
164C2×C32×C4#4112yes—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D414yes—
186C2×C3×Dic3C2×Q812yes—
187C2×C3×Dic3C2×Q812yes—
188C2×C3×Dic3#4112yes—
189C3×Dic6—44no—
190#627—48no—
191C2×C4⋊Q8—91no—
192C2×C22⋊Q8—31no—
193#400—92no—
194#393—92no—
195#391—92no—
196#391—91no—
197#391—91no—
198#388—92no—
199#380—91no—
200C4×C4⋊C4—91no—
201C4×C22⋊C4—31no—
202C24×C3—21no—
203C24×C3C22×D311yescharacteristic
204C24×C3C22×D311yescharacteristic
205C2×C3×Q8—62no—
206C2×C3×Q8—62no—
207C2×C3×Q8—62no—
208C22×C3×C4—24no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—32no—
221C22×C3×C4—31no—
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—32no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—62no—
234C22×Dic3—62no—
235C22×Dic3C22×D311yescharacteristic
236C22×Dic3C22×D312yes—
237C22×Dic3C22×D311yescharacteristic
238C22×Dic3C22×D311yescharacteristic
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D312yes—
241C2×Dic6—22no—
242C2×Dic6—22no—
243C2×Dic6—22no—
244C2×Dic6—64no—
245C2×Dic6—64no—
246C2×Dic6—64no—
247C2×Dic6—64no—
248C2×Dic6—122no—
249C2×Dic6—122no—
250C3×C4⋊C4—34no—
251C3×C4⋊C4—64no—
252C3×C22⋊C4—34no—
253C3×C22⋊C4—62no—
254C3×C22⋊C4—64no—
255C3×C42—62no—
256C3×C42—62no—
257#217—22no—
258#217—24no—
259#217—122no—
260#217—122no—
261#217—124no—
262#217Dic614yescomplemented
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3—64no—
268C4⋊Dic3—122no—
269C4⋊Dic3—122no—
270C4⋊Dic3#6714yes—
271Dic3⋊C4—24no—
272Dic3⋊C4—64no—
273C4×Dic3—22no—
274C4×Dic3—22no—
275C4×Dic3—122no—
276C4×Dic3—122no—
277C22×C32—22no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C22×D411yescharacteristic
285C22×C32C22×Q811yescharacteristic
286C22×C32C2×#4111yescharacteristic
287C22×C32C2×#4111yescharacteristic
288C22×C32C2×#4111yescharacteristic
289C22×C32H(5,𝔽2)11yescharacteristic
290C22×C322−1+411yescharacteristic
291C32×C4—41no—
292C32×C4#12414yes—
293C3⋊Dic3—42no—
294C3⋊Dic3—42no—
295C3×Dic3—22no—
296C3×Dic3—24no—
297C3×Dic3—22no—
298C3×Dic3—22no—
299C3×Dic3—42no—
300C3×Dic3—41no—
301C22×Q8—31no—
302C22×Q8—92no—
303C23×C4D3211yescharacteristic
304C4⋊Q8—184no—
305C22⋊Q8—64no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—32no—
313C2×C22⋊C4—31no—
314C2×C22⋊C4—92no—
315C2×C42—31no—
316C2×C42—31no—
317C2×C42—92no—
318#95—31no—
319#95—31no—
320#95—92no—
321#95—92no—
322#95—92no—
323#95—92no—
324#95—92no—
325#95—92no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
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—22no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3C2×Dic612yes—
347C23×C3D3×Q812yes—
348C23×C3C23×D311yescharacteristic
349C23×C3C23×D311yescharacteristic
350C3×Q8—124no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—34no—
362C2×C3×C4—32no—
363C2×C3×C4—32no—
364C2×C3×C4—32no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—48no—
368C2×C3×C4—44no—
369C2×C3×C4—44no—
370C2×C3×C4—62no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4—62no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4#23512yes—
385C2×C3×C4D3×D412yes—
386C2×C3×C4#23712yes—
387C2×C3×C4#23712yes—
388C2×C3×C4#23712yes—
389C2×C3×C4C2×#6712yes—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—22no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3C2×Dic612yes—
423C2×Dic3C2×Dic612yes—
424C2×Dic3#23512yes—
425C2×Dic3C2×#6714yes—
426Dic6—44no—
427Dic6—128no—
428Dic6—128no—
429C2×C32—42no—
430C2×C32C2×#12411yescharacteristic
431C2×C32#53311yescharacteristic
432C2×C32#54211yescharacteristic
433C2×C32#54611yescharacteristic
434C2×C32D4×Q811yescharacteristic
435C2×C32#55411yescharacteristic
436C2×C32#55611yescharacteristic
437C24C2×D3211yescharacteristic
438C2×Q8—62no—
439C2×Q8—62no—
440C2×Q8—62no—
441C2×Q8—184no—
442C2×Q8—184no—
443C2×Q8—362no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—32no—
451C22×C4—31no—
452C22×C4—32no—
453C22×C4—92no—
454C22×C4—92no—
455C22×C4C2×D3211yescharacteristic
456C22×C4C2×D3211yescharacteristic
457C4⋊C4—34no—
458C4⋊C4—64no—
459C4⋊C4—184no—
460C4⋊C4—182no—
461C4⋊C4—182no—
462C22⋊C4—34no—
463C22⋊C4—64no—
464C22⋊C4—62no—
465C22⋊C4—362no—
466C42—62no—
467C42—62no—
468C42—362no—
469C22×C3—24no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3C22×Dic611yescharacteristic
498C22×C3C2×#23511yescharacteristic
499C22×C3C2×#23511yescharacteristic
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C2×#23711yescharacteristic
502C22×C3C2×#23711yescharacteristic
503C22×C3C2×#23711yescharacteristic
504C22×C3C2×D3×Q811yescharacteristic
505C22×C3#100711yescharacteristic
506C22×C3D3×#4111yescharacteristic
507C22×C3#100911yescharacteristic
508C22×C3#100911yescharacteristic
509C22×C3#101011yescharacteristic
510C22×C3C22×#6711yescharacteristic
511C3×C4—24no—
512C3×C4—42no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—62no—
516C3×C4—64no—
517C3×C4—62no—
518C3×C4—62no—
519C3×C4—121no—
520C3×C4—122no—
521C3×C4#88514yes—
522C3×C4#93614yes—
523Dic3—22no—
524Dic3—22no—
525Dic3—22no—
526Dic3—24no—
527Dic3—42no—
528Dic3—41no—
529Dic3—122no—
530Dic3—122no—
531Dic3—122no—
532Dic3—122no—
533Dic3—242no—
534Dic3—242no—
535C32#249211yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23D3×Dic612yes—
543C23C22×D3211yescharacteristic
544Q8—124no—
545Q8—368no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—32no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—34no—
553C2×C4—44no—
554C2×C4—61no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—62no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—182no—
569C2×C4—182no—
570C2×C4—182no—
571C2×C4—182no—
572C2×C4—182no—
573C2×C4—182no—
574C2×C4#380412yes—
575C2×C4#380512yes—
576C2×C4D3×#6712yes—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—44no—
585C2×C3—42no—
586C2×C3—42no—
587C2×C3#547011yescharacteristic
588C2×C3C2×#88511yescharacteristic
589C2×C3#553411yescharacteristic
590C2×C3D4×Dic611yescharacteristic
591C2×C3#554211yescharacteristic
592C2×C3#554311yescharacteristic
593C2×C3#555011yescharacteristic
594C2×C3#562211yescharacteristic
595C2×C3#563511yescharacteristic
596C2×C3#564111yescharacteristic
597C2×C3#564311yescharacteristic
598C2×C3C2×#93611yescharacteristic
599C2×C3Q8×#6711yescharacteristic
600C2×C3#582911yescharacteristic
601C22—22no—
602C22—22no—
603C22—22no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22C2×D3×Dic611yescharacteristic
609C22#6429711yescharacteristic
610C22D3×#23511yescharacteristic
611C22#6430811yescharacteristic
612C22C2×#380411yescharacteristic
613C22C2×#380511yescharacteristic
614C22C2×D3×#6711yescharacteristic
615C4—41no—
616C4—62no—
617C4—62no—
618C4—62no—
619C4—64no—
620C4—121no—
621C4—122no—
622C4—362no—
623C4—362no—
624C4#6395914yes—
625C3—21no—
626C3#7350811yescharacteristic, complemented
627C3#8277311yescharacteristic, complemented
628C2—42no—
629C2#1059480811yescharacteristic
630C2#1059481411yescharacteristic
631C2#1059484111yescharacteristic
632C2Dic6×#6711yescharacteristic
633C2#1059499311yescharacteristic
634C2#1059506711yescharacteristic
635C2C2×#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×#63918C2semidirect
7. Dic3×C4⋊Dic3C2semidirect
8. #10591235C2semidirect
9. #10591220C2semidirect
10. #10591220C2semidirect
11. #10591196C2semidirect
87. C3×#217Q8semidirect
262. #217Dic6semidirect
535. C32#2492semidirect
626. C3#73508semidirect
627. 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×#639182
#105929112
C3×C4×#2172
#105917022
#105916922
Dic3×C4⋊Dic32
#105912352
#105912202
#105911962
#827733
#735083