Finite Group Databasebeta

← #11819081

Subgroups — #11819081

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#869C211yesmaximal, characteristic, complemented
2C2×#63857C211yesmaximal, characteristic
3#10592628C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5#10591343C212yesmaximal, complemented
6#10591313C211yesmaximal, characteristic
7#10591307C212yesmaximal
8#10591304C212yesmaximal
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591261C212yesmaximal, complemented
11#10591213C211yesmaximal, characteristic, complemented
12#83258—31nomaximal
13#73508—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4C2211yescharacteristic
20C2×C3×(C2×D3)⋊C4C2211yescharacteristic
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C3×#869—24no—
26C2×Dic3⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30#63857—24no—
31#63658C2212yes—
32#63658C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4⋊Q8—31no—
40C2×#924—31no—
41C2×#897—31no—
42C2×#869D311yescharacteristic, complemented
43C3×C4×C22⋊C4—31no—
44#5231—32no—
45#5229—32no—
46#5212—31no—
47#4990—32no—
48#4987—31no—
49#4986—32no—
50Dic3×C4⋊C4—31no—
51#4973—31no—
52#4951—32no—
53#4947—32no—
54C4×(C2×D3)⋊C4D311yescharacteristic
55C4×C4⋊Dic3—31no—
56#4929—31no—
57#4929—31no—
58#4929—31no—
59#4929—61no—
60#4660—32no—
61#4646—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C2×#634—22no—
69C2×#634—22no—
70C2×#634—22no—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6—24no—
80C2×C3×Dic6—24no—
81C2×C3×Dic6—42no—
82C32×C42—22no—
83C4⋊(C3⋊Dic3)—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4Q814yescomplemented
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—24no—
88C3×C4⋊Dic3D414yes—
89C3×C4×Dic3—22no—
90Dic3⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92(C2×D3)⋊Dic3—42no—
93Dic32—42no—
94#2492—91noSylow
95C22×C3×Q8—32no—
96C23×C3×C4—31no—
97C22×C4×D3C2×D311yescharacteristic
98C22×Dic6—31no—
99C22×Dic6—31no—
100C22×Dic6—61no—
101C22×Dic6C2×D312yes—
102C3×C4⋊Q8—64no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4—31no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C42—21no—
109C2×C3×C42—31no—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D311yescharacteristic
112C2×#217—32no—
113C2×#217—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4C2×D311yescharacteristic
117C2×(C2×D3)⋊C4C2×D311yescharacteristic
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D312yes—
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×C4⋊Dic3C2×D311yescharacteristic
125#924—64no—
126C2×Dic3⋊C4—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3C2×D311yescharacteristic
130#897—64no—
131#869—24no—
132C3×#95—31no—
133C3×#95—31no—
134C3⋊#95—32no—
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—62no—
147C3⋊#95—62no—
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D311yescharacteristic
150C23×C32C2411yescharacteristic
151C22×C3×D3—21no—
152C22×C3×D3—21no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3C2×Q812yes—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2×Q812yes—
164C2×C32×C4#4112yes—
165C2×C32×C4#4112yes—
166C2×C32×C4#4112yes—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173#634—44no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3C2×D414yes—
188C2×C3×Dic3C2×Q812yes—
189C3×C4×D3—44no—
190C3×Dic6—48no—
191C2×C4⋊Q8—31no—
192C2×C22⋊Q8—91no—
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—31no—
203C23×D3C22×D311yescharacteristic
204C2×C3×Q8—64no—
205C2×C3×Q8—64no—
206C2×C3×Q8—122no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—31no—
213C22×C3×C4—32no—
214C22×C3×C4—31no—
215C22×C3×C4—62no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—62no—
229C22×Dic3—62no—
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C2×C4×D3—22no—
236C2×C4×D3—22no—
237C2×C4×D3—22no—
238C2×Dic6—24no—
239C2×Dic6—24no—
240C2×Dic6—42no—
241C2×Dic6—64no—
242C2×Dic6—62no—
243C2×Dic6—62no—
244C2×Dic6—62no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—122no—
249C2×Dic6—122no—
250C3×C4⋊C4—34no—
251C3×C4⋊C4—64no—
252C3×C4⋊C4—62no—
253C3×C22⋊C4—34no—
254C3×C22⋊C4—62no—
255C3×C42—22no—
256C3×C42—22no—
257C3×C42—42no—
258C3×C42—62no—
259#217—64no—
260#217—122no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—122no—
264(C2×D3)⋊C4Dic614yescomplemented
265C4⋊Dic3—22no—
266C4⋊Dic3—24no—
267C4⋊Dic3—64no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3—122no—
271C4⋊Dic3#6714yes—
272Dic3⋊C4—64no—
273C4×Dic3—22no—
274C4×Dic3—122no—
275C4×Dic3—122no—
276C22×C32C22×D411yescharacteristic
277C22×C32C22×Q811yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C322−1+411yescharacteristic
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—22no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—22no—
291C32×C4—22no—
292C32×C4#12414yes—
293C3⋊Dic3—42no—
294C3⋊Dic3—42no—
295C3×Dic3—24no—
296C3×Dic3—22no—
297C3×Dic3—41no—
298C3×Dic3—42no—
299C3×Dic3—41no—
300C22×Q8—32no—
301C22×Q8—91no—
302C23×C4—31no—
303C4⋊Q8—64no—
304C22⋊Q8—184no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—92no—
309C2×C4⋊C4—91no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—92no—
314C2×C42—31no—
315C2×C42—92no—
316C2×C42D3211yescharacteristic
317#95—31no—
318#95—31no—
319#95—92no—
320#95—92no—
321#95—92no—
322#95—92no—
323#95—92no—
324#95—92no—
325C23×C3—21no—
326C23×C3—32no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—61no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3C23×D311yescharacteristic
334C23×C3C23×D311yescharacteristic
335C22×D3—21no—
336C22×D3—21no—
337C22×D3—21no—
338C22×D3—21no—
339C22×D3—21no—
340C22×D3—21no—
341C22×D3C2×Dic612yes—
342C3×Q8—128no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—34no—
357C2×C3×C4—32no—
358C2×C3×C4—41no—
359C2×C3×C4—41no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—62no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—62no—
374C2×C3×C4—61no—
375C2×C3×C4—124no—
376C2×C3×C4C2×Dic612yes—
377C2×C3×C4#23512yes—
378C2×C3×C4#23512yes—
379C2×C3×C4D3×D412yes—
380C2×C3×C4#23712yes—
381C2×C3×C4#23712yes—
382C2×C3×C4D3×Q812yes—
383C2×C3×C4#23912yes—
384C2×C3×C4#23912yes—
385C2×C3×C4C2×#6712yes—
386C2×Dic3—21no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—22no—
395C2×Dic3—21no—
396C2×Dic3—22no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—64no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
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—122no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3—122no—
416C2×Dic3—122no—
417C2×Dic3C2×Dic612yes—
418C2×Dic3C2×#6714yes—
419C4×D3—44no—
420Dic6—48no—
421Dic6—128no—
422Dic6—124no—
423Dic6—124no—
424C2×C32C2×#12411yescharacteristic
425C2×C32#53311yescharacteristic
426C2×C32#54211yescharacteristic
427C2×C32#54611yescharacteristic
428C2×C32D4×Q811yescharacteristic
429C2×C32#55411yescharacteristic
430C2×C32#55611yescharacteristic
431C3×D3—42no—
432C24—31no—
433C2×Q8—64no—
434C2×Q8—64no—
435C2×Q8—122no—
436C2×Q8—182no—
437C2×Q8—182no—
438C2×Q8—182no—
439C22×C4—31no—
440C22×C4—32no—
441C22×C4—31no—
442C22×C4—31no—
443C22×C4—32no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—92no—
448C22×C4—92no—
449C22×C4C2×D3211yescharacteristic
450C22×C4C2×D3211yescharacteristic
451C22×C4C2×D3211yescharacteristic
452C4⋊C4—34no—
453C4⋊C4—64no—
454C4⋊C4—62no—
455C4⋊C4—184no—
456C4⋊C4—182no—
457C22⋊C4—34no—
458C22⋊C4—62no—
459C22⋊C4—184no—
460C22⋊C4—362no—
461C42—22no—
462C42—62no—
463C42—362no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3—121no—
478C22×C3C22×Dic611yescharacteristic
479C22×C3C2×#23511yescharacteristic
480C22×C3C2×#23511yescharacteristic
481C22×C3C2×D3×D411yescharacteristic
482C22×C3C2×#23711yescharacteristic
483C22×C3C2×#23711yescharacteristic
484C22×C3#100411yescharacteristic
485C22×C3C2×D3×Q811yescharacteristic
486C22×C3C2×#23911yescharacteristic
487C22×C3C2×#23911yescharacteristic
488C22×C3#100711yescharacteristic
489C22×C3#100911yescharacteristic
490C22×C3#101011yescharacteristic
491C22×C3C22×#6711yescharacteristic
492C2×D3—22no—
493C2×D3—22no—
494C2×D3—22no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C3×C4—22no—
500C3×C4—22no—
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—24no—
504C3×C4—42no—
505C3×C4—42no—
506C3×C4—62no—
507C3×C4—64no—
508C3×C4—121no—
509C3×C4—122no—
510C3×C4—121no—
511C3×C4#88514yes—
512C3×C4#94714yes—
513Dic3—22no—
514Dic3—24no—
515Dic3—41no—
516Dic3—41no—
517Dic3—42no—
518Dic3—124no—
519Dic3—122no—
520Dic3—122no—
521Dic3—122no—
522Dic3—122no—
523Dic3—242no—
524C32#249211yescharacteristic, complemented, Sylow
525C23—32no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23—61no—
531C23—61no—
532C23C22×D3211yescharacteristic
533Q8—128no—
534Q8—364no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—32no—
540C2×C4—34no—
541C2×C4—62no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—62no—
545C2×C4—61no—
546C2×C4—62no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—61no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—61no—
554C2×C4—124no—
555C2×C4—182no—
556C2×C4—182no—
557C2×C4—182no—
558C2×C4—182no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4D3×Dic612yes—
562C2×C4#379512yes—
563C2×C4#379612yes—
564C2×C4#379912yes—
565C2×C4D3×#6712yes—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—122no—
574C2×C3#547011yescharacteristic
575C2×C3C2×#88511yescharacteristic
576C2×C3#553411yescharacteristic
577C2×C3D4×Dic611yescharacteristic
578C2×C3#554211yescharacteristic
579C2×C3#554311yescharacteristic
580C2×C3#555011yescharacteristic
581C2×C3#572811yescharacteristic
582C2×C3#573011yescharacteristic
583C2×C3#573211yescharacteristic
584C2×C3#573311yescharacteristic
585C2×C3#580611yescharacteristic
586C2×C3C2×#94711yescharacteristic
587C2×C3Q8×#6711yescharacteristic
588D3—42no—
589C22—62no—
590C22—62no—
591C22—62no—
592C22—121no—
593C22—121no—
594C22—121no—
595C22—121no—
596C22C2×D3×Dic611yescharacteristic
597C22C2×#379511yescharacteristic
598C22C2×#379611yescharacteristic
599C22#6429711yescharacteristic
600C22C2×#379911yescharacteristic
601C22#6430711yescharacteristic
602C22C2×D3×#6711yescharacteristic
603C4—22no—
604C4—22no—
605C4—64no—
606C4—62no—
607C4—122no—
608C4—121no—
609C4—121no—
610C4—362no—
611C4—362no—
612C4#6390714yes—
613C3—21no—
614C3#7350811yescharacteristic, complemented
615C3#8325811yescharacteristic, complemented
616C2—122no—
617C2#1059385911yescharacteristic
618C2#1059386311yescharacteristic
619C2#1059387711yescharacteristic
620C2#1059395611yescharacteristic
621C2#1059488611yescharacteristic
622C2Dic6×#6711yescharacteristic
623C2C2×#6390711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#869C2semidirect
3. #10592628C2semidirect
5. #10591343C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591261C2semidirect
11. #10591213C2semidirect
42. C2×#869D3semidirect
85. C3×(C2×D3)⋊C4Q8semidirect
264. (C2×D3)⋊C4Dic6semidirect
524. C32#2492semidirect
614. C3#73508semidirect
615. C3#83258semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8692
C2×#638572
#105926282
C3×C4×(C2×D3)⋊C42
#105913432
#105913132
#105913072
#105913042
Dic3×C4⋊Dic32
#105912612
#105912132
#832583
#735083