Finite Group Databasebeta

← #11819075

Subgroups — #11819075

Order 1152.

1113 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#897C211yesmaximal, characteristic
2C2×C3×#888C211yesmaximal, characteristic, complemented
3C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4#10591313C211yesmaximal, characteristic
5#10591304C212yesmaximal
6#10591283C212yesmaximal
7C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
8#10591225C212yesmaximal, complemented
9#10591221C211yesmaximal, characteristic, complemented
10#10591221C212yesmaximal, complemented
11#10591220C211yesmaximal, characteristic, complemented
12#83258—31nomaximal
13#82773—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2212yes—
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#897—24no—
27C3×#888—24no—
28C2×(C2×D3)⋊Dic3C2211yescharacteristic
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31#63658C2212yes—
32#63579C2211yescharacteristic
33#63579C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4⋊Q8—31no—
40C2×C3×C22⋊Q8—31no—
41C2×#897D311yescharacteristic
42C2×#888D311yescharacteristic, complemented
43#5231—32no—
44#5229—32no—
45#5229—31no—
46#5229—31no—
47#5212—31no—
48C4×#217—31no—
49#4990—32no—
50#4987—31no—
51#4986—32no—
52#4985—32no—
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—31no—
55Dic3×C4⋊C4—61no—
56#4973—31no—
57#4973—32no—
58#4947—32no—
59#4945—32no—
60C4×(C2×D3)⋊C4—31no—
61#4929—31no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×Dic6—24no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—24no—
81C2×C3×Dic6—42no—
82C32×C4⋊C4D414yes—
83C4⋊(C3⋊Dic3)—22no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3—42no—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—24no—
89C3×Dic3⋊C4—24no—
90C3×C4×Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—42no—
93(C2×D3)⋊Dic3Q814yescomplemented
94#2492—91noSylow
95C22×C3×Q8—31no—
96C22×C3×Q8—32no—
97C23×C3×C4—31no—
98C22×C4×D3C2×D311yescharacteristic
99C22×Dic6C2×D311yescharacteristic
100C22×Dic6C2×D312yes—
101C3×C4⋊Q8—64no—
102C3×C22⋊Q8—64no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C22⋊C4—32no—
110C2×C3×C42—31no—
111C2×#217—31no—
112C2×#217—31no—
113C2×#217—32no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—31no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4C2×D312yes—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—61no—
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×C4⋊Dic3C2×D312yes—
123C2×Dic3⋊C4C2×D312yes—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3—62no—
130C2×C4×Dic3C2×D311yescharacteristic
131#897—24no—
132#888—24no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—31no—
138C3⋊#95—31no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—62no—
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—22no—
159C2×C32×C4—22no—
160C2×C32×C4C2×D414yes—
161C2×C32×C4C2×D412yes—
162C2×C32×C4#4112yes—
163C2×C32×C4#4112yes—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3C2×Q812yes—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×Q812yes—
187C2×C3×Dic3#4112yes—
188C3×C4×D3—44no—
189C3×Dic6—48no—
190C3×Dic6—44no—
191C2×C4⋊Q8—31no—
192C2×C22⋊Q8—31no—
193#400—92no—
194#393—92no—
195#391—91no—
196#391—92no—
197#391—91no—
198#388—92no—
199#380—91no—
200C4×C4⋊C4—91no—
201C4×C22⋊C4—91no—
202C24×C3—31no—
203C23×D3C22×D311yescharacteristic
204C2×C3×Q8—64no—
205C2×C3×Q8—62no—
206C2×C3×Q8—62no—
207C2×C3×Q8—62no—
208C2×C3×Q8—64no—
209C2×C3×Q8—122no—
210C22×C3×C4—21no—
211C22×C3×C4—22no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—32no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C22×C3×C4—62no—
218C22×C3×C4—62no—
219C22×C3×C4—62no—
220C22×C3×C4C22×D312yes—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×Dic3—31no—
225C22×Dic3—31no—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—32no—
229C22×Dic3—32no—
230C22×Dic3—61no—
231C22×Dic3—61no—
232C22×Dic3—62no—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D312yes—
236C22×Dic3C22×D311yescharacteristic
237C22×Dic3C22×D311yescharacteristic
238C2×C4×D3—22no—
239C2×C4×D3—22no—
240C2×C4×D3—22no—
241C2×Dic6—22no—
242C2×Dic6—22no—
243C2×Dic6—24no—
244C2×Dic6—22no—
245C2×Dic6—24no—
246C2×Dic6—42no—
247C3×C4⋊C4—24no—
248C3×C4⋊C4—64no—
249C3×C4⋊C4—64no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4#6714yes—
252C3×C4⋊C4#6714yes—
253C3×C22⋊C4—64no—
254C3×C42—62no—
255#217—34no—
256#217—62no—
257#217—122no—
258(C2×D3)⋊C4—24no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—122no—
262C4⋊Dic3—22no—
263C4⋊Dic3—24no—
264C4⋊Dic3—64no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267Dic3⋊C4—24no—
268C4×Dic3—22no—
269C4×Dic3—64no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—122no—
273C4×Dic3—122no—
274C4×Dic3—124no—
275C22×C32C22×D411yescharacteristic
276C22×C32C22×Q811yescharacteristic
277C22×C32C2×#4111yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4111yescharacteristic
280C22×C32H(5,𝔽2)11yescharacteristic
281C22×C322−1+411yescharacteristic
282C2×C3×D3—22no—
283C2×C3×D3—22no—
284C2×C3×D3—22no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C32×C4—24no—
290C32×C4#12414yes—
291C3⋊Dic3—22no—
292C3⋊Dic3—42no—
293C3⋊Dic3—41no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C3×Dic3—42no—
299C22×Q8—31no—
300C22×Q8—32no—
301C23×C4—31no—
302C4⋊Q8—64no—
303C22⋊Q8—64no—
304C2×C4⋊C4—32no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—91no—
308C2×C4⋊C4D3211yescharacteristic
309C2×C22⋊C4—32no—
310C2×C22⋊C4—91no—
311C2×C22⋊C4—91no—
312C2×C22⋊C4—92no—
313C2×C42—31no—
314C2×C42—91no—
315C2×C42—92no—
316#95—91no—
317#95—91no—
318#95—92no—
319#95—92no—
320#95—92no—
321#95—92no—
322#95—92no—
323#95—92no—
324C23×C3—21no—
325C23×C3—32no—
326C23×C3—61no—
327C23×C3—61no—
328C23×C3—61no—
329C23×C3—61no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3C23×D311yescharacteristic
333C23×C3C23×D311yescharacteristic
334C22×D3—21no—
335C22×D3—21no—
336C22×D3—21no—
337C22×D3—21no—
338C22×D3—21no—
339C22×D3—21no—
340C22×D3D3×Q812yes—
341C3×Q8—128no—
342C3×Q8—124no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—24no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—124no—
369C2×C3×C4#23712yes—
370C2×C3×C4#23712yes—
371C2×C3×C4#23912yes—
372C2×C3×C4#23912yes—
373C2×C3×C4C2×#6714yes—
374C2×C3×C4C2×#6714yes—
375C2×C3×C4C2×#6712yes—
376C2×C3×C4C2×#6712yes—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—21no—
380C2×Dic3—21no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—64no—
401C2×Dic3—61no—
402C2×Dic3—62no—
403C2×Dic3—61no—
404C2×Dic3—62no—
405C2×Dic3—61no—
406C2×Dic3—62no—
407C2×Dic3—61no—
408C2×Dic3—62no—
409C2×Dic3—61no—
410C2×Dic3—62no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—122no—
414C2×Dic3—121no—
415C2×Dic3—121no—
416C2×Dic3—122no—
417C2×Dic3#23712yes—
418C2×Dic3D3×Q812yes—
419C4×D3—44no—
420Dic6—48no—
421Dic6—44no—
422C2×C32C2×#12411yescharacteristic
423C2×C32#53311yescharacteristic
424C2×C32#54211yescharacteristic
425C2×C32#54611yescharacteristic
426C2×C32D4×Q811yescharacteristic
427C2×C32#55411yescharacteristic
428C2×C32#55611yescharacteristic
429C3×D3—42no—
430C24—31no—
431C2×Q8—64no—
432C2×Q8—62no—
433C2×Q8—62no—
434C2×Q8—62no—
435C2×Q8—64no—
436C2×Q8—122no—
437C22×C4—31no—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—31no—
441C22×C4—32no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—62no—
445C22×C4—91no—
446C22×C4—91no—
447C22×C4—92no—
448C22×C4C2×D3212yes—
449C22×C4C2×D3211yescharacteristic
450C4⋊C4—64no—
451C4⋊C4—64no—
452C4⋊C4—62no—
453C4⋊C4—182no—
454C4⋊C4#62514yes—
455C22⋊C4—64no—
456C22⋊C4—94no—
457C22⋊C4—182no—
458C22⋊C4—362no—
459C42—62no—
460C42—182no—
461C42—362no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—121no—
473C22×C3—121no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3C2×#23711yescharacteristic
477C22×C3C2×#23711yescharacteristic
478C22×C3C2×#23711yescharacteristic
479C22×C3#100411yescharacteristic
480C22×C3C2×D3×Q811yescharacteristic
481C22×C3C2×D3×Q811yescharacteristic
482C22×C3C2×#23911yescharacteristic
483C22×C3C2×#23911yescharacteristic
484C22×C3#100711yescharacteristic
485C22×C3#100711yescharacteristic
486C22×C3D3×#4111yescharacteristic
487C22×C3#100911yescharacteristic
488C22×C3C22×#6711yescharacteristic
489C22×C3C22×#6711yescharacteristic
490C2×D3—22no—
491C2×D3—22no—
492C2×D3—22no—
493C2×D3—41no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C3×C4—24no—
498C3×C4—24no—
499C3×C4—24no—
500C3×C4—44no—
501C3×C4—62no—
502C3×C4—62no—
503C3×C4—121no—
504C3×C4—122no—
505C3×C4—122no—
506C3×C4#93614yes—
507C3×C4#94714yes—
508Dic3—22no—
509Dic3—22no—
510Dic3—42no—
511Dic3—41no—
512Dic3—42no—
513Dic3—64no—
514Dic3—62no—
515Dic3—62no—
516Dic3—124no—
517Dic3—122no—
518Dic3—121no—
519Dic3—122no—
520Dic3—121no—
521Dic3—122no—
522C32#249211yescharacteristic, complemented, Sylow
523C23—32no—
524C23—61no—
525C23—61no—
526C23—61no—
527C23—61no—
528C23—61no—
529C23—61no—
530C23C22×D3211yescharacteristic
531Q8—128no—
532Q8—124no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—32no—
536C2×C4—32no—
537C2×C4—61no—
538C2×C4—61no—
539C2×C4—61no—
540C2×C4—61no—
541C2×C4—61no—
542C2×C4—61no—
543C2×C4—62no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—61no—
549C2×C4—62no—
550C2×C4—92no—
551C2×C4—124no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—182no—
556C2×C4—181no—
557C2×C4—182no—
558C2×C4—182no—
559C2×C4—181no—
560C2×C4#379612yes—
561C2×C4#379612yes—
562C2×C4C2×#62514yes—
563C2×C4C2×#62512yes—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—122no—
572C2×C3#562211yescharacteristic
573C2×C3#563511yescharacteristic
574C2×C3#564111yescharacteristic
575C2×C3#564311yescharacteristic
576C2×C3#572811yescharacteristic
577C2×C3#573011yescharacteristic
578C2×C3#573211yescharacteristic
579C2×C3#573311yescharacteristic
580C2×C3C2×#93611yescharacteristic
581C2×C3#580611yescharacteristic
582C2×C3C2×#94711yescharacteristic
583C2×C3Q8×#6711yescharacteristic
584C2×C3Q8×#6711yescharacteristic
585C2×C3#582911yescharacteristic
586D3—42no—
587C22—62no—
588C22—62no—
589C22—62no—
590C22—121no—
591C22—121no—
592C22—121no—
593C22—121no—
594C22C2×#379611yescharacteristic
595C22C2×#379611yescharacteristic
596C22D3×#23711yescharacteristic
597C22#6431411yescharacteristic
598C22#6431611yescharacteristic
599C22D32×Q811yescharacteristic
600C22C22×#62511yescharacteristic
601C4—24no—
602C4—62no—
603C4—62no—
604C4—121no—
605C4—122no—
606C4—122no—
607C4—182no—
608C4—362no—
609C4—361no—
610C4#6386314yes—
611C3—21no—
612C3#8277311yescharacteristic, complemented
613C3#8325811yescharacteristic, complemented
614C2—122no—
615C2#1059434311yescharacteristic
616C2#1059438711yescharacteristic
617C2#1059439311yescharacteristic
618C2#1059455711yescharacteristic
619C2C2×#6386311yescharacteristic
620C2#1059524411yescharacteristic
621C2Q8×#62511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#888C2semidirect
3. C4⋊C4×C3⋊Dic3C2semidirect
8. #10591225C2semidirect
9. #10591221C2semidirect
10. #10591221C2semidirect
11. #10591220C2semidirect
42. C2×#888D3semidirect
93. (C2×D3)⋊Dic3Q8semidirect
522. C32#2492semidirect
612. C3#82773semidirect
613. C3#83258semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8972
C2×C3×#8882
C4⋊C4×C3⋊Dic32
#105913132
#105913042
#105912832
C4×(C2×D3)⋊Dic32
#105912252
#105912212
#105912202
#832583
#827733