Finite Group Databasebeta

← #11805783

Subgroups — #11805783

Order 1152.

1389 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic, complemented
3C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
4#10591711C212yesmaximal
5Dic3×#217C212yesmaximal, complemented
6#10591266C212yesmaximal, complemented
7#10591263C212yesmaximal, complemented
8#10591260C211yesmaximal, characteristic, complemented
9#10591252C211yesmaximal, characteristic, complemented
10#10591229C211yesmaximal, characteristic, complemented
11#10591219C211yesmaximal, characteristic, complemented
12#73884—31nomaximal
13#73336—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C2×#3757C2211yescharacteristic
19C4×#638C418yescomplemented
20C2×#3752C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×#3722C2212yes—
26C2×#3722C2212yes—
27C2×Dic32C2212yes—
28C2×Dic32C2212yes—
29C3×C3⋊#95C2211yescharacteristic
30C3×C3⋊#95C2211yescharacteristic
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×#67—31no—
40C2×C4×#67—61no—
41C3×#380—31no—
42C2×C3×#95—31no—
43#5213—32no—
44#5212D311yescharacteristic, complemented
45C4×#217—32no—
46C2×C3⋊#95D311yescharacteristic, complemented
47#4990—32no—
48#4978—32no—
49#4958—32no—
50Dic3×C22⋊C4—32no—
51#4670—32no—
52#4666—31no—
53#4666—31no—
54#4664—31no—
55#4664—31no—
56#4655—32no—
57#4651—31no—
58#4651—31no—
59#4648—31no—
60#4648—31no—
61C24×C32C2311yescharacteristic
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C2×#638—22no—
68C2×#638—22no—
69C2×#638C2×C414yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4×C3⋊D3—42no—
74C2×C4×C3⋊D3C2×C414yescomplemented
75C22×C3×Dic3—24no—
76C22×C3×Dic3—24no—
77C22×C3×Dic3—42no—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82#3757C2×C414yes—
83#3752C2×C414yescomplemented
84#3750C2×C414yescomplemented
85C4×C3⋊Dic3C2×C414yescomplemented
86C3×#217—24no—
87C3×C4⋊Dic3—42no—
88#3722—24no—
89#3722—42no—
90Dic32—24no—
91Dic32—42no—
92#2353—91noSylow
93C23×C3×C4—21no—
94C23×C3×C4—32no—
95C23×C3×C4C2×D311yescharacteristic
96C23×C3×C4C2×D311yescharacteristic
97C22×#67—31no—
98C22×#67—31no—
99C22×#67—61no—
100C23×Dic3C2×D312yes—
101C22×C4×D3—31no—
102C22×C4×D3—31no—
103C22×C4×D3—61no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C22⋊C4—32no—
106C2×#217—31no—
107C2×#217—31no—
108C2×#217—61no—
109C2×#217C2×D312yes—
110C4×#67—38no—
111C4×#67—38no—
112C4×#67—68no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—61no—
120C2×C4⋊Dic3C2×D312yes—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—31no—
123C2×Dic3⋊C4—61no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—61no—
131C3×#95—31no—
132C3×#95—31no—
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⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D311yescharacteristic
146C3⋊#95C2×D311yescharacteristic
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D312yes—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32C22×C412yes—
152C23×C32#4112yes—
153C23×C32#4112yes—
154C23×C32C2411yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3C22×C412yes—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—44no—
163C2×C32×C4C22×C412yes—
164C2×C32×C4C22×C412yes—
165#638—28no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3C22×C412yes—
171C2×C3⋊Dic3C22×C412yes—
172C2×C3⋊Dic3C22×C412yes—
173C4×C3⋊D3—44no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
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—48no—
186C2×C3×Dic3#4114yes—
187C2×C4×D4—91no—
188#388—92no—
189#387—92no—
190#386—92no—
191#383—91no—
192#381—91no—
193#380—31no—
194C4×C22⋊C4—91no—
195C4×C22⋊C4—92no—
196#376—91no—
197C2×#95—31no—
198C24×C3—21no—
199C24×C3C22×D311yescharacteristic
200C24×C3C22×D311yescharacteristic
201C23×D3—31no—
202C23×D3—31no—
203C23×D3—61no—
204C22×C3×C4—24no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—42no—
212C22×C3×C4—42no—
213C22×C3×C4—44no—
214C22×C3×C4—64no—
215C22×C3×C4—64no—
216C22×C3×C4—122no—
217C22×C3×C4C4×D314yes—
218C22×C3×C4C4×D314yes—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×#67—34no—
224C2×#67—34no—
225C2×#67—64no—
226C2×#67—64no—
227C2×#67—64no—
228C2×#67—62no—
229C2×#67—62no—
230C2×#67—62no—
231C2×#67—62no—
232C22×Dic3—24no—
233C22×Dic3—24no—
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—42no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3C22×D312yes—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C2×C4×D3—34no—
249C2×C4×D3—34no—
250C2×C4×D3—64no—
251C2×C4×D3—122no—
252C2×C4×D3—122no—
253C2×C4×D3—124no—
254C3×C4⋊C4—122no—
255C3×C22⋊C4—64no—
256#217—24no—
257#217—34no—
258#217—34no—
259#217—64no—
260(C2×D3)⋊C4—34no—
261(C2×D3)⋊C4—34no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—122no—
266(C2×D3)⋊C4—122no—
267C4⋊Dic3—42no—
268Dic3⋊C4—34no—
269Dic3⋊C4—34no—
270Dic3⋊C4—64no—
271C4×Dic3—34no—
272C4×Dic3—34no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C4×Dic3—64no—
276C4×Dic3—122no—
277C4×Dic3—122no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—24no—
281C22×C32—24no—
282C22×C32#11714yes—
283C22×C32C23×C411yescharacteristic
284C22×C32C2×#4112yes—
285C22×C32C2×#4111yescharacteristic
286C22×C32C2×#4111yescharacteristic
287C22×C32H(5,𝔽2)12yes—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—42no—
293C32×C4—22no—
294C32×C4—22no—
295C3⋊Dic3—22no—
296C3⋊Dic3—22no—
297C3⋊Dic3—22no—
298C3×Dic3—24no—
299C3×Dic3—42no—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C22×D4—91no—
303C23×C4—32no—
304C23×C4—91no—
305C23×C4D3211yescharacteristic
306C4×D4—98no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—91no—
309C2×C22⋊C4—32no—
310C2×C22⋊C4—91no—
311C2×C22⋊C4—91no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—92no—
314C2×C42—91no—
315C2×C42—92no—
316C2×C42—92no—
317#95—31no—
318#95—31no—
319#95—32no—
320#95—31no—
321#95—31no—
322#95—92no—
323#95—92no—
324#95—92no—
325#95—92no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—21no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3C2×C4×D312yes—
337C23×C3C2×C4×D312yes—
338C23×C3#23712yes—
339C23×C3#23712yes—
340C23×C3#23912yes—
341C23×C3#23912yes—
342C23×C3C23×D311yescharacteristic
343C23×C3C23×D311yescharacteristic
344C22×D3—32no—
345C22×D3—32no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—61no—
355C22×D3—61no—
356C22×D3—62no—
357C22×D3—122no—
358C22×D3—122no—
359C2×C3×C4—24no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—34no—
367C2×C3×C4—42no—
368C2×C3×C4—44no—
369C2×C3×C4—44no—
370C2×C3×C4—48no—
371C2×C3×C4—62no—
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—128no—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4C2×C4×D312yes—
385C2×C3×C4C2×C4×D312yes—
386C2×C3×C4C2×C4×D312yes—
387#67—616no—
388#67—68no—
389#67—68no—
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—22no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—48no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—62no—
421C2×Dic3—122no—
422C2×Dic3—122no—
423C2×Dic3#23514yes—
424C4×D3—124no—
425C4×D3—124no—
426C4×D3—128no—
427C2×C32—24no—
428C2×C32C2×#11711yescharacteristic
429C2×C32C4×#4111yescharacteristic
430C2×C32#51811yescharacteristic
431C2×C32#55112yes—
432C2×C32#55312yes—
433C3⋊D3—42no—
434C24—91no—
435C24C2×D3211yescharacteristic
436C2×D4—94no—
437C2×D4—182no—
438C2×D4—182no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—32no—
443C22×C4—42no—
444C22×C4—64no—
445C22×C4—64no—
446C22×C4—91no—
447C22×C4—91no—
448C22×C4—91no—
449C22×C4—94no—
450C22×C4—122no—
451C22×C4—362no—
452C22×C4#62414yes—
453C22×C4C2×D3211yescharacteristic
454C22×C4C2×D3211yescharacteristic
455C4⋊C4—94no—
456C4⋊C4—122no—
457C22⋊C4—64no—
458C22⋊C4—94no—
459C22⋊C4—94no—
460C22⋊C4—184no—
461C22⋊C4—362no—
462C42—94no—
463C42—184no—
464C42—362no—
465C22×C3—24no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—22no—
472C22×C3—24no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—22no—
478C22×C3—24no—
479C22×C3—42no—
480C22×C3—44no—
481C22×C3—44no—
482C22×C3—42no—
483C22×C3#89214yes—
484C22×C3#89214yes—
485C22×C3C22×C4×D311yescharacteristic
486C22×C3C22×C4×D311yescharacteristic
487C22×C3C2×#23512yes—
488C22×C3C2×#23711yescharacteristic
489C22×C3C2×#23711yescharacteristic
490C22×C3#100412yes—
491C22×C3#100412yes—
492C22×C3C2×#23911yescharacteristic
493C22×C3C2×#23911yescharacteristic
494C22×C3D3×#4112yes—
495C2×D3—64no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—124no—
505C2×D3—124no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—122no—
509C2×D3—122no—
510C3×C4—24no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—22no—
514C3×C4—22no—
515C3×C4—42no—
516C3×C4—64no—
517C3×C4—122no—
518C3×C4—122no—
519C3×C4—122no—
520Dic3—24no—
521Dic3—42no—
522Dic3—42no—
523Dic3—42no—
524Dic3—64no—
525Dic3—62no—
526Dic3—62no—
527Dic3—62no—
528Dic3—62no—
529Dic3—62no—
530Dic3—62no—
531Dic3—122no—
532Dic3—122no—
533C32#235311yescharacteristic, complemented, Sylow
534C23—22no—
535C23—22no—
536C23—92no—
537C23—181no—
538C23—181no—
539C23—182no—
540C23—182no—
541C23#379612yes—
542C23#379612yes—
543C23C2×#62412yes—
544C23C22×D3211yescharacteristic
545D4—188no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—34no—
549C2×C4—44no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—92no—
562C2×C4—92no—
563C2×C4—92no—
564C2×C4—128no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—182no—
568C2×C4—182no—
569C2×C4—364no—
570C2×C4C2×#62412yes—
571C2×C4C2×#62412yes—
572C2×C3—24no—
573C2×C3—24no—
574C2×C3—21no—
575C2×C3—22no—
576C2×C3—22no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—44no—
580C2×C3C4×#23511yescharacteristic
581C2×C3#548611yescharacteristic
582C2×C3#548611yescharacteristic
583C2×C3#549512yes—
584C2×C3C2×#89211yescharacteristic
585C2×C3C2×#89211yescharacteristic
586C2×C3#551412yes—
587C2×C3#552211yescharacteristic
588C2×C3#560112yes—
589C2×C3#563712yes—
590D3—124no—
591D3—122no—
592D3—122no—
593C22—24no—
594C22—24no—
595C22—22no—
596C22—22no—
597C22—182no—
598C22—182no—
599C22—182no—
600C22—362no—
601C22—362no—
602C22#6384914yes—
603C22C2×#379611yescharacteristic
604C22C2×#379611yescharacteristic
605C22D3×#23512yes—
606C22C22×#62411yescharacteristic
607C22#6433012yes—
608C4—22no—
609C4—22no—
610C4—64no—
611C4—122no—
612C4—122no—
613C4—122no—
614C4—182no—
615C4—182no—
616C4—182no—
617C3—21no—
618C3#7333611yescharacteristic, complemented
619C3#7388411yescharacteristic, complemented
620C2—24no—
621C2—362no—
622C2C2×#6384911yescharacteristic
623C2#1059494112yes—
624C2#1059495312yes—
625C2#1059495411yescharacteristic
626C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×#5212C2semidirect
3. C2×C3×C3⋊#95C2semidirect
5. Dic3×#217C2semidirect
6. #10591266C2semidirect
7. #10591263C2semidirect
8. #10591260C2semidirect
9. #10591252C2semidirect
10. #10591229C2semidirect
11. #10591219C2semidirect
19. C4×#638C4semidirect
44. #5212D3semidirect
46. C2×C3⋊#95D3semidirect
74. C2×C4×C3⋊D3C2×C4semidirect
83. #3752C2×C4semidirect
84. #3750C2×C4semidirect
85. C4×C3⋊Dic3C2×C4semidirect
533. C32#2353semidirect
618. C3#73336semidirect
619. C3#73884semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C3×#52122
C2×C3×C3⋊#952
#105917112
Dic3×#2172
#105912662
#105912632
#105912602
#105912522
#105912292
#105912192
#738843
#733363