Finite Group Databasebeta

← #11802777

Subgroups — #11802777

Order 1152.

1461 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic
2#10592641C211yesmaximal, characteristic, complemented
3C3×#4955C211yesmaximal, characteristic
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
5#10591720C211yesmaximal, characteristic, complemented
6#10591706C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic, complemented
8#10591282C212yesmaximal, complemented
9#10591281C212yesmaximal, complemented
10#10591280C212yesmaximal, complemented
11#10591279C212yesmaximal, complemented
12#73820—31nomaximal
13#73567—31nomaximal
14C24×C3×D3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×#3750C2212yescomplemented
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yescomplemented
25C2×#3724C2212yescomplemented
26C2×(C2×D3)⋊Dic3C418yescomplemented
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2211yescharacteristic
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×Dic32C2212yescomplemented
34#63658C2212yescomplemented
35C3×C3⋊#95C2212yescomplemented
36#63579C2212yescomplemented
37#63579C2212yescomplemented
38C22×#217—31no—
39C22×(C2×D3)⋊C4—31no—
40C3×#379—31no—
41C3×C4×C22⋊C4—31no—
42#5247—31no—
43C4×#217—31no—
44#4955—31no—
45#4955D311yescharacteristic
46#4945—32no—
47#4945—32no—
48#4944—32no—
49#4944—32no—
50#4942—31no—
51#4942—31no—
52#4942—31no—
53#4942—31no—
54#4942—61no—
55Dic3×C22⋊C4—31no—
56Dic3×C22⋊C4D311yescharacteristic, complemented
57#4940—32no—
58#4940—32no—
59#4669—32no—
60#4669—32no—
61C24×C32C2311yescharacteristic
62C23×C3×D3—22no—
63C23×C3×D3—22no—
64C23×C3×D3—42no—
65C23×C3×D3—42no—
66C23×C3×D3C2×C414yes—
67C23×C3×D3C2311yescharacteristic
68C23×C3×D3C2311yescharacteristic
69C22×C32×C4C2312yes—
70C22×C3⋊Dic3—42no—
71C22×C3⋊Dic3C2×C414yes—
72C22×C3⋊Dic3C2312yes—
73C22×C3⋊Dic3C2311yescharacteristic
74C22×C3⋊Dic3C2311yescharacteristic
75C22×C3×Dic3—42no—
76C22×C3×Dic3C2×C414yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C32×C22⋊C4—22no—
82#3757—22no—
83#3750—42no—
84C3×#217—22no—
85C3×#217—22no—
86C3×(C2×D3)⋊C4—42no—
87C3×(C2×D3)⋊C4—42no—
88C3×C4×Dic3—42no—
89#3724—42no—
90(C2×D3)⋊Dic3—42no—
91(C2×D3)⋊Dic3—42no—
92(C2×D3)⋊Dic3C2×C414yes—
93(C2×D3)⋊Dic3C2×C414yes—
94(C2×D3)⋊Dic3C2×C414yes—
95(C2×D3)⋊Dic3C2×C414yes—
96Dic32—42no—
97#2312—91noSylow
98C25×C3—31no—
99C24×D3C2×D311yescharacteristic
100C23×C3×C4—31no—
101C23×Dic3—31no—
102C23×Dic3—31no—
103C23×Dic3—61no—
104C23×Dic3C2×D311yescharacteristic
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4—31no—
107C2×C3×C22⋊C4—31no—
108C2×C3×C22⋊C4—32no—
109C2×C3×C22⋊C4—32no—
110C2×C3×C22⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C2×D311yescharacteristic
112C2×C3×C42—32no—
113C2×#217—38no—
114C2×#217—31no—
115C2×#217—31no—
116C2×#217—31no—
117C2×#217—31no—
118C2×#217—31no—
119C2×#217—31no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—61no—
123C2×#217C2×D311yescharacteristic
124C2×#217C2×D311yescharacteristic
125C2×(C2×D3)⋊C4—38no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4C2×D312yes—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—62no—
139C2×C4×Dic3—32no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3C2×D312yescomplemented
142C3×#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—62no—
150C3⋊#95C2×D312yescomplemented
151C23×C32—22no—
152C23×C32—22no—
153C23×C32C22×C412yes—
154C23×C32#4112yes—
155C23×C32#4112yes—
156C23×C32C2411yescharacteristic
157C22×C3×D3—28no—
158C22×C3×D3—21no—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—44no—
167C22×C3×D3—44no—
168C22×C3×D3—48no—
169C22×C3×D3—48no—
170C22×C3×D3C22×C412yes—
171C22×C3×D3C22×C412yes—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—44no—
181C2×C3⋊Dic3C22×C412yes—
182C2×C3⋊Dic3C22×C412yes—
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×Dic3—22no—
191C2×C3×Dic3—44no—
192C2×C3×Dic3C22×C412yes—
193C2×C3×Dic3C22×C412yes—
194C22×C22⋊C4—91no—
195#388—92no—
196#388—92no—
197#388—92no—
198#388—92no—
199#380—91no—
200#380—91no—
201#379—31no—
202#379—91no—
203C4×C22⋊C4—31no—
204C4×C22⋊C4—91no—
205C24×C3—21no—
206C24×C3—31no—
207C24×C3—31no—
208C24×C3—34no—
209C24×C3—62no—
210C24×C3—62no—
211C24×C3—122no—
212C24×C3—122no—
213C24×C3C22×D311yescharacteristic
214C24×C3C22×D311yescharacteristic
215C23×D3—22no—
216C23×D3—22no—
217C23×D3—42no—
218C23×D3—42no—
219C23×D3C4×D314yes—
220C23×D3C22×D311yescharacteristic
221C23×D3C22×D311yescharacteristic
222C22×C3×C4—22no—
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—34no—
226C22×C3×C4—32no—
227C22×C3×C4—32no—
228C22×C3×C4—122no—
229C22×C3×C4C22×D312yes—
230C22×C3×C4C22×D312yes—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—34no—
236C22×Dic3—34no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—42no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242C22×Dic3—64no—
243C22×Dic3—62no—
244C22×Dic3—122no—
245C22×Dic3—122no—
246C22×Dic3—124no—
247C22×Dic3C4×D314yes—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D311yescharacteristic
251C22×Dic3C22×D311yescharacteristic
252C3×C22⋊C4—22no—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—42no—
255C3×C22⋊C4—62no—
256C3×C22⋊C4—62no—
257C3×C22⋊C4—122no—
258C3×C22⋊C4—122no—
259C3×C42—122no—
260#217—22no—
261#217—22no—
262#217—34no—
263#217—34no—
264#217—34no—
265#217—34no—
266#217—62no—
267#217—62no—
268#217—122no—
269#217—122no—
270#217—122no—
271(C2×D3)⋊C4—34no—
272(C2×D3)⋊C4—34no—
273(C2×D3)⋊C4—34no—
274(C2×D3)⋊C4—34no—
275(C2×D3)⋊C4—42no—
276(C2×D3)⋊C4—42no—
277(C2×D3)⋊C4—122no—
278(C2×D3)⋊C4—122no—
279Dic3⋊C4—122no—
280Dic3⋊C4—122no—
281Dic3⋊C4—122no—
282Dic3⋊C4—122no—
283Dic3⋊C4—124no—
284C4×Dic3—42no—
285C4×Dic3—122no—
286C4×Dic3—122no—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32—24no—
290C22×C32—24no—
291C22×C32#11714yes—
292C22×C32C23×C411yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C22×C32C2×#4111yescharacteristic
295C22×C32H(5,𝔽2)12yes—
296C22×C32H(5,𝔽2)12yes—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—22no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—22no—
303C2×C3×D3—416no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—42no—
308C32×C4—42no—
309C3⋊Dic3—22no—
310C3⋊Dic3—22no—
311C3⋊Dic3—42no—
312C3×Dic3—22no—
313C3×Dic3—22no—
314C3×Dic3—42no—
315C3×Dic3—42no—
316C25—31no—
317C23×C4—31no—
318C23×C4—91no—
319C2×C4⋊C4—92no—
320C2×C4⋊C4—92no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—32no—
324C2×C22⋊C4—32no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—91no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—91no—
329C2×C22⋊C4—98no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4D3211yescharacteristic
334C2×C42—32no—
335C2×C42—92no—
336#95—32no—
337#95—92no—
338#95—92no—
339#95—92no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—21no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—32no—
349C23×C3—32no—
350C23×C3—42no—
351C23×C3—42no—
352C23×C3—68no—
353C23×C3—61no—
354C23×C3—61no—
355C23×C3—61no—
356C23×C3—61no—
357C23×C3—62no—
358C23×C3—62no—
359C23×C3—62no—
360C23×C3—62no—
361C23×C3—124no—
362C23×C3—124no—
363C23×C3—128no—
364C23×C3—128no—
365C23×C3C2×C4×D312yes—
366C23×C3C2×C4×D312yes—
367C23×C3#23512yes—
368C23×C3#23512yes—
369C23×C3#23712yes—
370C23×C3#23712yes—
371C23×C3C23×D311yescharacteristic
372C23×C3C23×D311yescharacteristic
373C22×D3—28no—
374C22×D3—21no—
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—22no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—44no—
383C22×D3—44no—
384C22×D3—48no—
385C22×D3—48no—
386C22×D3C2×C4×D312yes—
387C22×D3C2×C4×D312yes—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—42no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—62no—
407C2×C3×C4—124no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—32no—
420C2×Dic3—44no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—64no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—122no—
435C2×Dic3—122no—
436C2×Dic3—122no—
437C2×Dic3—122no—
438C2×Dic3—124no—
439C2×Dic3—124no—
440C2×Dic3—128no—
441C2×Dic3C2×C4×D312yes—
442C2×Dic3C2×C4×D312yes—
443C2×C32—24no—
444C2×C32C2×#11711yescharacteristic
445C2×C32#51811yescharacteristic
446C2×C32#51811yescharacteristic
447C2×C32#53812yes—
448C2×C32#53812yes—
449C3×D3—42no—
450C3×D3—42no—
451C24—31no—
452C24—31no—
453C24—34no—
454C24—62no—
455C24—62no—
456C24—122no—
457C24—122no—
458C24C2×D3211yescharacteristic
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—34no—
462C22×C4—32no—
463C22×C4—32no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—94no—
467C22×C4—92no—
468C22×C4—122no—
469C22×C4—362no—
470C22×C4C2×D3212yes—
471C4⋊C4—362no—
472C4⋊C4—362no—
473C22⋊C4—22no—
474C22⋊C4—62no—
475C22⋊C4—62no—
476C22⋊C4—94no—
477C22⋊C4—94no—
478C22⋊C4—94no—
479C22⋊C4—94no—
480C22⋊C4—122no—
481C22⋊C4—122no—
482C22⋊C4—182no—
483C22⋊C4—362no—
484C22⋊C4—362no—
485C42—122no—
486C42—362no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—24no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—21no—
500C22×C3—24no—
501C22×C3—42no—
502C22×C3—44no—
503C22×C3—42no—
504C22×C3—44no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—62no—
508C22×C3—62no—
509C22×C3—62no—
510C22×C3—62no—
511C22×C3—1216no—
512C22×C3—122no—
513C22×C3—122no—
514C22×C3—122no—
515C22×C3—122no—
516C22×C3#87214yes—
517C22×C3#87714yes—
518C22×C3C22×C4×D311yescharacteristic
519C22×C3C22×C4×D311yescharacteristic
520C22×C3C2×#23511yescharacteristic
521C22×C3C2×#23511yescharacteristic
522C22×C3C2×#23711yescharacteristic
523C22×C3C2×#23711yescharacteristic
524C22×C3#100412yes—
525C22×C3#100412yes—
526C22×C3#100412yes—
527C22×C3#100912yes—
528C2×D3—22no—
529C2×D3—22no—
530C2×D3—22no—
531C2×D3—22no—
532C2×D3—22no—
533C2×D3—22no—
534C2×D3—416no—
535C2×D3—42no—
536C2×D3—42no—
537C2×D3—42no—
538C2×D3—42no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—62no—
542C3×C4—62no—
543C3×C4—82no—
544C3×C4—122no—
545C3×C4—122no—
546Dic3—22no—
547Dic3—22no—
548Dic3—42no—
549Dic3—42no—
550Dic3—64no—
551Dic3—62no—
552Dic3—62no—
553Dic3—62no—
554Dic3—62no—
555Dic3—122no—
556Dic3—122no—
557Dic3—122no—
558Dic3—242no—
559C32#231211yescharacteristic, complemented, Sylow
560C23—22no—
561C23—22no—
562C23—32no—
563C23—32no—
564C23—61no—
565C23—61no—
566C23—62no—
567C23—62no—
568C23—62no—
569C23—62no—
570C23—61no—
571C23—61no—
572C23—68no—
573C23—124no—
574C23—124no—
575C23—128no—
576C23—128no—
577C23#379512yes—
578C23C4×D3212yes—
579C23#380412yes—
580C23C22×D3211yescharacteristic
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—62no—
591C2×C4—62no—
592C2×C4—62no—
593C2×C4—62no—
594C2×C4—92no—
595C2×C4—92no—
596C2×C4—124no—
597C2×C4—182no—
598C2×C4—182no—
599C2×C4—182no—
600C2×C4—182no—
601C2×C4—182no—
602C2×C4—364no—
603C2×C3—24no—
604C2×C3—24no—
605C2×C3—22no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—22no—
610C2×C3—44no—
611C2×C3—122no—
612C2×C3—122no—
613C2×C3C2×#87211yescharacteristic
614C2×C3C2×#87711yescharacteristic
615C2×C3#548611yescharacteristic
616C2×C3#548611yescharacteristic
617C2×C3#548611yescharacteristic
618C2×C3#552111yescharacteristic
619C2×C3#556012yes—
620C2×C3#556012yes—
621C2×C3#559312yes—
622C2×C3#559312yes—
623D3—42no—
624D3—42no—
625C22—24no—
626C22—22no—
627C22—22no—
628C22—24no—
629C22—62no—
630C22—62no—
631C22—62no—
632C22—62no—
633C22—62no—
634C22—62no—
635C22—1216no—
636C22—122no—
637C22—122no—
638C22—122no—
639C22—122no—
640C22#6387714yes—
641C22C2×#379511yescharacteristic
642C22C2×C4×D3211yescharacteristic
643C22#6431312yes—
644C22#6431412yes—
645C22C2×#380411yescharacteristic
646C4—42no—
647C4—62no—
648C4—62no—
649C4—122no—
650C4—122no—
651C4—182no—
652C4—182no—
653C4—362no—
654C3—21no—
655C3#7356711yescharacteristic, complemented
656C3#7382011yescharacteristic, complemented
657C2—24no—
658C2—122no—
659C2—122no—
660C2#1059418111yescharacteristic
661C2#1059418211yescharacteristic
662C2#1059423812yes—
663C2C2×#6387711yescharacteristic
664C2#1059512312yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592641C2semidirect
4. C3×Dic3×C22⋊C4C2semidirect
5. #10591720C2semidirect
7. Dic3×#217C2semidirect
8. #10591282C2semidirect
9. #10591281C2semidirect
10. #10591280C2semidirect
11. #10591279C2semidirect
19. C2×#3750C22semidirect
24. C2×C3×C4×Dic3C22semidirect
25. C2×#3724C22semidirect
26. C2×(C2×D3)⋊Dic3C4semidirect
33. C2×Dic32C22semidirect
34. #63658C22semidirect
35. C3×C3⋊#95C22semidirect
36. #63579C22semidirect
37. #63579C22semidirect
56. Dic3×C22⋊C4D3semidirect
141. C2×C4×Dic3C2×D3semidirect
150. C3⋊#95C2×D3semidirect
559. C32#2312semidirect
655. C3#73567semidirect
656. C3#73820semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D3)⋊Dic32
#105926412
C3×#49552
C3×Dic3×C22⋊C42
#105917202
#105917062
Dic3×#2172
#105912822
#105912812
#105912802
#105912792
#738203
#735673