Finite Group Databasebeta

← #11805032

Subgroups — #11805032

Order 1152.

1921 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63974C211yesmaximal, characteristic
3C2×#63849C211yesmaximal, characteristic, complemented
4C3×#4951C212yesmaximal, complemented
5#10591714C211yesmaximal, characteristic
6#10591703C212yesmaximal, complemented
7#10591378C212yesmaximal, complemented
8#10591355C211yesmaximal, characteristic, complemented
9C4×#3722C211yesmaximal, characteristic, complemented
10#10591233C212yesmaximal, complemented
11#10591219C211yesmaximal, characteristic, complemented
12#75833—32nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2212yes—
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×#3757C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C22⋊C4×C3⋊D3C418yescomplemented
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×C4⋊Dic3C2212yescomplemented
25C2×C3×C4×Dic3C2212yescomplemented
26#63974—24no—
27C2×#3724C2212yescomplemented
28C2×#3722C2212yes—
29C2×#3722C2211yescharacteristic
30C2×#3722C2211yescharacteristic
31C2×#3722C2211yescharacteristic
32C2×#3722C2211yescharacteristic
33C2×Dic32C2212yescomplemented
34#63849—24no—
35C3×C3⋊#95C2212yescomplemented
36C3×C3⋊#95C2212yescomplemented
37#63579C2212yescomplemented
38#63579C2212yescomplemented
39C2×#892—32no—
40C2×D3×C22⋊C4—32no—
41C2×D3×C22⋊C4—32no—
42C2×D3×C22⋊C4—61no—
43C3×#388—32no—
44#4989—32no—
45#4955—32no—
46#4951D312yescomplemented
47#4945—32no—
48#4944—32no—
49C4×(C2×D3)⋊C4—32no—
50C4×(C2×D3)⋊C4—32no—
51#4668—32no—
52#4667—32no—
53#4666—32no—
54#4664—32no—
55C24×C32C2311yescharacteristic
56C23×C3⋊D3—22no—
57C23×C3⋊D3—24no—
58C23×C3⋊D3—22no—
59C23×C3⋊D3—42no—
60C23×C3⋊D3C2×C414yes—
61C23×C3⋊D3C2311yescharacteristic
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—42no—
70C2×C4×C3⋊D3C2×C414yescomplemented
71C2×C4×C3⋊D3C2×C414yescomplemented
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×#624—24no—
77C2×#624—24no—
78C2×#624—42no—
79C32×C22⋊C4C2×C414yescomplemented
80#3757C2×C414yescomplemented
81#3752C2×C414yes—
82#3752C2×C414yes—
83C3×#217—24no—
84C3×#217—42no—
85C3×C4⋊Dic3—24no—
86C3×C4×Dic3—42no—
87#3724—42no—
88#3722—22no—
89#3722—22no—
90#3722—24no—
91#3722—22no—
92#3722D414yes—
93Dic32—24no—
94#2342—91noSylow
95C24×D3—32no—
96C24×D3—61no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3—61no—
102C22×C4×D3—61no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C22⋊C4C2×D312yes—
108C2×C3×C42—32no—
109C2×#217—32no—
110C2×#217—61no—
111C2×#217C2×D312yes—
112C2×#217C2×D312yes—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—61no—
122C2×(C2×D3)⋊C4—61no—
123C2×C4⋊Dic3C2×D312yescomplemented
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3C2×D312yescomplemented
129#892—68no—
130D3×C22⋊C4—316no—
131D3×C22⋊C4—68no—
132D3×C22⋊C4—68no—
133C3×#95—32no—
134C3×#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95C2×D312yescomplemented
140C3⋊#95C2×D312yescomplemented
141C23×C32—22no—
142C23×C32—21no—
143C23×C32—21no—
144C23×C32—22no—
145C23×C32C22×C412yes—
146C23×C32C2411yescharacteristic
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—28no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—28no—
154C22×C3⋊D3—44no—
155C22×C3⋊D3—48no—
156C22×C3⋊D3—48no—
157C22×C3⋊D3C22×C412yes—
158C22×C3⋊D3C22×C412yes—
159C22×C3⋊D3C2×D412yes—
160C22×C3⋊D3#4114yes—
161C22×C3⋊D3#4112yes—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—22no—
165C2×C32×C4C22×C412yes—
166C2×C32×C4C22×C412yes—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3C22×C412yes—
171C2×C3⋊Dic3C22×C412yes—
172C4×C3⋊D3—28no—
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×Dic3C2×D414yes—
186#624—48no—
187C2×#117—91no—
188C22×C22⋊C4—91no—
189C22×C22⋊C4—91no—
190#388—32no—
191#388—92no—
192#385—92no—
193#381—91no—
194#380—91no—
195#379—91no—
196C4×C22⋊C4—92no—
197C4×C22⋊C4—91no—
198C24×C3—21no—
199C24×C3C22×D312yes—
200C23×D3—32no—
201C23×D3—32no—
202C23×D3—38no—
203C23×D3—61no—
204C23×D3—64no—
205C23×D3—61no—
206C23×D3—64no—
207C23×D3—64no—
208C23×D3—64no—
209C23×D3—64no—
210C23×D3—68no—
211C23×D3—122no—
212C23×D3—122no—
213C23×D3—122no—
214C23×D3—122no—
215C23×D3—124no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D312yes—
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D312yes—
232C2×C4×D3—38no—
233C2×C4×D3—38no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—122no—
243C2×C4×D3—122no—
244C2×C4×D3—122no—
245C2×C4×D3—122no—
246C2×C4×D3—122no—
247C2×C4×D3—122no—
248C2×C4×D3—124no—
249C3×C4⋊C4—64no—
250C3×C22⋊C4—24no—
251C3×C22⋊C4—64no—
252C3×C22⋊C4—122no—
253C3×C22⋊C4C4×D318yescomplemented
254C3×C42—122no—
255#217—24no—
256#217—38no—
257#217—42no—
258#217—64no—
259(C2×D3)⋊C4—38no—
260(C2×D3)⋊C4—38no—
261(C2×D3)⋊C4—38no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—64no—
269C4⋊Dic3—24no—
270Dic3⋊C4—122no—
271Dic3⋊C4—122no—
272C4×Dic3—42no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C22×C32—22no—
276C22×C32—22no—
277C22×C32—22no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32C23×C411yescharacteristic
281C22×C32C22×D411yescharacteristic
282C22×C32C2×#4112yes—
283C22×C32C2×#4111yescharacteristic
284C22×C32H(5,𝔽2)12yes—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—24no—
288C2×C3⋊D3—24no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—24no—
292C2×C3⋊D3—24no—
293C2×C3⋊D3—416no—
294C2×C3⋊D3#11714yescomplemented
295C2×C3⋊D3C4×D414yes—
296C32×C4—22no—
297C32×C4—22no—
298C3⋊Dic3—22no—
299C3⋊Dic3—22no—
300C3×Dic3—24no—
301C3×Dic3—42no—
302C3×Dic3—42no—
303C3×Dic3—42no—
304C25—91no—
305C23×C4—92no—
306C23×C4—91no—
307C23×C4—91no—
308#117—184no—
309C2×C4⋊C4—32no—
310C2×C4⋊C4—92no—
311C2×C22⋊C4—32no—
312C2×C22⋊C4—32no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4—91no—
315C2×C22⋊C4—91no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—98no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—92no—
322C2×C22⋊C4—184no—
323C2×C22⋊C4D3211yescharacteristic
324C2×C42—32no—
325C2×C42—92no—
326#95—32no—
327#95—32no—
328#95—92no—
329#95—92no—
330C23×C3—24no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—22no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—21no—
338C23×C3—22no—
339C23×C3—41no—
340C23×C3—41no—
341C23×C3—42no—
342C23×C3C2×C4×D314yes—
343C23×C3C23×D312yes—
344C22×D3—34no—
345C22×D3—34no—
346C22×D3—34no—
347C22×D3—34no—
348C22×D3—34no—
349C22×D3—34no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—64no—
355C22×D3—616no—
356C22×D3—616no—
357C22×D3—64no—
358C22×D3—64no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—616no—
368C22×D3—128no—
369C22×D3—121no—
370C22×D3—121no—
371C22×D3—122no—
372C22×D3—128no—
373C22×D3—128no—
374C22×D3—128no—
375C22×D3—128no—
376C22×D3—128no—
377C22×D3—128no—
378C22×D3—1216no—
379C22×D3—1216no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—34no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—62no—
401C2×C3×C4C2×C4×D314yes—
402C2×C3×C4C2×C4×D314yes—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3—122no—
425C2×Dic3D3×D414yes—
426C4×D3—616no—
427C4×D3—128no—
428C4×D3—128no—
429C4×D3—128no—
430C4×D3—128no—
431C4×D3—128no—
432C2×C32—42no—
433C2×C32C2×#11711yescharacteristic
434C2×C32C2×C4×D411yescharacteristic
435C2×C32#51811yescharacteristic
436C2×C32#54612yes—
437C2×C32#55112yes—
438C3⋊D3—24no—
439C3⋊D3—24no—
440C24—91no—
441C24—91no—
442C24—94no—
443C24—182no—
444C24—184no—
445C24—182no—
446C24—362no—
447C24C2×D3211yescharacteristic
448C22×C4—32no—
449C22×C4—32no—
450C22×C4—32no—
451C22×C4—32no—
452C22×C4—91no—
453C22×C4—91no—
454C22×C4—94no—
455C22×C4—94no—
456C22×C4—182no—
457C22×C4—182no—
458C22×C4—184no—
459C22×C4—184no—
460C22×C4—362no—
461C22×C4—362no—
462C22×C4C2×D3211yescharacteristic
463C22×C4C2×D3211yescharacteristic
464C4⋊C4—64no—
465C4⋊C4—362no—
466C22⋊C4—64no—
467C22⋊C4—94no—
468C22⋊C4—94no—
469C22⋊C4—94no—
470C22⋊C4—94no—
471C22⋊C4—122no—
472C22⋊C4—182no—
473C22⋊C4—182no—
474C22⋊C4—184no—
475C22⋊C4—182no—
476C22⋊C4#62414yescomplemented
477C42—122no—
478C42—184no—
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—24no—
482C22×C3—24no—
483C22×C3—22no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—44no—
491C22×C3—44no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3C22×C4×D312yes—
497C22×C3C2×D3×D412yes—
498C22×C3#100412yes—
499C22×C3D3×#4112yes—
500C22×C3D3×#4112yes—
501C22×C3D3×#4112yes—
502C22×C3#100912yes—
503C2×D3—38no—
504C2×D3—38no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—64no—
508C2×D3—64no—
509C2×D3—68no—
510C2×D3—68no—
511C2×D3—64no—
512C2×D3—64no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—64no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—64no—
520C2×D3—64no—
521C2×D3—64no—
522C2×D3—64no—
523C2×D3—122no—
524C2×D3—122no—
525C2×D3—124no—
526C2×D3—124no—
527C2×D3—1232no—
528C2×D3—1232no—
529C3×C4—24no—
530C3×C4—24no—
531C3×C4—42no—
532C3×C4—42no—
533C3×C4—64no—
534C3×C4—122no—
535C3×C4—122no—
536C3×C4—122no—
537Dic3—24no—
538Dic3—42no—
539Dic3—42no—
540Dic3—42no—
541Dic3—64no—
542Dic3—64no—
543Dic3—122no—
544Dic3—122no—
545C32#234211yescharacteristic, complemented, Sylow
546C23—22no—
547C23—21no—
548C23—21no—
549C23—22no—
550C23—94no—
551C23—92no—
552C23—92no—
553C23—92no—
554C23—92no—
555C23—188no—
556C23—188no—
557C23—182no—
558C23—181no—
559C23—181no—
560C23—182no—
561C23—182no—
562C23—364no—
563C23—368no—
564C23—368no—
565C23C2×#62412yes—
566C23C22×D3211yescharacteristic
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—34no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—92no—
583C2×C4—92no—
584C2×C4—188no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—182no—
588C2×C4—364no—
589C2×C4—368no—
590C2×C4C2×#62412yes—
591C2×C4C2×#62412yes—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—44no—
598C2×C3—44no—
599C2×C3D3×#11712yes—
600C2×C3C4×D3×D412yes—
601C2×C3#554512yes—
602C2×C3#561012yes—
603C2×C3#565912yes—
604C2×C3#567612yes—
605C2×C3#570512yes—
606D3—68no—
607D3—68no—
608D3—68no—
609D3—124no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—42no—
614C22—42no—
615C22—94no—
616C22—94no—
617C22—182no—
618C22—182no—
619C22—182no—
620C22—182no—
621C22—184no—
622C22—184no—
623C22—184no—
624C22—184no—
625C22—3616no—
626C22#6430612yes—
627C22D32×D411yescharacteristic
628C22#6431211yescharacteristic
629C22#6431412yes—
630C22C22×#62411yescharacteristic
631C4—22no—
632C4—22no—
633C4—64no—
634C4—122no—
635C4—122no—
636C4—122no—
637C4—182no—
638C4—182no—
639C3—21no—
640C3#7583312yescomplemented
641C2—42no—
642C2—184no—
643C2—184no—
644C2#1059422812yes—
645C2#1059428512yes—
646C2#1059496911yescharacteristic
647C2D4×#62411yescharacteristic
648C2#1059522311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2342
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63849C2semidirect
4. C3×#4951C2semidirect
6. #10591703C2semidirect
7. #10591378C2semidirect
8. #10591355C2semidirect
9. C4×#3722C2semidirect
10. #10591233C2semidirect
11. #10591219C2semidirect
21. C22⋊C4×C3⋊D3C4semidirect
24. C2×C3×C4⋊Dic3C22semidirect
25. C2×C3×C4×Dic3C22semidirect
27. C2×#3724C22semidirect
33. C2×Dic32C22semidirect
35. C3×C3⋊#95C22semidirect
36. C3×C3⋊#95C22semidirect
37. #63579C22semidirect
38. #63579C22semidirect
46. #4951D3semidirect
70. C2×C4×C3⋊D3C2×C4semidirect
71. C2×C4×C3⋊D3C2×C4semidirect
79. C32×C22⋊C4C2×C4semidirect
80. #3757C2×C4semidirect
123. C2×C4⋊Dic3C2×D3semidirect
128. C2×C4×Dic3C2×D3semidirect
139. C3⋊#95C2×D3semidirect
140. C3⋊#95C2×D3semidirect
253. C3×C22⋊C4C4×D3semidirect
294. C2×C3⋊D3#117semidirect
476. C22⋊C4#624semidirect
545. C32#2342semidirect
640. C3#75833semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×C3⋊D32
C2×#639742
C2×#638492
C3×#49512
#105917142
#105917032
#105913782
#105913552
C4×#37222
#105912332
#105912192
#758333