Finite Group Databasebeta

← #11802772

Subgroups — #11802772

Order 1152.

1681 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×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
2C3×#4951C212yesmaximal, complemented
3#10591714C211yesmaximal, characteristic
4#10591714C211yesmaximal, characteristic
5#10591703C212yesmaximal, complemented
6#10591355C211yesmaximal, characteristic, complemented
7#10591325C211yesmaximal, characteristic, complemented
8C4×#3722C211yesmaximal, characteristic, complemented
9#10591266C212yesmaximal, complemented
10#10591260C211yesmaximal, characteristic, complemented
11#10591202C212yesmaximal, complemented
12#75825—32nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C22⋊C4×C3⋊D3C418yescomplemented
21C2×C3×#217C2212yes—
22C2×C3×#217C2212yes—
23C2×C3×C4⋊Dic3C2212yescomplemented
24C2×C3×C4×Dic3C2212yescomplemented
25C2×#3724C2212yescomplemented
26C2×#3722C2211yescharacteristic
27C2×#3722C2211yescharacteristic
28C2×#3722C2211yescharacteristic
29C2×#3722C2211yescharacteristic
30C2×#3722C2212yes—
31C2×#3722C2212yes—
32C2×Dic32C2212yescomplemented
33C3×C3⋊#95C2212yescomplemented
34C3×C3⋊#95C2212yescomplemented
35#63579C2212yescomplemented
36#63579C2212yescomplemented
37C2×D3×C22⋊C4—32no—
38C2×D3×C22⋊C4—61no—
39C3×#388—32no—
40#4990—32no—
41#4987—32no—
42#4955—32no—
43#4955—32no—
44#4951D312yescomplemented
45#4945—32no—
46#4944—32no—
47#4940—32no—
48C4×(C2×D3)⋊C4—32no—
49#4670—32no—
50#4669—32no—
51#4667—32no—
52#4666—32no—
53C24×C32C2311yescharacteristic
54C23×C3⋊D3—22no—
55C23×C3⋊D3—22no—
56C23×C3⋊D3—42no—
57C23×C3⋊D3—42no—
58C23×C3⋊D3C2×C414yes—
59C23×C3⋊D3C2311yescharacteristic
60C23×C3⋊D3C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C2×C4×C3⋊D3—42no—
66C2×C4×C3⋊D3—42no—
67C2×C4×C3⋊D3C2×C414yes—
68C2×C4×C3⋊D3C2×C414yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C32×C22⋊C4C2×C414yes—
74#3757C2×C414yes—
75#3752C2×C414yes—
76#3752C2×C414yes—
77C3×#217—42no—
78C3×#217—42no—
79C3×C4⋊Dic3—42no—
80C3×C4×Dic3—42no—
81#3724—42no—
82#3722—22no—
83#3722—22no—
84#3722—22no—
85#3722—22no—
86#3722—42no—
87#3722—42no—
88Dic32—42no—
89#2312—91noSylow
90C24×D3—32no—
91C24×D3—61no—
92C22×C4×D3—32no—
93C22×C4×D3—32no—
94C22×C4×D3—61no—
95C22×C4×D3—61no—
96C2×C3×C4⋊C4—32no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—32no—
99C2×C3×C22⋊C4—32no—
100C2×C3×C22⋊C4C2×D312yes—
101C2×C3×C42—32no—
102C2×#217—32no—
103C2×#217—61no—
104C2×#217C2×D312yes—
105C2×#217C2×D312yes—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—61no—
117C2×(C2×D3)⋊C4—61no—
118C2×C4⋊Dic3C2×D312yescomplemented
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3C2×D312yescomplemented
124D3×C22⋊C4—316no—
125D3×C22⋊C4—68no—
126C3×#95—32no—
127C3×#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95C2×D312yescomplemented
133C3⋊#95C2×D312yescomplemented
134C23×C32—21no—
135C23×C32—21no—
136C23×C32—22no—
137C23×C32—22no—
138C23×C32C22×C412yes—
139C23×C32C2411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—21no—
143C22×C3⋊D3—21no—
144C22×C3⋊D3—28no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3—22no—
147C22×C3⋊D3—44no—
148C22×C3⋊D3—44no—
149C22×C3⋊D3—48no—
150C22×C3⋊D3—48no—
151C22×C3⋊D3C22×C412yes—
152C22×C3⋊D3C22×C412yes—
153C22×C3⋊D3#4112yes—
154C22×C3⋊D3#4112yes—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C22×C412yes—
158C2×C32×C4C22×C412yes—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3C22×C412yes—
162C2×C3⋊Dic3C22×C412yes—
163C4×C3⋊D3—44no—
164C4×C3⋊D3—44no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C22×C22⋊C4—91no—
178#388—32no—
179#388—92no—
180#388—92no—
181#388—92no—
182#380—91no—
183#380—91no—
184#379—91no—
185#379—91no—
186C4×C22⋊C4—91no—
187C4×C22⋊C4—91no—
188C24×C3—21no—
189C24×C3C22×D312yes—
190C23×D3—32no—
191C23×D3—32no—
192C23×D3—38no—
193C23×D3—61no—
194C23×D3—64no—
195C23×D3—61no—
196C23×D3—64no—
197C23×D3—64no—
198C23×D3—64no—
199C23×D3—64no—
200C23×D3—122no—
201C23×D3—122no—
202C23×D3—122no—
203C23×D3—122no—
204C23×D3—124no—
205C23×D3—124no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—32no—
212C22×C3×C4C22×D312yes—
213C22×C3×C4C22×D312yes—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C2×C4×D3—38no—
223C2×C4×D3—38no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—122no—
227C2×C4×D3—122no—
228C2×C4×D3—122no—
229C2×C4×D3—122no—
230C2×C4×D3—124no—
231C2×C4×D3—124no—
232C3×C4⋊C4—122no—
233C3×C22⋊C4—24no—
234C3×C22⋊C4—122no—
235C3×C22⋊C4—122no—
236C3×C22⋊C4C4×D318yes—
237C3×C42—122no—
238#217—38no—
239#217—42no—
240#217—42no—
241#217—64no—
242(C2×D3)⋊C4—38no—
243(C2×D3)⋊C4—38no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—122no—
251(C2×D3)⋊C4—122no—
252(C2×D3)⋊C4—122no—
253(C2×D3)⋊C4—122no—
254C4⋊Dic3—42no—
255Dic3⋊C4—122no—
256Dic3⋊C4—122no—
257C4×Dic3—42no—
258C4×Dic3—122no—
259C4×Dic3—122no—
260C22×C32—22no—
261C22×C32—22no—
262C22×C32—22no—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32C23×C411yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32C2×#4111yescharacteristic
268C22×C32H(5,𝔽2)12yes—
269C22×C32H(5,𝔽2)12yes—
270C2×C3⋊D3—22no—
271C2×C3⋊D3—22no—
272C2×C3⋊D3—24no—
273C2×C3⋊D3—24no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—22no—
277C2×C3⋊D3—416no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3#11714yes—
281C32×C4—22no—
282C32×C4—22no—
283C3⋊Dic3—22no—
284C3⋊Dic3—22no—
285C3×Dic3—42no—
286C3×Dic3—42no—
287C3×Dic3—42no—
288C3×Dic3—42no—
289C25—91no—
290C23×C4—91no—
291C23×C4—91no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—92no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—32no—
296C2×C22⋊C4—91no—
297C2×C22⋊C4—91no—
298C2×C22⋊C4—91no—
299C2×C22⋊C4—98no—
300C2×C22⋊C4—91no—
301C2×C22⋊C4—91no—
302C2×C22⋊C4—91no—
303C2×C22⋊C4—91no—
304C2×C22⋊C4—92no—
305C2×C22⋊C4—92no—
306C2×C22⋊C4D3211yescharacteristic
307C2×C42—32no—
308C2×C42—92no—
309#95—32no—
310#95—32no—
311#95—92no—
312#95—92no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—22no—
320C23×C3—22no—
321C23×C3—21no—
322C23×C3—22no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3C2×C4×D314yes—
326C23×C3C23×D312yes—
327C22×D3—34no—
328C22×D3—34no—
329C22×D3—34no—
330C22×D3—34no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—616no—
336C22×D3—64no—
337C22×D3—64no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—616no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—122no—
352C22×D3—122no—
353C22×D3—128no—
354C22×D3—128no—
355C22×D3—128no—
356C22×D3—128no—
357C22×D3—1216no—
358C22×D3—1216no—
359C22×D3—128no—
360C22×D3—128no—
361C22×D3—128no—
362C22×D3—128no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—42no—
370C2×C3×C4—42no—
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—62no—
383C2×C3×C4C2×C4×D314yes—
384C2×C3×C4C2×C4×D314yes—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C4×D3—128no—
408C4×D3—128no—
409C4×D3—128no—
410C4×D3—128no—
411C2×C32—42no—
412C2×C32C2×#11711yescharacteristic
413C2×C32#51811yescharacteristic
414C2×C32#51811yescharacteristic
415C2×C32#53812yes—
416C2×C32#53812yes—
417C3⋊D3—24no—
418C3⋊D3—42no—
419C24—91no—
420C24—91no—
421C24—94no—
422C24—182no—
423C24—182no—
424C24—362no—
425C24—362no—
426C24C2×D3211yescharacteristic
427C22×C4—32no—
428C22×C4—32no—
429C22×C4—32no—
430C22×C4—32no—
431C22×C4—91no—
432C22×C4—91no—
433C22×C4—94no—
434C22×C4—94no—
435C22×C4—362no—
436C22×C4—362no—
437C22×C4C2×D3211yescharacteristic
438C22×C4C2×D3211yescharacteristic
439C4⋊C4—122no—
440C4⋊C4—362no—
441C22⋊C4—94no—
442C22⋊C4—94no—
443C22⋊C4—94no—
444C22⋊C4—122no—
445C22⋊C4—122no—
446C22⋊C4—182no—
447C22⋊C4—182no—
448C22⋊C4—182no—
449C22⋊C4—182no—
450C22⋊C4—362no—
451C22⋊C4—362no—
452C22⋊C4#62414yes—
453C42—122no—
454C42—362no—
455C22×C3—24no—
456C22×C3—24no—
457C22×C3—24no—
458C22×C3—24no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—44no—
467C22×C3—44no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3C22×C4×D312yes—
473C22×C3#100412yes—
474C22×C3#100412yes—
475C22×C3D3×#4112yes—
476C22×C3D3×#4112yes—
477C22×C3#100912yes—
478C22×C3#100912yes—
479C2×D3—38no—
480C2×D3—64no—
481C2×D3—64no—
482C2×D3—64no—
483C2×D3—68no—
484C2×D3—68no—
485C2×D3—64no—
486C2×D3—64no—
487C2×D3—64no—
488C2×D3—64no—
489C2×D3—64no—
490C2×D3—64no—
491C2×D3—64no—
492C2×D3—64no—
493C2×D3—64no—
494C2×D3—64no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—1232no—
498C2×D3—1232no—
499C2×D3—124no—
500C2×D3—124no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C3×C4—24no—
506C3×C4—24no—
507C3×C4—42no—
508C3×C4—42no—
509C3×C4—122no—
510C3×C4—122no—
511C3×C4—122no—
512C3×C4—122no—
513Dic3—42no—
514Dic3—42no—
515Dic3—42no—
516Dic3—42no—
517Dic3—64no—
518Dic3—64no—
519Dic3—122no—
520Dic3—122no—
521C32#231211yescharacteristic, complemented, Sylow
522C23—21no—
523C23—21no—
524C23—22no—
525C23—22no—
526C23—92no—
527C23—92no—
528C23—92no—
529C23—92no—
530C23—188no—
531C23—182no—
532C23—182no—
533C23—181no—
534C23—181no—
535C23—182no—
536C23—182no—
537C23—364no—
538C23—364no—
539C23—368no—
540C23—368no—
541C23C2×#62412yes—
542C23C22×D3211yescharacteristic
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4—364no—
562C2×C4—364no—
563C2×C4C2×#62412yes—
564C2×C4C2×#62412yes—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—22no—
569C2×C3—22no—
570C2×C3—44no—
571C2×C3—44no—
572C2×C3D3×#11712yes—
573C2×C3#554512yes—
574C2×C3#554512yes—
575C2×C3#561312yes—
576C2×C3#565712yes—
577C2×C3#567812yes—
578C2×C3#570412yes—
579D3—68no—
580D3—68no—
581D3—124no—
582D3—124no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—42no—
587C22—42no—
588C22—94no—
589C22—182no—
590C22—182no—
591C22—184no—
592C22—184no—
593C22—182no—
594C22—182no—
595C22—182no—
596C22—3616no—
597C22—362no—
598C22—362no—
599C22#6430611yescharacteristic
600C22#6430611yescharacteristic
601C22#6431412yes—
602C22#6431412yes—
603C22C22×#62411yescharacteristic
604C4—22no—
605C4—22no—
606C4—122no—
607C4—122no—
608C4—122no—
609C4—122no—
610C4—182no—
611C4—182no—
612C3—21no—
613C3#7582512yescomplemented
614C2—42no—
615C2—184no—
616C2—362no—
617C2#1059422512yes—
618C2#1059422612yes—
619C2#1059496911yescharacteristic
620C2#1059522311yescharacteristic
621C2#1059522311yescharacteristic
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. C3×#4951C2semidirect
5. #10591703C2semidirect
6. #10591355C2semidirect
7. #10591325C2semidirect
8. C4×#3722C2semidirect
9. #10591266C2semidirect
10. #10591260C2semidirect
11. #10591202C2semidirect
20. C22⋊C4×C3⋊D3C4semidirect
23. C2×C3×C4⋊Dic3C22semidirect
24. C2×C3×C4×Dic3C22semidirect
25. C2×#3724C22semidirect
32. C2×Dic32C22semidirect
33. C3×C3⋊#95C22semidirect
34. C3×C3⋊#95C22semidirect
35. #63579C22semidirect
36. #63579C22semidirect
44. #4951D3semidirect
118. C2×C4⋊Dic3C2×D3semidirect
123. C2×C4×Dic3C2×D3semidirect
132. C3⋊#95C2×D3semidirect
133. C3⋊#95C2×D3semidirect
521. C32#2312semidirect
613. C3#75825semidirect

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
C3×#49512
#105917142
#105917032
#105913552
#105913252
C4×#37222
#105912662
#105912602
#105912022
#758253