Finite Group Databasebeta

← #11808413

Subgroups — #11808413

Order 1152.

1511 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
2C2×Dic3×#67C212yesmaximal, complemented
3C2×#63877C211yesmaximal, characteristic, complemented
4#10592921C211yesmaximal, characteristic, complemented
5C3×#5223C211yesmaximal, characteristic
6#10591709C212yesmaximal, complemented
7Dic3×#217C212yesmaximal, complemented
8#10591691C212yesmaximal, complemented
9#10591358C211yesmaximal, characteristic, complemented
10#10591314C211yesmaximal, characteristic, complemented
11#10591242C211yesmaximal, characteristic, complemented
12#82401—31nomaximal
13#76666—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C23×C3×Dic3C2212yes—
17C22×D3×Dic3C2211yescharacteristic
18C2×#3757C2212yes—
19C2×#3757C2212yes—
20C2×#3750C2211yescharacteristic
21C2×C3×#217C2212yes—
22C2×C3×#217C2212yes—
23C3×D4×Dic3—24no—
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27Dic3×#67—28no—
28C2×#3724C2211yescharacteristic
29C2×Dic3⋊Dic3C2212yes—
30C2×Dic3⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×Dic32C2212yes—
34C2×Dic32C2211yescharacteristic
35#63877—24no—
36#63658C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×C4×D4—31no—
41C2×D4×Dic3—32no—
42C2×D4×Dic3D311yescharacteristic, complemented
43C2×C4×#67—32no—
44C2×#877—31no—
45C2×#872—31no—
46C3×#392—31no—
47#5223D311yescharacteristic
48#5222—31no—
49#5222—31no—
50#5222—32no—
51#5222—61no—
52C4×#217—32no—
53#4992—31no—
54#4983—31no—
55#4961—32no—
56#4953—31no—
57#4948—32no—
58#4948—32no—
59Dic3×C22⋊C4—32no—
60C4×C4⋊Dic3—31no—
61#4661—31no—
62#4649—31no—
63C24×C32C2312yes—
64C23×C3×D3C2311yescharacteristic
65C2×C32×D4—24no—
66C2×C32×D4—22no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C2×C3×#67—24no—
72C2×C3×#67—24no—
73C2×C3×#67—24no—
74C22×C3×Dic3—24no—
75C22×C3×Dic3—24no—
76C22×C3×Dic3—24no—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C2×D3×Dic3—22no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3D414yescomplemented
85#3757—24no—
86#3757—24no—
87#3750—22no—
88C3×#217—24no—
89C3×#217—24no—
90C3×(C2×D3)⋊C4—22no—
91C3×C4⋊Dic3—22no—
92C3×C4×Dic3D414yescomplemented
93#3724—22no—
94Dic3⋊Dic3—24no—
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—22no—
98Dic32—22no—
99Dic32—24no—
100#2392—91noSylow
101C22×C3×D4—21no—
102C22×C3×D4—32no—
103C22×C3×D4C2×D311yescharacteristic
104C22×C3×D4C2×D311yescharacteristic
105C23×C3×C4—32no—
106C22×#67C2×D312yes—
107C23×Dic3—31no—
108C23×Dic3C2×D312yes—
109C22×C4×D3—31no—
110C3×C4×D4—64no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C42—31no—
116C2×#217—32no—
117C2×#217—32no—
118C2×#217—32no—
119C2×#217—32no—
120C2×#217—32no—
121C2×#217—31no—
122C2×#217—62no—
123C2×#217—62no—
124C2×#217C2×D312yes—
125C2×#217C2×D312yes—
126D4×Dic3—24no—
127D4×Dic3—68no—
128C4×#67—68no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4C2×D311yescharacteristic
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—32no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—32no—
141C2×Dic3⋊C4—61no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—31no—
146C2×C4×Dic3C2×D311yescharacteristic
147#877—64no—
148#872—64no—
149C3×#95—31no—
150C3⋊#95—31no—
151C3⋊#95—31no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—61no—
157C3⋊#95C2×D311yescharacteristic
158C23×C32—22no—
159C23×C32—22no—
160C23×C32—22no—
161C23×C32—22no—
162C23×C32—22no—
163C23×C32—22no—
164C23×C32#4114yes—
165C23×C32C2411yescharacteristic
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3C2×D412yes—
171C32×D4—28no—
172C2×C32×C4—22no—
173C2×C32×C4C2×D412yes—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3C2×D412yes—
182C3×#67—216no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—48no—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195C2×C3×Dic3#4114yes—
196C2×C3×Dic3#4112yes—
197D3×Dic3—28no—
198C2×C4×D4—31no—
199C2×C4×D4—92no—
200C2×#117—91no—
201#398—91no—
202#397—91no—
203#396—92no—
204#394—92no—
205#394—91no—
206#392—31no—
207C4×C4⋊C4—91no—
208C4×C22⋊C4—92no—
209C24×C3—22no—
210C24×C3—31no—
211C24×C3C22×D312yes—
212C24×C3C22×D312yes—
213C23×D3C22×D311yescharacteristic
214C2×C3×D4—24no—
215C2×C3×D4—24no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—42no—
219C2×C3×D4—44no—
220C2×C3×D4—64no—
221C2×C3×D4—64no—
222C2×C3×D4—64no—
223C22×C3×C4—21no—
224C22×C3×C4—31no—
225C22×C3×C4—32no—
226C22×C3×C4—31no—
227C22×C3×C4—31no—
228C22×C3×C4—32no—
229C22×C3×C4—64no—
230C22×C3×C4—64no—
231C22×C3×C4—64no—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—24no—
235C2×#67—24no—
236C2×#67—24no—
237C22×Dic3—24no—
238C22×Dic3—24no—
239C22×Dic3—24no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—34no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—32no—
246C22×Dic3—32no—
247C22×Dic3—61no—
248C22×Dic3—62no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3C22×D311yescharacteristic
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D312yes—
255C22×Dic3C22×D311yescharacteristic
256C22×Dic3C22×D311yescharacteristic
257C2×C4×D3—34no—
258C2×C4×D3—62no—
259C2×C4×D3—62no—
260C3×C4⋊C4—62no—
261C3×C22⋊C4—64no—
262C3×C22⋊C4—64no—
263C3×C22⋊C4—62no—
264C3×C42—34no—
265#217—24no—
266#217—24no—
267#217—64no—
268#217—64no—
269#217—64no—
270#217—64no—
271#217—64no—
272#217—62no—
273#217—124no—
274#217—124no—
275(C2×D3)⋊C4—22no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—64no—
278C4⋊Dic3—22no—
279C4⋊Dic3—64no—
280C4⋊Dic3—64no—
281Dic3⋊C4—64no—
282Dic3⋊C4—62no—
283Dic3⋊C4—64no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—122no—
288C4×Dic3—62no—
289C4×Dic3—64no—
290C4×Dic3—64no—
291C4×Dic3—62no—
292C4×Dic3#6714yescomplemented
293C22×C32—24no—
294C22×C32—24no—
295C22×C32—24no—
296C22×C32—42no—
297C22×C32—42no—
298C22×C32—42no—
299C22×C32—42no—
300C22×C32C22×D411yescharacteristic
301C22×C32C22×D411yescharacteristic
302C22×C32C2×#4112yes—
303C22×C32C2×#4111yescharacteristic
304C22×C32C2×#4112yes—
305C2×C3×D3—22no—
306C2×C3×D3—24no—
307C2×C3×D3—41no—
308C2×C3×D3—42no—
309C2×C3×D3—41no—
310C32×C4—22no—
311C3⋊Dic3—22no—
312C3⋊Dic3—41no—
313C3⋊Dic3—42no—
314C3×Dic3—24no—
315C3×Dic3—22no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3#12114yes—
319C22×D4—32no—
320C22×D4D3211yescharacteristic
321C23×C4—32no—
322C23×C4—91no—
323C4×D4—64no—
324C4×D4—188no—
325#117—184no—
326C2×C4⋊C4—31no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—92no—
329C2×C4⋊C4—92no—
330C2×C4⋊C4—91no—
331C2×C22⋊C4—32no—
332C2×C22⋊C4—32no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—91no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4—92no—
338C2×C42—31no—
339C2×C42—91no—
340C2×C42—92no—
341#95—31no—
342#95—92no—
343#95—92no—
344#95—91no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—22no—
357C23×C3—21no—
358C23×C3—24no—
359C23×C3—32no—
360C23×C3—42no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3—62no—
367C23×C3—61no—
368C23×C3—62no—
369C23×C3—61no—
370C23×C3#23514yes—
371C23×C3#23714yes—
372C23×C3C23×D311yescharacteristic
373C23×C3C23×D311yescharacteristic
374C22×D3—21no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—21no—
378C22×D3D3×D412yes—
379C3×D4—28no—
380C3×D4—28no—
381C3×D4—48no—
382C3×D4—616no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—32no—
387C2×C3×C4—32no—
388C2×C3×C4—32no—
389C2×C3×C4—32no—
390C2×C3×C4—34no—
391C2×C3×C4—42no—
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—61no—
400C2×C3×C4—128no—
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6712yes—
403#67—216no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—32no—
413C2×Dic3—32no—
414C2×Dic3—48no—
415C2×Dic3—62no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—68no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—61no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—61no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3—121no—
434C2×Dic3—122no—
435C2×Dic3—122no—
436C2×Dic3—122no—
437C2×Dic3—122no—
438C2×Dic3D3×D412yes—
439C2×Dic3#23714yes—
440C2×Dic3#23712yes—
441C2×Dic3C2×#6712yes—
442C2×Dic3C2×#6712yes—
443C4×D3—68no—
444C2×C32—44no—
445C2×C32C2×#12111yescharacteristic
446C2×C32#52511yescharacteristic
447C2×C32#52512yes—
448C2×C32#52912yes—
449C2×C32#53211yescharacteristic
450C3×D3—42no—
451C24—31no—
452C24C2×D3212yes—
453C2×D4—24no—
454C2×D4—22no—
455C2×D4—64no—
456C2×D4—64no—
457C2×D4—64no—
458C22×C4—31no—
459C22×C4—32no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—32no—
463C22×C4—64no—
464C22×C4—64no—
465C22×C4—64no—
466C22×C4—94no—
467C22×C4—91no—
468C22×C4—92no—
469C22×C4—91no—
470C22×C4—182no—
471C22×C4—182no—
472C22×C4C2×D3211yescharacteristic
473C4⋊C4—62no—
474C4⋊C4—182no—
475C4⋊C4—184no—
476C4⋊C4—184no—
477C4⋊C4—182no—
478C22⋊C4—64no—
479C22⋊C4—64no—
480C22⋊C4—62no—
481C22⋊C4—182no—
482C22⋊C4—184no—
483C22⋊C4—184no—
484C22⋊C4—184no—
485C42—34no—
486C42—182no—
487C42—184no—
488C22×C3—24no—
489C22×C3—24no—
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—21no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3—44no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—42no—
510C22×C3—62no—
511C22×C3—64no—
512C22×C3—82no—
513C22×C3—82no—
514C22×C3—82no—
515C22×C3—82no—
516C22×C3—121no—
517C22×C3—122no—
518C22×C3—121no—
519C22×C3C2×#23512yes—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C2×D3×D411yescharacteristic
522C22×C3C2×D3×D411yescharacteristic
523C22×C3C2×#23712yes—
524C22×C3C2×#23711yescharacteristic
525C22×C3C2×#23712yes—
526C22×C3D3×#4112yes—
527C22×C3D3×#4111yescharacteristic
528C22×C3C22×#6711yescharacteristic
529C2×D3—24no—
530C2×D3—22no—
531C2×D3—41no—
532C2×D3—41no—
533C2×D3—42no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—34no—
537C3×C4—42no—
538C3×C4—62no—
539C3×C4—64no—
540C3×C4—121no—
541C3×C4—122no—
542Dic3—22no—
543Dic3—24no—
544Dic3—41no—
545Dic3—42no—
546Dic3—62no—
547Dic3—62no—
548Dic3—122no—
549Dic3—121no—
550Dic3—122no—
551Dic3—122no—
552Dic3—121no—
553Dic3—242no—
554Dic3—241no—
555Dic3#93814yes—
556C32#239211yescharacteristic, complemented, Sylow
557C23—22no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—32no—
564C23—61no—
565C23—62no—
566C23—62no—
567C23—61no—
568C23#380414yes—
569C23C22×D3211yescharacteristic
570D4—28no—
571D4—616no—
572C2×C4—22no—
573C2×C4—32no—
574C2×C4—32no—
575C2×C4—32no—
576C2×C4—34no—
577C2×C4—32no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—61no—
585C2×C4—62no—
586C2×C4—92no—
587C2×C4—128no—
588C2×C4—188no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—182no—
592C2×C4—182no—
593C2×C4—182no—
594C2×C4—182no—
595C2×C4—181no—
596C2×C4D3×#6712yes—
597C2×C3—22no—
598C2×C3—21no—
599C2×C3—22no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—44no—
603C2×C3—44no—
604C2×C3—84no—
605C2×C3—122no—
606C2×C3#553812yes—
607C2×C3#554712yes—
608C2×C3#558612yes—
609C2×C3#558611yescharacteristic
610C2×C3#560012yes—
611C2×C3D3×#12111yescharacteristic
612C2×C3#571611yescharacteristic
613C2×C3#579111yescharacteristic
614C2×C3C2×#93811yescharacteristic
615C2×C3#583211yescharacteristic
616D3—42no—
617C22—24no—
618C22—24no—
619C22—24no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—64no—
625C22—62no—
626C22—121no—
627C22—122no—
628C22—121no—
629C22D32×D411yescharacteristic
630C22D3×#23712yes—
631C22D3×#23711yescharacteristic
632C22C2×#380412yes—
633C22C2×D3×#6711yescharacteristic
634C4—22no—
635C4—34no—
636C4—64no—
637C4—62no—
638C4—121no—
639C4—122no—
640C4—182no—
641C4—362no—
642C4—361no—
643C3—21no—
644C3#7666611yescharacteristic, complemented
645C3#8240111yescharacteristic, complemented
646C2—44no—
647C2—122no—
648C2#1059512912yes—
649C2#1059515211yescharacteristic
650C2#1059518712yes—
651C2D3×#93811yescharacteristic
652C2#1059549811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC3×#5223C2
hypercenterC22×D4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Dic3C2semidirect
2. C2×Dic3×#67C2semidirect
3. C2×#63877C2semidirect
4. #10592921C2semidirect
6. #10591709C2semidirect
7. Dic3×#217C2semidirect
8. #10591691C2semidirect
9. #10591358C2semidirect
10. #10591314C2semidirect
11. #10591242C2semidirect
42. C2×D4×Dic3D3semidirect
84. C2×D3×Dic3D4semidirect
92. C3×C4×Dic3D4semidirect
292. C4×Dic3#67semidirect
556. C32#2392semidirect
644. C3#76666semidirect
645. C3#82401semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×Dic3×#672
C2×#638772
#105929212
C3×#52232
#105917092
Dic3×#2172
#105916912
#105913582
#105913142
#105912422
#824013
#766663