Finite Group Databasebeta

← #11808464

Subgroups — #11808464

Order 1152.

1477 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic, complemented
2C2×#63880C212yesmaximal, complemented
3C2×#63836C211yesmaximal, characteristic, complemented
4#10592373C211yesmaximal, characteristic, complemented
5C3×#4672C211yesmaximal, characteristic, complemented
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591391C211yesmaximal, characteristic
8Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
9#10591353C211yesmaximal, characteristic, complemented
10#10591306C212yesmaximal, complemented
11#10591291C212yesmaximal, complemented
12#76891—31nomaximal
13#73776—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×#626C2212yes—
16C22×#624C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×#3752C2212yes—
19C2×#3752C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2211yescharacteristic
29C2×#3722C2211yescharacteristic
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×Dic32C2211yescharacteristic
33Dic3×D12—24no—
34#63880—28no—
35#63836—24no—
36C32×#95C2211yescharacteristic
37#63658C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39#63579C2212yes—
40C2×D4×Dic3—31no—
41C2×#892—31no—
42C2×#67⋊C4—32no—
43C2×C4×D12—31no—
44C2×C4×D12—32no—
45C2×#872—31no—
46C3×#394—31no—
47C3×C4×C4⋊C4—31no—
48#5223—31no—
49#4994—32no—
50#4991—32no—
51#4981—31no—
52#4959—32no—
53#4948—32no—
54Dic3×C22⋊C4—32no—
55C4×(C2×D3)⋊C4—32no—
56#4674—31no—
57#4674—31no—
58#4674—61no—
59#4672D311yescharacteristic, complemented
60#4671—31no—
61#4661—31no—
62#4649D311yescharacteristic, complemented
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×D12—24no—
75C2×C3×D12—22no—
76C2×#626—24no—
77C2×#626—24no—
78C2×#626—24no—
79C2×#624—22no—
80C2×#624—22no—
81C2×#624D414yescomplemented
82C2×D3×Dic3—24no—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85#3752—24no—
86#3752—22no—
87C4⋊(C3⋊Dic3)—22no—
88C3×(C2×D3)⋊C4—24no—
89C3×(C2×D3)⋊C4—24no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—24no—
92C3×C4×Dic3—24no—
93C3×C4×Dic3D414yescomplemented
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—24no—
96#3722—22no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3—24no—
99Dic32—22no—
100#2392—91noSylow
101C22×C3×D4—31no—
102C22×#67—32no—
103C23×Dic3—32no—
104C22×D12—32no—
105C22×D12C2×D311yescharacteristic
106C22×C4×D3—31no—
107C22×C4×D3—31no—
108C22×C4×D3—32no—
109C2×C3×C4⋊C4—31no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C22⋊C4—32no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C42—31no—
114C2×C3×C42—32no—
115C2×#217—32no—
116C2×#217—32no—
117D4×Dic3—64no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—61no—
127C2×(C2×D3)⋊C4—62no—
128C2×(C2×D3)⋊C4C2×D312yes—
129C2×(C2×D3)⋊C4C2×D312yes—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—31no—
132C2×C4⋊Dic3—32no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—61no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4C2×D312yes—
138C2×Dic3⋊C4C2×D311yescharacteristic
139C2×C4×Dic3—31no—
140C2×C4×Dic3—31no—
141C2×C4×Dic3C2×D312yes—
142C2×C4×Dic3C2×D311yescharacteristic
143#892—64no—
144#67⋊C4—68no—
145C4×D12—68no—
146C4×D12—64no—
147#872—64no—
148C3×#95—21no—
149C3×#95—31no—
150C3×#95C2×D311yescharacteristic
151C3×#95C2×D311yescharacteristic
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—62no—
157C3⋊#95C2×D311yescharacteristic
158C23×C32C2411yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3⋊D3—21no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3C2×D412yes—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3#4114yes—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4C2×D412yes—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D412yes—
189C2×C3×Dic3C2×D412yes—
190C2×C3×Dic3C2×D412yes—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3#4114yes—
193C2×C3×Dic3#4112yes—
194C3×D12—28no—
195#626—216no—
196#624—28no—
197D3×Dic3—48no—
198C2×C4×D4—92no—
199C2×C4×D4—91no—
200C2×#117—91no—
201#398—91no—
202#397—91no—
203#396—92no—
204#394—31no—
205#394—92no—
206#392—91no—
207C4×C4⋊C4—31no—
208C4×C22⋊C4—92no—
209C24×C3—32no—
210C23×D3—31no—
211C23×D3—31no—
212C23×D3—61no—
213C23×D3C22×D312yes—
214C2×C3×D4—64no—
215C2×C3×D4—62no—
216C22×C3×C4—21no—
217C22×C3×C4—22no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4C22×D312yes—
224C22×C3×C4C22×D312yes—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—64no—
228C2×#67—64no—
229C2×#67—64no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—32no—
233C22×Dic3—32no—
234C22×Dic3—61no—
235C22×Dic3—62no—
236C22×Dic3—64no—
237C22×Dic3—64no—
238C22×Dic3—64no—
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D311yescharacteristic
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D311yescharacteristic
243C22×Dic3C22×D311yescharacteristic
244C2×D12—24no—
245C2×D12—22no—
246C2×D12—64no—
247C2×D12—64no—
248C2×D12—64no—
249C2×C4×D3—34no—
250C2×C4×D3—34no—
251C2×C4×D3—62no—
252C2×C4×D3—62no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C3×C4⋊C4—64no—
259C3×C4⋊C4—62no—
260C3×C22⋊C4—64no—
261C3×C22⋊C4—64no—
262C3×C42—34no—
263C3×C42—64no—
264#217—64no—
265#217—64no—
266(C2×D3)⋊C4—24no—
267(C2×D3)⋊C4—24no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—64no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—122no—
277(C2×D3)⋊C4—124no—
278C4⋊Dic3—62no—
279C4⋊Dic3—62no—
280C4⋊Dic3—62no—
281C4⋊Dic3—64no—
282C4⋊Dic3—122no—
283Dic3⋊C4—22no—
284Dic3⋊C4—24no—
285Dic3⋊C4—62no—
286Dic3⋊C4—64no—
287C4×Dic3—24no—
288C4×Dic3—62no—
289C4×Dic3—62no—
290C4×Dic3D1214yescomplemented
291C22×C32C22×D411yescharacteristic
292C22×C32C22×D411yescharacteristic
293C22×C32C2×#4112yes—
294C22×C32C2×#4112yes—
295C22×C32C2×#4111yescharacteristic
296C2×C3⋊D3—22no—
297C2×C3⋊D3—24no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3—42no—
300C2×C3⋊D3—41no—
301C2×C3×D3—24no—
302C2×C3×D3—24no—
303C2×C3×D3—24no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—42no—
308C32×C4—22no—
309C32×C4—42no—
310C3⋊Dic3—42no—
311C3⋊Dic3—41no—
312C3×Dic3—22no—
313C3×Dic3—24no—
314C3×Dic3—22no—
315C3×Dic3—41no—
316C3×Dic3#12114yes—
317C22×D4—31no—
318C22×D4—92no—
319C23×C4—91no—
320C23×C4—92no—
321C4×D4—184no—
322C4×D4—188no—
323#117—184no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—32no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—92no—
328C2×C4⋊C4—91no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—91no—
335C2×C22⋊C4—92no—
336C2×C42—31no—
337C2×C42—32no—
338C2×C42—91no—
339#95—31no—
340#95—92no—
341#95—92no—
342#95D3211yescharacteristic
343C23×C3—21no—
344C23×C3—34no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—62no—
349C23×C3—62no—
350C23×C3—62no—
351C23×C3C23×D311yescharacteristic
352C23×C3C23×D311yescharacteristic
353C22×D3—22no—
354C22×D3—22no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—32no—
360C22×D3—32no—
361C22×D3—62no—
362C22×D3—61no—
363C22×D3—62no—
364C22×D3—61no—
365C22×D3—62no—
366C22×D3—61no—
367C22×D3—61no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—121no—
371C22×D3—122no—
372C22×D3—122no—
373C22×D3—121no—
374C22×D3#23714yes—
375C3×D4—68no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—32no—
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—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—61no—
399C2×C3×C4—62no—
400C2×C3×C4—61no—
401C2×C3×C4—62no—
402C2×C3×C4C2×D1212yes—
403C2×C3×C4D3×D412yes—
404#67—616no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—21no—
411C2×Dic3—22no—
412C2×Dic3—61no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—61no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—122no—
423C2×Dic3—121no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—128no—
428C2×Dic3C2×D1212yes—
429C2×Dic3C2×D1212yes—
430C2×Dic3#23514yes—
431C2×Dic3D3×D412yes—
432C2×Dic3D3×D412yes—
433C2×Dic3#23912yes—
434D12—28no—
435D12—616no—
436C4×D3—68no—
437C4×D3—68no—
438C4×D3—128no—
439C2×C32C2×#12111yescharacteristic
440C2×C32#52511yescharacteristic
441C2×C32#52512yes—
442C2×C32#52912yes—
443C2×C32#53211yescharacteristic
444C3⋊D3—42no—
445C3×D3—44no—
446C24—32no—
447C24—91no—
448C2×D4—64no—
449C2×D4—62no—
450C2×D4—184no—
451C2×D4—184no—
452C2×D4—184no—
453C22×C4—31no—
454C22×C4—32no—
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—31no—
458C22×C4—94no—
459C22×C4—91no—
460C22×C4—92no—
461C22×C4—182no—
462C22×C4—182no—
463C22×C4—184no—
464C22×C4—184no—
465C22×C4—184no—
466C22×C4C2×D3212yes—
467C22×C4C2×D3211yescharacteristic
468C4⋊C4—64no—
469C4⋊C4—62no—
470C4⋊C4—182no—
471C4⋊C4—184no—
472C4⋊C4—182no—
473C22⋊C4—64no—
474C22⋊C4—64no—
475C22⋊C4—184no—
476C22⋊C4—182no—
477C22⋊C4—184no—
478C22⋊C4—184no—
479C22⋊C4—182no—
480C42—34no—
481C42—64no—
482C42—182no—
483C22×C3—21no—
484C22×C3—22no—
485C22×C3—21no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—64no—
489C22×C3—64no—
490C22×C3—64no—
491C22×C3—122no—
492C22×C3—122no—
493C22×C3—122no—
494C22×C3—122no—
495C22×C3C22×D1211yescharacteristic
496C22×C3C2×#23512yes—
497C22×C3C2×D3×D411yescharacteristic
498C22×C3C2×D3×D411yescharacteristic
499C22×C3C2×D3×D411yescharacteristic
500C22×C3C2×#23712yes—
501C22×C3C2×#23911yescharacteristic
502C22×C3D3×#4112yes—
503C22×C3D3×#4112yes—
504C22×C3D3×#4111yescharacteristic
505C2×D3—24no—
506C2×D3—24no—
507C2×D3—24no—
508C2×D3—42no—
509C2×D3—42no—
510C2×D3—42no—
511C2×D3—42no—
512C2×D3—62no—
513C2×D3—64no—
514C2×D3—62no—
515C2×D3—64no—
516C2×D3—122no—
517C2×D3—124no—
518C2×D3—122no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—122no—
523C2×D3—121no—
524C2×D3—241no—
525C2×D3—242no—
526C2×D3—241no—
527C3×C4—22no—
528C3×C4—22no—
529C3×C4—34no—
530C3×C4—42no—
531C3×C4—42no—
532C3×C4—42no—
533C3×C4—62no—
534C3×C4—62no—
535C3×C4—64no—
536C3×C4—82no—
537C3×C4—121no—
538Dic3—22no—
539Dic3—24no—
540Dic3—22no—
541Dic3—41no—
542Dic3—121no—
543Dic3—121no—
544Dic3—122no—
545Dic3—122no—
546Dic3—242no—
547Dic3—241no—
548Dic3#89514yes—
549C32#239211yescharacteristic, complemented, Sylow
550C23—34no—
551C23—62no—
552C23—62no—
553C23—62no—
554C23—62no—
555C23—62no—
556C23—62no—
557C23—92no—
558C23—181no—
559C23—182no—
560C23—182no—
561C23—181no—
562C23C22×D3211yescharacteristic
563D4—68no—
564D4—1816no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—32no—
570C2×C4—32no—
571C2×C4—32no—
572C2×C4—32no—
573C2×C4—34no—
574C2×C4—32no—
575C2×C4—61no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—61no—
580C2×C4—61no—
581C2×C4—62no—
582C2×C4—188no—
583C2×C4—181no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—368no—
589C2×C4D3×D1212yes—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—22no—
593C2×C3—21no—
594C2×C3—22no—
595C2×C3—124no—
596C2×C3#547711yescharacteristic
597C2×C3C2×#89511yescharacteristic
598C2×C3#552411yescharacteristic
599C2×C3#554712yes—
600C2×C3#558012yes—
601C2×C3#558611yescharacteristic
602C2×C3D3×#12111yescharacteristic
603C2×C3#560612yes—
604C2×C3#564912yes—
605C2×C3#566811yescharacteristic
606D3—44no—
607D3—122no—
608D3—122no—
609D3—242no—
610C22—64no—
611C22—64no—
612C22—64no—
613C22—122no—
614C22—122no—
615C22—122no—
616C22—122no—
617C22—182no—
618C22—184no—
619C22—361no—
620C22—362no—
621C22—361no—
622C22C2×D3×D1211yescharacteristic
623C22D3×#23512yes—
624C22D32×D411yescharacteristic
625C22D3×#23712yes—
626C22D3×#23911yescharacteristic
627C4—22no—
628C4—34no—
629C4—42no—
630C4—62no—
631C4—62no—
632C4—64no—
633C4—121no—
634C4—362no—
635C4—361no—
636C3—21no—
637C3#7377611yescharacteristic, complemented
638C3#7689111yescharacteristic, complemented
639C2—124no—
640C2—362no—
641C2#1059396911yescharacteristic
642C2#1059407811yescharacteristic
643C2#1059428612yes—
644C2#1059441612yes—
645C2D3×#89511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radical#10591391C2
hypercenter#95D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×Dic3×D12C2semidirect
2. C2×#63880C2semidirect
3. C2×#63836C2semidirect
4. #10592373C2semidirect
5. C3×#4672C2semidirect
6. C3×#4649C2semidirect
8. Dic3×(C2×D3)⋊C4C2semidirect
9. #10591353C2semidirect
10. #10591306C2semidirect
11. #10591291C2semidirect
59. #4672D3semidirect
62. #4649D3semidirect
81. C2×#624D4semidirect
93. C3×C4×Dic3D4semidirect
290. C4×Dic3D12semidirect
549. C32#2392semidirect
637. C3#73776semidirect
638. C3#76891semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C2×#638802
C2×#638362
#105923732
C3×#46722
C3×#46492
#105913912
Dic3×(C2×D3)⋊C42
#105913532
#105913062
#105912912
#768913
#737763