Finite Group Databasebeta

← #11808450

Subgroups — #11808450

Order 1152.

1467 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C2×#63879C212yesmaximal, complemented
4#10592680C211yesmaximal, characteristic, complemented
5C3×#4991C211yesmaximal, characteristic, complemented
6#10591390C212yesmaximal, complemented
7#10591389C211yesmaximal, characteristic
8Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
9#10591315C211yesmaximal, characteristic, complemented
10#10591308C212yesmaximal, complemented
11#10591242C211yesmaximal, characteristic, complemented
12#82273—31nomaximal
13#76891—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×#625C2212yes—
17C22×D3×Dic3C2212yes—
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750C2212yes—
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#892—24no—
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×(C2×D3)⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×Dic32C2212yes—
34Dic3×D12—24no—
35#63879—28no—
36#63658C2211yescharacteristic
37#63658C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39#63579C2212yes—
40C2×C3×#117—31no—
41C2×D4×Dic3—31no—
42C2×C4×#67—32no—
43C2×#892D311yescharacteristic, complemented
44C2×#67⋊C4—32no—
45C2×C4×D12—31no—
46C3×#394—31no—
47#5223—31no—
48#4994—32no—
49#4991D311yescharacteristic, complemented
50#4981—31no—
51#4981—31no—
52#4981—61no—
53#4961—32no—
54#4960—31no—
55#4959—32no—
56#4953—31no—
57#4948—32no—
58Dic3×C22⋊C4—32no—
59C4×(C2×D3)⋊C4—32no—
60C4×C4⋊Dic3—31no—
61#4674—31no—
62#4649—31no—
63C23×C3×D3C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×D12—24no—
75C2×C3×D12—22no—
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3D414yescomplemented
79C2×#625—24no—
80C2×#625—24no—
81C2×#625—24no—
82C2×D3×Dic3—24no—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—24no—
85C32×C4⋊C4—22no—
86C4⋊(C3⋊Dic3)—22no—
87#3750—24no—
88C3×(C2×D3)⋊C4—24no—
89C3×(C2×D3)⋊C4—22no—
90C3×(C2×D3)⋊C4—24no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3—22no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3D414yescomplemented
95Dic3⋊Dic3—24no—
96(C2×D3)⋊Dic3—24no—
97(C2×D3)⋊Dic3—24no—
98(C2×D3)⋊Dic3—24no—
99Dic32—24no—
100#2392—91noSylow
101C22×C3×D4—31no—
102C23×C3×C4—31no—
103C22×#67—32no—
104C22×#67—32no—
105C23×Dic3—32no—
106C22×D12C2×D311yescharacteristic
107C22×C4×D3—32no—
108C22×C4×D3C2×D311yescharacteristic
109C3×#117—64no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×C3×C22⋊C4—32no—
115C2×C3×C22⋊C4—32no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—31no—
118C2×C3×C42—31no—
119C2×C3×C42—31no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—32no—
123D4×Dic3—64no—
124C4×#67—68no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4C2×D311yescharacteristic
129C2×(C2×D3)⋊C4C2×D312yes—
130C2×(C2×D3)⋊C4C2×D311yescharacteristic
131C2×(C2×D3)⋊C4C2×D312yes—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—32no—
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—32no—
139C2×Dic3⋊C4—32no—
140C2×Dic3⋊C4—62no—
141C2×C4×Dic3—32no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3C2×D311yescharacteristic
144C2×C4×Dic3C2×D311yescharacteristic
145#892—24no—
146#67⋊C4—68no—
147C4×D12—64no—
148C3×#95—31no—
149C3⋊#95—31no—
150C3⋊#95—31no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—62no—
156C3⋊#95—61no—
157C3⋊#95C2×D311yescharacteristic
158C23×C32C2411yescharacteristic
159C22×C3×D3—22no—
160C22×C3×D3—21no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C22×C3×D3—22no—
169C22×C3×D3C2×D412yes—
170C22×C3×D3#4114yes—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—22no—
174C2×C32×C4—21no—
175C2×C32×C4—22no—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2×D412yes—
178C2×C3⋊Dic3—22no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3#4114yes—
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×Dic3C2×D412yes—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3#4112yes—
194C3×D12—28no—
195C3×C4×D3—28no—
196#625—216no—
197D3×Dic3—48no—
198C2×C4×D4—91no—
199C2×C4×D4—92no—
200C2×#117—31no—
201#398—91no—
202#397—91no—
203#396—92no—
204#394—31no—
205#394—92no—
206#392—91no—
207C4×C4⋊C4—91no—
208C4×C22⋊C4—92no—
209C24×C3—32no—
210C24×C3—31no—
211C23×D3C22×D311yescharacteristic
212C23×D3C22×D312yes—
213C2×C3×D4—64no—
214C2×C3×D4—62no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—34no—
221C22×C3×C4—31no—
222C22×C3×C4—32no—
223C22×C3×C4—62no—
224C22×C3×C4—62no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—64no—
232C2×#67—64no—
233C2×#67—64no—
234C2×#67—64no—
235C2×#67—64no—
236C2×#67—64no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—32no—
241C22×Dic3—62no—
242C22×Dic3—62no—
243C22×Dic3—64no—
244C22×Dic3—64no—
245C22×Dic3—64no—
246C22×Dic3C22×D311yescharacteristic
247C22×Dic3C22×D312yes—
248C22×Dic3C22×D311yescharacteristic
249C22×Dic3C22×D311yescharacteristic
250C2×D12—24no—
251C2×D12—22no—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3D1214yescomplemented
258C3×C4⋊C4—22no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—42no—
261C3×C4⋊C4—62no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—64no—
264C3×C22⋊C4—64no—
265C3×C22⋊C4—62no—
266C3×C42—34no—
267C3×C42—62no—
268#217—64no—
269#217—64no—
270#217—64no—
271(C2×D3)⋊C4—24no—
272(C2×D3)⋊C4—24no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—22no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—64no—
278C4⋊Dic3—22no—
279C4⋊Dic3—64no—
280C4⋊Dic3—62no—
281C4⋊Dic3—62no—
282C4⋊Dic3—122no—
283Dic3⋊C4—64no—
284Dic3⋊C4—64no—
285Dic3⋊C4—64no—
286Dic3⋊C4—124no—
287C4×Dic3—22no—
288C4×Dic3—64no—
289C4×Dic3—64no—
290C4×Dic3#6714yescomplemented
291C22×C32C22×D411yescharacteristic
292C22×C32C22×D411yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C22×C32C2×#4112yes—
295C22×C32C2×#4112yes—
296C2×C3×D3—22no—
297C2×C3×D3—24no—
298C2×C3×D3—24no—
299C2×C3×D3—24no—
300C2×C3×D3—24no—
301C2×C3×D3—42no—
302C2×C3×D3—41no—
303C2×C3×D3—42no—
304C2×C3×D3—42no—
305C2×C3×D3—42no—
306C2×C3×D3—42no—
307C2×C3×D3—41no—
308C32×C4—22no—
309C32×C4—22no—
310C32×C4—41no—
311C3⋊Dic3—24no—
312C3⋊Dic3—42no—
313C3×Dic3—22no—
314C3×Dic3—42no—
315C3×Dic3—41no—
316C3×Dic3#12114yes—
317C22×D4—31no—
318C22×D4—92no—
319C23×C4—31no—
320C23×C4—92no—
321C4×D4—184no—
322C4×D4—188no—
323#117—64no—
324C2×C4⋊C4—31no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—92no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4D3211yescharacteristic
329C2×C22⋊C4—31no—
330C2×C22⋊C4—31no—
331C2×C22⋊C4—32no—
332C2×C22⋊C4—32no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—92no—
336C2×C42—31no—
337C2×C42—31no—
338C2×C42—92no—
339#95—31no—
340#95—92no—
341#95—92no—
342#95—91no—
343C23×C3—21no—
344C23×C3—32no—
345C23×C3—34no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—61no—
349C23×C3—62no—
350C23×C3—62no—
351C23×C3—62no—
352C23×C3—62no—
353C23×C3—61no—
354C23×C3—62no—
355C23×C3—62no—
356C23×C3C23×D311yescharacteristic
357C23×C3C23×D311yescharacteristic
358C22×D3—21no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—22no—
364C22×D3—22no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—21no—
368C22×D3C2×D1212yes—
369C22×D3#23714yes—
370C3×D4—68no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—32no—
384C2×C3×C4—32no—
385C2×C3×C4—32no—
386C2×C3×C4—32no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—42no—
390C2×C3×C4—41no—
391C2×C3×C4—42no—
392C2×C3×C4—68no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4C2×D1212yes—
400C2×C3×C4D3×D412yes—
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6712yes—
403#67—616no—
404#67—616no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—21no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—64no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—62no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—122no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427C2×Dic3—122no—
428C2×Dic3—122no—
429C2×Dic3—128no—
430C2×Dic3C2×D1212yes—
431C2×Dic3#23512yes—
432C2×Dic3C2×#6712yes—
433C2×Dic3C2×#6712yes—
434D12—28no—
435C4×D3—28no—
436C4×D3—128no—
437C2×C32C2×#12111yescharacteristic
438C2×C32#52512yes—
439C2×C32#52511yescharacteristic
440C2×C32#52912yes—
441C2×C32#53211yescharacteristic
442C3×D3—44no—
443C3×D3—42no—
444C24—31no—
445C24—32no—
446C2×D4—64no—
447C2×D4—62no—
448C2×D4—184no—
449C2×D4—184no—
450C2×D4—184no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—34no—
454C22×C4—32no—
455C22×C4—31no—
456C22×C4—62no—
457C22×C4—62no—
458C22×C4—92no—
459C22×C4—92no—
460C22×C4—184no—
461C22×C4—184no—
462C22×C4—184no—
463C22×C4C2×D3211yescharacteristic
464C22×C4C2×D3211yescharacteristic
465C22×C4C2×D3211yescharacteristic
466C4⋊C4—22no—
467C4⋊C4—62no—
468C4⋊C4—184no—
469C4⋊C4—184no—
470C4⋊C4—182no—
471C22⋊C4—62no—
472C22⋊C4—64no—
473C22⋊C4—64no—
474C22⋊C4—62no—
475C22⋊C4—184no—
476C22⋊C4—184no—
477C22⋊C4—184no—
478C42—34no—
479C42—62no—
480C42—184no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—21no—
486C22×C3—64no—
487C22×C3—64no—
488C22×C3—64no—
489C22×C3—62no—
490C22×C3—64no—
491C22×C3—122no—
492C22×C3—121no—
493C22×C3—122no—
494C22×C3—122no—
495C22×C3—122no—
496C22×C3—122no—
497C22×C3—121no—
498C22×C3C22×D1211yescharacteristic
499C22×C3C2×#23511yescharacteristic
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C22×C3C2×#23712yes—
503C22×C3D3×#4111yescharacteristic
504C22×C3D3×#4112yes—
505C22×C3D3×#4112yes—
506C22×C3D3×#4112yes—
507C22×C3C22×#6711yescharacteristic
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—22no—
511C2×D3—24no—
512C2×D3—24no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—42no—
516C2×D3—41no—
517C2×D3—41no—
518C2×D3—42no—
519C2×D3—42no—
520C3×C4—22no—
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—34no—
525C3×C4—42no—
526C3×C4—42no—
527C3×C4—41no—
528C3×C4—41no—
529C3×C4—62no—
530C3×C4—81no—
531C3×C4—121no—
532C3×C4—122no—
533Dic3—22no—
534Dic3—41no—
535Dic3—42no—
536Dic3—64no—
537Dic3—64no—
538Dic3—124no—
539Dic3—122no—
540Dic3—122no—
541Dic3—242no—
542Dic3#93014yes—
543C32#239211yescharacteristic, complemented, Sylow
544C23—32no—
545C23—34no—
546C23—62no—
547C23—61no—
548C23—62no—
549C23—62no—
550C23—62no—
551C23—62no—
552C23—62no—
553C23—62no—
554C23—61no—
555C23—62no—
556C23C22×D3211yescharacteristic
557D4—68no—
558D4—1816no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—32no—
565C2×C4—32no—
566C2×C4—32no—
567C2×C4—32no—
568C2×C4—68no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—61no—
575C2×C4—94no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—182no—
579C2×C4—182no—
580C2×C4—182no—
581C2×C4—368no—
582C2×C4D3×D1212yes—
583C2×C4D3×#6712yes—
584C2×C3—21no—
585C2×C3—22no—
586C2×C3—21no—
587C2×C3—22no—
588C2×C3—21no—
589C2×C3—122no—
590C2×C3—124no—
591C2×C3#552412yes—
592C2×C3#552812yes—
593C2×C3#558611yescharacteristic
594C2×C3D3×#12111yescharacteristic
595C2×C3#560612yes—
596C2×C3#564912yes—
597C2×C3#566811yescharacteristic
598C2×C3C2×#93011yescharacteristic
599C2×C3#582811yescharacteristic
600C2×C3#583211yescharacteristic
601D3—44no—
602D3—42no—
603C22—64no—
604C22—64no—
605C22—64no—
606C22—64no—
607C22—62no—
608C22—122no—
609C22—121no—
610C22—122no—
611C22—121no—
612C22—122no—
613C22—122no—
614C22—122no—
615C22C2×D3×D1211yescharacteristic
616C22D3×#23511yescharacteristic
617C22D3×#23712yes—
618C22#6431912yes—
619C22C2×D3×#6711yescharacteristic
620C4—22no—
621C4—22no—
622C4—34no—
623C4—41no—
624C4—62no—
625C4—121no—
626C4—122no—
627C4—184no—
628C4—362no—
629C3—21no—
630C3#7689111yescharacteristic, complemented
631C3#8227311yescharacteristic, complemented
632C2—122no—
633C2—124no—
634C2#1059440412yes—
635C2#1059462612yes—
636C2D3×#93011yescharacteristic
637C2#1059515411yescharacteristic
638C2#1059535911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radical#10591389C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#892C2semidirect
2. C2×Dic3×D12C2semidirect
3. C2×#63879C2semidirect
4. #10592680C2semidirect
5. C3×#4991C2semidirect
6. #10591390C2semidirect
8. Dic3×(C2×D3)⋊C4C2semidirect
9. #10591315C2semidirect
10. #10591308C2semidirect
11. #10591242C2semidirect
43. C2×#892D3semidirect
49. #4991D3semidirect
78. C2×C3×C4×D3D4semidirect
94. C3×C4×Dic3D4semidirect
257. C2×C4×D3D12semidirect
290. C4×Dic3#67semidirect
543. C32#2392semidirect
630. C3#76891semidirect
631. C3#82273semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×Dic3×D122
C2×#638792
#105926802
C3×#49912
#105913902
#105913892
Dic3×(C2×D3)⋊C42
#105913152
#105913082
#105912422
#822733
#768913