Finite Group Databasebeta

← C4×#63836 #11800780

Subgroups — C4×#63836 #11800780

Order 1152.

1633 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#624C211yesmaximal, characteristic
2C2×#63836C212yesmaximal
3C4×#3752C211yesmaximal, characteristic
4C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C3×C42×Dic3C211yesmaximal, characteristic, complemented
6C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7C4×#3722C211yesmaximal, characteristic
8Dic3×Dic3⋊C4C212yesmaximal, complemented
9#10591239C212yesmaximal, complemented
10C4×Dic32C211yesmaximal, characteristic, complemented
11#10591233C212yesmaximal
12C4×#892—31nomaximal
13C4×#872—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#624C2211yescharacteristic
16C22×#624C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×#3752C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2211yescharacteristic
31C2×Dic32C2211yescharacteristic
32C2×Dic32C2212yes—
33C4×#624C418yescomplemented
34#63836C4116yesdirect product factor
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#892—32no—
40C2×#872—32no—
41C2×C42×D3—31no—
42C2×C42×D3—31no—
43C3×C4×C4⋊C4—31no—
44C3×C43—31no—
45Dic3×C4⋊C4—32no—
46C4×(C2×D3)⋊C4—31no—
47C4×(C2×D3)⋊C4—31no—
48C4×(C2×D3)⋊C4—31no—
49C4×(C2×D3)⋊C4—31no—
50C4×(C2×D3)⋊C4—32no—
51C4×(C2×D3)⋊C4—61no—
52C4×C4⋊Dic3—31no—
53#4932—32no—
54C4×Dic3⋊C4—32no—
55C4×Dic3⋊C4—31no—
56C4×Dic3⋊C4D311yescharacteristic, complemented
57C42×Dic3—31no—
58C42×Dic3—31no—
59C42×Dic3D311yescharacteristic, complemented
60#4666—32no—
61#4648—32no—
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3C2×C414yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C2×#624—24no—
77C2×#624C2×C414yes—
78C2×#624C2×C418yes—
79C2×#624C2×C414yes—
80C32×C42—22no—
81#3752C2×C418yes—
82C4×C3⋊Dic3—22no—
83C3×Dic3⋊C4C2×C418yescomplemented
84C3×C4×Dic3—22no—
85C3×C4×Dic3—22no—
86C3×C4×Dic3—24no—
87C3×C4×Dic3C2×C414yes—
88C3×C4×Dic3C2×C414yes—
89C3×C4×Dic3C2×C418yescomplemented
90Dic3⋊Dic3C2×C418yescomplemented
91#3722C2×C418yes—
92Dic32—24no—
93Dic32C2×C414yes—
94Dic32C2×C414yes—
95Dic32C2×C418yescomplemented
96C4×#117—91noSylow
97C22×C4×D3—31no—
98C22×C4×D3—31no—
99C22×C4×D3—31no—
100C22×C4×D3—31no—
101C22×C4×D3—31no—
102C22×C4×D3—31no—
103C22×C4×D3—61no—
104C2×C3×C4⋊C4—32no—
105C2×C3×C42—21no—
106C2×C3×C42—31no—
107C2×C3×C42—32no—
108C2×C3×C42—31no—
109C2×C3×C42—31no—
110C2×C3×C42—32no—
111C2×C3×C42—31no—
112C2×C3×C42C2×D311yescharacteristic
113C2×C3×C42C2×D311yescharacteristic
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—62no—
119C2×C4⋊Dic3—32no—
120C2×Dic3⋊C4—32no—
121C2×Dic3⋊C4C2×D312yes—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—32no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3C2×D312yes—
134C2×C4×Dic3C2×D311yescharacteristic
135C2×C4×Dic3C2×D311yescharacteristic
136C2×C4×Dic3C2×D311yescharacteristic
137C2×C4×Dic3C2×D311yescharacteristic
138C2×C4×Dic3C2×D312yes—
139#892—316no—
140#872—316no—
141C42×D3—38no—
142C42×D3—38no—
143C3×#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—62no—
151C3⋊#95C2×D312yes—
152C23×C32C2411yescharacteristic
153C22×C3⋊D3—22no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3C22×C414yes—
157C22×C3⋊D3C22×C412yes—
158C2×C32×C4—22no—
159C2×C32×C4—22no—
160C2×C32×C4C22×C414yes—
161C2×C32×C4C22×C412yes—
162C2×C32×C4#4112yes—
163C2×C32×C4#4112yes—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3C22×C412yes—
169C2×C3⋊Dic3C22×C414yes—
170C4×C3⋊D3—28no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C22×C414yes—
178C2×C3×Dic3C22×C414yes—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C414yes—
182C2×C3×Dic3C22×C414yes—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3#4114yes—
185#624—28no—
186#624C42116yescomplemented
187C2×#117—92no—
188C22×C42—91no—
189C4×C4⋊C4—31no—
190C4×C4⋊C4—91no—
191C4×C4⋊C4—92no—
192C4×C22⋊C4—92no—
193C4×C22⋊C4—91no—
194C4×C22⋊C4—91no—
195#376—92no—
196C43—31no—
197C43—91no—
198C23×D3—31no—
199C23×D3—31no—
200C23×D3—61no—
201C22×C3×C4—22no—
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—61no—
218C22×Dic3—62no—
219C22×Dic3C22×D311yescharacteristic
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D311yescharacteristic
225C2×C4×D3—34no—
226C2×C4×D3—34no—
227C2×C4×D3—38no—
228C2×C4×D3—38no—
229C2×C4×D3—34no—
230C2×C4×D3—34no—
231C2×C4×D3—34no—
232C2×C4×D3—34no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3—64no—
240C2×C4×D3—122no—
241C2×C4×D3—122no—
242C3×C4⋊C4—38no—
243C3×C42—22no—
244C3×C42—22no—
245C3×C42—34no—
246C3×C42—34no—
247C3×C42—38no—
248C3×C42—42no—
249C3×C42—64no—
250C3×C42—62no—
251C3×C42—62no—
252(C2×D3)⋊C4—38no—
253(C2×D3)⋊C4—38no—
254(C2×D3)⋊C4—38no—
255(C2×D3)⋊C4—38no—
256(C2×D3)⋊C4—68no—
257C4⋊Dic3—38no—
258Dic3⋊C4—38no—
259Dic3⋊C4C4×D318yescomplemented
260C4×Dic3—22no—
261C4×Dic3—22no—
262C4×Dic3—24no—
263C4×Dic3—34no—
264C4×Dic3—34no—
265C4×Dic3—34no—
266C4×Dic3—34no—
267C4×Dic3—38no—
268C4×Dic3—38no—
269C4×Dic3—64no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C4×Dic3—64no—
273C4×Dic3—122no—
274C4×Dic3C4×D314yes—
275C4×Dic3C4×D314yes—
276C4×Dic3C4×D318yescomplemented
277C22×C32C23×C411yescharacteristic
278C22×C32C23×C412yes—
279C22×C32C2×#4111yescharacteristic
280C22×C32C2×#4111yescharacteristic
281C22×C32C2×#4112yes—
282C2×C3⋊D3—22no—
283C2×C3⋊D3—22no—
284C2×C3⋊D3—24no—
285C2×C3⋊D3—24no—
286C2×C3⋊D3C2×C4214yes—
287C32×C4—24no—
288C32×C4#11714yescomplemented
289C3⋊Dic3—22no—
290C3⋊Dic3—24no—
291C3×Dic3—22no—
292C3×Dic3—24no—
293C3×Dic3—24no—
294C3×Dic3C2×C4214yes—
295C3×Dic3C2×C4214yes—
296C3×Dic3#11714yescomplemented
297C23×C4—91no—
298C23×C4—91no—
299C23×C4—91no—
300#117—916no—
301C2×C4⋊C4—32no—
302C2×C4⋊C4—92no—
303C2×C22⋊C4—92no—
304C2×C22⋊C4—92no—
305C2×C42—32no—
306C2×C42—31no—
307C2×C42—31no—
308C2×C42—32no—
309C2×C42—31no—
310C2×C42—31no—
311C2×C42—98no—
312C2×C42—92no—
313C2×C42—91no—
314C2×C42—91no—
315C2×C42—92no—
316C2×C42—91no—
317C2×C42D3211yescharacteristic
318#95—32no—
319#95—92no—
320#95—92no—
321#95—92no—
322C23×C3—21no—
323C23×C3C23×D311yescharacteristic
324C23×C3C23×D311yescharacteristic
325C22×D3—34no—
326C22×D3—34no—
327C22×D3—32no—
328C22×D3—32no—
329C22×D3—64no—
330C22×D3—62no—
331C22×D3—61no—
332C22×D3—62no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—62no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—122no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—24no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—34no—
351C2×C3×C4—32no—
352C2×C3×C4—34no—
353C2×C3×C4—34no—
354C2×C3×C4—34no—
355C2×C3×C4—32no—
356C2×C3×C4—34no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4C2×C4×D314yes—
365C2×C3×C4C2×C4×D314yes—
366C2×C3×C4C2×C4×D312yes—
367C2×C3×C4C2×C4×D312yes—
368C2×C3×C4#23512yes—
369C2×C3×C4#23512yes—
370C2×C3×C4#23712yes—
371C2×C3×C4#23912yes—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—34no—
380C2×Dic3—34no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—62no—
389C2×Dic3—61no—
390C2×Dic3—62no—
391C2×Dic3—122no—
392C2×Dic3—121no—
393C2×Dic3—121no—
394C2×Dic3—122no—
395C2×Dic3C2×C4×D312yes—
396C2×Dic3C2×C4×D314yes—
397C2×Dic3C2×C4×D314yes—
398C2×Dic3C2×C4×D312yes—
399C2×Dic3C2×C4×D312yes—
400C2×Dic3C2×C4×D314yes—
401C2×Dic3C2×C4×D314yes—
402C2×Dic3C2×C4×D312yes—
403C2×Dic3#23514yes—
404C4×D3—316no—
405C4×D3—316no—
406C4×D3—68no—
407C4×D3—68no—
408C4×D3—68no—
409C4×D3—68no—
410C4×D3—128no—
411C2×C32C22×C4211yescharacteristic
412C2×C32C2×#11711yescharacteristic
413C2×C32C2×#11711yescharacteristic
414C2×C32C4×#4112yes—
415C2×C32C4×#4112yes—
416C3⋊D3—24no—
417C24—91no—
418C22×C4—31no—
419C22×C4—31no—
420C22×C4—31no—
421C22×C4—31no—
422C22×C4—32no—
423C22×C4—32no—
424C22×C4—94no—
425C22×C4—98no—
426C22×C4—94no—
427C22×C4—91no—
428C22×C4—92no—
429C22×C4—94no—
430C22×C4—184no—
431C22×C4—182no—
432C22×C4—182no—
433C22×C4C2×D3212yes—
434C22×C4C2×D3211yescharacteristic
435C4⋊C4—38no—
436C4⋊C4—98no—
437C22⋊C4—98no—
438C22⋊C4—98no—
439C42—22no—
440C42—34no—
441C42—34no—
442C42—38no—
443C42—64no—
444C42—62no—
445C42—62no—
446C42—94no—
447C42—94no—
448C42—98no—
449C42—184no—
450C42—182no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—21no—
456C22×C3C22×C4×D311yescharacteristic
457C22×C3C22×C4×D312yes—
458C22×C3C22×C4×D311yescharacteristic
459C22×C3C22×C4×D312yes—
460C22×C3C2×#23511yescharacteristic
461C22×C3C2×#23512yes—
462C22×C3C2×#23511yescharacteristic
463C22×C3C2×#23711yescharacteristic
464C22×C3C2×#23911yescharacteristic
465C22×C3D3×#4112yes—
466C2×D3—34no—
467C2×D3—34no—
468C2×D3—64no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—64no—
472C2×D3—64no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—64no—
476C2×D3—64no—
477C2×D3—122no—
478C2×D3—124no—
479C2×D3—124no—
480C2×D3—122no—
481C3×C4—24no—
482C3×C4—24no—
483C3×C4—24no—
484C3×C4—34no—
485C3×C4—34no—
486C3×C4—34no—
487C3×C4—44no—
488C3×C4—62no—
489C3×C4—64no—
490C3×C4—64no—
491C3×C4#87214yescomplemented
492C3×C4#89214yescomplemented
493Dic3—24no—
494Dic3—22no—
495Dic3—24no—
496Dic3—62no—
497Dic3—64no—
498Dic3—62no—
499Dic3—64no—
500Dic3—122no—
501Dic3—124no—
502Dic3C42×D314yes—
503Dic3C42×D314yes—
504Dic3#87214yescomplemented
505C32C4×#11711yescharacteristic, complemented, Sylow
506C23—94no—
507C23—92no—
508C23—181no—
509C23—182no—
510C23—181no—
511C23C22×D3211yescharacteristic
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—34no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—32no—
518C2×C4—34no—
519C2×C4—34no—
520C2×C4—32no—
521C2×C4—34no—
522C2×C4—34no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—916no—
529C2×C4—92no—
530C2×C4—94no—
531C2×C4—188no—
532C2×C4—182no—
533C2×C4—181no—
534C2×C4—182no—
535C2×C4—181no—
536C2×C4—188no—
537C2×C4#379912yes—
538C2×C4C4×D3214yes—
539C2×C4C4×D3212yes—
540C2×C4#380412yes—
541C2×C3—22no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3C2×C42×D311yescharacteristic
547C2×C3C2×C42×D311yescharacteristic
548C2×C3C2×#87211yescharacteristic
549C2×C3C2×#87211yescharacteristic
550C2×C3C4×#23512yes—
551C2×C3C4×#23512yes—
552C2×C3C2×#89211yescharacteristic
553C2×C3D3×#11711yescharacteristic
554C2×C3C4×#23712yes—
555C2×C3C4×#23912yes—
556D3—64no—
557D3—64no—
558D3—124no—
559C22—94no—
560C22—184no—
561C22—184no—
562C22—182no—
563C22—182no—
564C22C2×#379911yescharacteristic
565C22C2×C4×D3212yes—
566C22C2×C4×D3211yescharacteristic
567C22D3×#23512yes—
568C22C2×#380411yescharacteristic
569C4—24no—
570C4—34no—
571C4—34no—
572C4—34no—
573C4—64no—
574C4—64no—
575C4—62no—
576C4—184no—
577C4—182no—
578C4#6383614yesdirect product factor
579C3—21no—
580C3C4×#87211yescharacteristic, complemented
581C3C4×#89211yescharacteristic, complemented
582C2—184no—
583C2C4×#379912yes—
584C2C42×D3211yescharacteristic
585C2D3×#87211yescharacteristic
586C2C2×#6383611yescharacteristic
587C2C4×#380412yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C22×C42
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C4×#117
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C3×C4×Dic3⋊C4C2semidirect
5. C3×C42×Dic3C2semidirect
6. C4×Dic3⋊Dic3C2semidirect
8. Dic3×Dic3⋊C4C2semidirect
9. #10591239C2semidirect
10. C4×Dic32C2semidirect
33. C4×#624C4semidirect
34. #63836C4direct (N × H)
56. C4×Dic3⋊C4D3semidirect
59. C42×Dic3D3semidirect
83. C3×Dic3⋊C4C2×C4semidirect
89. C3×C4×Dic3C2×C4semidirect
90. Dic3⋊Dic3C2×C4semidirect
95. Dic32C2×C4semidirect
186. #624C42semidirect
259. Dic3⋊C4C4×D3semidirect
276. C4×Dic3C4×D3semidirect
288. C32×C4#117semidirect
296. C3×Dic3#117semidirect
491. C3×C4#872semidirect
492. C3×C4#892semidirect
504. Dic3#872semidirect
505. C32C4×#117semidirect
578. C4#63836direct (N × H)
580. C3C4×#872semidirect
581. C3C4×#892semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6242
C2×#638362
C4×#37522
C3×C4×Dic3⋊C42
C3×C42×Dic32
C4×Dic3⋊Dic32
C4×#37222
Dic3×Dic3⋊C42
#105912392
C4×Dic322
#105912332
C4×#8923
C4×#8723