Finite Group Databasebeta

← C4×#63877 #11800782

Subgroups — C4×#63877 #11800782

Order 1152.

1601 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63877C212yesmaximal
2C2×C4×D3×Dic3C211yesmaximal, characteristic
3C4×#3750C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
5C3×C42×Dic3C211yesmaximal, characteristic, complemented
6Dic3×(C2×D3)⋊C4C212yesmaximal
7C4×#3724C211yesmaximal, characteristic, complemented
8C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
9#10591243C212yesmaximal, complemented
10#10591239C212yesmaximal, complemented
11C4×Dic32C211yesmaximal, characteristic, complemented
12C4×#877—31nomaximal
13C4×#872—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3C2211yescharacteristic
16C22×D3×Dic3C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×#3750C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C2×#3724C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2211yescharacteristic
31C2×Dic32C2211yescharacteristic
32C2×Dic32C2212yes—
33#63877C4116yesdirect product factor
34C4×D3×Dic3C418yescomplemented
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C22×C4×Dic3—31no—
40C2×#877—32no—
41C2×#872—32no—
42C2×C42×D3—31no—
43C3×C4×C22⋊C4—31no—
44C3×C43—31no—
45C4×#217—31no—
46Dic3×C22⋊C4—32no—
47C4×(C2×D3)⋊C4—31no—
48C4×(C2×D3)⋊C4—32no—
49C4×(C2×D3)⋊C4D311yescharacteristic
50#4932—32no—
51C4×Dic3⋊C4—31no—
52C4×Dic3⋊C4—31no—
53C4×Dic3⋊C4—31no—
54C4×Dic3⋊C4—31no—
55C4×Dic3⋊C4—32no—
56C4×Dic3⋊C4—61no—
57C42×Dic3—31no—
58C42×Dic3—31no—
59C42×Dic3D311yescharacteristic, complemented
60#4649—32no—
61#4648—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2×C414yes—
76C2×D3×Dic3—24no—
77C2×D3×Dic3C2×C414yes—
78C2×D3×Dic3C2×C414yes—
79C2×D3×Dic3C2×C418yes—
80C32×C42—22no—
81#3750C2×C418yescomplemented
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3C2×C414yes—
84C3×(C2×D3)⋊C4C2×C418yes—
85C3×C4×Dic3—22no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3—24no—
88C3×C4×Dic3C2×C414yes—
89C3×C4×Dic3C2×C418yescomplemented
90#3724C2×C418yescomplemented
91(C2×D3)⋊Dic3C2×C418yes—
92Dic32—24no—
93Dic32C2×C414yes—
94Dic32C2×C414yes—
95Dic32C2×C418yescomplemented
96C4×#117—91noSylow
97C23×C3×C4—31no—
98C23×Dic3—31no—
99C23×Dic3—31no—
100C22×C4×D3—31no—
101C22×C4×D3—31no—
102C22×C4×D3C2×D311yescharacteristic
103C2×C3×C22⋊C4—32no—
104C2×C3×C42—21no—
105C2×C3×C42—31no—
106C2×C3×C42—32no—
107C2×C3×C42—31no—
108C2×C3×C42—32no—
109C2×C3×C42—31no—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D311yescharacteristic
112C2×#217—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4C2×D312yes—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—62no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—38no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—61no—
134C2×C4×Dic3—61no—
135C2×C4×Dic3C2×D312yes—
136C2×C4×Dic3C2×D311yescharacteristic
137C2×C4×Dic3C2×D311yescharacteristic
138C2×C4×Dic3C2×D311yescharacteristic
139C2×C4×Dic3C2×D312yes—
140#877—316no—
141#872—316no—
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—22no—
167C2×C3⋊Dic3C22×C412yes—
168C2×C3⋊Dic3C22×C414yes—
169C2×C3⋊Dic3C22×C412yes—
170C2×C3⋊Dic3C22×C414yes—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C22×C412yes—
178C2×C3×Dic3C22×C414yes—
179C2×C3×Dic3C22×C414yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C414yes—
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3#4114yes—
184C3×C4×D3—28no—
185D3×Dic3—28no—
186D3×Dic3C42116yescomplemented
187C2×#117—92no—
188C22×C42—91no—
189C4×C4⋊C4—92no—
190C4×C4⋊C4—91no—
191C4×C4⋊C4—91no—
192C4×C22⋊C4—31no—
193C4×C22⋊C4—92no—
194C4×C22⋊C4—91no—
195#376—92no—
196C43—31no—
197C43—91no—
198C24×C3—31no—
199C23×D3C22×D311yescharacteristic
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—31no—
203C22×C3×C4—31no—
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—34no—
208C22×C3×C4—62no—
209C22×C3×C4—62no—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D312yes—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—38no—
217C22×Dic3—34no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—32no—
221C22×Dic3—32no—
222C22×Dic3—34no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225C22×Dic3—62no—
226C22×Dic3—64no—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D311yescharacteristic
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—34no—
235C2×C4×D3—38no—
236C2×C4×D3—34no—
237C2×C4×D3—64no—
238C2×C4×D3C4×D314yes—
239C3×C22⋊C4—38no—
240C3×C42—22no—
241C3×C42—22no—
242C3×C42—34no—
243C3×C42—38no—
244C3×C42—42no—
245C3×C42—64no—
246C3×C42—62no—
247C3×C42—62no—
248#217—38no—
249(C2×D3)⋊C4—38no—
250(C2×D3)⋊C4C4×D318yes—
251Dic3⋊C4—38no—
252Dic3⋊C4—38no—
253Dic3⋊C4—38no—
254Dic3⋊C4—38no—
255Dic3⋊C4—68no—
256C4×Dic3—22no—
257C4×Dic3—22no—
258C4×Dic3—24no—
259C4×Dic3—34no—
260C4×Dic3—34no—
261C4×Dic3—34no—
262C4×Dic3—34no—
263C4×Dic3—38no—
264C4×Dic3—38no—
265C4×Dic3—34no—
266C4×Dic3—34no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3—64no—
272C4×Dic3—122no—
273C4×Dic3C4×D314yes—
274C4×Dic3C4×D318yescomplemented
275C22×C32C23×C411yescharacteristic
276C22×C32C23×C412yes—
277C22×C32C2×#4111yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32C2×#4112yes—
280C2×C3×D3—22no—
281C2×C3×D3—22no—
282C2×C3×D3—24no—
283C2×C3×D3—24no—
284C2×C3×D3C2×C4214yes—
285C32×C4—24no—
286C32×C4#11714yescomplemented
287C3⋊Dic3—22no—
288C3⋊Dic3—24no—
289C3⋊Dic3C2×C4214yes—
290C3×Dic3—22no—
291C3×Dic3—24no—
292C3×Dic3—24no—
293C3×Dic3C2×C4214yes—
294C3×Dic3#11714yescomplemented
295C23×C4—31no—
296C23×C4—91no—
297C23×C4—91no—
298#117—916no—
299C2×C4⋊C4—92no—
300C2×C4⋊C4—92no—
301C2×C22⋊C4—32no—
302C2×C22⋊C4—92no—
303C2×C42—32no—
304C2×C42—31no—
305C2×C42—32no—
306C2×C42—31no—
307C2×C42—31no—
308C2×C42—98no—
309C2×C42—92no—
310C2×C42—91no—
311C2×C42—91no—
312C2×C42—91no—
313C2×C42—92no—
314C2×C42—91no—
315C2×C42D3211yescharacteristic
316#95—32no—
317#95—92no—
318#95—92no—
319#95—92no—
320C23×C3—21no—
321C23×C3—34no—
322C23×C3—32no—
323C23×C3—62no—
324C23×C3—61no—
325C23×C3—61no—
326C23×C3C23×D311yescharacteristic
327C23×C3C23×D311yescharacteristic
328C22×D3—21no—
329C22×D3—21no—
330C22×D3—22no—
331C22×D3C2×C4×D314yes—
332C22×D3C2×C4×D312yes—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—32no—
342C2×C3×C4—34no—
343C2×C3×C4—32no—
344C2×C3×C4—34no—
345C2×C3×C4—32no—
346C2×C3×C4—34no—
347C2×C3×C4—34no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—68no—
357C2×C3×C4C2×C4×D314yes—
358C2×C3×C4C2×C4×D314yes—
359C2×C3×C4C2×C4×D312yes—
360C2×C3×C4C2×C4×D312yes—
361C2×C3×C4#23512yes—
362C2×C3×C4#23512yes—
363C2×C3×C4#23712yes—
364C2×C3×C4#23712yes—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—32no—
372C2×Dic3—32no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—316no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—34no—
379C2×Dic3—34no—
380C2×Dic3—62no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—64no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—62no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—68no—
391C2×Dic3—122no—
392C2×Dic3—122no—
393C2×Dic3—122no—
394C2×Dic3C2×C4×D312yes—
395C2×Dic3C2×C4×D314yes—
396C2×Dic3C2×C4×D314yes—
397C2×Dic3C2×C4×D312yes—
398C2×Dic3C2×C4×D314yes—
399C2×Dic3C2×C4×D312yes—
400C2×Dic3#23514yes—
401C4×D3—28no—
402C4×D3—316no—
403C4×D3—68no—
404C2×C32C22×C4211yescharacteristic
405C2×C32C2×#11711yescharacteristic
406C2×C32C2×#11711yescharacteristic
407C2×C32C4×#4112yes—
408C2×C32C4×#4112yes—
409C3×D3—24no—
410C24—31no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—34no—
417C22×C4—62no—
418C22×C4—62no—
419C22×C4—94no—
420C22×C4—98no—
421C22×C4—94no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—92no—
425C22×C4—184no—
426C22×C4C2×D3212yes—
427C22×C4C2×D3211yescharacteristic
428C4⋊C4—98no—
429C4⋊C4—98no—
430C22⋊C4—38no—
431C22⋊C4—98no—
432C42—22no—
433C42—34no—
434C42—38no—
435C42—64no—
436C42—62no—
437C42—62no—
438C42—94no—
439C42—94no—
440C42—98no—
441C42—94no—
442C42—184no—
443C42—182no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—21no—
449C22×C3—34no—
450C22×C3—62no—
451C22×C3—62no—
452C22×C3—64no—
453C22×C3—64no—
454C22×C3C22×C4×D311yescharacteristic
455C22×C3C22×C4×D312yes—
456C22×C3C22×C4×D311yescharacteristic
457C22×C3C22×C4×D312yes—
458C22×C3C2×#23511yescharacteristic
459C22×C3C2×#23512yes—
460C22×C3C2×#23511yescharacteristic
461C22×C3C2×#23711yescharacteristic
462C22×C3C2×#23711yescharacteristic
463C22×C3D3×#4112yes—
464C2×D3—22no—
465C2×D3—22no—
466C2×D3—24no—
467C2×D3—24no—
468C2×D3C42×D314yes—
469C3×C4—24no—
470C3×C4—24no—
471C3×C4—24no—
472C3×C4—34no—
473C3×C4—34no—
474C3×C4—44no—
475C3×C4—62no—
476C3×C4—64no—
477C3×C4—64no—
478C3×C4#87214yescomplemented
479C3×C4#87714yescomplemented
480Dic3—24no—
481Dic3—22no—
482Dic3—24no—
483Dic3—34no—
484Dic3—34no—
485Dic3—64no—
486Dic3—62no—
487Dic3—64no—
488Dic3—62no—
489Dic3—64no—
490Dic3—124no—
491Dic3—122no—
492Dic3C42×D314yes—
493Dic3#87214yescomplemented
494C32C4×#11711yescharacteristic, complemented, Sylow
495C23—34no—
496C23—32no—
497C23—61no—
498C23—62no—
499C23—61no—
500C23C22×D3211yescharacteristic
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—32no—
504C2×C4—34no—
505C2×C4—32no—
506C2×C4—34no—
507C2×C4—34no—
508C2×C4—32no—
509C2×C4—34no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—61no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—61no—
516C2×C4—68no—
517C2×C4—916no—
518C2×C4—92no—
519C2×C4—94no—
520C2×C4—92no—
521C2×C4—94no—
522C2×C4—188no—
523C2×C4—182no—
524C2×C4—182no—
525C2×C4—182no—
526C2×C4#379512yes—
527C2×C4C4×D3214yes—
528C2×C4C4×D3212yes—
529C2×C4#380412yes—
530C2×C3—21no—
531C2×C3—22no—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—64no—
536C2×C3C2×C42×D311yescharacteristic
537C2×C3C2×C42×D311yescharacteristic
538C2×C3C2×#87211yescharacteristic
539C2×C3C2×#87211yescharacteristic
540C2×C3C4×#23512yes—
541C2×C3C4×#23512yes—
542C2×C3C2×#87711yescharacteristic
543C2×C3D3×#11711yescharacteristic
544C2×C3C4×#23712yes—
545C2×C3C4×#23712yes—
546D3—24no—
547C22—34no—
548C22—62no—
549C22—64no—
550C22—64no—
551C22—62no—
552C22C2×#379511yescharacteristic
553C22C2×C4×D3211yescharacteristic
554C22C2×C4×D3212yes—
555C22D3×#23512yes—
556C22C2×#380411yescharacteristic
557C4—24no—
558C4—34no—
559C4—34no—
560C4—62no—
561C4—64no—
562C4—64no—
563C4—94no—
564C4—184no—
565C4—182no—
566C4#6387714yesdirect product factor
567C3—21no—
568C3C4×#87211yescharacteristic, complemented
569C3C4×#87711yescharacteristic, complemented
570C2—64no—
571C2C4×#379512yes—
572C2C42×D3211yescharacteristic
573C2D3×#87211yescharacteristic
574C2C2×#6387711yescharacteristic
575C2C4×#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
3. C4×#3750C2semidirect
5. C3×C42×Dic3C2semidirect
7. C4×#3724C2semidirect
9. #10591243C2semidirect
10. #10591239C2semidirect
11. C4×Dic32C2semidirect
33. #63877C4direct (N × H)
34. C4×D3×Dic3C4semidirect
59. C42×Dic3D3semidirect
81. #3750C2×C4semidirect
89. C3×C4×Dic3C2×C4semidirect
90. #3724C2×C4semidirect
95. Dic32C2×C4semidirect
186. D3×Dic3C42semidirect
274. C4×Dic3C4×D3semidirect
286. C32×C4#117semidirect
294. C3×Dic3#117semidirect
478. C3×C4#872semidirect
479. C3×C4#877semidirect
493. Dic3#872semidirect
494. C32C4×#117semidirect
566. C4#63877direct (N × H)
568. C3C4×#872semidirect
569. C3C4×#877semidirect

Maximal subgroups

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

subgroupindex
C2×#638772
C2×C4×D3×Dic32
C4×#37502
C3×C4×(C2×D3)⋊C42
C3×C42×Dic32
Dic3×(C2×D3)⋊C42
C4×#37242
C4×(C2×D3)⋊Dic32
#105912432
#105912392
C4×Dic322
C4×#8773
C4×#8723