Finite Group Databasebeta

← C4×#88646 #13147702

Subgroups — C4×#88646 #13147702

Order 1728.

1386 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88646C211yesmaximal, characteristic
2C2×C4×D3×D9C212yesmaximal, complemented
3C42×C3⋊D9C211yesmaximal, characteristic, complemented
4C4×C9×D12C211yesmaximal, characteristic, complemented
5C3×C4×D36C211yesmaximal, characteristic, complemented
6#11721048C212yesmaximal, complemented
7#11721028C212yesmaximal, complemented
8C4×#6194C212yesmaximal, complemented
9#11721025C211yesmaximal, characteristic, complemented
10#11721000C211yesmaximal, characteristic, complemented
11#11720998C211yesmaximal, characteristic, complemented
12C4×#3802—31nomaximal
13C4×D4×D9—31nomaximal
14C22×D3×D9C2212yes—
15C2×C4×C3⋊D9C2211yescharacteristic
16C2×C4×C3⋊D9C2211yescharacteristic
17C2×C4×C3⋊D9C2211yescharacteristic
18C2×C9×D12C2211yescharacteristic
19C2×C4×D3×C9C2212yescomplemented
20C2×C3×D36C2211yescharacteristic
21C2×C3×C4×D9C2212yescomplemented
22C2×#6194C2212yes—
23C2×D3×Dic9C2212yescomplemented
24C2×(C3⋊D9)⋊C4C2212yes—
25C2×Dic3×D9C2212yescomplemented
26#88646C418yesdirect product factor
27C4×D3×D9—28no—
28C3×C42×C9C2211yescharacteristic, complemented
29C4×C3⋊Dic9C2211yescharacteristic, complemented
30C4×C3⋊Dic9C2211yescharacteristic, complemented
31C4×C3⋊Dic9C2211yescharacteristic, complemented
32C9×(C2×D3)⋊C4C2212yescomplemented
33C3×(C2×D9)⋊C4C2212yescomplemented
34C9×C4⋊Dic3C2211yescharacteristic, complemented
35C3×C4⋊Dic9C2211yescharacteristic, complemented
36(C2×D3)⋊Dic9C2212yescomplemented
37(C2×D9)⋊Dic3C2212yescomplemented
38#88442C2212yescomplemented
39C2×#3802—31no—
40C2×C4×D32—32no—
41C42×C3⋊D3—31no—
42C3×C4×D12—31no—
43C3×C4×D12D311yescharacteristic
44#63921—32no—
45#63902—32no—
46C4×#625—32no—
47#63900—31no—
48#63898—31no—
49#63898—31no—
50C2×D4×D9—31no—
51C22×C4×D9—32no—
52C4×D4×C9—31no—
53D4×Dic9—31no—
54C4×#611—32no—
55#63455—31no—
56C4⋊C4×D9—31no—
57#611⋊C4—32no—
58C22⋊C4×D9—32no—
59C4×D36D311yescharacteristic, complemented
60C42×D9—31no—
61C42×D9—61no—
62C22×C3⋊D9C2311yescharacteristic
63C22×D3×C9C2312yes—
64C22×C3×D9C2312yes—
65C2×D3×D9—24no—
66C2×D3×D9—24no—
67C2×D3×D9C2×C418yescomplemented
68C2×C3×C4×C9C2311yescharacteristic
69C2×C3×C4×C9C2311yescharacteristic
70C2×C3×C4×C9C2311yescharacteristic
71C2×C3⋊Dic9C2311yescharacteristic
72C2×C3⋊Dic9C2311yescharacteristic
73C2×C3⋊Dic9C2311yescharacteristic
74C4×C3⋊D9—22no—
75C4×C3⋊D9C2×C414yescomplemented
76C4×C3⋊D9D414yescomplemented
77C2×C9×Dic3C2312yes—
78C2×C3×Dic9C2312yes—
79C9×D12C2×C414yescomplemented
80C4×D3×C9—24no—
81C3×D36C2×C414yescomplemented
82C3×C4×D9—24no—
83#6194C2×C418yescomplemented
84D3×Dic9—24no—
85(C3⋊D9)⋊C4—24no—
86Dic3×D9—24no—
87C4×D3×D4—91no—
88C4×D3×D4—91no—
89C22×D32—32no—
90C2×C4×C3⋊D3—31no—
91C2×C4×C3⋊D3—31no—
92C2×C4×C3⋊D3—31no—
93C2×C3×D12—31no—
94C2×C3×D12C2×D311yescharacteristic
95C2×C3×C4×D3—32no—
96C2×C3×C4×D3C2×D312yes—
97C2×#625—32no—
98C2×#624—32no—
99C2×D3×Dic3—32no—
100C2×D3×Dic3—32no—
101#3802—38no—
102C4×D32—68no—
103C23×D9—32no—
104C32×C42C2×D311yescharacteristic
105C4×C3⋊Dic3—31no—
106C4×C3⋊Dic3—31no—
107C4×C3⋊Dic3—31no—
108C3×(C2×D3)⋊C4—32no—
109C3×(C2×D3)⋊C4C2×D312yes—
110C3×C4⋊Dic3—31no—
111C3×C4⋊Dic3C2×D311yescharacteristic
112#3724—32no—
113(C2×D3)⋊Dic3—32no—
114(C2×D3)⋊Dic3—32no—
115C2×D4×C9—31no—
116C22×C4×C9—32no—
117C2×#611—32no—
118C22×Dic9—32no—
119D4×D9—38no—
120C2×D36C2×D311yescharacteristic
121C2×C4×D9—31no—
122C2×C4×D9—31no—
123C2×C4×D9—32no—
124C2×C4×D9—31no—
125C2×C4×D9—32no—
126C2×C4×D9—68no—
127C2×C4×D9—61no—
128C2×C4×D9—61no—
129C2×C4×D9—61no—
130C2×C4×D9C2×D312yescomplemented
131C9×C4⋊C4—31no—
132C9×C22⋊C4—32no—
133C42×C9—21no—
134C42×C9C2×D311yescharacteristic, complemented
135#3676—32no—
136(C2×D9)⋊C4—32no—
137(C2×D9)⋊C4C2×D312yescomplemented
138C4⋊Dic9C2×D311yescharacteristic, complemented
139Dic9⋊C4—32no—
140C4×Dic9—31no—
141C4×Dic9—31no—
142C4×Dic9—31no—
143C4×Dic9—61no—
144C4×Dic9—61no—
145C4×Dic9—61no—
146C22×C3×C9C2411yescharacteristic
147C2×C3⋊D9C22×C412yes—
148C2×C3⋊D9C2×D412yes—
149C2×C3⋊D9#4112yes—
150C2×D3×C9—22no—
151C2×D3×C9—22no—
152C2×D3×C9C22×C414yescomplemented
153C2×C3×D9—22no—
154C2×C3×D9—22no—
155C2×C3×D9C22×C414yescomplemented
156D3×D9—216no—
157C3×C4×C9—21no—
158C3×C4×C9C22×C412yescomplemented
159C3×C4×C9C2×D412yescomplemented
160C3⋊Dic9—21no—
161C3⋊Dic9C22×C412yescomplemented
162C3⋊Dic9C2×D412yescomplemented
163C9×Dic3—22no—
164C3×Dic9—22no—
165C2×D3×D4—91no—
166C2×D3×D4—91no—
167C22×C4×D3—92no—
168C22×C4×D3—92no—
169C3×C4×D4—31no—
170C3×C4×D4—91no—
171D4×Dic3—91no—
172D4×Dic3—91no—
173C4×#67—92no—
174C4×#67—92no—
175#893—91no—
176#893—91no—
177D3×C4⋊C4—91no—
178D3×C4⋊C4—91no—
179#67⋊C4—92no—
180#67⋊C4—92no—
181D3×C22⋊C4—92no—
182D3×C22⋊C4—92no—
183C4×D12—31no—
184C4×D12D911yescharacteristic, complemented
185C42×D3—91no—
186C42×D3—91no—
187C42×D3—181no—
188C22×C3⋊D3—31no—
189C22×C3×D3—32no—
190C22×C3×D3C22×D312yes—
191C2×D32—38no—
192C2×D32—64no—
193C2×D32—64no—
194C2×C32×C4C22×D311yescharacteristic
195C2×C32×C4C22×D311yescharacteristic
196C2×C32×C4C22×D311yescharacteristic
197C2×C3⋊Dic3—31no—
198C2×C3⋊Dic3—31no—
199C2×C3⋊Dic3—31no—
200C4×C3⋊D3—34no—
201C4×C3⋊D3—34no—
202C4×C3⋊D3—62no—
203C2×C3×Dic3—32no—
204C2×C3×Dic3C22×D312yes—
205C3×D12—34no—
206C3×D12C4×D314yes—
207C3×C4×D3—24no—
208C3×C4×D3—64no—
209#625—38no—
210#624—64no—
211D3×Dic3—64no—
212D3×Dic3—64no—
213C23×C9—32no—
214C22×D9—31no—
215C22×D9—38no—
216C22×D9—61no—
217C22×D9—64no—
218C22×D9—64no—
219C22×D9C22×D312yes—
220D4×C9—34no—
221C2×C4×C9—21no—
222C2×C4×C9—21no—
223C2×C4×C9—21no—
224C2×C4×C9—32no—
225C2×C4×C9—64no—
226C2×C4×C9C22×D311yescharacteristic
227C2×C4×C9C22×D311yescharacteristic
228C2×C4×C9C22×D311yescharacteristic
229#611—38no—
230C2×Dic9—31no—
231C2×Dic9—31no—
232C2×Dic9—31no—
233C2×Dic9—61no—
234C2×Dic9—61no—
235C2×Dic9—61no—
236C2×Dic9—64no—
237C2×Dic9C22×D312yes—
238D36C4×D314yescomplemented
239C4×D9—24no—
240C4×D9—34no—
241C4×D9—34no—
242C4×D9—64no—
243C4×D9—64no—
244C4×D9—64no—
245C4×D9—64no—
246C4×D9—62no—
247C4×D9—64no—
248C2×C4×D4—271noSylow
249C2×C3×C9C23×C411yescharacteristic
250C2×C3×C9C22×D411yescharacteristic
251C2×C3×C9C2×#4111yescharacteristic
252C3⋊D9C4×D414yescomplemented
253D3×C9—24no—
254C3×D9—24no—
255C23×D3—92no—
256C23×D3—92no—
257C2×C3×D4—31no—
258C2×C3×D4—91no—
259C22×C3×C4—32no—
260C22×C3×C4—92no—
261C2×#67—92no—
262C2×#67—92no—
263C22×Dic3—92no—
264C22×Dic3—92no—
265D3×D4—98no—
266D3×D4—98no—
267C2×D12—31no—
268C2×D12C2×D911yescharacteristic
269C2×C4×D3—32no—
270C2×C4×D3—91no—
271C2×C4×D3—91no—
272C2×C4×D3—91no—
273C2×C4×D3—91no—
274C2×C4×D3—92no—
275C2×C4×D3—92no—
276C2×C4×D3—92no—
277C2×C4×D3—91no—
278C2×C4×D3—91no—
279C2×C4×D3—92no—
280C2×C4×D3—181no—
281C2×C4×D3—181no—
282C2×C4×D3—181no—
283C2×C4×D3—188no—
284C2×C4×D3—188no—
285C2×C4×D3C2×D912yescomplemented
286C3×C4⋊C4—31no—
287C3×C4⋊C4—91no—
288C3×C22⋊C4—32no—
289C3×C22⋊C4—92no—
290C3×C42—21no—
291C3×C42C2×D911yescharacteristic, complemented
292C3×C42D3211yescharacteristic
293#217—92no—
294#217—92no—
295(C2×D3)⋊C4—32no—
296(C2×D3)⋊C4—92no—
297(C2×D3)⋊C4—92no—
298(C2×D3)⋊C4C2×D912yescomplemented
299C4⋊Dic3—31no—
300C4⋊Dic3C2×D911yescharacteristic, complemented
301Dic3⋊C4—92no—
302Dic3⋊C4—92no—
303C4×Dic3—91no—
304C4×Dic3—91no—
305C4×Dic3—91no—
306C4×Dic3—91no—
307C4×Dic3—91no—
308C4×Dic3—91no—
309C4×Dic3—181no—
310C4×Dic3—181no—
311C4×Dic3—181no—
312C22×C32C23×D311yescharacteristic
313C2×C3⋊D3—32no—
314C2×C3⋊D3—32no—
315C2×C3⋊D3—32no—
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—34no—
319C2×C3×D3—62no—
320C2×C3×D3—62no—
321C2×C3×D3C2×C4×D314yes—
322D32—616no—
323C32×C4—21no—
324C32×C4C2×C4×D312yes—
325C32×C4D3×D412yes—
326C3⋊Dic3—32no—
327C3⋊Dic3—32no—
328C3⋊Dic3—61no—
329C3×Dic3—22no—
330C3×Dic3—62no—
331C22×C9—21no—
332C22×C9—34no—
333C22×C9—62no—
334C22×C9—62no—
335C22×C9C23×D311yescharacteristic
336C2×D9—22no—
337C2×D9—22no—
338C2×D9—32no—
339C2×D9—32no—
340C2×D9—32no—
341C2×D9—62no—
342C2×D9—62no—
343C2×D9—62no—
344C2×D9—616no—
345C2×D9C2×C4×D314yescomplemented
346C4×C9—22no—
347C4×C9—21no—
348C4×C9—22no—
349C4×C9—22no—
350C4×C9—62no—
351C4×C9C2×C4×D312yescomplemented
352C4×C9D3×D412yescomplemented
353Dic9—22no—
354Dic9—32no—
355Dic9—32no—
356Dic9—62no—
357Dic9—62no—
358Dic9—62no—
359Dic9—61no—
360C22×D4—271no—
361C23×C4—272no—
362C4×D4—31no—
363C4×D4—91no—
364C4×D4—272no—
365C4×D4—271no—
366C4×D4—271no—
367C4×D4—272no—
368C2×C4⋊C4—271no—
369C2×C22⋊C4—272no—
370C2×C42—271no—
371C3×C9C2×C4×D411yescharacteristic, complemented, Sylow
372C23×C3—32no—
373C23×C3—92no—
374C22×D3—32no—
375C22×D3—98no—
376C22×D3—91no—
377C22×D3—91no—
378C22×D3—98no—
379C22×D3—181no—
380C22×D3—184no—
381C22×D3—184no—
382C22×D3—184no—
383C22×D3—184no—
384C22×D3C22×D912yes—
385C3×D4—34no—
386C3×D4—94no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—32no—
391C2×C3×C4—64no—
392C2×C3×C4—92no—
393C2×C3×C4—184no—
394C2×C3×C4C22×D911yescharacteristic
395C2×C3×C4C22×D911yescharacteristic
396C2×C3×C4C22×D911yescharacteristic
397C2×C3×C4C2×D3211yescharacteristic
398C2×C3×C4C2×D3211yescharacteristic
399C2×C3×C4C2×D3211yescharacteristic
400#67—98no—
401#67—98no—
402C2×Dic3—32no—
403C2×Dic3—91no—
404C2×Dic3—91no—
405C2×Dic3—91no—
406C2×Dic3—91no—
407C2×Dic3—91no—
408C2×Dic3—91no—
409C2×Dic3—181no—
410C2×Dic3—181no—
411C2×Dic3—181no—
412C2×Dic3—184no—
413C2×Dic3—184no—
414C2×Dic3C22×D912yes—
415D12—34no—
416D12C4×D914yescomplemented
417C4×D3—24no—
418C4×D3—64no—
419C4×D3—94no—
420C4×D3—94no—
421C4×D3—94no—
422C4×D3—94no—
423C4×D3—184no—
424C4×D3—184no—
425C4×D3—184no—
426C4×D3—184no—
427C4×D3—184no—
428C4×D3—184no—
429C4×D3—182no—
430C4×D3—182no—
431C4×D3—184no—
432C2×C32C22×C4×D311yescharacteristic
433C2×C32C2×D3×D411yescharacteristic
434C2×C32D3×#4111yescharacteristic
435C3⋊D3—34no—
436C3×D3—24no—
437C3×D3—64no—
438C2×C9—21no—
439C2×C9—21no—
440C2×C9—21no—
441C2×C9—64no—
442C2×C9C22×C4×D311yescharacteristic
443C2×C9C2×D3×D411yescharacteristic
444C2×C9D3×#4111yescharacteristic
445D9—24no—
446D9—34no—
447D9—64no—
448C24—272no—
449C2×D4—31no—
450C2×D4—91no—
451C2×D4—278no—
452C2×D4—272no—
453C22×C4—32no—
454C22×C4—92no—
455C22×C4—272no—
456C22×C4—272no—
457C22×C4—272no—
458C22×C4—271no—
459C22×C4—271no—
460C22×C4—271no—
461C22×C4—548no—
462C4⋊C4—31no—
463C4⋊C4—91no—
464C4⋊C4—272no—
465C22⋊C4—32no—
466C22⋊C4—92no—
467C22⋊C4—272no—
468C22⋊C4—272no—
469C42—271no—
470C42—271no—
471C42—271no—
472C42D3×D911yescharacteristic, complemented
473C22×C3—21no—
474C22×C3—34no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3—94no—
478C22×C3—182no—
479C22×C3—182no—
480C22×C3C23×D911yescharacteristic
481C22×C3C22×D3211yescharacteristic
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—34no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—92no—
488C2×D3—92no—
489C2×D3—92no—
490C2×D3—92no—
491C2×D3—92no—
492C2×D3—92no—
493C2×D3—182no—
494C2×D3—182no—
495C2×D3—182no—
496C2×D3—1816no—
497C2×D3—1816no—
498C2×D3C2×C4×D914yescomplemented
499C3×C4—22no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—22no—
503C3×C4—22no—
504C3×C4—62no—
505C3×C4—182no—
506C3×C4C2×C4×D912yescomplemented
507C3×C4D4×D912yescomplemented
508C3×C4C4×D3212yes—
509C3×C4#380212yes—
510Dic3—22no—
511Dic3—62no—
512Dic3—92no—
513Dic3—92no—
514Dic3—92no—
515Dic3—92no—
516Dic3—182no—
517Dic3—182no—
518Dic3—182no—
519Dic3—181no—
520Dic3—181no—
521C32C4×D3×D411yescharacteristic
522C9—21no—
523C9C4×D3×D411yescharacteristic, complemented
524C23—32no—
525C23—92no—
526C23—278no—
527C23—271no—
528C23—544no—
529C23—544no—
530D4—34no—
531D4—94no—
532D4—278no—
533C2×C4—32no—
534C2×C4—64no—
535C2×C4—92no—
536C2×C4—184no—
537C2×C4—271no—
538C2×C4—271no—
539C2×C4—274no—
540C2×C4—274no—
541C2×C4—271no—
542C2×C4—542no—
543C2×C4—544no—
544C2×C4—544no—
545C2×C4—544no—
546C2×C4C2×D3×D911yescharacteristic
547C2×C4C2×D3×D911yescharacteristic
548C2×C4C2×D3×D911yescharacteristic
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—64no—
553C2×C3—184no—
554C2×C3C22×C4×D911yescharacteristic
555C2×C3C2×D4×D911yescharacteristic
556C2×C3#41×D911yescharacteristic
557C2×C3C2×C4×D3211yescharacteristic
558C2×C3C2×#380211yescharacteristic
559C2×C3#6430611yescharacteristic
560D3—24no—
561D3—64no—
562D3—94no—
563D3—94no—
564D3—184no—
565C22—34no—
566C22—62no—
567C22—62no—
568C22—94no—
569C22—182no—
570C22—182no—
571C22—272no—
572C22—272no—
573C22—272no—
574C22—5416no—
575C22C22×D3×D911yescharacteristic
576C4—21no—
577C4—62no—
578C4—182no—
579C4—272no—
580C4—272no—
581C4—541no—
582C4C4×D3×D912yescomplemented
583C4#8864612yesdirect product factor
584C3—21no—
585C3C4×D4×D911yescharacteristic, complemented
586C3C4×#380211yescharacteristic
587C2—64no—
588C2—184no—
589C2—274no—
590C2C2×C4×D3×D911yescharacteristic
591C2C2×#8864611yescharacteristic
592C2#1172247511yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC3×C42×C9C22
socleC22×C32C23×D3
prime radicalC2×#88646C2
cosocleC22×C3×C9C24
hypercenterC42D3×D9
hypocenterC3×C9C2×C4×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×D9C2semidirect
3. C42×C3⋊D9C2semidirect
4. C4×C9×D12C2semidirect
5. C3×C4×D36C2semidirect
6. #11721048C2semidirect
7. #11721028C2semidirect
8. C4×#6194C2semidirect
9. #11721025C2semidirect
10. #11721000C2semidirect
11. #11720998C2semidirect
19. C2×C4×D3×C9C22semidirect
21. C2×C3×C4×D9C22semidirect
23. C2×D3×Dic9C22semidirect
25. C2×Dic3×D9C22semidirect
26. #88646C4direct (N × H)
28. C3×C42×C9C22semidirect
29. C4×C3⋊Dic9C22semidirect
30. C4×C3⋊Dic9C22semidirect
31. C4×C3⋊Dic9C22semidirect
32. C9×(C2×D3)⋊C4C22semidirect
33. C3×(C2×D9)⋊C4C22semidirect
34. C9×C4⋊Dic3C22semidirect
35. C3×C4⋊Dic9C22semidirect
36. (C2×D3)⋊Dic9C22semidirect
37. (C2×D9)⋊Dic3C22semidirect
38. #88442C22semidirect
59. C4×D36D3semidirect
67. C2×D3×D9C2×C4semidirect
75. C4×C3⋊D9C2×C4semidirect
76. C4×C3⋊D9D4semidirect
79. C9×D12C2×C4semidirect
81. C3×D36C2×C4semidirect
83. #6194C2×C4semidirect
130. C2×C4×D9C2×D3semidirect
134. C42×C9C2×D3semidirect
137. (C2×D9)⋊C4C2×D3semidirect
138. C4⋊Dic9C2×D3semidirect
152. C2×D3×C9C22×C4semidirect
155. C2×C3×D9C22×C4semidirect
158. C3×C4×C9C22×C4semidirect
159. C3×C4×C9C2×D4semidirect
161. C3⋊Dic9C22×C4semidirect
162. C3⋊Dic9C2×D4semidirect
184. C4×D12D9semidirect
238. D36C4×D3semidirect
252. C3⋊D9C4×D4semidirect
285. C2×C4×D3C2×D9semidirect
291. C3×C42C2×D9semidirect
298. (C2×D3)⋊C4C2×D9semidirect
300. C4⋊Dic3C2×D9semidirect
345. C2×D9C2×C4×D3semidirect
351. C4×C9C2×C4×D3semidirect
352. C4×C9D3×D4semidirect
371. C3×C9C2×C4×D4semidirect
416. D12C4×D9semidirect
472. C42D3×D9semidirect
498. C2×D3C2×C4×D9semidirect
506. C3×C4C2×C4×D9semidirect
507. C3×C4D4×D9semidirect
523. C9C4×D3×D4semidirect
582. C4C4×D3×D9semidirect
583. C4#88646direct (N × H)
585. C3C4×D4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#886462
C2×C4×D3×D92
C42×C3⋊D92
C4×C9×D122
C3×C4×D362
#117210482
#117210282
C4×#61942
#117210252
#117210002
#117209982
C4×#38023
C4×D4×D93