Finite Group Databasebeta

← C3×C4×#3830 #13179299

Subgroups — C3×C4×#3830 #13179299

Order 1728.

2236 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic
2C33×C4×D4C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×C4×#638C212yesmaximal, complemented
5C2×C3×C4×C3⋊Dic3C212yesmaximal, complemented
6C3×#64101C211yesmaximal, characteristic, complemented
7C3×#64096C211yesmaximal, characteristic, complemented
8C3×#64090C212yesmaximal, complemented
9C3×#64086C212yesmaximal, complemented
10C3×C42×C3⋊D3C211yesmaximal, characteristic, complemented
11C3×C4×#634C211yesmaximal, characteristic, complemented
12C4×#3830C311yesmaximal, characteristic, direct product factor
13C3×C4×#237—34nomaximal
14C2×C33×D4C2211yescharacteristic
15C22×C33×C4C2212yes—
16C2×C3×#638C2212yes—
17C22×C3×C3⋊Dic3C2212yes—
18C22×C3×C3⋊Dic3C2212yes—
19C3×#3830C418yesdirect product factor
20C2×C3×C4×C3⋊D3C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×C3×C4×C3⋊D3C2211yescharacteristic
23C2×C3×#634C2211yescharacteristic
24C33×C4⋊C4C2211yescharacteristic
25C33×C22⋊C4C2212yes—
26C33×C42C2211yescharacteristic
27C3×#3757C2212yes—
28C3×#3752C2212yes—
29C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C3×#3750C2212yes—
31C3×#3750C2212yes—
32C3×C4×C3⋊Dic3C2212yes—
33C3×C4×C3⋊Dic3C2211yescharacteristic
34C3×C4×C3⋊Dic3C2211yescharacteristic
35C3×C4×C3⋊Dic3C2211yescharacteristic
36C3×C4×C3⋊Dic3C2212yes—
37C3×C4×C3⋊Dic3C2212yes—
38C2×#3830C2×C311yescharacteristic
39C2×C3×#237—34no—
40C32×C4×D4—24no—
41C32×C4×D4D314yescomplemented
42C32×C4×D4C2×C311yescharacteristic, complemented
43D4×C3⋊Dic3C2×C311yescharacteristic, complemented
44C4×#638C2×C312yescomplemented
45C2×C4×C3⋊Dic3C2×C312yescomplemented
46#64101C2×C311yescharacteristic, complemented
47#64096C2×C311yescharacteristic, complemented
48#64090C2×C312yescomplemented
49#64086C2×C312yescomplemented
50C42×C3⋊D3C2×C311yescharacteristic, complemented
51C4×#634C2×C311yescharacteristic, complemented
52C3×D4×Dic3—34no—
53C3×C4×#67—38no—
54C2×C3×C4×Dic3—38no—
55C3×#892—34no—
56C3×#887—34no—
57C3×#67⋊C4—38no—
58C3×#877—38no—
59C3×C42×D3—34no—
60C3×C4×Dic6—34no—
61C23×C33C2312yes—
62C22×C3×C3⋊D3C2311yescharacteristic
63C33×D4C2×C414yescomplemented
64C2×C33×C4—24no—
65C2×C33×C4C2312yes—
66C2×C33×C4C2311yescharacteristic
67C2×C33×C4C2311yescharacteristic
68C2×C33×C4C2311yescharacteristic
69C3×#638C2×C418yescomplemented
70C2×C3×C3⋊Dic3—24no—
71C2×C3×C3⋊Dic3C2×C418yescomplemented
72C2×C3×C3⋊Dic3C2311yescharacteristic
73C2×C3×C3⋊Dic3C2312yes—
74C2×C3×C3⋊Dic3C2311yescharacteristic
75C2×C3×C3⋊Dic3C2312yes—
76C2×C3×C3⋊Dic3C2311yescharacteristic
77C3×C4×C3⋊D3—22no—
78C3×C4×C3⋊D3—22no—
79C3×C4×C3⋊D3C2×C414yescomplemented
80C3×#634C2×C414yescomplemented
81C3×C4×#41—91no—
82C4×#237—34no—
83C2×C32×D4—24no—
84C2×C32×D4C2×D314yes—
85C2×C32×D4C22×C311yescharacteristic
86C22×C32×C4—28no—
87C22×C32×C4C2×D318yes—
88C22×C32×C4C22×C312yes—
89C2×#638C22×C312yes—
90C22×C3⋊Dic3C22×C312yes—
91C22×C3⋊Dic3C22×C312yes—
92#3830C3×C418yesdirect product factor
93C2×C4×C3⋊D3C22×C311yescharacteristic
94C2×C4×C3⋊D3C22×C311yescharacteristic
95C2×C4×C3⋊D3C22×C311yescharacteristic
96C2×#634C22×C311yescharacteristic
97C2×C3×#67—38no—
98C22×C3×Dic3—38no—
99C22×C3×Dic3—38no—
100C3×#237—332no—
101C2×C3×C4×D3—34no—
102C2×C3×C4×D3—34no—
103C2×C3×C4×D3—34no—
104C2×C3×Dic6—34no—
105C32×C4⋊C4—24no—
106C32×C4⋊C4C2×D314yes—
107C32×C4⋊C4C22×C311yescharacteristic
108C32×C22⋊C4—28no—
109C32×C22⋊C4C2×D318yes—
110C32×C22⋊C4C22×C312yes—
111C32×C42—24no—
112C32×C42C2×D314yes—
113C32×C42C22×C311yescharacteristic
114#3757C22×C312yes—
115#3752C22×C312yes—
116C4⋊(C3⋊Dic3)C22×C311yescharacteristic
117#3750C22×C312yes—
118#3750C22×C312yes—
119C4×C3⋊Dic3C22×C312yes—
120C4×C3⋊Dic3C22×C311yescharacteristic
121C4×C3⋊Dic3C22×C311yescharacteristic
122C4×C3⋊Dic3C22×C311yescharacteristic
123C4×C3⋊Dic3C22×C312yes—
124C4×C3⋊Dic3C22×C312yes—
125C3×#217—38no—
126C3×(C2×D3)⋊C4—38no—
127C3×C4⋊Dic3—34no—
128C3×Dic3⋊C4—38no—
129C3×Dic3⋊C4—38no—
130C3×C4×Dic3—34no—
131C3×C4×Dic3—38no—
132C3×C4×Dic3—38no—
133C3×C4×Dic3—34no—
134C3×C4×Dic3—34no—
135C3×C4×Dic3—38no—
136C22×C33—22no—
137C22×C33—22no—
138C22×C33C22×C414yes—
139C22×C33C2411yescharacteristic
140C2×C3×C3⋊D3—21no—
141C2×C3×C3⋊D3—21no—
142C2×C3×C3⋊D3C22×C412yes—
143C33×C4—21no—
144C33×C4—22no—
145C33×C4C22×C412yes—
146C33×C4#4112yescomplemented
147C3×C3⋊Dic3—21no—
148C3×C3⋊Dic3—22no—
149C3×C3⋊Dic3C22×C414yes—
150C3×C3⋊Dic3C22×C412yes—
151C3×C3⋊Dic3#4112yescomplemented
152C2×C3×#41—91no—
153C2×#237—34no—
154C3×C4×Q8—91no—
155C3×C4×Q8—91no—
156C3×C4×D4—24no—
157C3×C4×D4—91no—
158C3×C4×D4—92no—
159C3×C4×D4—92no—
160C3×C4×D4C3×D314yescomplemented
161C3×C4×D4C3⋊D311yescharacteristic, complemented
162C3×#117—91no—
163C3×#117—92no—
164C2×C3×C42—92no—
165C2×C3×C42—91no—
166D4×Dic3—34no—
167C4×#67—38no—
168C2×C4×Dic3—38no—
169#892—34no—
170#887—34no—
171#67⋊C4—38no—
172#877—38no—
173C42×D3—34no—
174C4×Dic6—34no—
175C23×C32—28no—
176C23×C32C22×D318yes—
177C23×C32C23×C312yes—
178C22×C3⋊D3C23×C311yescharacteristic
179C22×C3×D3—34no—
180C32×D4—216no—
181C32×D4C4×D3116yescomplemented
182C32×D4C2×C3×C414yescomplemented
183C2×C32×C4—24no—
184C2×C32×C4—24no—
185C2×C32×C4—24no—
186C2×C32×C4—24no—
187C2×C32×C4—28no—
188C2×C32×C4—216no—
189C2×C32×C4—416no—
190C2×C32×C4C22×D318yes—
191C2×C32×C4C22×D314yes—
192C2×C32×C4C22×D314yes—
193C2×C32×C4C22×D314yes—
194C2×C32×C4C23×C312yes—
195C2×C32×C4C23×C311yescharacteristic
196C2×C32×C4C23×C311yescharacteristic
197C2×C32×C4C23×C311yescharacteristic
198#638C2×C3×C418yescomplemented
199C2×C3⋊Dic3—24no—
200C2×C3⋊Dic3C2×C3×C418yescomplemented
201C2×C3⋊Dic3C23×C311yescharacteristic
202C2×C3⋊Dic3C23×C312yes—
203C2×C3⋊Dic3C23×C311yescharacteristic
204C2×C3⋊Dic3C23×C312yes—
205C2×C3⋊Dic3C23×C311yescharacteristic
206C4×C3⋊D3—22no—
207C4×C3⋊D3—22no—
208C4×C3⋊D3C2×C3×C414yescomplemented
209#634C2×C3×C414yescomplemented
210C3×#67—332no—
211C2×C3×Dic3—332no—
212C2×C3×Dic3—34no—
213C2×C3×Dic3—34no—
214C2×C3×Dic3—38no—
215C2×C3×Dic3—34no—
216C2×C3×Dic3—38no—
217C2×C3×Dic3—616no—
218C3×C4×D3—316no—
219C3×C4×D3—68no—
220C3×C4×D3—68no—
221C3×Dic6—316no—
222C4×#41—91noSylow
223C2×C33—24no—
224C2×C33C23×C411yescharacteristic
225C2×C33C2×#4111yescharacteristic
226C2×C33C2×#4111yescharacteristic
227C3×C3⋊D3—22no—
228C3×#41—98no—
229C2×C3×Q8—91no—
230C2×C3×D4—24no—
231C2×C3×D4—92no—
232C2×C3×D4C2×C3×D314yes—
233C2×C3×D4C2×C3⋊D311yescharacteristic
234C22×C3×C4—28no—
235C22×C3×C4—92no—
236C22×C3×C4—91no—
237C22×C3×C4—92no—
238C22×C3×C4—91no—
239C22×C3×C4—91no—
240C22×C3×C4C2×C3×D318yes—
241C22×C3×C4C2×C3⋊D312yes—
242C2×#67—38no—
243C22×Dic3—38no—
244C22×Dic3—38no—
245#237—332no—
246C2×C4×D3—34no—
247C2×C4×D3—34no—
248C2×C4×D3—34no—
249C2×Dic6—34no—
250C3×C4⋊C4—24no—
251C3×C4⋊C4—92no—
252C3×C4⋊C4—92no—
253C3×C4⋊C4—91no—
254C3×C4⋊C4C2×C3×D314yes—
255C3×C4⋊C4C2×C3⋊D311yescharacteristic
256C3×C22⋊C4—28no—
257C3×C22⋊C4—92no—
258C3×C22⋊C4—92no—
259C3×C22⋊C4C2×C3×D318yes—
260C3×C22⋊C4C2×C3⋊D312yes—
261C3×C42—24no—
262C3×C42—92no—
263C3×C42—91no—
264C3×C42—92no—
265C3×C42—91no—
266C3×C42—91no—
267C3×C42—92no—
268C3×C42C2×C3×D314yes—
269C3×C42C2×C3⋊D311yescharacteristic
270#217—38no—
271(C2×D3)⋊C4—38no—
272C4⋊Dic3—34no—
273Dic3⋊C4—38no—
274Dic3⋊C4—38no—
275C4×Dic3—38no—
276C4×Dic3—34no—
277C4×Dic3—34no—
278C4×Dic3—34no—
279C4×Dic3—38no—
280C4×Dic3—38no—
281C22×C32—22no—
282C22×C32—22no—
283C22×C32—24no—
284C22×C32—216no—
285C22×C32—28no—
286C22×C32—28no—
287C22×C32—48no—
288C22×C32—48no—
289C22×C32C2×C4×D3116yes—
290C22×C32C22×C3×C414yes—
291C22×C32C23×D314yes—
292C22×C32C24×C311yescharacteristic
293C2×C3⋊D3—21no—
294C2×C3⋊D3—21no—
295C2×C3⋊D3C22×C3×C412yes—
296C2×C3×D3—38no—
297C2×C3×D3—64no—
298C2×C3×D3—64no—
299C32×C4—21no—
300C32×C4—22no—
301C32×C4—28no—
302C32×C4—28no—
303C32×C4—28no—
304C32×C4—24no—
305C32×C4—44no—
306C32×C4—48no—
307C32×C4C2×C4×D318yes—
308C32×C4#23718yescomplemented
309C32×C4C22×C3×C412yes—
310C32×C4C3×#4112yescomplemented
311C3⋊Dic3—21no—
312C3⋊Dic3—22no—
313C3⋊Dic3C22×C3×C414yes—
314C3⋊Dic3C22×C3×C412yes—
315C3⋊Dic3C3×#4112yescomplemented
316C3×Dic3—316no—
317C3×Dic3—38no—
318C3×Dic3—38no—
319C3×Dic3—64no—
320C3×Dic3—68no—
321C2×#41—91no—
322C4×Q8—91no—
323C4×Q8—91no—
324C4×D4—91no—
325C4×D4—92no—
326C4×D4—92no—
327C4×D4C3×C3⋊D311yescharacteristic, complemented
328#117—91no—
329#117—92no—
330C2×C42—92no—
331C2×C42—91no—
332C33C4×#4111yescharacteristic, complemented, Sylow
333C23×C3—28no—
334C23×C3—91no—
335C23×C3C22×C3×D318yes—
336C23×C3C22×C3⋊D312yes—
337C22×D3—34no—
338C3×Q8—94no—
339C3×D4—216no—
340C3×D4—98no—
341C3×D4C3×C4×D3116yescomplemented
342C3×D4C4×C3⋊D314yescomplemented
343C2×C3×C4—216no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—28no—
349C2×C3×C4—416no—
350C2×C3×C4—91no—
351C2×C3×C4—91no—
352C2×C3×C4—92no—
353C2×C3×C4—98no—
354C2×C3×C4—94no—
355C2×C3×C4—91no—
356C2×C3×C4—92no—
357C2×C3×C4—182no—
358C2×C3×C4—184no—
359C2×C3×C4—182no—
360C2×C3×C4C22×C3×D318yes—
361C2×C3×C4C22×C3×D314yes—
362C2×C3×C4C22×C3×D314yes—
363C2×C3×C4C22×C3×D314yes—
364C2×C3×C4C22×C3⋊D312yes—
365C2×C3×C4C22×C3⋊D311yescharacteristic
366C2×C3×C4C22×C3⋊D311yescharacteristic
367C2×C3×C4C22×C3⋊D311yescharacteristic
368#67—332no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—38no—
372C2×Dic3—332no—
373C2×Dic3—34no—
374C2×Dic3—38no—
375C2×Dic3—616no—
376C4×D3—316no—
377C4×D3—68no—
378C4×D3—68no—
379Dic6—316no—
380C2×C32—24no—
381C2×C32—24no—
382C2×C32—24no—
383C2×C32—24no—
384C2×C32—216no—
385C2×C32—416no—
386C2×C32C22×C4×D314yes—
387C2×C32C2×#23714yes—
388C2×C32D3×#4114yes—
389C2×C32C23×C3×C411yescharacteristic
390C2×C32C2×C3×#4111yescharacteristic
391C2×C32C2×C3×#4111yescharacteristic
392C3⋊D3—22no—
393C3×D3—68no—
394#41—98no—
395C2×Q8—91no—
396C2×D4—92no—
397C2×D4C2×C3×C3⋊D311yescharacteristic
398C22×C4—92no—
399C22×C4—91no—
400C22×C4—92no—
401C22×C4—91no—
402C22×C4—91no—
403C22×C4C2×C3×C3⋊D312yes—
404C4⋊C4—92no—
405C4⋊C4—92no—
406C4⋊C4—91no—
407C4⋊C4C2×C3×C3⋊D311yescharacteristic
408C22⋊C4—92no—
409C22⋊C4—92no—
410C22⋊C4C2×C3×C3⋊D312yes—
411C42—91no—
412C42—92no—
413C42—91no—
414C42—92no—
415C42—91no—
416C42—92no—
417C42C2×C3×C3⋊D311yescharacteristic
418C22×C3—28no—
419C22×C3—28no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—24no—
423C22×C3—216no—
424C22×C3—48no—
425C22×C3—48no—
426C22×C3—92no—
427C22×C3—181no—
428C22×C3—181no—
429C22×C3C2×C3×C4×D3116yes—
430C22×C3C2×C4×C3⋊D314yes—
431C22×C3C23×C3×D314yes—
432C22×C3C23×C3⋊D311yescharacteristic
433C2×D3—38no—
434C2×D3—64no—
435C2×D3—64no—
436C3×C4—28no—
437C3×C4—24no—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—28no—
441C3×C4—28no—
442C3×C4—48no—
443C3×C4—44no—
444C3×C4—92no—
445C3×C4—94no—
446C3×C4—92no—
447C3×C4—181no—
448C3×C4—182no—
449C3×C4C2×C3×C4×D318yes—
450C3×C4C3×#23718yescomplemented
451C3×C4C2×C4×C3⋊D312yes—
452C3×C4#383012yesdirect product factor
453Dic3—316no—
454Dic3—38no—
455Dic3—38no—
456Dic3—64no—
457Dic3—68no—
458C32—24no—
459C32C4×#23714yescomplemented
460C32C3×C4×#4111yescharacteristic, complemented
461C23—91no—
462C23C22×C3×C3⋊D312yes—
463Q8—94no—
464D4—98no—
465D4C3×C4×C3⋊D314yescomplemented
466C2×C4—24no—
467C2×C4—91no—
468C2×C4—91no—
469C2×C4—92no—
470C2×C4—98no—
471C2×C4—94no—
472C2×C4—91no—
473C2×C4—92no—
474C2×C4—182no—
475C2×C4—184no—
476C2×C4—182no—
477C2×C4C22×C3×C3⋊D312yes—
478C2×C4C22×C3×C3⋊D311yescharacteristic
479C2×C4C22×C3×C3⋊D311yescharacteristic
480C2×C4C22×C3×C3⋊D311yescharacteristic
481C2×C3—216no—
482C2×C3—24no—
483C2×C3—24no—
484C2×C3—24no—
485C2×C3—24no—
486C2×C3—416no—
487C2×C3—182no—
488C2×C3C22×C3×C4×D314yes—
489C2×C3C2×C3×#23714yes—
490C2×C3C3×D3×#4114yes—
491C2×C3C22×C4×C3⋊D311yescharacteristic
492C2×C3C2×#383011yescharacteristic
493C2×C3#41×C3⋊D311yescharacteristic
494D3—68no—
495C22—22no—
496C22—22no—
497C22—92no—
498C22—181no—
499C22—181no—
500C22C2×C3×C4×C3⋊D314yes—
501C22C23×C3×C3⋊D311yescharacteristic
502C4—22no—
503C4—21no—
504C4—92no—
505C4—94no—
506C4—92no—
507C4—181no—
508C4—182no—
509C4C2×C3×C4×C3⋊D312yes—
510C4C3×#383012yesdirect product factor
511C3—24no—
512C3C3×C4×#23714yescomplemented
513C3C4×#383011yescharacteristic, direct product factor
514C2—24no—
515C2—182no—
516C2C22×C3×C4×C3⋊D311yescharacteristic
517C2C2×C3×#383011yescharacteristic
518C2C3×#41×C3⋊D311yescharacteristic
subgroupG/H
centerC2×C3×C4C22×C3⋊D3
commutatorC2×C32C23×C3×C4
FrattiniC22C23×C3×C3⋊D3
FittingC33×C4×D4C2
socleC22×C33C24
prime radicalC2×C3×#3830C2
cosocleC22×C32C24×C3
hypercenterC3×C4×D4C3⋊D3
hypocenterC32C3×C4×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3×C4 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C33×C4×D4C2semidirect
3. C3×D4×C3⋊Dic3C2semidirect
4. C3×C4×#638C2semidirect
5. C2×C3×C4×C3⋊Dic3C2semidirect
6. C3×#64101C2semidirect
7. C3×#64096C2semidirect
8. C3×#64090C2semidirect
9. C3×#64086C2semidirect
10. C3×C42×C3⋊D3C2semidirect
11. C3×C4×#634C2semidirect
12. C4×#3830C3direct (N × H)
19. C3×#3830C4direct (N × H)
41. C32×C4×D4D3semidirect
42. C32×C4×D4C2×C3semidirect
43. D4×C3⋊Dic3C2×C3semidirect
44. C4×#638C2×C3semidirect
45. C2×C4×C3⋊Dic3C2×C3semidirect
46. #64101C2×C3semidirect
47. #64096C2×C3semidirect
48. #64090C2×C3semidirect
49. #64086C2×C3semidirect
50. C42×C3⋊D3C2×C3semidirect
51. C4×#634C2×C3semidirect
63. C33×D4C2×C4semidirect
69. C3×#638C2×C4semidirect
71. C2×C3×C3⋊Dic3C2×C4semidirect
79. C3×C4×C3⋊D3C2×C4semidirect
80. C3×#634C2×C4semidirect
92. #3830C3×C4direct (N × H)
146. C33×C4#41semidirect
151. C3×C3⋊Dic3#41semidirect
160. C3×C4×D4C3×D3semidirect
161. C3×C4×D4C3⋊D3semidirect
181. C32×D4C4×D3semidirect
182. C32×D4C2×C3×C4semidirect
198. #638C2×C3×C4semidirect
200. C2×C3⋊Dic3C2×C3×C4semidirect
208. C4×C3⋊D3C2×C3×C4semidirect
209. #634C2×C3×C4semidirect
308. C32×C4#237semidirect
310. C32×C4C3×#41semidirect
315. C3⋊Dic3C3×#41semidirect
327. C4×D4C3×C3⋊D3semidirect
332. C33C4×#41semidirect
341. C3×D4C3×C4×D3semidirect
342. C3×D4C4×C3⋊D3semidirect
450. C3×C4C3×#237semidirect
452. C3×C4#3830direct (N × H)
459. C32C4×#237semidirect
460. C32C3×C4×#41semidirect
465. D4C3×C4×C3⋊D3semidirect
510. C4C3×#3830direct (N × H)
512. C3C3×C4×#237semidirect
513. C3C4×#3830direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C33×C4×D42
C3×D4×C3⋊Dic32
C3×C4×#6382
C2×C3×C4×C3⋊Dic32
C3×#641012
C3×#640962
C3×#640902
C3×#640862
C3×C42×C3⋊D32
C3×C4×#6342
C4×#38303
C3×C4×#2373