Finite Group Databasebeta

← C2×#611⋊Dic3 #13151991

Subgroups — C2×#611⋊Dic3 #13151991

Order 1728.

1514 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3⋊Dic9C211yesmaximal, characteristic, complemented
2C22×C3×#611C211yesmaximal, characteristic
3C22×Dic3×D9C211yesmaximal, characteristic, complemented
4C2×C9×#217C211yesmaximal, characteristic, complemented
5#611⋊Dic3C218yesmaximal, direct product factor
6C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
7C2×Dic9⋊Dic3C211yesmaximal, characteristic, complemented
8C2×Dic3×Dic9C211yesmaximal, characteristic, complemented
9C2×#67⋊Dic3—31nomaximal
10C2×#611⋊C4—31nomaximal
11C24×C3×C9C2211yescharacteristic
12C23×C3×D9C2211yescharacteristic
13C22×C3⋊Dic9—24no—
14C22×C3⋊Dic9C2211yescharacteristic
15C22×C3⋊Dic9C2211yescharacteristic
16C22×C3⋊Dic9C2214yescomplemented
17C2×C3×#611C418yescomplemented
18C2×C3×#611C2214yes—
19C22×C9×Dic3C2211yescharacteristic
20C22×C9×Dic3C2211yescharacteristic
21C22×C3×Dic9C2211yescharacteristic
22C2×Dic3×D9—24no—
23C2×Dic3×D9C2214yescomplemented
24C9×#217C2214yescomplemented
25(C2×D9)⋊Dic3C2214yescomplemented
26Dic9⋊Dic3C2214yescomplemented
27Dic3×Dic9C2214yescomplemented
28C23×C3⋊Dic3—31no—
29C22×C3×#67—31no—
30C22×D3×Dic3—31no—
31C2×C3×#217D311yescharacteristic
32#67⋊Dic3—38no—
33C2×Dic3⋊Dic3—31no—
34C2×(C2×D3)⋊Dic3—31no—
35C2×Dic32—31no—
36C22×#611D311yescharacteristic
37C23×Dic9—31no—
38C23×Dic9—61no—
39C22×C4×D9—31no—
40C2×C9×C22⋊C4—31no—
41C2×(C2×D9)⋊C4—31no—
42C2×Dic9⋊C4—31no—
43C2×C4×Dic9—31no—
44#611⋊C4—38no—
45C23×C3×C9—22no—
46C23×C3×C9—22no—
47C23×C3×C9C2×C414yescomplemented
48C23×C3×C9C2312yes—
49C23×C3×C9C2311yescharacteristic
50C22×C3×D9—22no—
51C22×C3×D9—22no—
52C22×C3×D9C2×C414yescomplemented
53C22×C3×D9C2312yes—
54C2×C3⋊Dic9—22no—
55C2×C3⋊Dic9—28no—
56C2×C3⋊Dic9D414yescomplemented
57C2×C3⋊Dic9C2312yes—
58C2×C3⋊Dic9C2312yes—
59C3×#611C2×C4116yescomplemented
60C2×C9×Dic3—22no—
61C2×C9×Dic3—22no—
62C2×C9×Dic3C2312yes—
63C2×C9×Dic3C2312yes—
64C2×C3×Dic9C2×C414yescomplemented
65C2×C3×Dic9C2312yes—
66Dic3×D9—28no—
67C2×D4×Dic3—91no—
68C2×#67⋊C4—91no—
69C24×C32C2×D311yescharacteristic
70C23×C3×D3—31no—
71C22×C3⋊Dic3—31no—
72C22×C3⋊Dic3—31no—
73C22×C3⋊Dic3—34no—
74C22×C3⋊Dic3—64no—
75C2×C3×#67—38no—
76C2×C3×#67—34no—
77C22×C3×Dic3—31no—
78C22×C3×Dic3C2×D311yescharacteristic
79C22×C3×Dic3C2×D311yescharacteristic
80C2×D3×Dic3—34no—
81C2×D3×Dic3—64no—
82C24×C9—21no—
83C24×C9C2×D311yescharacteristic
84C23×D9C2×D311yescharacteristic
85C3×#217C2×D314yes—
86Dic3⋊Dic3—34no—
87(C2×D3)⋊Dic3—34no—
88Dic32—34no—
89C22×C4×C9—31no—
90C22×C4×C9—31no—
91C2×#611Dic318yescomplemented
92C2×#611C2×D314yes—
93C22×Dic9—31no—
94C22×Dic9—31no—
95C22×Dic9—34no—
96C22×Dic9—64no—
97C22×Dic9—61no—
98C22×Dic9—61no—
99C22×Dic9—64no—
100C22×Dic9—68no—
101C22×Dic9C2×D311yescharacteristic
102C2×C4×D9—34no—
103C2×C4×D9—64no—
104C9×C22⋊C4—34no—
105(C2×D9)⋊C4—34no—
106Dic9⋊C4—34no—
107C4×Dic9—34no—
108C22×C3×C9—28no—
109C22×C3×C9—22no—
110C22×C3×C9—22no—
111C22×C3×C9C22×C412yes—
112C22×C3×C9C22×C414yescomplemented
113C22×C3×C9C2×D412yes—
114C22×C3×C9#4112yes—
115C22×C3×C9C2411yescharacteristic
116C2×C3×D9—28no—
117C2×C3×D9—22no—
118C2×C3×D9—22no—
119C2×C3×D9C22×C414yescomplemented
120C3⋊Dic9—22no—
121C3⋊Dic9C2×D414yescomplemented
122C9×Dic3—22no—
123C9×Dic3—22no—
124C3×Dic9C22×C414yescomplemented
125C22×C3×D4—91no—
126C22×#67—31no—
127C23×Dic3—91no—
128C23×Dic3—91no—
129C23×Dic3—91no—
130C23×Dic3—181no—
131C22×C4×D3—91no—
132C2×C3×C22⋊C4—31no—
133C2×#217—91no—
134C2×#217D911yescharacteristic, complemented
135D4×Dic3—98no—
136C2×(C2×D3)⋊C4—91no—
137C2×C4⋊Dic3—91no—
138C2×Dic3⋊C4—91no—
139C2×C4×Dic3—91no—
140C2×C4×Dic3—91no—
141#67⋊C4—98no—
142C23×C32—22no—
143C23×C32—22no—
144C23×C32C4×D314yes—
145C23×C32C22×D312yes—
146C23×C32C22×D311yescharacteristic
147C22×C3×D3—34no—
148C22×C3×D3—32no—
149C22×C3×D3—62no—
150C22×C3×D3—62no—
151C2×C3⋊Dic3—34no—
152C2×C3⋊Dic3—32no—
153C2×C3⋊Dic3—32no—
154C2×C3⋊Dic3—68no—
155C2×C3⋊Dic3—62no—
156C3×#67—316no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—34no—
160C2×C3×Dic3—32no—
161C2×C3×Dic3C22×D312yes—
162C2×C3×Dic3C22×D312yes—
163D3×Dic3—68no—
164C23×C9—24no—
165C23×C9—24no—
166C23×C9—22no—
167C23×C9—22no—
168C23×C9—24no—
169C23×C9—22no—
170C23×C9—21no—
171C23×C9C2×Dic314yescomplemented
172C23×C9C22×D312yes—
173C23×C9C22×D311yescharacteristic
174C22×D9—22no—
175C22×D9—22no—
176C22×D9C2×Dic314yescomplemented
177C22×D9C22×D312yes—
178C2×C4×C9—32no—
179C2×C4×C9—32no—
180C2×C4×C9—62no—
181C2×C4×C9—62no—
182#611C2×Dic3116yescomplemented
183C2×Dic9—34no—
184C2×Dic9—32no—
185C2×Dic9—32no—
186C2×Dic9—64no—
187C2×Dic9—62no—
188C2×Dic9—62no—
189C2×Dic9—68no—
190C2×Dic9—616no—
191C2×Dic9—64no—
192C2×Dic9—62no—
193C2×Dic9C2×Dic314yescomplemented
194C2×Dic9C22×D312yes—
195C4×D9—68no—
196C2×C4×D4—271noSylow
197C2×C3×C9—24no—
198C2×C3×C9C4×D414yescomplemented
199C2×C3×C9C23×C411yescharacteristic
200C2×C3×C9C22×D411yescharacteristic
201C2×C3×C9C2×#4111yescharacteristic
202C3×D9—24no—
203C24×C3—21no—
204C24×C3—91no—
205C24×C3C2×D911yescharacteristic
206C24×C3D3211yescharacteristic
207C23×D3—31no—
208C2×C3×D4—98no—
209C2×C3×D4—94no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—91no—
213C2×#67—38no—
214C2×#67—34no—
215C22×Dic3—31no—
216C22×Dic3—91no—
217C22×Dic3—91no—
218C22×Dic3—91no—
219C22×Dic3—94no—
220C22×Dic3—94no—
221C22×Dic3—91no—
222C22×Dic3—94no—
223C22×Dic3—181no—
224C22×Dic3—184no—
225C22×Dic3—181no—
226C22×Dic3—184no—
227C22×Dic3—184no—
228C22×Dic3—184no—
229C22×Dic3—188no—
230C22×Dic3C2×D911yescharacteristic
231C22×Dic3C2×D911yescharacteristic
232C2×C4×D3—94no—
233C2×C4×D3—184no—
234C3×C22⋊C4—34no—
235#217—94no—
236#217C2×D914yescomplemented
237(C2×D3)⋊C4—94no—
238C4⋊Dic3—94no—
239Dic3⋊C4—94no—
240C4×Dic3—94no—
241C4×Dic3—94no—
242C22×C32—28no—
243C22×C32—22no—
244C22×C32—22no—
245C22×C32C2×C4×D312yes—
246C22×C32C2×C4×D314yes—
247C22×C32D3×D412yes—
248C22×C32#23712yes—
249C22×C32C23×D311yescharacteristic
250C2×C3×D3—34no—
251C2×C3×D3—68no—
252C2×C3×D3—62no—
253C2×C3×D3—62no—
254C3⋊Dic3—34no—
255C3⋊Dic3—62no—
256C3×Dic3—22no—
257C3×Dic3—22no—
258C3×Dic3—34no—
259C22×C9—24no—
260C22×C9—24no—
261C22×C9—216no—
262C22×C9—28no—
263C22×C9—22no—
264C22×C9—22no—
265C22×C9—21no—
266C22×C9—22no—
267C22×C9—24no—
268C22×C9—22no—
269C22×C9—22no—
270C22×C9D3×D412yes—
271C22×C9#23712yes—
272C22×C9C22×Dic312yes—
273C22×C9C22×Dic314yescomplemented
274C22×C9C23×D311yescharacteristic
275C2×D9—28no—
276C2×D9—22no—
277C2×D9—22no—
278C2×D9C22×Dic314yescomplemented
279C4×C9—62no—
280C4×C9—62no—
281Dic9—34no—
282Dic9—64no—
283Dic9—64no—
284Dic9—62no—
285Dic9C22×Dic314yescomplemented
286C22×D4—91no—
287C23×C4—271no—
288C23×C4—271no—
289C4×D4—278no—
290C2×C4⋊C4—271no—
291C2×C22⋊C4—31no—
292C2×C22⋊C4—271no—
293C2×C42—271no—
294C3×C9C2×C4×D411yescharacteristic, complemented, Sylow
295C23×C3—24no—
296C23×C3—24no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—24no—
302C23×C3—22no—
303C23×C3—21no—
304C23×C3—94no—
305C23×C3—92no—
306C23×C3—182no—
307C23×C3—182no—
308C23×C3C4×D914yescomplemented
309C23×C3C22×D912yes—
310C23×C3C22×D911yescharacteristic
311C23×C3D3×Dic314yes—
312C23×C3C2×D3212yes—
313C23×C3C2×D3211yescharacteristic
314C22×D3—32no—
315C22×D3—34no—
316C22×D3—62no—
317C22×D3—62no—
318C3×D4—916no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—94no—
324C2×C3×C4—92no—
325#67—316no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—32no—
329C2×Dic3—34no—
330C2×Dic3—92no—
331C2×Dic3—94no—
332C2×Dic3—92no—
333C2×Dic3—94no—
334C2×Dic3—92no—
335C2×Dic3—92no—
336C2×Dic3—182no—
337C2×Dic3—184no—
338C2×Dic3—182no—
339C2×Dic3—188no—
340C2×Dic3—188no—
341C2×Dic3—188no—
342C2×Dic3—1816no—
343C2×Dic3—184no—
344C2×Dic3—182no—
345C2×Dic3—182no—
346C2×Dic3C22×D912yes—
347C2×Dic3C22×D912yes—
348C4×D3—188no—
349C2×C32—24no—
350C2×C32#67⋊C414yes—
351C2×C32C22×C4×D311yescharacteristic
352C2×C32C2×D3×D411yescharacteristic
353C2×C32C2×#23711yescharacteristic
354C3×D3—64no—
355C2×C9—28no—
356C2×C9—24no—
357C2×C9—21no—
358C2×C9—21no—
359C2×C9—21no—
360C2×C9—24no—
361C2×C9D4×Dic314yescomplemented
362C2×C9C2×D3×D411yescharacteristic
363C2×C9C2×#23711yescharacteristic
364C2×C9C23×Dic311yescharacteristic
365D9—24no—
366C24—91no—
367C24D3×D911yescharacteristic
368C2×D4—98no—
369C2×D4—94no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—91no—
373C22×C4—274no—
374C22×C4—271no—
375C22×C4—274no—
376C22×C4—271no—
377C22×C4—544no—
378C22×C4—544no—
379C4⋊C4—274no—
380C22⋊C4—34no—
381C22⋊C4—274no—
382C42—274no—
383C22×C3—24no—
384C22×C3—24no—
385C22×C3—216no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—28no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3—28no—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—24no—
395C22×C3—22no—
396C22×C3—22no—
397C22×C3—94no—
398C22×C3—188no—
399C22×C3—182no—
400C22×C3—182no—
401C22×C3C2×C4×D912yes—
402C22×C3C2×C4×D914yescomplemented
403C22×C3D4×D912yes—
404C22×C3#369912yes—
405C22×C3C23×D911yescharacteristic
406C22×C3C2×D3×Dic312yes—
407C22×C3C2×D3×Dic314yes—
408C22×C3#380512yes—
409C22×C3#381112yes—
410C22×C3C22×D3211yescharacteristic
411C2×D3—34no—
412C2×D3—62no—
413C2×D3—62no—
414C2×D3—68no—
415C3×C4—62no—
416C3×C4—62no—
417C3×C4—94no—
418Dic3—22no—
419Dic3—22no—
420Dic3—34no—
421Dic3—94no—
422Dic3—94no—
423Dic3—184no—
424Dic3—184no—
425Dic3—182no—
426Dic3—182no—
427C32C2×#67⋊C411yescharacteristic
428C9—21no—
429C9C2×D4×Dic311yescharacteristic, complemented
430C23—22no—
431C23—22no—
432C23—92no—
433C23—94no—
434C23—182no—
435C23—182no—
436C23Dic3×D914yescomplemented
437C23C2×D3×D912yes—
438C23C2×D3×D911yescharacteristic
439D4—916no—
440C2×C4—32no—
441C2×C4—32no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—92no—
445C2×C4—94no—
446C2×C4—272no—
447C2×C4—274no—
448C2×C4—272no—
449C2×C4—548no—
450C2×C4—548no—
451C2×C4—542no—
452C2×C3—28no—
453C2×C3—24no—
454C2×C3—24no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—24no—
459C2×C3—184no—
460C2×C3#611⋊C414yescomplemented
461C2×C3C22×C4×D911yescharacteristic
462C2×C3C2×D4×D911yescharacteristic
463C2×C3C2×#369911yescharacteristic
464C2×C3#67⋊Dic314yes—
465C2×C3C22×D3×Dic311yescharacteristic
466C2×C3C2×#380511yescharacteristic
467C2×C3C2×#381111yescharacteristic
468D3—64no—
469C22—22no—
470C22—22no—
471C22—28no—
472C22—94no—
473C22—182no—
474C22—182no—
475C22—188no—
476C22C2×Dic3×D912yes—
477C22C2×Dic3×D914yescomplemented
478C22#8866312yes—
479C22#8866812yes—
480C22C22×D3×D911yescharacteristic
481C4—62no—
482C4—62no—
483C4—94no—
484C4—274no—
485C4—542no—
486C3—21no—
487C3C2×#611⋊C411yescharacteristic, complemented
488C3C2×#67⋊Dic311yescharacteristic
489C2—24no—
490C2—184no—
491C2#611⋊Dic314yesdirect product factor
492C2C22×Dic3×D911yescharacteristic
493C2C2×#8866311yescharacteristic
494C2C2×#8866811yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC24×C3×C9C22
socleC23×C32C22×D3
prime radicalC22×C3×#611C2
cosocleC22×C3×C9C24
hypercenterC24D3×D9
hypocenterC3×C9C2×C4×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C23×C3⋊Dic9C2semidirect
3. C22×Dic3×D9C2semidirect
4. C2×C9×#217C2semidirect
5. #611⋊Dic3C2direct (N × H)
6. C2×(C2×D9)⋊Dic3C2semidirect
7. C2×Dic9⋊Dic3C2semidirect
8. C2×Dic3×Dic9C2semidirect
16. C22×C3⋊Dic9C22semidirect
17. C2×C3×#611C4semidirect
23. C2×Dic3×D9C22semidirect
24. C9×#217C22semidirect
25. (C2×D9)⋊Dic3C22semidirect
26. Dic9⋊Dic3C22semidirect
27. Dic3×Dic9C22semidirect
47. C23×C3×C9C2×C4semidirect
52. C22×C3×D9C2×C4semidirect
56. C2×C3⋊Dic9D4semidirect
59. C3×#611C2×C4semidirect
64. C2×C3×Dic9C2×C4semidirect
91. C2×#611Dic3semidirect
112. C22×C3×C9C22×C4semidirect
119. C2×C3×D9C22×C4semidirect
121. C3⋊Dic9C2×D4semidirect
124. C3×Dic9C22×C4semidirect
134. C2×#217D9semidirect
171. C23×C9C2×Dic3semidirect
176. C22×D9C2×Dic3semidirect
182. #611C2×Dic3semidirect
193. C2×Dic9C2×Dic3semidirect
198. C2×C3×C9C4×D4semidirect
236. #217C2×D9semidirect
273. C22×C9C22×Dic3semidirect
278. C2×D9C22×Dic3semidirect
285. Dic9C22×Dic3semidirect
294. C3×C9C2×C4×D4semidirect
308. C23×C3C4×D9semidirect
361. C2×C9D4×Dic3semidirect
402. C22×C3C2×C4×D9semidirect
429. C9C2×D4×Dic3semidirect
436. C23Dic3×D9semidirect
460. C2×C3#611⋊C4semidirect
477. C22C2×Dic3×D9semidirect
487. C3C2×#611⋊C4semidirect
491. C2#611⋊Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊Dic92
C22×C3×#6112
C22×Dic3×D92
C2×C9×#2172
#611⋊Dic32
C2×(C2×D9)⋊Dic32
C2×Dic9⋊Dic32
C2×Dic3×Dic92
C2×#67⋊Dic33
C2×#611⋊C43