Finite Group Databasebeta

← C2×#11720946 #13150085

Subgroups — C2×#11720946 #13150085

Order 1728.

830 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88534C211yesmaximal, characteristic, complemented
2C2×C3×(C2×D9)⋊C4C211yesmaximal, characteristic
3C2×C9×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic
5C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic
6C2×Dic3⋊Dic9C211yesmaximal, characteristic, complemented
7C2×Dic3×Dic9C211yesmaximal, characteristic, complemented
8#11720946C218yesmaximal, direct product factor
9C2×#63858—31nomaximal
10C2×#63460—31nomaximal
11C23×C3×D9C2211yescharacteristic
12C22×C3×C4×C9C2211yescharacteristic
13C22×C3⋊Dic9C2211yescharacteristic
14C22×C3⋊Dic9C2211yescharacteristic
15C22×C9×Dic3C2211yescharacteristic
16C22×C9×Dic3C2211yescharacteristic
17C22×C3×Dic9C2211yescharacteristic
18#88534C2214yescomplemented
19C3×(C2×D9)⋊C4C2214yes—
20C9×C4⋊Dic3C2214yescomplemented
21(C2×D9)⋊Dic3C2214yes—
22(C2×D9)⋊Dic3C2214yes—
23Dic3⋊Dic9C2214yescomplemented
24Dic3×Dic9C2214yescomplemented
25C2×#3750—31no—
26C2×C3×(C2×D3)⋊C4—31no—
27C2×C3×C4⋊Dic3D311yescharacteristic
28C2×Dic3⋊Dic3—31no—
29C2×(C2×D3)⋊Dic3—31no—
30C2×(C2×D3)⋊Dic3—31no—
31C2×Dic32—31no—
32#63858—38no—
33C2×C9×C4⋊C4—31no—
34C2×(C2×D9)⋊C4—31no—
35C2×(C2×D9)⋊C4—31no—
36C2×(C2×D9)⋊C4D311yescharacteristic
37C2×C4⋊Dic9—31no—
38C2×Dic9⋊C4—31no—
39C2×Dic9⋊C4—61no—
40C2×C4×Dic9—31no—
41#63460—38no—
42C23×C3×C9C2311yescharacteristic
43C22×C3×D9—22no—
44C22×C3×D9—22no—
45C22×C3×D9—22no—
46C22×C3×D9C2312yes—
47C2×C3×C4×C9—22no—
48C2×C3×C4×C9C2312yes—
49C2×C3⋊Dic9—22no—
50C2×C3⋊Dic9—22no—
51C2×C3⋊Dic9C2312yes—
52C2×C3⋊Dic9C2312yes—
53C2×C9×Dic3—22no—
54C2×C9×Dic3—22no—
55C2×C9×Dic3C2312yes—
56C2×C9×Dic3C2312yes—
57C2×C3×Dic9—22no—
58C2×C3×Dic9C2312yes—
59C2×#898—91no—
60C2×#879—91no—
61C23×C3×D3—31no—
62C22×C32×C4C2×D311yescharacteristic
63C22×C3⋊Dic3—31no—
64C22×C3⋊Dic3—31no—
65C22×C3×Dic3—31no—
66C22×C3×Dic3C2×D311yescharacteristic
67C22×C3×Dic3C2×D311yescharacteristic
68C23×D9C2×D311yescharacteristic
69#3750—34no—
70C3×(C2×D3)⋊C4—34no—
71C3×C4⋊Dic3C2×D314yes—
72Dic3⋊Dic3—34no—
73(C2×D3)⋊Dic3—34no—
74(C2×D3)⋊Dic3—34no—
75Dic32—34no—
76C22×C4×C9—21no—
77C22×C4×C9—31no—
78C22×C4×C9—31no—
79C22×C4×C9C2×D311yescharacteristic
80C22×Dic9—31no—
81C22×Dic9—31no—
82C22×Dic9—61no—
83C22×Dic9—61no—
84C22×Dic9C2×D311yescharacteristic
85C9×C4⋊C4—34no—
86(C2×D9)⋊C4—34no—
87(C2×D9)⋊C4—34no—
88(C2×D9)⋊C4C2×D314yes—
89C4⋊Dic9—34no—
90Dic9⋊C4—34no—
91Dic9⋊C4—64no—
92C4×Dic9—34no—
93C22×C3×C9#4112yes—
94C22×C3×C9#4112yes—
95C22×C3×C9#4112yes—
96C22×C3×C9C2411yescharacteristic
97C2×C3×D9—22no—
98C2×C3×D9—22no—
99C2×C3×D9—22no—
100C2×C3×D9—44no—
101C3×C4×C9—22no—
102C3⋊Dic9—22no—
103C3⋊Dic9—22no—
104C9×Dic3—22no—
105C9×Dic3—22no—
106C3×Dic9—22no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C22⋊C4—91no—
109C2×#217—91no—
110C2×#217—91no—
111C2×(C2×D3)⋊C4—31no—
112C2×(C2×D3)⋊C4—91no—
113C2×(C2×D3)⋊C4—91no—
114C2×C4⋊Dic3—91no—
115C2×C4⋊Dic3D911yescharacteristic, complemented
116C2×Dic3⋊C4—91no—
117C2×Dic3⋊C4—91no—
118C2×Dic3⋊C4—91no—
119C2×Dic3⋊C4—181no—
120C2×C4×Dic3—91no—
121C2×C4×Dic3—91no—
122#898—98no—
123#879—98no—
124C23×C32C22×D311yescharacteristic
125C22×C3×D3—32no—
126C22×C3×D3—62no—
127C22×C3×D3—62no—
128C22×C3×D3—62no—
129C2×C32×C4—22no—
130C2×C32×C4C22×D312yes—
131C2×C3⋊Dic3—32no—
132C2×C3⋊Dic3—32no—
133C2×C3⋊Dic3—62no—
134C2×C3⋊Dic3—62no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—32no—
138C2×C3×Dic3—62no—
139C2×C3×Dic3C22×D312yes—
140C2×C3×Dic3C22×D312yes—
141C23×C9—21no—
142C23×C9C22×D311yescharacteristic
143C22×D9—22no—
144C22×D9—22no—
145C22×D9—22no—
146C22×D9C22×D312yes—
147C2×C4×C9—22no—
148C2×C4×C9—22no—
149C2×C4×C9—32no—
150C2×C4×C9—32no—
151C2×C4×C9—42no—
152C2×C4×C9—62no—
153C2×C4×C9—62no—
154C2×C4×C9C22×D312yes—
155C2×Dic9—22no—
156C2×Dic9—32no—
157C2×Dic9—32no—
158C2×Dic9—62no—
159C2×Dic9—62no—
160C2×Dic9—64no—
161C2×Dic9—62no—
162C2×Dic9—62no—
163C2×Dic9—122no—
164C2×Dic9C22×D312yes—
165C2×#126—271noSylow
166C2×C3×C9#12614yescomplemented
167C2×C3×C9C2×#4111yescharacteristic
168C2×C3×C9C2×#4111yescharacteristic
169C2×C3×C9C2×#4111yescharacteristic
170C3×D9—42no—
171C24×C3—91no—
172C23×D3—31no—
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—91no—
177C22×C3×C4C2×D911yescharacteristic
178C22×C3×C4D3211yescharacteristic
179C22×Dic3—31no—
180C22×Dic3—91no—
181C22×Dic3—91no—
182C22×Dic3—91no—
183C22×Dic3—91no—
184C22×Dic3—181no—
185C22×Dic3—181no—
186C22×Dic3C2×D911yescharacteristic
187C22×Dic3C2×D911yescharacteristic
188C3×C4⋊C4—34no—
189C3×C22⋊C4—94no—
190#217—94no—
191#217—94no—
192(C2×D3)⋊C4—34no—
193(C2×D3)⋊C4—94no—
194(C2×D3)⋊C4—94no—
195C4⋊Dic3—94no—
196C4⋊Dic3C2×D914yescomplemented
197Dic3⋊C4—94no—
198Dic3⋊C4—94no—
199Dic3⋊C4—94no—
200Dic3⋊C4—184no—
201C4×Dic3—94no—
202C4×Dic3—94no—
203C22×C32#23512yes—
204C22×C32#23712yes—
205C22×C32#23912yes—
206C22×C32C23×D311yescharacteristic
207C2×C3×D3—62no—
208C2×C3×D3—62no—
209C2×C3×D3—62no—
210C2×C3×D3—124no—
211C32×C4—22no—
212C3⋊Dic3—62no—
213C3⋊Dic3—62no—
214C3×Dic3—22no—
215C3×Dic3—22no—
216C3×Dic3—62no—
217C22×C9—21no—
218C22×C9—22no—
219C22×C9—22no—
220C22×C9—22no—
221C22×C9#23512yes—
222C22×C9#23712yes—
223C22×C9#23712yes—
224C22×C9C23×D311yescharacteristic
225C2×D9—22no—
226C2×D9—22no—
227C2×D9—22no—
228C2×D9—44no—
229C4×C9—22no—
230C4×C9—42no—
231C4×C9—62no—
232C4×C9—62no—
233Dic9—22no—
234Dic9—64no—
235Dic9—62no—
236Dic9—62no—
237Dic9—122no—
238#126—278no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—271no—
241C2×C4⋊C4—271no—
242C2×C22⋊C4—91no—
243C2×C22⋊C4—271no—
244C2×C22⋊C4—271no—
245C2×C42—271no—
246C3×C9C2×#12611yescharacteristic, complemented, Sylow
247C23×C3—21no—
248C23×C3—92no—
249C23×C3—182no—
250C23×C3—182no—
251C23×C3—182no—
252C23×C3C22×D911yescharacteristic
253C23×C3C2×D3211yescharacteristic
254C22×D3—32no—
255C22×D3—62no—
256C22×D3—62no—
257C22×D3—62no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—32no—
262C2×C3×C4—32no—
263C2×C3×C4—42no—
264C2×C3×C4—62no—
265C2×C3×C4—62no—
266C2×C3×C4—92no—
267C2×C3×C4—182no—
268C2×C3×C4C22×D912yes—
269C2×C3×C4C2×D3212yes—
270C2×Dic3—22no—
271C2×Dic3—22no—
272C2×Dic3—32no—
273C2×Dic3—62no—
274C2×Dic3—92no—
275C2×Dic3—92no—
276C2×Dic3—92no—
277C2×Dic3—92no—
278C2×Dic3—182no—
279C2×Dic3—182no—
280C2×Dic3—184no—
281C2×Dic3—182no—
282C2×Dic3—182no—
283C2×Dic3—182no—
284C2×Dic3—182no—
285C2×Dic3—362no—
286C2×Dic3C22×D912yes—
287C2×Dic3C22×D912yes—
288C2×C32#89814yes—
289C2×C32C2×#23511yescharacteristic
290C2×C32C2×#23711yescharacteristic
291C2×C32C2×#23911yescharacteristic
292C3×D3—122no—
293C2×C9—21no—
294C2×C9—21no—
295C2×C9—21no—
296C2×C9—24no—
297C2×C9#87914yescomplemented
298C2×C9C2×#23511yescharacteristic
299C2×C9C2×#23711yescharacteristic
300C2×C9C2×#23711yescharacteristic
301D9—42no—
302C24—91no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—91no—
306C22×C4—271no—
307C22×C4—271no—
308C22×C4D3×D911yescharacteristic
309C4⋊C4—34no—
310C4⋊C4—274no—
311C4⋊C4—274no—
312C22⋊C4—94no—
313C22⋊C4—274no—
314C22⋊C4—274no—
315C42—274no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—21no—
319C22×C3—22no—
320C22×C3—182no—
321C22×C3—182no—
322C22×C3—182no—
323C22×C3—364no—
324C22×C3#369712yes—
325C22×C3#369912yes—
326C22×C3#370112yes—
327C22×C3C23×D911yescharacteristic
328C22×C3#379512yes—
329C22×C3#379612yes—
330C22×C3#380412yes—
331C22×C3C22×D3211yescharacteristic
332C2×D3—62no—
333C2×D3—62no—
334C2×D3—62no—
335C2×D3—124no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—42no—
339C3×C4—62no—
340C3×C4—62no—
341C3×C4—182no—
342Dic3—22no—
343Dic3—22no—
344Dic3—62no—
345Dic3—184no—
346Dic3—182no—
347Dic3—182no—
348Dic3—182no—
349Dic3—182no—
350Dic3—362no—
351C32C2×#89811yescharacteristic
352C9—21no—
353C9C2×#87911yescharacteristic, complemented
354C23—92no—
355C23—182no—
356C23—182no—
357C23—182no—
358C23C2×D3×D911yescharacteristic
359C2×C4—22no—
360C2×C4—32no—
361C2×C4—32no—
362C2×C4—62no—
363C2×C4—62no—
364C2×C4—92no—
365C2×C4—182no—
366C2×C4—272no—
367C2×C4—272no—
368C2×C4—542no—
369C2×C4—542no—
370C2×C4C2×D3×D912yes—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—24no—
375C2×C3—362no—
376C2×C3#6346014yescomplemented
377C2×C3C2×#369711yescharacteristic
378C2×C3C2×#369911yescharacteristic
379C2×C3C2×#370111yescharacteristic
380C2×C3#6385814yes—
381C2×C3C2×#379511yescharacteristic
382C2×C3C2×#379611yescharacteristic
383C2×C3C2×#380411yescharacteristic
384D3—122no—
385C22—182no—
386C22—182no—
387C22—182no—
388C22—364no—
389C22#8863412yes—
390C22#8863812yes—
391C22#8865812yes—
392C22C22×D3×D911yescharacteristic
393C4—22no—
394C4—62no—
395C4—62no—
396C4—182no—
397C4—542no—
398C4—542no—
399C3—21no—
400C3C2×#6346011yescharacteristic, complemented
401C3C2×#6385811yescharacteristic
402C2—362no—
403C2#1172094614yesdirect product factor
404C2C2×#8863411yescharacteristic
405C2C2×#8863811yescharacteristic
406C2C2×#8865811yescharacteristic
subgroupG/H
centerC23C2×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC23×C32C22×D3
prime radicalC23×C3×D9C22
hypercenterC22×C4D3×D9
hypocenterC3×C9C2×#126
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#88534C2semidirect
3. C2×C9×C4⋊Dic3C2semidirect
6. C2×Dic3⋊Dic9C2semidirect
7. C2×Dic3×Dic9C2semidirect
8. #11720946C2direct (N × H)
18. #88534C22semidirect
20. C9×C4⋊Dic3C22semidirect
23. Dic3⋊Dic9C22semidirect
24. Dic3×Dic9C22semidirect
115. C2×C4⋊Dic3D9semidirect
166. C2×C3×C9#126semidirect
196. C4⋊Dic3C2×D9semidirect
246. C3×C9C2×#126semidirect
297. C2×C9#879semidirect
353. C9C2×#879semidirect
376. C2×C3#63460semidirect
400. C3C2×#63460semidirect
403. C2#11720946direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#885342
C2×C3×(C2×D9)⋊C42
C2×C9×C4⋊Dic32
C2×(C2×D9)⋊Dic32
C2×Dic3⋊Dic92
C2×Dic3×Dic92
#117209462
C2×#638583
C2×#634603