Finite Group Databasebeta

← C2×#11720260 #13139303

Subgroups — C2×#11720260 #13139303

Order 1728.

578 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3697C211yesmaximal, characteristic
2C2×#88532C211yesmaximal, characteristic, complemented
3C2×C4×C9×Dic3C211yesmaximal, characteristic, complemented
4#11720260C214yesmaximal, direct product factor
5C2×#63569—31nomaximal
6C2×#63364—31nomaximal
7C22×C3×C4×C9C2211yescharacteristic
8C2×C3×#611—21no—
9C22×C9×Dic3—21no—
10C3×#3697—21no—
11C3×#3697—21no—
12C3×#3697C412yescomplemented
13C3×#3697C2212yes—
14C2×C3×D36C411yescharacteristic, complemented
15C2×C3×C4×D9—21no—
16C2×C3×Dic18C411yescharacteristic, complemented
17#88532—21no—
18#88532C2212yescomplemented
19C2×C3⋊(C9⋊C8)—21no—
20C4×C9×Dic3—21no—
21C4×C9×Dic3C2212yescomplemented
22C2×C3×#235—31no—
23C2×#3748—31no—
24C2×C3×C4×Dic3D311yescharacteristic
25C2×#3697D311yescharacteristic
26#63569—34no—
27C2×C42×C9—31no—
28C2×#3667—31no—
29C2×#3667—61no—
30#63364—34no—
31C23×C3×C9D411yescharacteristic
32C22×C3×D9—21no—
33C2×C3×C4×C9C2×C411yescharacteristic
34C2×C3×C4×C9C2×C411yescharacteristic
35C2×C3×C4×C9D411yescharacteristic
36C2×C3×C4×C9D411yescharacteristic
37C2×C3×C4×C9D411yescharacteristic
38C2×C3×C4×C9C2311yescharacteristic
39C3×#611—22no—
40C3×#611—22no—
41C2×C9×Dic3—24no—
42C2×C9×Dic3—22no—
43C2×C3×Dic9—21no—
44C3×D36—21no—
45C3×D36C2×C412yescomplemented
46C3×C4×D9—22no—
47C3×C4×D9—22no—
48C3×Dic18—21no—
49C3×Dic18C2×C412yescomplemented
50C3⋊(C9⋊C8)—22no—
51C2×#837—91no—
52C2×#805—91no—
53C22×C32×C4C2×D311yescharacteristic
54C2×C3×#67—61no—
55C22×C3×Dic3—21no—
56C3×#235—32no—
57C3×#235—32no—
58C3×#235—61no—
59C3×#235—61no—
60C2×C3×D12—31no—
61C2×C3×C4×D3—61no—
62C2×C3×Dic6—31no—
63#3748—32no—
64#3748—61no—
65C2×C3⋊(C3⋊C8)—61no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3C2×D312yes—
68C22×C4×C9—21no—
69C22×C4×C9—61no—
70C22×C4×C9C2×D311yescharacteristic
71C2×#611—21no—
72#3697—21no—
73#3697—21no—
74#3697Dic312yescomplemented
75#3697C2×D312yes—
76C2×D36Dic311yescharacteristic, complemented
77C2×C4×D9—21no—
78C2×Dic18Dic311yescharacteristic, complemented
79C42×C9—32no—
80C42×C9—61no—
81#3667—32no—
82#3667—62no—
83#3667—62no—
84#3667—61no—
85C2×C9⋊C8—62no—
86C2×C9⋊C8—61no—
87C22×C3×C9—22no—
88C22×C3×C9C22⋊C411yescharacteristic
89C22×C3×C9C22⋊C411yescharacteristic
90C22×C3×C9C2×D411yescharacteristic
91C2×C3×D9—22no—
92C2×C3×D9—42no—
93C3×C4×C9C22⋊C411yescharacteristic
94C3×C4×C9C22⋊C411yescharacteristic
95C3×C4×C9C22×C411yescharacteristic
96C3×C4×C9C2×D411yescharacteristic
97C9×Dic3—24no—
98C3×Dic9—22no—
99C2×C3×#41—91no—
100C2×#235—31no—
101C2×C3×C42—31no—
102C2×C4×Dic3D911yescharacteristic, complemented
103C2×#208—91no—
104C2×#208—91no—
105C2×#208—181no—
106#837—94no—
107#805—94no—
108C23×C32#6711yescharacteristic
109C22×C3×D3—61no—
110C2×C32×C4C4×D311yescharacteristic
111C2×C32×C4C4×D311yescharacteristic
112C2×C32×C4D1211yescharacteristic
113C2×C32×C4D1211yescharacteristic
114C2×C32×C4#6711yescharacteristic
115C2×C32×C4C22×D311yescharacteristic
116C3×#67—62no—
117C3×#67—62no—
118C2×C3×Dic3—24no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—61no—
121C3×D12—32no—
122C3×D12—61no—
123C3×C4×D3—62no—
124C3×C4×D3—62no—
125C3×Dic6—32no—
126C3×Dic6—61no—
127C23×C9—21no—
128C23×C9#6711yescharacteristic
129C22×D9—21no—
130C3⋊(C3⋊C8)—62no—
131C2×C4×C9—21no—
132C2×C4×C9—21no—
133C2×C4×C9—21no—
134C2×C4×C9—21no—
135C2×C4×C9—21no—
136C2×C4×C9—21no—
137C2×C4×C9—64no—
138C2×C4×C9—62no—
139C2×C4×C9C2×Dic311yescharacteristic
140C2×C4×C9C2×Dic311yescharacteristic
141C2×C4×C9#6711yescharacteristic
142C2×C4×C9#6711yescharacteristic
143C2×C4×C9#6711yescharacteristic
144C2×C4×C9C22×D311yescharacteristic
145#611—22no—
146#611—22no—
147C2×Dic9—21no—
148D36—21no—
149D36C2×Dic312yescomplemented
150C4×D9—22no—
151C4×D9—22no—
152Dic18—21no—
153Dic18C2×Dic312yescomplemented
154C9⋊C8—64no—
155C9⋊C8—62no—
156C2×#104—271noSylow
157C2×C3×C9—21no—
158C2×C3×C9—21no—
159C2×C3×C9#10412yescomplemented
160C2×C3×C9C2×C22⋊C411yescharacteristic
161C3×D9—42no—
162C3×#41—92no—
163C3×#41—92no—
164C3×#41—181no—
165C3×#41—181no—
166C2×C3×Q8—91no—
167C2×C3×D4—91no—
168C2×C3×D4—181no—
169C22×C3×C4—21no—
170C22×C3×C4—61no—
171C22×C3×C4—181no—
172C22×C3×C4C2×D911yescharacteristic
173C22×C3×C4D3211yescharacteristic
174C2×#67—61no—
175C22×Dic3—21no—
176#235—32no—
177#235—32no—
178#235—61no—
179#235—61no—
180C2×D12—31no—
181C2×C4×D3—61no—
182C2×Dic6—31no—
183C3×C42—32no—
184C3×C42—61no—
185C4×Dic3—21no—
186C4×Dic3C2×D912yescomplemented
187#208—92no—
188#208—92no—
189#208—182no—
190#208—182no—
191#208—181no—
192#208—181no—
193C2×C3⋊C8—182no—
194C2×C3⋊C8—181no—
195C2×C3⋊C8—181no—
196C22×C32—22no—
197C22×C32(C2×D3)⋊C411yescharacteristic
198C22×C32(C2×D3)⋊C411yescharacteristic
199C22×C32C2×#6711yescharacteristic
200C2×C3×D3—62no—
201C2×C3×D3—122no—
202C32×C4(C2×D3)⋊C411yescharacteristic
203C32×C4(C2×D3)⋊C411yescharacteristic
204C32×C4C2×C4×D311yescharacteristic
205C32×C4C2×D1211yescharacteristic
206C3×Dic3—24no—
207C3×Dic3—62no—
208C22×C9—22no—
209C22×C9—21no—
210C22×C9—21no—
211C22×C9—21no—
212C22×C9—42no—
213C22×C9#21711yescharacteristic
214C22×C9#21711yescharacteristic
215C22×C9C2×#6711yescharacteristic
216C2×D9—22no—
217C2×D9—42no—
218C4×C9—21no—
219C4×C9—21no—
220C4×C9—21no—
221C4×C9—21no—
222C4×C9—64no—
223C4×C9#21711yescharacteristic
224C4×C9#21711yescharacteristic
225C4×C9C22×Dic311yescharacteristic
226C4×C9C2×#6711yescharacteristic
227Dic9—22no—
228C2×#41—91no—
229C2×M16—271no—
230C2×C42—31no—
231#104—274no—
232C3×C9C2×#10411yescharacteristic, complemented, Sylow
233C23×C3—21no—
234C23×C3—181no—
235C23×C3#61111yescharacteristic
236C23×C3#62511yescharacteristic
237C22×D3—61no—
238C3×Q8—92no—
239C3×Q8—181no—
240C3×D4—92no—
241C3×D4—182no—
242C3×D4—182no—
243C3×D4—181no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—64no—
251C2×C3×C4—62no—
252C2×C3×C4—181no—
253C2×C3×C4—182no—
254C2×C3×C4—182no—
255C2×C3×C4C4×D911yescharacteristic
256C2×C3×C4C4×D911yescharacteristic
257C2×C3×C4D3611yescharacteristic
258C2×C3×C4D3611yescharacteristic
259C2×C3×C4#61111yescharacteristic
260C2×C3×C4C22×D911yescharacteristic
261C2×C3×C4D3×Dic311yescharacteristic
262C2×C3×C4D3×Dic311yescharacteristic
263C2×C3×C4#62511yescharacteristic
264C2×C3×C4#62611yescharacteristic
265C2×C3×C4#62611yescharacteristic
266C2×C3×C4C2×D3211yescharacteristic
267#67—62no—
268#67—62no—
269C2×Dic3—24no—
270C2×Dic3—22no—
271C2×Dic3—61no—
272D12—32no—
273D12—61no—
274C4×D3—62no—
275C4×D3—62no—
276Dic6—32no—
277Dic6—61no—
278C3⋊C8—184no—
279C3⋊C8—182no—
280C3⋊C8—182no—
281C2×C32—21no—
282C2×C32—21no—
283C2×C32#80512yes—
284C2×C32C2×(C2×D3)⋊C411yescharacteristic
285C3×D3—122no—
286C2×C9—21no—
287C2×C9—21no—
288C2×C9—22no—
289C2×C9—21no—
290C2×C9—41no—
291C2×C9—41no—
292C2×C9#83712yescomplemented
293C2×C9C2×#21711yescharacteristic
294D9—42no—
295#41—92no—
296#41—92no—
297#41—181no—
298#41—181no—
299C2×Q8—91no—
300C2×D4—91no—
301C2×D4—181no—
302C22×C4—61no—
303C22×C4—181no—
304C22×C4D3×D911yescharacteristic
305M16—272no—
306M16—541no—
307C2×C8—541no—
308C42—32no—
309C42—61no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—42no—
316C22×C3—182no—
317C22×C3—362no—
318C22×C3(C2×D9)⋊C411yescharacteristic
319C22×C3(C2×D9)⋊C411yescharacteristic
320C22×C3C2×#61111yescharacteristic
321C22×C3(C2×D3)⋊Dic311yescharacteristic
322C22×C3(C2×D3)⋊Dic311yescharacteristic
323C22×C3C2×#62511yescharacteristic
324C2×D3—62no—
325C2×D3—122no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—64no—
331C3×C4—182no—
332C3×C4(C2×D9)⋊C411yescharacteristic
333C3×C4(C2×D9)⋊C411yescharacteristic
334C3×C4C2×C4×D911yescharacteristic
335C3×C4C2×D3611yescharacteristic
336C3×C4(C2×D3)⋊Dic311yescharacteristic
337C3×C4(C2×D3)⋊Dic311yescharacteristic
338C3×C4C2×D3×Dic311yescharacteristic
339C3×C4C2×#62611yescharacteristic
340Dic3—24no—
341Dic3—62no—
342C32C2×#80511yescharacteristic
343C9—21no—
344C9C2×#83711yescharacteristic, complemented
345C23—181no—
346C23#619411yescharacteristic
347Q8—92no—
348Q8—181no—
349D4—92no—
350D4—182no—
351D4—182no—
352D4—181no—
353C2×C4—64no—
354C2×C4—62no—
355C2×C4—181no—
356C2×C4—182no—
357C2×C4—182no—
358C2×C4Dic3×D911yescharacteristic
359C2×C4Dic3×D911yescharacteristic
360C2×C4#619211yescharacteristic
361C2×C4#619211yescharacteristic
362C2×C4#619411yescharacteristic
363C2×C4C2×D3×D911yescharacteristic
364C8—542no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—22no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3—362no—
374C2×C3#6336412yescomplemented
375C2×C3C2×(C2×D9)⋊C411yescharacteristic
376C2×C3#6356912yes—
377C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
378D3—122no—
379C22—22no—
380C22—182no—
381C22—362no—
382C22(C2×D9)⋊Dic311yescharacteristic
383C22(C2×D9)⋊Dic311yescharacteristic
384C22C2×#619411yescharacteristic
385C4—64no—
386C4—182no—
387C4(C2×D9)⋊Dic311yescharacteristic
388C4(C2×D9)⋊Dic311yescharacteristic
389C4C2×Dic3×D911yescharacteristic
390C4C2×#619211yescharacteristic
391C3—21no—
392C3C2×#6336411yescharacteristic, complemented
393C3C2×#6356911yescharacteristic
394C2—21no—
395C2—21no—
396C2—362no—
397C2#1172026012yesdirect product factor
398C2C2×(C2×D9)⋊Dic311yescharacteristic
subgroupG/H
centerC2×C4#6192
commutatorC3×C4×C9C22×C4
FrattiniC2×C3×C4C2×D32
FittingC22×C3×C4×C9C22
socleC22×C32(C2×D3)⋊C4
prime radicalC2×C3×#3697C2
cosocleC2×C3×C4×C9C23
hypercenterC22×C4D3×D9
hypocenterC3×C9C2×#104
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#88532C2semidirect
3. C2×C4×C9×Dic3C2semidirect
4. #11720260C2direct (N × H)
12. C3×#3697C4semidirect
14. C2×C3×D36C4semidirect
16. C2×C3×Dic18C4semidirect
18. #88532C22semidirect
21. C4×C9×Dic3C22semidirect
45. C3×D36C2×C4semidirect
49. C3×Dic18C2×C4semidirect
74. #3697Dic3semidirect
76. C2×D36Dic3semidirect
78. C2×Dic18Dic3semidirect
102. C2×C4×Dic3D9semidirect
149. D36C2×Dic3semidirect
153. Dic18C2×Dic3semidirect
159. C2×C3×C9#104semidirect
186. C4×Dic3C2×D9semidirect
232. C3×C9C2×#104semidirect
292. C2×C9#837semidirect
344. C9C2×#837semidirect
374. C2×C3#63364semidirect
392. C3C2×#63364semidirect
397. C2#11720260direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#36972
C2×#885322
C2×C4×C9×Dic32
#117202602
C2×#635693
C2×#633643