Finite Group Databasebeta

← C2×#11720523 #13144280

Subgroups — C2×#11720523 #13144280

Order 1728.

1050 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6233C211yesmaximal, characteristic
2C2×C3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×#88551C211yesmaximal, characteristic, complemented
4#11720523C214yesmaximal, direct product factor
5C2×#63633—31nomaximal
6C2×#63365—33nomaximal
7C24×C3×C9C2211yescharacteristic
8C23×C3⋊D9C411yescharacteristic, complemented
9C22×C3×C4×C9—21no—
10C2×#6233—21no—
11C2×#6233—21no—
12C2×#6233—21no—
13C2×#6233—21no—
14C2×#6233C412yescomplemented
15C2×#6233C2212yes—
16C22×C3⋊Dic9—21no—
17C22×C3⋊Dic9C411yescharacteristic, complemented
18C3×C9×C22⋊C4—21no—
19C3×C9×C22⋊C4C2212yescomplemented
20#88551—21no—
21#88551C2212yescomplemented
22C22×#638—31no—
23C2×C32×C22⋊C4D311yescharacteristic
24C2×#3757—31no—
25C22×#611—33no—
26#63633—34no—
27C2×C9×C22⋊C4D313yescomplemented
28C2×#3676—33no—
29#63365—312no—
30C23×C3×C9—42no—
31C23×C3×C9C2×C411yescharacteristic
32C23×C3×C9C2×C411yescharacteristic
33C23×C3×C9D411yescharacteristic
34C23×C3×C9D411yescharacteristic
35C23×C3×C9D411yescharacteristic
36C23×C3×C9D411yescharacteristic
37C23×C3×C9C2311yescharacteristic
38C22×C3⋊D9—21no—
39C22×C3⋊D9—21no—
40C22×C3⋊D9—42no—
41C22×C3⋊D9C2×C412yescomplemented
42C2×C3×C4×C9—22no—
43C2×C3×C4×C9—42no—
44#6233—22no—
45#6233—22no—
46#6233—22no—
47#6233—22no—
48C2×C3⋊Dic9—21no—
49C2×C3⋊Dic9—21no—
50C2×C3⋊Dic9—22no—
51C2×C3⋊Dic9—42no—
52C2×C3⋊Dic9C2×C412yescomplemented
53C2×#806—93no—
54C2×#806—91no—
55C24×C32C2×D311yescharacteristic
56C23×C3⋊D3—31no—
57C22×C32×C4—21no—
58C2×#638—32no—
59C2×#638—32no—
60C2×#638—61no—
61C2×#638—61no—
62C2×#638—61no—
63C2×#638—61no—
64C22×C3⋊Dic3—31no—
65C22×C3⋊Dic3—61no—
66C24×C9C2×D313yes—
67C23×D9—33no—
68C32×C22⋊C4—21no—
69C32×C22⋊C4C2×D312yes—
70#3757—32no—
71#3757—61no—
72C22×C4×C9—23no—
73C2×#611—36no—
74C2×#611—36no—
75C2×#611—63no—
76C2×#611—63no—
77C2×#611—63no—
78C2×#611—63no—
79C22×Dic9—33no—
80C22×Dic9—63no—
81C9×C22⋊C4—23no—
82C9×C22⋊C4C2×D316yescomplemented
83#3676—36no—
84#3676—63no—
85C22×C3×C9—22no—
86C22×C3×C9—22no—
87C22×C3×C9—22no—
88C22×C3×C9—41no—
89C22×C3×C9—41no—
90C22×C3×C9—41no—
91C22×C3×C9—41no—
92C22×C3×C9C22⋊C411yescharacteristic
93C22×C3×C9C22⋊C411yescharacteristic
94C22×C3×C9C22⋊C411yescharacteristic
95C22×C3×C9C22⋊C411yescharacteristic
96C22×C3×C9C22×C411yescharacteristic
97C22×C3×C9C2×D411yescharacteristic
98C22×C3×C9C2×D411yescharacteristic
99C2×C3⋊D9—22no—
100C2×C3⋊D9—42no—
101C2×C3⋊D9—42no—
102C2×C3⋊D9—42no—
103C3×C4×C9—42no—
104C3⋊Dic9—22no—
105C3⋊Dic9—42no—
106C22×#67—93no—
107C22×#67—91no—
108C2×C3×C22⋊C4D913yescomplemented
109C2×C3×C22⋊C4C3⋊D311yescharacteristic
110C2×#217—93no—
111C2×#217—91no—
112#806—912no—
113#806—94no—
114C23×C32—42no—
115C23×C32C4×D311yescharacteristic
116C23×C32C4×D311yescharacteristic
117C23×C32D1211yescharacteristic
118C23×C32D1211yescharacteristic
119C23×C32#6711yescharacteristic
120C23×C32#6711yescharacteristic
121C23×C32C22×D311yescharacteristic
122C22×C3⋊D3—32no—
123C22×C3⋊D3—61no—
124C22×C3⋊D3—61no—
125C22×C3⋊D3—122no—
126C2×C32×C4—22no—
127C2×C32×C4—42no—
128#638—62no—
129#638—62no—
130#638—62no—
131#638—62no—
132C2×C3⋊Dic3—32no—
133C2×C3⋊Dic3—61no—
134C2×C3⋊Dic3—61no—
135C2×C3⋊Dic3—62no—
136C2×C3⋊Dic3—122no—
137C23×C9—46no—
138C23×C9C4×D313yes—
139C23×C9C4×D313yes—
140C23×C9D1213yes—
141C23×C9D1213yes—
142C23×C9#6713yes—
143C23×C9#6713yes—
144C23×C9C22×D313yes—
145C22×D9—36no—
146C22×D9—63no—
147C22×D9—63no—
148C22×D9—126no—
149C2×C4×C9—26no—
150C2×C4×C9—46no—
151#611—66no—
152#611—66no—
153#611—66no—
154#611—66no—
155C2×Dic9—36no—
156C2×Dic9—63no—
157C2×Dic9—63no—
158C2×Dic9—66no—
159C2×Dic9—126no—
160C2×#99—271noSylow
161C2×C3×C9—21no—
162C2×C3×C9—21no—
163C2×C3×C9—21no—
164C2×C3×C9—21no—
165C2×C3×C9—21no—
166C2×C3×C9—21no—
167C2×C3×C9#9912yescomplemented
168C2×C3×C9C2×C22⋊C411yescharacteristic
169C3⋊D9—42no—
170C24×C3C2×D913yes—
171C24×C3C2×C3⋊D311yescharacteristic
172C23×D3—93no—
173C23×D3—91no—
174C22×C3×C4—23no—
175C22×C3×C4—21no—
176C2×#67—96no—
177C2×#67—96no—
178C2×#67—92no—
179C2×#67—92no—
180C2×#67—183no—
181C2×#67—183no—
182C2×#67—183no—
183C2×#67—183no—
184C2×#67—181no—
185C2×#67—181no—
186C2×#67—181no—
187C2×#67—181no—
188C22×Dic3—93no—
189C22×Dic3—91no—
190C22×Dic3—183no—
191C22×Dic3—181no—
192C3×C22⋊C4—23no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4C2×D916yescomplemented
195C3×C22⋊C4C2×C3⋊D312yes—
196#217—96no—
197#217—92no—
198#217—183no—
199#217—181no—
200C22×C32—22no—
201C22×C32—22no—
202C22×C32—22no—
203C22×C32—41no—
204C22×C32—41no—
205C22×C32—41no—
206C22×C32—41no—
207C22×C32(C2×D3)⋊C411yescharacteristic
208C22×C32(C2×D3)⋊C411yescharacteristic
209C22×C32(C2×D3)⋊C411yescharacteristic
210C22×C32(C2×D3)⋊C411yescharacteristic
211C22×C32C2×C4×D311yescharacteristic
212C22×C32C2×D1211yescharacteristic
213C22×C32C2×#6711yescharacteristic
214C2×C3⋊D3—62no—
215C2×C3⋊D3—122no—
216C2×C3⋊D3—122no—
217C2×C3⋊D3—122no—
218C32×C4—42no—
219C3⋊Dic3—62no—
220C3⋊Dic3—122no—
221C22×C9—26no—
222C22×C9—26no—
223C22×C9—26no—
224C22×C9—43no—
225C22×C9—43no—
226C22×C9—43no—
227C22×C9—43no—
228C22×C9(C2×D3)⋊C413yes—
229C22×C9(C2×D3)⋊C413yes—
230C22×C9(C2×D3)⋊C413yes—
231C22×C9(C2×D3)⋊C413yes—
232C22×C9C2×C4×D313yes—
233C22×C9C2×D1213yes—
234C22×C9C2×#6713yes—
235C2×D9—66no—
236C2×D9—126no—
237C2×D9—126no—
238C2×D9—126no—
239C4×C9—46no—
240Dic9—66no—
241Dic9—126no—
242C22×D4—271no—
243C2×C22⋊C4—271no—
244C2×C22⋊C4C3⋊D911yescharacteristic, complemented
245#99—274no—
246C3×C9C2×#9911yescharacteristic, complemented, Sylow
247C23×C3—42no—
248C23×C3—46no—
249C23×C3C4×D913yes—
250C23×C3C4×D913yes—
251C23×C3D3613yes—
252C23×C3D3613yes—
253C23×C3#61113yes—
254C23×C3#61113yes—
255C23×C3C22×D913yes—
256C23×C3C4×C3⋊D311yescharacteristic
257C23×C3C4×C3⋊D311yescharacteristic
258C23×C3C4⋊(C3⋊D3)11yescharacteristic
259C23×C3C4⋊(C3⋊D3)11yescharacteristic
260C23×C3#63811yescharacteristic
261C23×C3#63811yescharacteristic
262C23×C3C22×C3⋊D311yescharacteristic
263C22×D3—96no—
264C22×D3—92no—
265C22×D3—183no—
266C22×D3—183no—
267C22×D3—181no—
268C22×D3—181no—
269C22×D3—362no—
270C22×D3—366no—
271C2×C3×C4—26no—
272C2×C3×C4—22no—
273C2×C3×C4—42no—
274C2×C3×C4—46no—
275#67—186no—
276#67—186no—
277#67—186no—
278#67—186no—
279#67—182no—
280#67—182no—
281#67—182no—
282#67—182no—
283C2×Dic3—96no—
284C2×Dic3—92no—
285C2×Dic3—183no—
286C2×Dic3—183no—
287C2×Dic3—181no—
288C2×Dic3—181no—
289C2×Dic3—186no—
290C2×Dic3—182no—
291C2×Dic3—362no—
292C2×Dic3—366no—
293C2×C32—21no—
294C2×C32—21no—
295C2×C32—21no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32—21no—
299C2×C32#80612yes—
300C2×C32C2×(C2×D3)⋊C411yescharacteristic
301C3⋊D3—122no—
302C2×C9—23no—
303C2×C9—23no—
304C2×C9—23no—
305C2×C9—23no—
306C2×C9—23no—
307C2×C9—23no—
308C2×C9#80616yescomplemented
309C2×C9C2×(C2×D3)⋊C413yes—
310D9—126no—
311C24—271no—
312C24C2×C3⋊D911yescharacteristic
313C2×D4—272no—
314C2×D4—272no—
315C2×D4—541no—
316C2×D4—541no—
317C2×D4—541no—
318C2×D4—541no—
319C22×C4—21no—
320C22×C4—271no—
321C22×C4—541no—
322C22⋊C4—21no—
323C22⋊C4—272no—
324C22⋊C4—541no—
325C22⋊C4C2×C3⋊D912yescomplemented
326C22×C3—26no—
327C22×C3—26no—
328C22×C3—26no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—43no—
333C22×C3—43no—
334C22×C3—43no—
335C22×C3—43no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3(C2×D9)⋊C413yes—
341C22×C3(C2×D9)⋊C413yes—
342C22×C3(C2×D9)⋊C413yes—
343C22×C3(C2×D9)⋊C413yes—
344C22×C3C2×C4×D913yes—
345C22×C3C2×D3613yes—
346C22×C3C2×#61113yes—
347C22×C3#375211yescharacteristic
348C22×C3#375211yescharacteristic
349C22×C3#375211yescharacteristic
350C22×C3#375211yescharacteristic
351C22×C3C2×C4×C3⋊D311yescharacteristic
352C22×C3C2×C4⋊(C3⋊D3)11yescharacteristic
353C22×C3C2×#63811yescharacteristic
354C2×D3—186no—
355C2×D3—182no—
356C2×D3—362no—
357C2×D3—366no—
358C2×D3—366no—
359C2×D3—362no—
360C2×D3—362no—
361C2×D3—366no—
362C3×C4—42no—
363C3×C4—46no—
364Dic3—186no—
365Dic3—182no—
366Dic3—362no—
367Dic3—366no—
368C32C2×#80611yescharacteristic
369C9C2×#80613yescomplemented
370C23—42no—
371C23—272no—
372C23—541no—
373C23—541no—
374C23—1082no—
375C23C4×C3⋊D911yescharacteristic
376C23C4×C3⋊D911yescharacteristic
377C23C4⋊(C3⋊D9)11yescharacteristic
378C23C4⋊(C3⋊D9)11yescharacteristic
379C23#623311yescharacteristic
380C23#623311yescharacteristic
381C23C22×C3⋊D911yescharacteristic
382D4—542no—
383D4—542no—
384D4—542no—
385D4—542no—
386C2×C4—22no—
387C2×C4—42no—
388C2×C4—272no—
389C2×C4—541no—
390C2×C4—541no—
391C2×C4—542no—
392C2×C4—1082no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—23no—
400C2×C3—23no—
401C2×C3—23no—
402C2×C3—23no—
403C2×C3—23no—
404C2×C3—23no—
405C2×C3#6336516yescomplemented
406C2×C3C2×(C2×D9)⋊C413yes—
407C2×C3#6363312yes—
408C2×C3C2×#375211yescharacteristic
409D3—362no—
410D3—366no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—542no—
419C22—1082no—
420C22—1082no—
421C22—1082no—
422C22#8853611yescharacteristic
423C22#8853611yescharacteristic
424C22#8853611yescharacteristic
425C22#8853611yescharacteristic
426C22C2×C4×C3⋊D911yescharacteristic
427C22C2×C4⋊(C3⋊D9)11yescharacteristic
428C22C2×#623311yescharacteristic
429C4—42no—
430C4—542no—
431C4—1082no—
432C3C2×#6336513yescomplemented
433C3C2×#6363311yescharacteristic
434C2—21no—
435C2—21no—
436C2—21no—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—1082no—
441C2#1172052312yesdirect product factor
442C2C2×#8853611yescharacteristic
subgroupG/H
centerC22#88536
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C22×C3⋊D3
FittingC2×C3×C9×C22⋊C4C2
socleC22×C32(C2×D3)⋊C4
prime radicalC22×#6233C2
cosocleC23×C3×C9C23
hypercenterC2×C22⋊C4C3⋊D9
hypocenterC3×C9C2×#99
LCSG ▷ C22×C3×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C9×C22⋊C4C2semidirect
3. C2×#88551C2semidirect
4. #11720523C2direct (N × H)
8. C23×C3⋊D9C4semidirect
14. C2×#6233C4semidirect
17. C22×C3⋊Dic9C4semidirect
19. C3×C9×C22⋊C4C22semidirect
21. #88551C22semidirect
27. C2×C9×C22⋊C4D3semidirect
41. C22×C3⋊D9C2×C4semidirect
52. C2×C3⋊Dic9C2×C4semidirect
82. C9×C22⋊C4C2×D3semidirect
108. C2×C3×C22⋊C4D9semidirect
167. C2×C3×C9#99semidirect
194. C3×C22⋊C4C2×D9semidirect
244. C2×C22⋊C4C3⋊D9semidirect
246. C3×C9C2×#99semidirect
308. C2×C9#806semidirect
325. C22⋊C4C2×C3⋊D9semidirect
369. C9C2×#806semidirect
405. C2×C3#63365semidirect
432. C3C2×#63365semidirect
441. C2#11720523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62332
C2×C3×C9×C22⋊C42
C2×#885512
#117205232
C2×#636333
C2×#633653