Finite Group Databasebeta

← C2×#11720332 #13141094

Subgroups — C2×#11720332 #13141094

Order 1728.

762 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×#67C211yesmaximal, characteristic
2C2×#88551C211yesmaximal, characteristic, complemented
3C2×C3×#3676C211yesmaximal, characteristic, complemented
4#11720332C214yesmaximal, direct product factor
5C2×#63580—31nomaximal
6C2×#63393—31nomaximal
7C24×C3×C9C2211yescharacteristic
8C23×D3×C9C411yescharacteristic, complemented
9C22×C3⋊Dic9—21no—
10C2×C9×#67—21no—
11C2×C9×#67—21no—
12C2×C9×#67—21no—
13C2×C9×#67—21no—
14C2×C9×#67C412yescomplemented
15C2×C9×#67C2212yes—
16C22×C9×Dic3C411yescharacteristic, complemented
17C22×C3×Dic9—21no—
18#88551—21no—
19#88551C2212yescomplemented
20C3×#3676—21no—
21C3×#3676C2212yescomplemented
22C22×C3×#67D311yescharacteristic
23C2×#3757—31no—
24C2×C3×#217—31no—
25C22×D4×C9—31no—
26#63580—34no—
27C2×#3676—31no—
28C2×#3676—61no—
29C2×#3676D311yescharacteristic, complemented
30#63393—34no—
31C23×C3×C9—42no—
32C23×C3×C9C2×C411yescharacteristic
33C23×C3×C9C2×C411yescharacteristic
34C23×C3×C9D411yescharacteristic
35C23×C3×C9D411yescharacteristic
36C23×C3×C9D411yescharacteristic
37C23×C3×C9D411yescharacteristic
38C23×C3×C9C2311yescharacteristic
39C22×D3×C9—21no—
40C22×D3×C9—21no—
41C22×D3×C9—42no—
42C22×D3×C9C2×C412yescomplemented
43C2×C3⋊Dic9—22no—
44C2×C3⋊Dic9—42no—
45C9×#67—22no—
46C9×#67—22no—
47C9×#67—22no—
48C9×#67—22no—
49C2×C9×Dic3—21no—
50C2×C9×Dic3—21no—
51C2×C9×Dic3C2×C412yescomplemented
52C2×C3×Dic9—22no—
53C2×C3×Dic9—42no—
54C2×#834—91no—
55C2×#806—91no—
56C24×C32C2×D311yescharacteristic
57C23×C3×D3Dic311yescharacteristic
58C22×C3⋊Dic3—61no—
59C2×C3×#67—21no—
60C2×C3×#67—21no—
61C2×C3×#67—21no—
62C2×C3×#67—21no—
63C2×C3×#67Dic312yes—
64C2×C3×#67C2×D312yes—
65C22×C3×Dic3—61no—
66C22×C3×Dic3Dic311yescharacteristic
67C24×C9—21no—
68C24×C9—31no—
69C24×C9C2×D311yescharacteristic
70#3757—32no—
71#3757—61no—
72C3×#217—32no—
73C3×#217—61no—
74C2×D4×C9—32no—
75C2×D4×C9—32no—
76C2×D4×C9—61no—
77C2×D4×C9—61no—
78C2×D4×C9—61no—
79C2×D4×C9—61no—
80C22×C4×C9—31no—
81C22×Dic9—21no—
82C22×Dic9—62no—
83C22×Dic9—61no—
84#3676—21no—
85#3676—32no—
86#3676—62no—
87#3676—62no—
88#3676—61no—
89#3676C2×D312yescomplemented
90C22×C3×C9—22no—
91C22×C3×C9—22no—
92C22×C3×C9—22no—
93C22×C3×C9—41no—
94C22×C3×C9—41no—
95C22×C3×C9—41no—
96C22×C3×C9—41no—
97C22×C3×C9C22⋊C411yescharacteristic
98C22×C3×C9C22⋊C411yescharacteristic
99C22×C3×C9C22⋊C411yescharacteristic
100C22×C3×C9C22⋊C411yescharacteristic
101C22×C3×C9C22×C411yescharacteristic
102C22×C3×C9C2×D411yescharacteristic
103C22×C3×C9C2×D411yescharacteristic
104C2×D3×C9—22no—
105C2×D3×C9—42no—
106C2×D3×C9—42no—
107C2×D3×C9—42no—
108C3⋊Dic9—42no—
109C9×Dic3—22no—
110C3×Dic9—42no—
111C22×C3×D4—31no—
112C22×#67D911yescharacteristic
113C2×C3×C22⋊C4—91no—
114C2×#217—31no—
115C2×#217—91no—
116C2×#217—91no—
117C2×#217—181no—
118#834—94no—
119#806—94no—
120C23×C32—42no—
121C23×C32C2×Dic311yescharacteristic
122C23×C32C2×Dic311yescharacteristic
123C23×C32#6711yescharacteristic
124C23×C32#6711yescharacteristic
125C23×C32#6711yescharacteristic
126C23×C32#6711yescharacteristic
127C23×C32C22×D311yescharacteristic
128C22×C3×D3—21no—
129C22×C3×D3—21no—
130C22×C3×D3—42no—
131C22×C3×D3C2×Dic312yes—
132C2×C3⋊Dic3—62no—
133C2×C3⋊Dic3—122no—
134C3×#67—22no—
135C3×#67—22no—
136C3×#67—22no—
137C3×#67—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—62no—
141C2×C3×Dic3—122no—
142C2×C3×Dic3C2×Dic312yes—
143C23×C9—21no—
144C23×C9—21no—
145C23×C9—21no—
146C23×C9—21no—
147C23×C9—21no—
148C23×C9—21no—
149C23×C9—21no—
150C23×C9—32no—
151C23×C9—42no—
152C23×C9—44no—
153C23×C9—61no—
154C23×C9—61no—
155C23×C9—122no—
156C23×C9C4×D311yescharacteristic
157C23×C9C4×D311yescharacteristic
158C23×C9D1211yescharacteristic
159C23×C9D1211yescharacteristic
160C23×C9#6711yescharacteristic
161C23×C9#6711yescharacteristic
162C23×C9C22×D311yescharacteristic
163D4×C9—62no—
164D4×C9—62no—
165D4×C9—62no—
166D4×C9—62no—
167C2×C4×C9—32no—
168C2×C4×C9—61no—
169C2×C4×C9—61no—
170C2×Dic9—22no—
171C2×Dic9—42no—
172C2×Dic9—64no—
173C2×Dic9—62no—
174C2×Dic9—124no—
175C2×Dic9—122no—
176C2×#99—271noSylow
177C2×C3×C9—21no—
178C2×C3×C9—21no—
179C2×C3×C9—21no—
180C2×C3×C9—21no—
181C2×C3×C9—21no—
182C2×C3×C9—21no—
183C2×C3×C9#9912yescomplemented
184C2×C3×C9C2×C22⋊C411yescharacteristic
185D3×C9—42no—
186C24×C3—21no—
187C24×C3—31no—
188C24×C3C2×D911yescharacteristic
189C24×C3D3211yescharacteristic
190C23×D3Dic911yescharacteristic, complemented
191C2×C3×D4—32no—
192C2×C3×D4—32no—
193C2×C3×D4—61no—
194C2×C3×D4—61no—
195C2×C3×D4—61no—
196C2×C3×D4—61no—
197C22×C3×C4—31no—
198C22×C3×C4—181no—
199C2×#67—21no—
200C2×#67—21no—
201C2×#67—21no—
202C2×#67—21no—
203C2×#67Dic912yescomplemented
204C2×#67C2×D912yes—
205C22×Dic3—61no—
206C22×Dic3—182no—
207C22×Dic3—181no—
208C22×Dic3—181no—
209C22×Dic3Dic911yescharacteristic, complemented
210C3×C22⋊C4—92no—
211C3×C22⋊C4—181no—
212#217—32no—
213#217—61no—
214#217—92no—
215#217—92no—
216#217—182no—
217#217—182no—
218#217—181no—
219#217—181no—
220C22×C32—22no—
221C22×C32—22no—
222C22×C32—22no—
223C22×C32—41no—
224C22×C32—41no—
225C22×C32—41no—
226C22×C32—41no—
227C22×C32#21711yescharacteristic
228C22×C32#21711yescharacteristic
229C22×C32#21711yescharacteristic
230C22×C32#21711yescharacteristic
231C22×C32C22×Dic311yescharacteristic
232C22×C32C2×#6711yescharacteristic
233C22×C32C2×#6711yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C3⋊Dic3—122no—
239C3×Dic3—22no—
240C3×Dic3—122no—
241C22×C9—24no—
242C22×C9—22no—
243C22×C9—22no—
244C22×C9—22no—
245C22×C9—21no—
246C22×C9—21no—
247C22×C9—21no—
248C22×C9—21no—
249C22×C9—21no—
250C22×C9—21no—
251C22×C9—21no—
252C22×C9—42no—
253C22×C9—42no—
254C22×C9—41no—
255C22×C9—41no—
256C22×C9—41no—
257C22×C9—41no—
258C22×C9—42no—
259C22×C9—42no—
260C22×C9—42no—
261C22×C9—42no—
262C22×C9—62no—
263C22×C9—122no—
264C22×C9—122no—
265C22×C9—122no—
266C22×C9(C2×D3)⋊C411yescharacteristic
267C22×C9(C2×D3)⋊C411yescharacteristic
268C22×C9(C2×D3)⋊C411yescharacteristic
269C22×C9(C2×D3)⋊C411yescharacteristic
270C22×C9C2×C4×D311yescharacteristic
271C22×C9C2×D1211yescharacteristic
272C22×C9C2×#6711yescharacteristic
273C4×C9—62no—
274Dic9—42no—
275Dic9—124no—
276Dic9—122no—
277C22×D4—31no—
278C2×C22⋊C4—91no—
279C2×C22⋊C4—271no—
280#99—274no—
281C3×C9C2×#9911yescharacteristic, complemented, Sylow
282C23×C3—21no—
283C23×C3—21no—
284C23×C3—21no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3—21no—
288C23×C3—21no—
289C23×C3—32no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—44no—
293C23×C3—61no—
294C23×C3—61no—
295C23×C3—122no—
296C23×C3C2×Dic911yescharacteristic
297C23×C3C2×Dic911yescharacteristic
298C23×C3#61111yescharacteristic
299C23×C3#61111yescharacteristic
300C23×C3#61111yescharacteristic
301C23×C3#61111yescharacteristic
302C23×C3C22×D911yescharacteristic
303C23×C3D3×Dic311yescharacteristic
304C23×C3D3×Dic311yescharacteristic
305C23×C3#62511yescharacteristic
306C23×C3#62511yescharacteristic
307C23×C3#62611yescharacteristic
308C23×C3#62611yescharacteristic
309C23×C3C2×D3211yescharacteristic
310C22×D3—21no—
311C22×D3—21no—
312C22×D3—42no—
313C22×D3C2×Dic912yescomplemented
314C3×D4—62no—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—62no—
318C2×C3×C4—32no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—182no—
322C2×C3×C4—362no—
323#67—22no—
324#67—22no—
325#67—22no—
326#67—22no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—62no—
330C2×Dic3—122no—
331C2×Dic3—184no—
332C2×Dic3—182no—
333C2×Dic3—182no—
334C2×Dic3—362no—
335C2×Dic3—364no—
336C2×Dic3—362no—
337C2×Dic3C2×Dic912yescomplemented
338C2×C32—21no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32#83412yes—
345C2×C32C2×#21711yescharacteristic
346C3×D3—42no—
347C2×C9—22no—
348C2×C9—22no—
349C2×C9—21no—
350C2×C9—21no—
351C2×C9—21no—
352C2×C9—21no—
353C2×C9—21no—
354C2×C9—21no—
355C2×C9—22no—
356C2×C9—21no—
357C2×C9—41no—
358C2×C9—41no—
359C2×C9—41no—
360C2×C9—41no—
361C2×C9—122no—
362C2×C9#80612yescomplemented
363C2×C9C2×(C2×D3)⋊C411yescharacteristic
364C24—31no—
365C24D3×D911yescharacteristic
366C2×D4—32no—
367C2×D4—32no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C22×C4—31no—
373C22×C4—181no—
374C22×C4—541no—
375C22⋊C4—92no—
376C22⋊C4—181no—
377C22⋊C4—272no—
378C22⋊C4—541no—
379C22×C3—24no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—62no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3#367611yescharacteristic
412C22×C3#367611yescharacteristic
413C22×C3#367611yescharacteristic
414C22×C3#367611yescharacteristic
415C22×C3C22×Dic911yescharacteristic
416C22×C3C2×#61111yescharacteristic
417C22×C3C2×#61111yescharacteristic
418C22×C3(C2×D3)⋊Dic311yescharacteristic
419C22×C3(C2×D3)⋊Dic311yescharacteristic
420C22×C3(C2×D3)⋊Dic311yescharacteristic
421C22×C3(C2×D3)⋊Dic311yescharacteristic
422C22×C3C2×D3×Dic311yescharacteristic
423C22×C3C2×#62511yescharacteristic
424C22×C3C2×#62611yescharacteristic
425C2×D3—22no—
426C2×D3—42no—
427C2×D3—42no—
428C2×D3—42no—
429C3×C4—62no—
430C3×C4—362no—
431Dic3—22no—
432Dic3—122no—
433Dic3—362no—
434Dic3—364no—
435Dic3—362no—
436C32C2×#83411yescharacteristic
437C9—21no—
438C9C2×#80611yescharacteristic, complemented
439C23—32no—
440C23—42no—
441C23—61no—
442C23—61no—
443C23—122no—
444C23D3×Dic911yescharacteristic
445C23D3×Dic911yescharacteristic
446C23#619411yescharacteristic
447C23#619411yescharacteristic
448C23#619511yescharacteristic
449C23#619511yescharacteristic
450C23C2×D3×D911yescharacteristic
451D4—62no—
452D4—62no—
453D4—62no—
454D4—62no—
455C2×C4—32no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—182no—
459C2×C4—362no—
460C2×C4—542no—
461C2×C4—1082no—
462C2×C3—22no—
463C2×C3—22no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—22no—
478C2×C3—41no—
479C2×C3—41no—
480C2×C3—41no—
481C2×C3—41no—
482C2×C3—122no—
483C2×C3#6339312yescomplemented
484C2×C3C2×#367611yescharacteristic
485C2×C3#6358012yes—
486C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
487D3—42no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—62no—
496C22—122no—
497C22—122no—
498C22—122no—
499C22(C2×D3)⋊Dic911yescharacteristic
500C22(C2×D3)⋊Dic911yescharacteristic
501C22(C2×D3)⋊Dic911yescharacteristic
502C22(C2×D3)⋊Dic911yescharacteristic
503C22C2×D3×Dic911yescharacteristic
504C22C2×#619411yescharacteristic
505C22C2×#619511yescharacteristic
506C4—62no—
507C4—362no—
508C4—1082no—
509C3—21no—
510C3C2×#6339311yescharacteristic, complemented
511C3C2×#6358011yescharacteristic
512C2—21no—
513C2—21no—
514C2—21no—
515C2—21no—
516C2—21no—
517C2—21no—
518C2—122no—
519C2#1172033212yesdirect product factor
520C2C2×(C2×D3)⋊Dic911yescharacteristic
subgroupG/H
centerC22(C2×D3)⋊Dic9
commutatorC22×C3×C9C22×C4
FrattiniC23×C3C2×D32
FittingC24×C3×C9C22
socleC22×C32#217
prime radicalC22×C3×#67D3
cosocleC23×C3×C9C23
hypercenterC24D3×D9
hypocenterC3×C9C2×#99
LCSG ▷ C22×C3×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
2. C2×#88551C2semidirect
3. C2×C3×#3676C2semidirect
4. #11720332C2direct (N × H)
8. C23×D3×C9C4semidirect
14. C2×C9×#67C4semidirect
16. C22×C9×Dic3C4semidirect
19. #88551C22semidirect
21. C3×#3676C22semidirect
29. C2×#3676D3semidirect
42. C22×D3×C9C2×C4semidirect
51. C2×C9×Dic3C2×C4semidirect
89. #3676C2×D3semidirect
183. C2×C3×C9#99semidirect
190. C23×D3Dic9semidirect
203. C2×#67Dic9semidirect
209. C22×Dic3Dic9semidirect
281. C3×C9C2×#99semidirect
313. C22×D3C2×Dic9semidirect
337. C2×Dic3C2×Dic9semidirect
362. C2×C9#806semidirect
438. C9C2×#806semidirect
483. C2×C3#63393semidirect
510. C3C2×#63393semidirect
519. C2#11720332direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×#672
C2×#885512
C2×C3×#36762
#117203322
C2×#635803
C2×#633933