Finite Group Databasebeta

← C22⋊C9×(C2×D3)⋊C4 #13147263

Subgroups — C22⋊C9×(C2×D3)⋊C4 #13147263

Order 1728.

674 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 674 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C22⋊C9C211yesmaximal, characteristic
2C2×C3×C4×C22⋊C9C211yesmaximal, characteristic, complemented
3C2×Dic3×C22⋊C9C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C311yesmaximal, characteristic
5C22⋊C4×C22⋊C9—31nomaximal
6C22×C3×C22⋊C9C2211yescharacteristic
7C2×D3×C22⋊C9—21no—
8C2×D3×C22⋊C9—21no—
9C2×D3×C22⋊C9C412yescomplemented
10C3×C4×C22⋊C9—21no—
11Dic3×C22⋊C9—21no—
12C9×(C2×D3)⋊C4—41nomaximal
13C24×C3×D3C2×C311yescharacteristic
14C23×C32×C4C2×C311yescharacteristic
15C23×C3×Dic3C2×C311yescharacteristic
16C23×C22⋊C9—31no—
17C2×C3×(C2×D3)⋊C4—31no—
18C2×C3×(C2×D3)⋊C4—31no—
19C2×C3×(C2×D3)⋊C4—31no—
20C2×C3×(C2×D3)⋊C4—31no—
21C2×C4×C22⋊C9—21no—
22C2×C4×C22⋊C9—31no—
23C2×C4×C22⋊C9D311yescharacteristic, complemented
24C22×D3×C9—41no—
25C2×C3×C22⋊C9C2×C411yescharacteristic
26C2×C3×C22⋊C9D411yescharacteristic
27C2×C3×C22⋊C9D411yescharacteristic
28D3×C22⋊C9—22no—
29C2×C3×C4×C9—41no—
30C2×C9×Dic3—41no—
31C22×C3×C22⋊C4—31no—
32C22×(C2×D3)⋊C4C911yescharacteristic, complemented
33C24×C32C22×C311yescharacteristic
34C23×C3×D3—21no—
35C23×C3×D3—21no—
36C23×C3×D3—31no—
37C23×C3×D3—31no—
38C23×C3×D3—32no—
39C23×C3×D3—61no—
40C23×C3×D3—61no—
41C23×C3×D3C3×C412yes—
42C22×C32×C4—21no—
43C22×C32×C4—31no—
44C22×C32×C4—31no—
45C22×C32×C4—61no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—31no—
48C22×C3×Dic3—31no—
49C22×C3×Dic3—61no—
50C22×C22⋊C9—21no—
51C22×C22⋊C9—32no—
52C22×C22⋊C9—61no—
53C22×C22⋊C9—61no—
54C22×C22⋊C9C2×D311yescharacteristic
55C3×(C2×D3)⋊C4—32no—
56C3×(C2×D3)⋊C4—31no—
57C3×(C2×D3)⋊C4—31no—
58C3×(C2×D3)⋊C4—31no—
59C3×(C2×D3)⋊C4A411yescharacteristic
60C4×C22⋊C9—22no—
61C4×C22⋊C9—21no—
62C4×C22⋊C9—61no—
63C9×C22⋊C4—121no—
64C22×C3×C9—41no—
65C2×D3×C9—42no—
66C2×D3×C9—81no—
67C2×D3×C9—81no—
68C3×C22⋊C9C22⋊C411yescharacteristic, complemented
69C3×C4×C9—81no—
70C9×Dic3—81no—
71C25×C3—31no—
72C24×D3C2×C911yescharacteristic
73C23×C3×C4—21no—
74C23×C3×C4—31no—
75C23×C3×C4C2×C911yescharacteristic, complemented
76C23×C3×C4C3×D311yescharacteristic
77C23×Dic3C2×C911yescharacteristic, complemented
78C2×C3×C22⋊C4—91no—
79C2×C3×C22⋊C4—91no—
80C2×C3×C22⋊C4—91no—
81C2×C3×C22⋊C4—91no—
82C2×(C2×D3)⋊C4—31no—
83C2×(C2×D3)⋊C4—31no—
84C2×(C2×D3)⋊C4—31no—
85C2×(C2×D3)⋊C4—31no—
86C23×C32—31no—
87C23×C32—31no—
88C23×C32—31no—
89C23×C32—31no—
90C23×C32C2×C3×C411yescharacteristic
91C23×C32C3×D411yescharacteristic
92C23×C32C3×D411yescharacteristic
93C22×C3×D3—22no—
94C22×C3×D3—32no—
95C22×C3×D3—31no—
96C22×C3×D3—32no—
97C22×C3×D3—32no—
98C22×C3×D3—32no—
99C22×C3×D3—61no—
100C22×C3×D3—61no—
101C22×C3×D3—61no—
102C22×C3×D3—61no—
103C22×C3×D3—64no—
104C22×C3×D3—62no—
105C22×C3×D3—62no—
106C22×C3×D3—61no—
107C22×C3×D3—61no—
108C22×C3×D3—61no—
109C22×C3×D3—61no—
110C22×C3×D3—62no—
111C22×C3×D3C2×A411yescharacteristic
112C2×C32×C4—31no—
113C2×C32×C4—61no—
114C2×C32×C4—61no—
115C2×C32×C4—61no—
116C2×C32×C4—61no—
117C2×C32×C4C2×A411yescharacteristic
118C2×C3×Dic3—31no—
119C2×C3×Dic3—61no—
120C2×C3×Dic3—61no—
121C2×C3×Dic3—61no—
122C2×C3×Dic3—61no—
123C2×C3×Dic3C2×A411yescharacteristic
124C23×C9—121no—
125C2×C22⋊C9—21no—
126C2×C22⋊C9—21no—
127C2×C22⋊C9—21no—
128C2×C22⋊C9—62no—
129C2×C22⋊C9C4×D311yescharacteristic
130C2×C22⋊C9D1211yescharacteristic
131C2×C22⋊C9#6711yescharacteristic
132C2×C4×C9—41no—
133C2×C4×C9—81no—
134C2×C4×C9—121no—
135C22×C22⋊C4—31noSylow
136C2×C3×C9—41no—
137C2×C3×C9—41no—
138C2×C3×C9—41no—
139D3×C9—82no—
140C24×C3—21no—
141C24×C3—32no—
142C24×C3—61no—
143C24×C3—61no—
144C24×C3—91no—
145C24×C3—92no—
146C24×C3—91no—
147C24×C3—181no—
148C24×C3—181no—
149C24×C3C22×C911yescharacteristic
150C24×C3C2×C3×D311yescharacteristic
151C23×D3—21no—
152C23×D3—21no—
153C23×D3—31no—
154C23×D3—31no—
155C23×D3—32no—
156C23×D3—61no—
157C23×D3—61no—
158C23×D3C4×C912yescomplemented
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—62no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4—91no—
173C22×C3×C4—91no—
174C22×C3×C4—181no—
175C22×Dic3—21no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—61no—
179C3×C22⋊C4—31no—
180C3×C22⋊C4—91no—
181C3×C22⋊C4—91no—
182C3×C22⋊C4—92no—
183C3×C22⋊C4—91no—
184(C2×D3)⋊C4—32no—
185(C2×D3)⋊C4—31no—
186(C2×D3)⋊C4—31no—
187(C2×D3)⋊C4—31no—
188(C2×D3)⋊C4C22⋊C911yescharacteristic, direct product factor
189C22×C32—31no—
190C22×C32—31no—
191C22×C32—31no—
192C22×C32—32no—
193C22×C32—31no—
194C22×C32—31no—
195C22×C32—31no—
196C22×C32—31no—
197C22×C32—31no—
198C22×C32—31no—
199C22×C32C3×C22⋊C411yescharacteristic
200C22×C32C22×A411yescharacteristic
201C2×C3×D3—21no—
202C2×C3×D3—21no—
203C2×C3×D3—32no—
204C2×C3×D3—62no—
205C2×C3×D3—62no—
206C2×C3×D3—62no—
207C2×C3×D3—62no—
208C2×C3×D3—62no—
209C2×C3×D3—62no—
210C2×C3×D3—61no—
211C2×C3×D3—61no—
212C2×C3×D3—62no—
213C2×C3×D3—62no—
214C2×C3×D3C4×A412yes—
215C32×C4—21no—
216C32×C4—61no—
217C3×Dic3—21no—
218C3×Dic3—61no—
219C22×C9—41no—
220C22×C9—81no—
221C22×C9—122no—
222C22×C9—241no—
223C22×C9—241no—
224C22⋊C9—21no—
225C22⋊C9(C2×D3)⋊C411yescharacteristic, direct product factor
226C4×C9—81no—
227C4×C9—82no—
228C4×C9—241no—
229C25—31no—
230C23×C4—31no—
231C23×C4D3×C911yescharacteristic, complemented
232C2×C22⋊C4—91no—
233C2×C22⋊C4—91no—
234C2×C22⋊C4—91no—
235C2×C22⋊C4—91no—
236C3×C9—41noSylow
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—21no—
240C23×C3—31no—
241C23×C3—31no—
242C23×C3—31no—
243C23×C3—31no—
244C23×C3—31no—
245C23×C3—31no—
246C23×C3—31no—
247C23×C3—31no—
248C23×C3—31no—
249C23×C3—61no—
250C23×C3—61no—
251C23×C3—61no—
252C23×C3—61no—
253C23×C3—62no—
254C23×C3—92no—
255C23×C3—92no—
256C23×C3—92no—
257C23×C3—92no—
258C23×C3—91no—
259C23×C3—181no—
260C23×C3—181no—
261C23×C3—181no—
262C23×C3—181no—
263C23×C3—182no—
264C23×C3—182no—
265C23×C3—182no—
266C23×C3—181no—
267C23×C3—181no—
268C23×C3—181no—
269C23×C3—181no—
270C23×C3—184no—
271C23×C3C2×C4×C911yescharacteristic
272C23×C3D4×C911yescharacteristic
273C23×C3D4×C911yescharacteristic
274C23×C3C3×C4×D311yescharacteristic
275C23×C3C3×D1211yescharacteristic
276C23×C3C3×#6711yescharacteristic
277C22×D3—22no—
278C22×D3—32no—
279C22×D3—31no—
280C22×D3—32no—
281C22×D3—32no—
282C22×D3—32no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—64no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—61no—
291C22×D3—61no—
292C22×D3—61no—
293C22×D3—61no—
294C22×D3—62no—
295C22×D3C2×C22⋊C911yescharacteristic
296C2×C3×C4—21no—
297C2×C3×C4—31no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—61no—
304C2×C3×C4—61no—
305C2×C3×C4—62no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—62no—
313C2×C3×C4—91no—
314C2×C3×C4—181no—
315C2×C3×C4—181no—
316C2×C3×C4—181no—
317C2×C3×C4—181no—
318C2×C3×C4C2×C22⋊C911yescharacteristic, complemented
319C2×C3×C4D3×A411yescharacteristic
320C2×Dic3—31no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3C2×C22⋊C911yescharacteristic, complemented
326C2×C32—31no—
327C2×C32—31no—
328C2×C32—31no—
329C2×C32—31no—
330C2×C32C2×C4×A411yescharacteristic
331C2×C32D4×A411yescharacteristic
332C2×C32D4×A411yescharacteristic
333C3×D3—22no—
334C3×D3—62no—
335C2×C9—41no—
336C2×C9—41no—
337C2×C9—41no—
338C2×C9—81no—
339C2×C9—81no—
340C2×C9—81no—
341C2×C9—242no—
342C24—32no—
343C24—61no—
344C24—61no—
345C24—91no—
346C24—91no—
347C24—92no—
348C24—181no—
349C24—181no—
350C24C2×D3×C911yescharacteristic
351C22×C4—21no—
352C22×C4—31no—
353C22×C4—31no—
354C22×C4—61no—
355C22×C4—61no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—181no—
359C22⋊C4—31no—
360C22⋊C4—91no—
361C22⋊C4—91no—
362C22⋊C4—92no—
363C22⋊C4—91no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—31no—
367C22×C3—31no—
368C22×C3—31no—
369C22×C3—31no—
370C22×C3—31no—
371C22×C3—31no—
372C22×C3—32no—
373C22×C3—32no—
374C22×C3—31no—
375C22×C3—31no—
376C22×C3—31no—
377C22×C3—31no—
378C22×C3—31no—
379C22×C3—31no—
380C22×C3—31no—
381C22×C3—31no—
382C22×C3—31no—
383C22×C3—31no—
384C22×C3—31no—
385C22×C3—31no—
386C22×C3—32no—
387C22×C3—61no—
388C22×C3—61no—
389C22×C3—61no—
390C22×C3—61no—
391C22×C3—61no—
392C22×C3—61no—
393C22×C3—61no—
394C22×C3—61no—
395C22×C3—61no—
396C22×C3—62no—
397C22×C3—61no—
398C22×C3—61no—
399C22×C3—92no—
400C22×C3—182no—
401C22×C3—182no—
402C22×C3—182no—
403C22×C3—182no—
404C22×C3—182no—
405C22×C3—182no—
406C22×C3—182no—
407C22×C3—182no—
408C22×C3—181no—
409C22×C3—181no—
410C22×C3C9×C22⋊C411yescharacteristic, complemented
411C22×C3C3×(C2×D3)⋊C411yescharacteristic
412C22×C3C22×C22⋊C911yescharacteristic
413C22×C3C2×D3×A411yescharacteristic
414C2×D3—21no—
415C2×D3—21no—
416C2×D3—32no—
417C2×D3—62no—
418C2×D3—62no—
419C2×D3—62no—
420C2×D3—62no—
421C2×D3—62no—
422C2×D3—62no—
423C2×D3—61no—
424C2×D3—61no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3C4×C22⋊C912yescomplemented
428C3×C4—22no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—62no—
432C3×C4—61no—
433C3×C4—61no—
434C3×C4—61no—
435C3×C4—181no—
436Dic3—21no—
437Dic3—61no—
438C32A4×C22⋊C411yescharacteristic
439C9—41no—
440C9—81no—
441C23—31no—
442C23—31no—
443C23—31no—
444C23—31no—
445C23—31no—
446C23—62no—
447C23—92no—
448C23—92no—
449C23—92no—
450C23—92no—
451C23—91no—
452C23—181no—
453C23—181no—
454C23—181no—
455C23—181no—
456C23—182no—
457C23—182no—
458C23—182no—
459C23—181no—
460C23—181no—
461C23—181no—
462C23—181no—
463C23—184no—
464C23C4×D3×C911yescharacteristic
465C23C9×D1211yescharacteristic
466C23C9×#6711yescharacteristic
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—91no—
474C2×C4—181no—
475C2×C4—181no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4D3×C22⋊C911yescharacteristic, complemented
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—31no—
483C2×C3—31no—
484C2×C3—31no—
485C2×C3—31no—
486C2×C3—31no—
487C2×C3—31no—
488C2×C3—31no—
489C2×C3—31no—
490C2×C3—61no—
491C2×C3—61no—
492C2×C3—61no—
493C2×C3—61no—
494C2×C3—62no—
495C2×C3—182no—
496C2×C3C2×C4×C22⋊C911yescharacteristic
497C2×C3D4×C22⋊C911yescharacteristic
498C2×C3D4×C22⋊C911yescharacteristic
499C2×C3C4×D3×A411yescharacteristic
500C2×C3A4×D1211yescharacteristic
501C2×C3A4×#6711yescharacteristic
502D3—22no—
503D3—62no—
504C22—31no—
505C22—31no—
506C22—31no—
507C22—32no—
508C22—31no—
509C22—31no—
510C22—31no—
511C22—31no—
512C22—31no—
513C22—31no—
514C22—32no—
515C22—61no—
516C22—61no—
517C22—92no—
518C22—182no—
519C22—182no—
520C22—182no—
521C22—182no—
522C22—182no—
523C22—182no—
524C22—182no—
525C22—182no—
526C22—181no—
527C22—181no—
528C22C9×(C2×D3)⋊C411yescharacteristic, complemented
529C22C2×D3×C22⋊C911yescharacteristic
530C4—21no—
531C4—61no—
532C4—61no—
533C4—181no—
534C3—21no—
535C3C22⋊C4×C22⋊C911yescharacteristic, complemented
536C3A4×(C2×D3)⋊C411yescharacteristic
537C2—31no—
538C2—31no—
539C2—31no—
540C2—31no—
541C2—62no—
542C2—182no—
543C2C4×D3×C22⋊C911yescharacteristic
544C2D12×C22⋊C911yescharacteristic
545C2#67×C22⋊C911yescharacteristic
subgroupG/H
center, FrattiniC22×C3C2×D3×A4
commutatorC23×C3C2×C4×C9
FittingC23×C32×C4C2×C3
socle, cosocleC24×C32C22×C3
prime radicalC24×C3×D3C2×C3
hypercenterC2×C3×C4D3×A4
hypocenterC22×C3C9×C22⋊C4
LCSG ▷ C23×C3 ▷ C22×C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C22⋊C9C2semidirect
3. C2×Dic3×C22⋊C9C2semidirect
9. C2×D3×C22⋊C9C4semidirect
23. C2×C4×C22⋊C9D3semidirect
32. C22×(C2×D3)⋊C4C9semidirect
68. C3×C22⋊C9C22⋊C4semidirect
75. C23×C3×C4C2×C9semidirect
77. C23×Dic3C2×C9semidirect
158. C23×D3C4×C9semidirect
188. (C2×D3)⋊C4C22⋊C9direct (N × H)
225. C22⋊C9(C2×D3)⋊C4direct (N × H)
231. C23×C4D3×C9semidirect
318. C2×C3×C4C2×C22⋊C9semidirect
325. C2×Dic3C2×C22⋊C9semidirect
410. C22×C3C9×C22⋊C4semidirect
427. C2×D3C4×C22⋊C9semidirect
478. C2×C4D3×C22⋊C9semidirect
528. C22C9×(C2×D3)⋊C4semidirect
535. C3C22⋊C4×C22⋊C9semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C22⋊C92
C2×C3×C4×C22⋊C92
C2×Dic3×C22⋊C92
C22×C3×(C2×D3)⋊C43
C22⋊C4×C22⋊C93
C9×(C2×D3)⋊C44