Finite Group Databasebeta

← C22⋊Q8×AGL(1,ℤ/9) #13152977

Subgroups — C22⋊Q8×AGL(1,ℤ/9) #13152977

Order 1728.

1003 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
2C22×C4×AGL(1,ℤ/9)C211yesmaximal, characteristic
33−1+2×C22⋊Q8C211yesmaximal, characteristic, complemented
4#63508⋊C3C211yesmaximal, characteristic, complemented
5#63486⋊C3C211yesmaximal, characteristic, complemented
6#63459⋊C3C211yesmaximal, characteristic, complemented
7#63458⋊C3C212yesmaximal, complemented
8C4⋊C4×AGL(1,ℤ/9)C212yesmaximal, complemented
9C4⋊C4×AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
10C22⋊C4×AGL(1,ℤ/9)C212yesmaximal
11#63440⋊C3C212yesmaximal, complemented
12C3×D3×C22⋊Q8—31nomaximal
13D9×C22⋊Q8C311yesmaximal, characteristic, complemented
14C23×AGL(1,ℤ/9)C2211yescharacteristic
15C2×Q8×3−1+2C2211yescharacteristic, complemented
16C22×C4×3−1+2C2211yescharacteristic
17C22×3−1+2⋊C4C2211yescharacteristic
18Q8×AGL(1,ℤ/9)—24no—
19C2×C4×AGL(1,ℤ/9)—24no—
20C2×C4×AGL(1,ℤ/9)C2211yescharacteristic
21C2×C4×AGL(1,ℤ/9)C2212yes—
22C2×C4×AGL(1,ℤ/9)C2212yes—
23C2×C4×AGL(1,ℤ/9)C2211yescharacteristic
24C2×C4×AGL(1,ℤ/9)C2211yescharacteristic
25C2×C4×AGL(1,ℤ/9)C2211yescharacteristic
26C2×3−1+2⋊Q8C2212yescomplemented
27C2×3−1+2⋊Q8C2211yescharacteristic, complemented
28C4⋊C4×3−1+2C2212yescomplemented
29C4⋊C4×3−1+2C2211yescharacteristic, complemented
30C22⋊C4×3−1+2C2212yes—
31#3676⋊C3C2212yes—
32(C2×AGL(1,ℤ/9))⋊C4C2212yes—
33(C2×AGL(1,ℤ/9))⋊C4C2212yes—
34C4⋊(3−1+2⋊C4)C2212yescomplemented
35C4⋊(3−1+2⋊C4)C2211yescharacteristic, complemented
36(3−1+2⋊C4)⋊C4C2212yescomplemented
37(3−1+2⋊C4)⋊C4C2212yescomplemented
38(3−1+2⋊C4)⋊C4C2212yescomplemented
39C2×C3×D3×Q8—31no—
40C22×C3×C4×D3—31no—
41C32×C22⋊Q8D311yescharacteristic
42C3×#946—31no—
43C3×#924—31no—
44C3×#897—31no—
45C3×#896—32no—
46C3×D3×C4⋊C4—31no—
47C3×D3×C4⋊C4—32no—
48C3×D3×C22⋊C4—32no—
49C3×#878—32no—
50C2×Q8×D9C2×C311yescharacteristic, complemented
51C22×C4×D9C2×C311yescharacteristic
52C9×C22⋊Q8—21no—
53C9×C22⋊Q8C2×C311yescharacteristic, complemented
54#63508C2×C311yescharacteristic, complemented
55#63486C2×C311yescharacteristic, complemented
56#63459C2×C311yescharacteristic, complemented
57#63458C2×C312yescomplemented
58C4⋊C4×D9C2×C312yescomplemented
59C4⋊C4×D9C2×C311yescharacteristic, complemented
60C22⋊C4×D9C2×C312yes—
61#63440C2×C312yescomplemented
62C23×3−1+2C2311yescharacteristic
63C22×AGL(1,ℤ/9)—22no—
64C22×AGL(1,ℤ/9)—22no—
65C22×AGL(1,ℤ/9)Q814yescomplemented
66C22×AGL(1,ℤ/9)C2311yescharacteristic
67C22×AGL(1,ℤ/9)C2311yescharacteristic
68Q8×3−1+2—22no—
69C2×C4×3−1+2—22no—
70C2×C4×3−1+2C2312yes—
71C2×C4×3−1+2C2311yescharacteristic
72C2×C4×3−1+2C2312yes—
73C2×C4×3−1+2C2311yescharacteristic
74C2×3−1+2⋊C4—22no—
75C2×3−1+2⋊C4C2312yes—
76C2×3−1+2⋊C4C2311yescharacteristic
77C2×3−1+2⋊C4C2312yes—
78C2×3−1+2⋊C4C2311yescharacteristic
79C4×AGL(1,ℤ/9)—22no—
80C4×AGL(1,ℤ/9)—24no—
81C4×AGL(1,ℤ/9)—24no—
82C4×AGL(1,ℤ/9)—22no—
83C4×AGL(1,ℤ/9)—22no—
84C4×AGL(1,ℤ/9)D414yes—
853−1+2⋊Q8—22no—
863−1+2⋊Q8—24no—
87C2×C3×C22⋊Q8—91no—
88D3×C22⋊Q8—31no—
89C23×C3×D3—31no—
90C2×C32×Q8C2×D311yescharacteristic
91C22×C32×C4C2×D311yescharacteristic
92C22×C3×Dic3—31no—
93C3×D3×Q8—64no—
94C2×C3×C4×D3—31no—
95C2×C3×C4×D3—32no—
96C2×C3×C4×D3—32no—
97C2×C3×C4×D3—31no—
98C2×C3×C4×D3—31no—
99C2×C3×C4×D3—31no—
100C2×C3×C4×D3—64no—
101C2×C3×Dic6—32no—
102C2×C3×Dic6—31no—
103C23×D9C22×C311yescharacteristic
104C32×C4⋊C4C2×D312yes—
105C32×C4⋊C4C2×D311yescharacteristic
106C32×C22⋊C4C2×D312yes—
107C3×#217—32no—
108C3×(C2×D3)⋊C4—32no—
109C3×(C2×D3)⋊C4—32no—
110C3×C4⋊Dic3—32no—
111C3×C4⋊Dic3—31no—
112C3×Dic3⋊C4—32no—
113C3×Dic3⋊C4—32no—
114C3×Dic3⋊C4—32no—
115C2×Q8×C9—21no—
116C2×Q8×C9C22×C311yescharacteristic, complemented
117C22×C4×C9—21no—
118C22×C4×C9C22×C311yescharacteristic
119C22×Dic9C22×C311yescharacteristic
120Q8×D9—24no—
121C2×C4×D9—24no—
122C2×C4×D9C22×C311yescharacteristic
123C2×C4×D9C22×C312yes—
124C2×C4×D9C22×C312yes—
125C2×C4×D9C22×C311yescharacteristic
126C2×C4×D9C22×C311yescharacteristic
127C2×C4×D9C22×C311yescharacteristic
128C2×Dic18C22×C312yescomplemented
129C2×Dic18C22×C311yescharacteristic, complemented
130C9×C4⋊C4—21no—
131C9×C4⋊C4—22no—
132C9×C4⋊C4C22×C312yescomplemented
133C9×C4⋊C4C22×C311yescharacteristic, complemented
134C9×C22⋊C4—22no—
135C9×C22⋊C4C22×C312yes—
136#3676C22×C312yes—
137(C2×D9)⋊C4C22×C312yes—
138(C2×D9)⋊C4C22×C312yes—
139C4⋊Dic9C22×C311yescharacteristic, complemented
140C4⋊Dic9C22×C312yescomplemented
141Dic9⋊C4C22×C312yescomplemented
142Dic9⋊C4C22×C312yescomplemented
143Dic9⋊C4C22×C312yescomplemented
144C22×3−1+2—21no—
145C22×3−1+2—21no—
146C22×3−1+2C2×Q812yescomplemented
147C22×3−1+2C2411yescharacteristic
148C2×AGL(1,ℤ/9)—21no—
149C2×AGL(1,ℤ/9)—21no—
150C2×AGL(1,ℤ/9)—28no—
151C2×AGL(1,ℤ/9)C2×D412yes—
152C2×AGL(1,ℤ/9)C2×Q812yes—
153C2×AGL(1,ℤ/9)C2×Q812yescomplemented
154C2×AGL(1,ℤ/9)#4112yes—
155C4×3−1+2—22no—
156C4×3−1+2—21no—
157C4×3−1+2—22no—
158C4×3−1+2C2×D412yes—
1593−1+2⋊C4—22no—
1603−1+2⋊C4—21no—
1613−1+2⋊C4—22no—
1623−1+2⋊C4C2×D412yes—
163C22×C3×Q8—91no—
164C23×C3×C4—91no—
165C2×D3×Q8—31no—
166C22×C4×D3—31no—
167C3×C22⋊Q8—31no—
168C3×C22⋊Q8—92no—
169C3×C22⋊Q8—92no—
170C3×C22⋊Q8—91no—
171C3×C22⋊Q8—91no—
172C3×C22⋊Q8—91no—
173C3×C22⋊Q8C3×D311yescharacteristic
174C2×C3×C4⋊C4—91no—
175C2×C3×C4⋊C4—92no—
176C2×C3×C22⋊C4—92no—
177#946—31no—
178#924—31no—
179#897—31no—
180#896—32no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—32no—
183D3×C22⋊C4—32no—
184#878—32no—
185C23×C32C22×D311yescharacteristic
186C22×C3×D3—31no—
187C22×C3×D3—34no—
188C22×C3×D3—31no—
189C22×C3×D3—62no—
190C22×C3×D3—62no—
191C32×Q8—22no—
192C2×C32×C4—22no—
193C2×C32×C4C22×D311yescharacteristic
194C2×C32×C4C22×D312yes—
195C2×C32×C4C22×D312yes—
196C2×C32×C4C22×D311yescharacteristic
197C2×C3×Dic3—31no—
198C2×C3×Dic3—32no—
199C2×C3×Dic3—31no—
200C2×C3×Dic3—32no—
201C2×C3×Dic3—62no—
202C3×C4×D3—34no—
203C3×C4×D3—62no—
204C3×C4×D3—64no—
205C3×C4×D3—62no—
206C3×C4×D3—64no—
207C3×C4×D3—62no—
208C3×Dic6—64no—
209C3×Dic6—62no—
210C23×C9—21no—
211C23×C9C23×C311yescharacteristic
212C22×D9—22no—
213C22×D9—22no—
214C22×D9C3×Q814yescomplemented
215C22×D9C23×C311yescharacteristic
216C22×D9C23×C311yescharacteristic
217Q8×C9—22no—
218Q8×C9—42no—
219C2×C4×C9—22no—
220C2×C4×C9—21no—
221C2×C4×C9—22no—
222C2×C4×C9—22no—
223C2×C4×C9—21no—
224C2×C4×C9—42no—
225C2×C4×C9C23×C311yescharacteristic
226C2×C4×C9C23×C312yes—
227C2×C4×C9C23×C312yes—
228C2×C4×C9C23×C311yescharacteristic
229C2×Dic9—22no—
230C2×Dic9C23×C312yes—
231C2×Dic9C23×C311yescharacteristic
232C2×Dic9C23×C312yes—
233C2×Dic9C23×C311yescharacteristic
234C4×D9—22no—
235C4×D9—24no—
236C4×D9—24no—
237C4×D9—22no—
238C4×D9—22no—
239C4×D9C3×D414yes—
240Dic18—22no—
241Dic18—24no—
242C2×C22⋊Q8—91noSylow
243C2×3−1+2—22no—
244C2×3−1+2C22×D411yescharacteristic
245C2×3−1+2C22×Q811yescharacteristic
246C2×3−1+2C2×#4111yescharacteristic
247AGL(1,ℤ/9)—22no—
248AGL(1,ℤ/9)C22⋊Q814yesdirect product factor
249C24×C3—91no—
250C23×D3—31no—
251C2×C3×Q8—31no—
252C2×C3×Q8—91no—
253C2×C3×Q8—92no—
254C2×C3×Q8—184no—
255C2×C3×Q8C2×C3×D311yescharacteristic
256C22×C3×C4—31no—
257C22×C3×C4—91no—
258C22×C3×C4—92no—
259C22×C3×C4—92no—
260C22×C3×C4—91no—
261C22×C3×C4—91no—
262C22×C3×C4—91no—
263C22×C3×C4—91no—
264C22×C3×C4—184no—
265C22×C3×C4C2×C3×D311yescharacteristic
266C22×Dic3—31no—
267D3×Q8—64no—
268C2×C4×D3—31no—
269C2×C4×D3—32no—
270C2×C4×D3—32no—
271C2×C4×D3—31no—
272C2×C4×D3—31no—
273C2×C4×D3—31no—
274C2×C4×D3—64no—
275C2×Dic6—32no—
276C2×Dic6—31no—
277C3×C4⋊C4—31no—
278C3×C4⋊C4—32no—
279C3×C4⋊C4—92no—
280C3×C4⋊C4—92no—
281C3×C4⋊C4—92no—
282C3×C4⋊C4—91no—
283C3×C4⋊C4—92no—
284C3×C4⋊C4C2×C3×D312yes—
285C3×C4⋊C4C2×C3×D311yescharacteristic
286C3×C22⋊C4—32no—
287C3×C22⋊C4—92no—
288C3×C22⋊C4—92no—
289C3×C22⋊C4—92no—
290C3×C22⋊C4C2×C3×D312yes—
291#217—32no—
292(C2×D3)⋊C4—32no—
293(C2×D3)⋊C4—32no—
294C4⋊Dic3—32no—
295C4⋊Dic3—31no—
296Dic3⋊C4—32no—
297Dic3⋊C4—32no—
298Dic3⋊C4—32no—
299C22×C32—21no—
300C22×C32—21no—
301C22×C32D3×Q812yes—
302C22×C32C23×D311yescharacteristic
303C2×C3×D3—32no—
304C2×C3×D3—32no—
305C2×C3×D3—32no—
306C2×C3×D3—32no—
307C2×C3×D3—68no—
308C2×C3×D3—61no—
309C2×C3×D3—61no—
310C32×C4—22no—
311C32×C4—21no—
312C32×C4—22no—
313C32×C4D3×D412yes—
314C3×Dic3—32no—
315C3×Dic3—62no—
316C3×Dic3—61no—
317C3×Dic3—62no—
318C22×C9—21no—
319C22×C9—21no—
320C22×C9—21no—
321C22×C9—22no—
322C22×C9—41no—
323C22×C9—41no—
324C22×C9C2×C3×Q812yescomplemented
325C22×C9C24×C311yescharacteristic
326C2×D9—21no—
327C2×D9—21no—
328C2×D9—28no—
329C2×D9C2×C3×D412yes—
330C2×D9C2×C3×Q812yes—
331C2×D9C2×C3×Q812yescomplemented
332C2×D9C3×#4112yes—
333C4×C9—22no—
334C4×C9—21no—
335C4×C9—22no—
336C4×C9—22no—
337C4×C9—42no—
338C4×C9—41no—
339C4×C9—42no—
340C4×C9C2×C3×D412yes—
341Dic9—22no—
342Dic9—21no—
343Dic9—22no—
344Dic9C2×C3×D412yes—
345C22×Q8—91no—
346C23×C4—91no—
347C22⋊Q8—91no—
348C22⋊Q8—91no—
349C22⋊Q8—92no—
350C22⋊Q8—91no—
351C22⋊Q8—92no—
352C22⋊Q8AGL(1,ℤ/9)11yescharacteristic, direct product factor
353C2×C4⋊C4—91no—
354C2×C4⋊C4—92no—
355C2×C22⋊C4—92no—
3563−1+2C2×C22⋊Q811yescharacteristic, complemented, Sylow
357C23×C3—31no—
358C23×C3—91no—
359C23×C3—91no—
360C23×C3—94no—
361C23×C3—182no—
362C23×C3—182no—
363C23×C3C22×C3×D311yescharacteristic
364C22×D3—31no—
365C22×D3—31no—
366C22×D3—34no—
367C22×D3—62no—
368C22×D3—62no—
369C3×Q8—22no—
370C3×Q8—62no—
371C3×Q8—182no—
372C3×Q8—184no—
373C2×C3×C4—22no—
374C2×C3×C4—31no—
375C2×C3×C4—32no—
376C2×C3×C4—32no—
377C2×C3×C4—31no—
378C2×C3×C4—62no—
379C2×C3×C4—94no—
380C2×C3×C4—91no—
381C2×C3×C4—92no—
382C2×C3×C4—92no—
383C2×C3×C4—91no—
384C2×C3×C4—182no—
385C2×C3×C4—182no—
386C2×C3×C4—184no—
387C2×C3×C4—182no—
388C2×C3×C4—184no—
389C2×C3×C4—182no—
390C2×C3×C4C22×C3×D311yescharacteristic
391C2×C3×C4C22×C3×D312yes—
392C2×C3×C4C22×C3×D312yes—
393C2×C3×C4C22×C3×D311yescharacteristic
394C2×Dic3—31no—
395C2×Dic3—32no—
396C2×Dic3—31no—
397C2×Dic3—32no—
398C2×Dic3—62no—
399C4×D3—34no—
400C4×D3—62no—
401C4×D3—64no—
402C4×D3—62no—
403C4×D3—64no—
404C4×D3—62no—
405Dic6—64no—
406Dic6—62no—
407C2×C32—22no—
408C2×C32C2×D3×D411yescharacteristic
409C2×C32C2×D3×Q811yescharacteristic
410C2×C32D3×#4111yescharacteristic
411C3×D3—34no—
412C3×D3—62no—
413C2×C9—22no—
414C2×C9—21no—
415C2×C9—21no—
416C2×C9—21no—
417C2×C9—42no—
418C2×C9C22×C3×D411yescharacteristic
419C2×C9C22×C3×Q811yescharacteristic
420C2×C9C2×C3×#4111yescharacteristic
421D9—22no—
422D9C3×C22⋊Q814yescomplemented
423C24—91no—
424C2×Q8—92no—
425C2×Q8—91no—
426C2×Q8—184no—
427C2×Q8C2×AGL(1,ℤ/9)11yescharacteristic, complemented
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—92no—
431C22×C4—92no—
432C22×C4—91no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—184no—
436C22×C4C2×AGL(1,ℤ/9)11yescharacteristic
437C4⋊C4—92no—
438C4⋊C4—92no—
439C4⋊C4—92no—
440C4⋊C4—91no—
441C4⋊C4—92no—
442C4⋊C4C2×AGL(1,ℤ/9)11yescharacteristic, complemented
443C4⋊C4C2×AGL(1,ℤ/9)12yescomplemented
444C22⋊C4—92no—
445C22⋊C4—92no—
446C22⋊C4—92no—
447C22⋊C4C2×AGL(1,ℤ/9)12yes—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—31no—
451C22×C3—32no—
452C22×C3—61no—
453C22×C3—61no—
454C22×C3—92no—
455C22×C3—92no—
456C22×C3—92no—
457C22×C3—92no—
458C22×C3—181no—
459C22×C3—181no—
460C22×C3—188no—
461C22×C3C3×D3×Q812yes—
462C22×C3C23×C3×D311yescharacteristic
463C2×D3—32no—
464C2×D3—32no—
465C2×D3—32no—
466C2×D3—32no—
467C2×D3—68no—
468C2×D3—61no—
469C2×D3—61no—
470C3×C4—22no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—32no—
474C3×C4—61no—
475C3×C4—62no—
476C3×C4—62no—
477C3×C4—92no—
478C3×C4—181no—
479C3×C4—182no—
480C3×C4—182no—
481C3×C4C3×D3×D412yes—
482Dic3—32no—
483Dic3—62no—
484Dic3—61no—
485Dic3—62no—
486C32D3×C22⋊Q811yescharacteristic
487C9—21no—
488C9C2×C3×C22⋊Q811yescharacteristic, complemented
489C23—91no—
490C23—91no—
491C23—94no—
492C23—182no—
493C23—182no—
494C23C22×AGL(1,ℤ/9)11yescharacteristic
495Q8—22no—
496Q8—184no—
497Q8—182no—
498C2×C4—22no—
499C2×C4—91no—
500C2×C4—94no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—91no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—184no—
507C2×C4—184no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4C22×AGL(1,ℤ/9)12yes—
511C2×C4C22×AGL(1,ℤ/9)12yes—
512C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
513C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
514C2×C3—22no—
515C2×C3—31no—
516C2×C3—31no—
517C2×C3—31no—
518C2×C3—62no—
519C2×C3—94no—
520C2×C3—182no—
521C2×C3C2×C3×D3×D411yescharacteristic
522C2×C3C2×C3×D3×Q811yescharacteristic
523C2×C3C3×D3×#4111yescharacteristic
524D3—34no—
525D3—62no—
526C22—21no—
527C22—21no—
528C22—92no—
529C22—92no—
530C22—92no—
531C22—92no—
532C22—188no—
533C22—181no—
534C22—181no—
535C22Q8×AGL(1,ℤ/9)12yescomplemented
536C22C23×AGL(1,ℤ/9)11yescharacteristic
537C4—21no—
538C4—22no—
539C4—22no—
540C4—92no—
541C4—181no—
542C4—182no—
543C4—182no—
544C4D4×AGL(1,ℤ/9)12yes—
545C3—31no—
546C3C3×D3×C22⋊Q811yescharacteristic
547C2—22no—
548C2—94no—
549C2—182no—
550C2C2×D4×AGL(1,ℤ/9)11yescharacteristic
551C2C2×Q8×AGL(1,ℤ/9)11yescharacteristic
552C2#41×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
centerC22C23×AGL(1,ℤ/9)
commutator, cosocleC22×C9C24×C3
Frattini, socleC22×C3C23×C3×D3
Fitting3−1+2×C22⋊Q8C2
prime radicalC23×AGL(1,ℤ/9)C22
hypercenterC22⋊Q8AGL(1,ℤ/9)
hypocenterC9C2×C3×C22⋊Q8
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×AGL(1,ℤ/9)C2semidirect
3. 3−1+2×C22⋊Q8C2semidirect
4. #63508⋊C3C2semidirect
5. #63486⋊C3C2semidirect
6. #63459⋊C3C2semidirect
7. #63458⋊C3C2semidirect
8. C4⋊C4×AGL(1,ℤ/9)C2semidirect
9. C4⋊C4×AGL(1,ℤ/9)C2semidirect
11. #63440⋊C3C2semidirect
13. D9×C22⋊Q8C3semidirect
15. C2×Q8×3−1+2C22semidirect
26. C2×3−1+2⋊Q8C22semidirect
27. C2×3−1+2⋊Q8C22semidirect
28. C4⋊C4×3−1+2C22semidirect
29. C4⋊C4×3−1+2C22semidirect
34. C4⋊(3−1+2⋊C4)C22semidirect
35. C4⋊(3−1+2⋊C4)C22semidirect
36. (3−1+2⋊C4)⋊C4C22semidirect
37. (3−1+2⋊C4)⋊C4C22semidirect
38. (3−1+2⋊C4)⋊C4C22semidirect
50. C2×Q8×D9C2×C3semidirect
53. C9×C22⋊Q8C2×C3semidirect
54. #63508C2×C3semidirect
55. #63486C2×C3semidirect
56. #63459C2×C3semidirect
57. #63458C2×C3semidirect
58. C4⋊C4×D9C2×C3semidirect
59. C4⋊C4×D9C2×C3semidirect
61. #63440C2×C3semidirect
65. C22×AGL(1,ℤ/9)Q8semidirect
116. C2×Q8×C9C22×C3semidirect
128. C2×Dic18C22×C3semidirect
129. C2×Dic18C22×C3semidirect
132. C9×C4⋊C4C22×C3semidirect
133. C9×C4⋊C4C22×C3semidirect
139. C4⋊Dic9C22×C3semidirect
140. C4⋊Dic9C22×C3semidirect
141. Dic9⋊C4C22×C3semidirect
142. Dic9⋊C4C22×C3semidirect
143. Dic9⋊C4C22×C3semidirect
146. C22×3−1+2C2×Q8semidirect
153. C2×AGL(1,ℤ/9)C2×Q8semidirect
214. C22×D9C3×Q8semidirect
248. AGL(1,ℤ/9)C22⋊Q8direct (N × H)
324. C22×C9C2×C3×Q8semidirect
331. C2×D9C2×C3×Q8semidirect
352. C22⋊Q8AGL(1,ℤ/9)direct (N × H)
356. 3−1+2C2×C22⋊Q8semidirect
422. D9C3×C22⋊Q8semidirect
427. C2×Q8C2×AGL(1,ℤ/9)semidirect
442. C4⋊C4C2×AGL(1,ℤ/9)semidirect
443. C4⋊C4C2×AGL(1,ℤ/9)semidirect
488. C9C2×C3×C22⋊Q8semidirect
535. C22Q8×AGL(1,ℤ/9)semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×AGL(1,ℤ/9)2
C22×C4×AGL(1,ℤ/9)2
3−1+2×C22⋊Q82
#63508⋊C32
#63486⋊C32
#63459⋊C32
#63458⋊C32
C4⋊C4×AGL(1,ℤ/9)2
C22⋊C4×AGL(1,ℤ/9)2
#63440⋊C32
C3×D3×C22⋊Q83
D9×C22⋊Q83