Finite Group Databasebeta

← C4×#41×AGL(1,ℤ/9) #72268968

Subgroups — C4×#41×AGL(1,ℤ/9) #72268968

Order 3456.

5339 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×AGL(1,ℤ/9)C211yesmaximal, characteristic
2C4×#41×3−1+2C211yesmaximal, characteristic, complemented
3#41×3−1+2⋊C4C211yesmaximal, characteristic, complemented
4C4×#88724C212yesmaximal, complemented
5C4×Q8×AGL(1,ℤ/9)C212yesmaximal, complemented
6C4×#3699⋊C3C216yesmaximal, complemented
7C4×D4×AGL(1,ℤ/9)C216yesmaximal, complemented
8#10589624⋊C3C213yesmaximal, complemented
9#117×AGL(1,ℤ/9)C213yesmaximal, complemented
10C4×#3697⋊C3C213yesmaximal, complemented
11C2×C42×AGL(1,ℤ/9)C213yesmaximal, complemented
12C3×C4×D3×#41—31nomaximal
13C4×#41×D9C311yesmaximal, characteristic, complemented
14C2×#41×3−1+2C2211yescharacteristic
15#41×AGL(1,ℤ/9)C4116yesdirect product factor
16C2×#88724C2211yescharacteristic
17C2×Q8×AGL(1,ℤ/9)C2211yescharacteristic
18C2×#3699⋊C3C2213yes—
19C2×D4×AGL(1,ℤ/9)C2213yes—
20C2×#3697⋊C3C2213yes—
21C22×C4×AGL(1,ℤ/9)C2216yes—
22C22×C4×AGL(1,ℤ/9)C2213yes—
23C4×Q8×3−1+2C2212yescomplemented
24C4×D4×3−1+2C2216yescomplemented
253−1+2×#117C2213yescomplemented
26C2×C42×3−1+2C2213yescomplemented
27Q8×3−1+2⋊C4C2212yescomplemented
28D4×3−1+2⋊C4C2216yescomplemented
29C4×#611⋊C3C22112yescomplemented
30#63488⋊C3C2213yescomplemented
31C2×C4×3−1+2⋊C4C2213yescomplemented
32C2×C4×3−1+2⋊C4C2216yescomplemented
33#63455⋊C3C2216yescomplemented
34#63454⋊C3C2216yescomplemented
35C4⋊C4×AGL(1,ℤ/9)C2216yes—
36#63449⋊C3C2216yescomplemented
37(#611⋊C3)⋊C4C22112yescomplemented
38C22⋊C4×AGL(1,ℤ/9)C2216yes—
39#63439⋊C3C2216yescomplemented
40C4×C4⋊AGL(1,ℤ/9)C2216yescomplemented
41#63434⋊C3C2216yescomplemented
42C42×AGL(1,ℤ/9)C2213yes—
43C42×AGL(1,ℤ/9)C2211yescharacteristic
44C42×AGL(1,ℤ/9)C2216yes—
45C42×AGL(1,ℤ/9)C2213yescomplemented
46C42×AGL(1,ℤ/9)C2213yescomplemented
47C42×AGL(1,ℤ/9)C2216yescomplemented
48C4×3−1+2⋊Q8C2216yescomplemented
49C2×C3×D3×#41—31no—
50C32×C4×#41D311yescharacteristic
51C3×Dic3×#41—31no—
52C3×C4×#239—32no—
53C3×C4×D3×Q8—32no—
54C3×C4×D3×D4—36no—
55C3×C4×#237—36no—
56C3×#5522—33no—
57C3×D3×#117—33no—
58C3×C4×#235—33no—
59C2×C3×C42×D3—33no—
60C2×#41×D9C2×C311yescharacteristic
61C4×C9×#41—21no—
62C4×C9×#41C2×C311yescharacteristic, complemented
63#41×Dic9C2×C311yescharacteristic, complemented
64C4×#3701C2×C312yescomplemented
65C4×Q8×D9C2×C312yescomplemented
66C4×D4×D9C2×C316yescomplemented
67C4×#3699C2×C316yescomplemented
68#10589624C2×C313yescomplemented
69D9×#117C2×C313yescomplemented
70C4×#3697C2×C313yescomplemented
71C2×C42×D9C2×C313yescomplemented
72C23×AGL(1,ℤ/9)C2313yes—
73#41×3−1+2C2×C418yescomplemented
74C2×Q8×3−1+2C2311yescharacteristic
75C2×D4×3−1+2C2313yes—
76C22×C4×3−1+2C2316yes—
77C22×C4×3−1+2C2313yes—
78C2×#611⋊C3C2316yes—
79C22×3−1+2⋊C4C2316yes—
80C22×3−1+2⋊C4C2313yes—
81#88724C2×C418yescomplemented
82Q8×AGL(1,ℤ/9)C2×C418yescomplemented
83#3699⋊C3C2×C4124yescomplemented
84D4×AGL(1,ℤ/9)C2×C4124yescomplemented
85#3697⋊C3C2×C4124yescomplemented
86C2×C4⋊AGL(1,ℤ/9)C2313yes—
87C2×C4×AGL(1,ℤ/9)—224no—
88C2×C4×AGL(1,ℤ/9)C2×C4124yescomplemented
89C2×C4×AGL(1,ℤ/9)C2316yes—
90C2×C4×AGL(1,ℤ/9)C2316yes—
91C2×C4×AGL(1,ℤ/9)C2316yes—
92C2×C4×AGL(1,ℤ/9)C2313yes—
93C2×C4×AGL(1,ℤ/9)C2311yescharacteristic
94C2×C4×AGL(1,ℤ/9)C2313yes—
95C2×C4×AGL(1,ℤ/9)C2313yes—
96C2×C4×AGL(1,ℤ/9)C2312yes—
97C2×3−1+2⋊Q8C2313yes—
98C4⋊C4×3−1+2C2316yes—
99C22⋊C4×3−1+2C2316yes—
100C42×3−1+2C2311yescharacteristic
101C42×3−1+2C2313yes—
102C42×3−1+2C2316yes—
103#3676⋊C3C2316yes—
104(C2×AGL(1,ℤ/9))⋊C4C23112yes—
105C4⋊(3−1+2⋊C4)C2316yes—
106(3−1+2⋊C4)⋊C4C23112yes—
107C4×3−1+2⋊C4C2316yes—
108C4×3−1+2⋊C4C2316yes—
109C4×3−1+2⋊C4C2316yes—
110C4×3−1+2⋊C4C2312yes—
111C4×3−1+2⋊C4C2311yescharacteristic
112C4×3−1+2⋊C4C2313yes—
113C4×3−1+2⋊C4C2316yes—
114C2×C3×C4×#41—91no—
115C4×D3×#41—31no—
116C2×C32×#41C2×D311yescharacteristic
117C3×D3×#41—316no—
118C2×C3×#239—31no—
119C2×C3×D3×Q8—31no—
120C2×C3×#237—33no—
121C2×C3×D3×D4—33no—
122C2×C3×#235—33no—
123C22×C3×C4×D3—33no—
124C22×C3×C4×D3—36no—
125C32×C4×Q8C2×D312yes—
126C32×C4×D4C2×D316yes—
127C32×#117C2×D313yes—
128C2×C32×C42C2×D313yes—
129C3×Q8×Dic3—32no—
130C3×D4×Dic3—36no—
131C3×C4×#67—312no—
132C3×#926—33no—
133C2×C3×C4×Dic3—33no—
134C2×C3×C4×Dic3—36no—
135C3×#893—36no—
136C3×#892—36no—
137C3×D3×C4⋊C4—36no—
138C3×#887—36no—
139C3×#67⋊C4—312no—
140C3×D3×C22⋊C4—36no—
141C3×#877—36no—
142C3×C4×D12—36no—
143C3×#872—36no—
144C3×C42×D3—33no—
145C3×C42×D3—33no—
146C3×C42×D3—36no—
147C3×C42×D3—36no—
148C3×C42×D3—31no—
149C3×C42×D3—33no—
150C3×C4×Dic6—36no—
151C2×C9×#41—21no—
152C2×C9×#41C22×C311yescharacteristic
153#41×D9C3×C4116yescomplemented
154C2×#3701C22×C311yescharacteristic
155C2×Q8×D9C22×C311yescharacteristic
156C2×#3699C22×C313yes—
157C2×D4×D9C22×C313yes—
158C2×#3697C22×C313yes—
159C22×C4×D9C22×C316yes—
160C22×C4×D9C22×C313yes—
161C4×Q8×C9—22no—
162C4×Q8×C9C22×C312yescomplemented
163C4×D4×C9—26no—
164C4×D4×C9C22×C316yescomplemented
165C9×#117—23no—
166C9×#117C22×C313yescomplemented
167C2×C42×C9—23no—
168C2×C42×C9C22×C313yescomplemented
169Q8×Dic9C22×C312yescomplemented
170D4×Dic9C22×C316yescomplemented
171C4×#611C22×C3112yescomplemented
172#63488C22×C313yescomplemented
173C2×C4×Dic9C22×C313yescomplemented
174C2×C4×Dic9C22×C316yescomplemented
175#63455C22×C316yescomplemented
176#63454C22×C316yescomplemented
177C4⋊C4×D9C22×C316yes—
178#63449C22×C316yescomplemented
179#611⋊C4C22×C3112yescomplemented
180C22⋊C4×D9C22×C316yes—
181#63439C22×C316yescomplemented
182C4×D36C22×C316yescomplemented
183#63434C22×C316yescomplemented
184C42×D9C22×C311yescharacteristic
185C42×D9C22×C313yes—
186C42×D9C22×C316yes—
187C42×D9C22×C313yescomplemented
188C42×D9C22×C313yescomplemented
189C42×D9C22×C316yescomplemented
190C4×Dic18C22×C316yescomplemented
191C23×3−1+2C2413yes—
192C22×AGL(1,ℤ/9)—212no—
193C22×AGL(1,ℤ/9)C22×C4112yes—
194C22×AGL(1,ℤ/9)C2413yes—
195C22×AGL(1,ℤ/9)C2411yescharacteristic
196Q8×3−1+2C22×C414yescomplemented
197D4×3−1+2C22×C4112yescomplemented
198C2×C4×3−1+2—212no—
199C2×C4×3−1+2C22×C4112yescomplemented
200C2×C4×3−1+2C2416yes—
201C2×C4×3−1+2C2413yes—
202C2×C4×3−1+2C2411yescharacteristic
203C2×C4×3−1+2C2412yes—
204#611⋊C3C22×C4124yescomplemented
205C2×3−1+2⋊C4—212no—
206C2×3−1+2⋊C4C22×C4112yescomplemented
207C2×3−1+2⋊C4C2416yes—
208C2×3−1+2⋊C4C2413yes—
209C2×3−1+2⋊C4C2411yescharacteristic
210C2×3−1+2⋊C4C2412yes—
211C4⋊AGL(1,ℤ/9)C22×C4112yescomplemented
212C4×AGL(1,ℤ/9)—212no—
213C4×AGL(1,ℤ/9)—212no—
214C4×AGL(1,ℤ/9)—212no—
215C4×AGL(1,ℤ/9)C22×C414yes—
216C4×AGL(1,ℤ/9)C22×C4112yes—
217C4×AGL(1,ℤ/9)C22×C4112yescomplemented
218C4×AGL(1,ℤ/9)C22×C4112yescomplemented
219C4×AGL(1,ℤ/9)#4118yesdirect product factor
2203−1+2⋊Q8C22×C4112yescomplemented
221C22×C3×#41—91no—
222C2×D3×#41—31no—
223C3×C4×#41—61no—
224C3×C4×#41—93no—
225C3×C4×#41—93no—
226C3×C4×#41—96no—
227C3×C4×#41—92no—
228C3×C4×#41—91no—
229C3×C4×#41C3×D311yescharacteristic
230C2×C3×C4×Q8—92no—
231C2×C3×C4×D4—96no—
232C2×C3×#117—93no—
233C22×C3×C42—93no—
234Dic3×#41—31no—
235C4×#239—32no—
236C4×D3×Q8—32no—
237C4×D3×D4—36no—
238C4×#237—36no—
239#5522—33no—
240D3×#117—33no—
241C4×#235—33no—
242C2×C42×D3—33no—
243C23×C3×D3—33no—
244C32×#41C4×D318yes—
245C2×C32×Q8C22×D311yescharacteristic
246C2×C32×D4C22×D313yes—
247C22×C32×C4C22×D316yes—
248C22×C32×C4C22×D313yes—
249C2×C3×#67—36no—
250C22×C3×Dic3—33no—
251C22×C3×Dic3—36no—
252C3×#239—38no—
253C3×D3×Q8—38no—
254C3×#237—324no—
255C3×D3×D4—324no—
256C3×#235—324no—
257C2×C3×D12—33no—
258C2×C3×C4×D3—324no—
259C2×C3×C4×D3—33no—
260C2×C3×C4×D3—33no—
261C2×C3×C4×D3—31no—
262C2×C3×C4×D3—32no—
263C2×C3×C4×D3—33no—
264C2×C3×C4×D3—36no—
265C2×C3×C4×D3—36no—
266C2×C3×C4×D3—36no—
267C2×C3×C4×D3—624no—
268C2×C3×Dic6—33no—
269C23×D9C23×C313yes—
270C32×C4⋊C4C22×D316yes—
271C32×C22⋊C4C22×D316yes—
272C32×C42C22×D311yescharacteristic
273C32×C42C22×D313yes—
274C32×C42C22×D316yes—
275C3×#217—36no—
276C3×(C2×D3)⋊C4—312no—
277C3×C4⋊Dic3—36no—
278C3×Dic3⋊C4—312no—
279C3×C4×Dic3—36no—
280C3×C4×Dic3—36no—
281C3×C4×Dic3—36no—
282C3×C4×Dic3—31no—
283C3×C4×Dic3—32no—
284C3×C4×Dic3—33no—
285C3×C4×Dic3—36no—
286C9×#41—28no—
287C9×#41C2×C3×C418yescomplemented
288C2×Q8×C9—21no—
289C2×Q8×C9C23×C311yescharacteristic
290C2×D4×C9—23no—
291C2×D4×C9C23×C313yes—
292C22×C4×C9—23no—
293C22×C4×C9—26no—
294C22×C4×C9C23×C316yes—
295C22×C4×C9C23×C313yes—
296C2×#611C23×C316yes—
297C22×Dic9C23×C316yes—
298C22×Dic9C23×C313yes—
299#3701C2×C3×C418yescomplemented
300Q8×D9C2×C3×C418yescomplemented
301#3699C2×C3×C4124yescomplemented
302D4×D9C2×C3×C4124yescomplemented
303#3697C2×C3×C4124yescomplemented
304C2×D36C23×C313yes—
305C2×C4×D9—224no—
306C2×C4×D9C2×C3×C4124yescomplemented
307C2×C4×D9C23×C316yes—
308C2×C4×D9C23×C316yes—
309C2×C4×D9C23×C316yes—
310C2×C4×D9C23×C311yescharacteristic
311C2×C4×D9C23×C313yes—
312C2×C4×D9C23×C313yes—
313C2×C4×D9C23×C313yes—
314C2×C4×D9C23×C312yes—
315C2×Dic18C23×C313yes—
316C9×C4⋊C4—26no—
317C9×C4⋊C4C23×C316yes—
318C9×C22⋊C4—26no—
319C9×C22⋊C4C23×C316yes—
320C42×C9—21no—
321C42×C9—23no—
322C42×C9—26no—
323C42×C9C23×C311yescharacteristic
324C42×C9C23×C313yes—
325C42×C9C23×C316yes—
326#3676C23×C316yes—
327(C2×D9)⋊C4C23×C3112yes—
328C4⋊Dic9C23×C316yes—
329Dic9⋊C4C23×C3112yes—
330C4×Dic9C23×C313yes—
331C4×Dic9C23×C316yes—
332C4×Dic9C23×C316yes—
333C4×Dic9C23×C312yes—
334C4×Dic9C23×C311yescharacteristic
335C4×Dic9C23×C316yes—
336C4×Dic9C23×C316yes—
337C2×C4×#41—91noSylow
338C22×3−1+2—26no—
339C22×3−1+2C23×C416yes—
340C22×3−1+2C2511yescharacteristic
341C2×AGL(1,ℤ/9)—26no—
342C2×AGL(1,ℤ/9)—224no—
343C2×AGL(1,ℤ/9)C23×C416yes—
344C2×AGL(1,ℤ/9)C23×C412yes—
345C2×AGL(1,ℤ/9)C2×#4114yes—
346C4×3−1+2—26no—
347C4×3−1+2C23×C416yes—
348C4×3−1+2C23×C412yes—
349C4×3−1+2C2×#4114yescomplemented
3503−1+2⋊C4—26no—
3513−1+2⋊C4C23×C416yes—
3523−1+2⋊C4C23×C412yes—
3533−1+2⋊C4C2×#4114yescomplemented
354C2×C3×#41—61no—
355C2×C3×#41—93no—
356C2×C3×#41—93no—
357C2×C3×#41—91no—
358C2×C3×#41—916no—
359C2×C3×#41C2×C3×D311yescharacteristic
360C22×C3×Q8—91no—
361C22×C3×D4—93no—
362C23×C3×C4—93no—
363C23×C3×C4—96no—
364D3×#41—316no—
365C2×#239—31no—
366C2×D3×Q8—31no—
367C2×#237—33no—
368C2×D3×D4—33no—
369C2×#235—33no—
370C22×C4×D3—33no—
371C22×C4×D3—36no—
372C3×C4×Q8—62no—
373C3×C4×Q8—96no—
374C3×C4×Q8—96no—
375C3×C4×Q8—92no—
376C3×C4×Q8C2×C3×D312yes—
377C3×C4×D4—66no—
378C3×C4×D4—96no—
379C3×C4×D4—912no—
380C3×C4×D4—96no—
381C3×C4×D4—912no—
382C3×C4×D4—96no—
383C3×C4×D4C2×C3×D316yes—
384C3×#117—63no—
385C3×#117—96no—
386C3×#117—96no—
387C3×#117—96no—
388C3×#117—93no—
389C3×#117C2×C3×D313yes—
390C2×C3×C4⋊C4—96no—
391C2×C3×C22⋊C4—96no—
392C2×C3×C42—63no—
393C2×C3×C42—91no—
394C2×C3×C42—93no—
395C2×C3×C42—96no—
396C2×C3×C42—93no—
397C2×C3×C42—96no—
398C2×C3×C42—93no—
399C2×C3×C42—93no—
400C2×C3×C42—96no—
401C2×C3×C42C2×C3×D313yes—
402Q8×Dic3—32no—
403D4×Dic3—36no—
404C4×#67—312no—
405#926—33no—
406C2×C4×Dic3—33no—
407C2×C4×Dic3—36no—
408#893—36no—
409#892—36no—
410D3×C4⋊C4—36no—
411#887—36no—
412#67⋊C4—312no—
413D3×C22⋊C4—36no—
414#877—36no—
415C4×D12—36no—
416#872—36no—
417C42×D3—31no—
418C42×D3—33no—
419C42×D3—33no—
420C42×D3—33no—
421C42×D3—36no—
422C42×D3—36no—
423C4×Dic6—36no—
424C23×C32C23×D313yes—
425C22×C3×D3—31no—
426C22×C3×D3—312no—
427C22×C3×D3—33no—
428C22×C3×D3—612no—
429C32×Q8C2×C4×D314yes—
430C32×D4C2×C4×D3112yes—
431C2×C32×C4—212no—
432C2×C32×C4C2×C4×D3112yes—
433C2×C32×C4C23×D316yes—
434C2×C32×C4C23×D311yescharacteristic
435C2×C32×C4C23×D313yes—
436C2×C32×C4C23×D312yes—
437C3×#67—324no—
438C2×C3×Dic3—312no—
439C2×C3×Dic3—31no—
440C2×C3×Dic3—32no—
441C2×C3×Dic3—33no—
442C2×C3×Dic3—36no—
443C2×C3×Dic3—612no—
444C3×D12—312no—
445C3×C4×D3—34no—
446C3×C4×D3—312no—
447C3×C4×D3—312no—
448C3×C4×D3—312no—
449C3×C4×D3—38no—
450C3×C4×D3—612no—
451C3×C4×D3—612no—
452C3×C4×D3—612no—
453C3×Dic6—312no—
454C23×C9—23no—
455C23×C9C24×C313yes—
456C22×D9—212no—
457C22×D9C22×C3×C4112yes—
458C22×D9C24×C313yes—
459C22×D9C24×C311yescharacteristic
460Q8×C9—24no—
461Q8×C9C22×C3×C414yescomplemented
462D4×C9—212no—
463D4×C9C22×C3×C4112yescomplemented
464C2×C4×C9—212no—
465C2×C4×C9—21no—
466C2×C4×C9—22no—
467C2×C4×C9—23no—
468C2×C4×C9—26no—
469C2×C4×C9—212no—
470C2×C4×C9—412no—
471C2×C4×C9C22×C3×C4112yescomplemented
472C2×C4×C9C24×C316yes—
473C2×C4×C9C24×C311yescharacteristic
474C2×C4×C9C24×C313yes—
475C2×C4×C9C24×C312yes—
476#611C22×C3×C4124yescomplemented
477C2×Dic9—212no—
478C2×Dic9C22×C3×C4112yescomplemented
479C2×Dic9C24×C316yes—
480C2×Dic9C24×C311yescharacteristic
481C2×Dic9C24×C313yes—
482C2×Dic9C24×C312yes—
483D36C22×C3×C4112yescomplemented
484C4×D9—212no—
485C4×D9—212no—
486C4×D9—212no—
487C4×D9C22×C3×C414yes—
488C4×D9C22×C3×C4112yes—
489C4×D9C22×C3×C4112yescomplemented
490C4×D9C22×C3×C4112yescomplemented
491C4×D9C3×#4118yescomplemented
492Dic18C22×C3×C4112yescomplemented
493C22×#41—91no—
494C4×#41—91no—
495C4×#41—92no—
496C4×#41—96no—
497C4×#41—93no—
498C4×#41—93no—
499C4×#41AGL(1,ℤ/9)11yescharacteristic, direct product factor
500C2×C4×Q8—92no—
501C2×C4×D4—96no—
502C2×#117—93no—
503C22×C42—93no—
504C2×3−1+2—26no—
505C2×3−1+2C24×C411yescharacteristic
506C2×3−1+2C22×#4112yes—
507AGL(1,ℤ/9)—26no—
508AGL(1,ℤ/9)C4×#4114yesdirect product factor
509C24×C3—93no—
510C23×D3—33no—
511C3×#41—68no—
512C3×#41—924no—
513C3×#41—924no—
514C3×#41—98no—
515C3×#41C3×C4×D318yes—
516C2×C3×Q8—61no—
517C2×C3×Q8—93no—
518C2×C3×Q8—98no—
519C2×C3×Q8C22×C3×D311yescharacteristic
520C2×C3×D4—63no—
521C2×C3×D4—93no—
522C2×C3×D4—924no—
523C2×C3×D4—96no—
524C2×C3×D4C22×C3×D313yes—
525C22×C3×C4—63no—
526C22×C3×C4—66no—
527C22×C3×C4—91no—
528C22×C3×C4—92no—
529C22×C3×C4—93no—
530C22×C3×C4—93no—
531C22×C3×C4—93no—
532C22×C3×C4—924no—
533C22×C3×C4—96no—
534C22×C3×C4—96no—
535C22×C3×C4—96no—
536C22×C3×C4—93no—
537C22×C3×C4—96no—
538C22×C3×C4—1824no—
539C22×C3×C4C22×C3×D316yes—
540C22×C3×C4C22×C3×D313yes—
541C2×#67—36no—
542C22×Dic3—33no—
543C22×Dic3—36no—
544#239—38no—
545D3×Q8—38no—
546#237—324no—
547D3×D4—324no—
548#235—324no—
549C2×D12—33no—
550C2×C4×D3—31no—
551C2×C4×D3—32no—
552C2×C4×D3—33no—
553C2×C4×D3—33no—
554C2×C4×D3—33no—
555C2×C4×D3—324no—
556C2×C4×D3—36no—
557C2×C4×D3—36no—
558C2×C4×D3—36no—
559C2×C4×D3—624no—
560C2×Dic6—33no—
561C3×C4⋊C4—66no—
562C3×C4⋊C4—912no—
563C3×C4⋊C4—96no—
564C3×C4⋊C4C22×C3×D316yes—
565C3×C22⋊C4—66no—
566C3×C22⋊C4—912no—
567C3×C22⋊C4—96no—
568C3×C22⋊C4C22×C3×D316yes—
569C3×C42—63no—
570C3×C42—66no—
571C3×C42—61no—
572C3×C42—91no—
573C3×C42—92no—
574C3×C42—93no—
575C3×C42—96no—
576C3×C42—96no—
577C3×C42—96no—
578C3×C42—96no—
579C3×C42C22×C3×D316yes—
580C3×C42C22×C3×D313yes—
581C3×C42C22×C3×D311yescharacteristic
582#217—36no—
583(C2×D3)⋊C4—312no—
584C4⋊Dic3—36no—
585Dic3⋊C4—312no—
586C4×Dic3—36no—
587C4×Dic3—31no—
588C4×Dic3—32no—
589C4×Dic3—33no—
590C4×Dic3—36no—
591C4×Dic3—36no—
592C4×Dic3—36no—
593C22×C32—26no—
594C22×C32C22×C4×D316yes—
595C22×C32C24×D311yescharacteristic
596C2×C3×D3—32no—
597C2×C3×D3—34no—
598C2×C3×D3—36no—
599C2×C3×D3—624no—
600C2×C3×D3—66no—
601C32×C4—26no—
602C32×C4C22×C4×D316yes—
603C32×C4C22×C4×D312yes—
604C32×C4D3×#4114yes—
605C3×Dic3—36no—
606C3×Dic3—32no—
607C3×Dic3—34no—
608C3×Dic3—66no—
609C22×C9—26no—
610C22×C9—26no—
611C22×C9—21no—
612C22×C9—46no—
613C22×C9C23×C3×C416yes—
614C22×C9C25×C311yescharacteristic
615C2×D9—26no—
616C2×D9—224no—
617C2×D9C23×C3×C416yes—
618C2×D9C23×C3×C412yes—
619C2×D9C2×C3×#4114yes—
620C4×C9—26no—
621C4×C9—22no—
622C4×C9—26no—
623C4×C9—24no—
624C4×C9—46no—
625C4×C9C23×C3×C416yes—
626C4×C9C23×C3×C412yes—
627C4×C9C2×C3×#4114yescomplemented
628Dic9—26no—
629Dic9C23×C3×C416yes—
630Dic9C23×C3×C412yes—
631Dic9C2×C3×#4114yescomplemented
632C2×#41—916no—
633C2×#41—91no—
634C2×#41—93no—
635C2×#41—93no—
636C2×#41C2×AGL(1,ℤ/9)11yescharacteristic
637C22×Q8—91no—
638C22×D4—93no—
639C23×C4—93no—
640C23×C4—96no—
641C4×Q8—92no—
642C4×Q8—96no—
643C4×Q8—96no—
644C4×Q8C2×AGL(1,ℤ/9)12yescomplemented
645C4×D4—96no—
646C4×D4—912no—
647C4×D4—96no—
648C4×D4—912no—
649C4×D4—96no—
650C4×D4C2×AGL(1,ℤ/9)16yescomplemented
651#117—93no—
652#117—96no—
653#117—96no—
654#117—96no—
655#117C2×AGL(1,ℤ/9)13yescomplemented
656C2×C4⋊C4—96no—
657C2×C22⋊C4—96no—
658C2×C42—96no—
659C2×C42—93no—
660C2×C42—93no—
661C2×C42—96no—
662C2×C42—96no—
663C2×C42—93no—
664C2×C42—93no—
665C2×C42—91no—
666C2×C42C2×AGL(1,ℤ/9)13yescomplemented
6673−1+2C2×C4×#4111yescharacteristic, complemented, Sylow
668C23×C3—63no—
669C23×C3—91no—
670C23×C3—93no—
671C23×C3—912no—
672C23×C3—1812no—
673C23×C3C23×C3×D313yes—
674C22×D3—31no—
675C22×D3—312no—
676C22×D3—33no—
677C22×D3—612no—
678C3×Q8—64no—
679C3×Q8—912no—
680C3×Q8C2×C3×C4×D314yes—
681C3×D4—612no—
682C3×D4—912no—
683C3×D4—924no—
684C3×D4C2×C3×C4×D3112yes—
685C2×C3×C4—212no—
686C2×C3×C4—61no—
687C2×C3×C4—62no—
688C2×C3×C4—63no—
689C2×C3×C4—66no—
690C2×C3×C4—612no—
691C2×C3×C4—94no—
692C2×C3×C4—912no—
693C2×C3×C4—912no—
694C2×C3×C4—912no—
695C2×C3×C4—98no—
696C2×C3×C4—91no—
697C2×C3×C4—92no—
698C2×C3×C4—93no—
699C2×C3×C4—912no—
700C2×C3×C4—96no—
701C2×C3×C4—1212no—
702C2×C3×C4—1812no—
703C2×C3×C4—1812no—
704C2×C3×C4—1812no—
705C2×C3×C4—1812no—
706C2×C3×C4C2×C3×C4×D3112yes—
707C2×C3×C4C23×C3×D316yes—
708C2×C3×C4C23×C3×D311yescharacteristic
709C2×C3×C4C23×C3×D313yes—
710C2×C3×C4C23×C3×D312yes—
711#67—324no—
712C2×Dic3—312no—
713C2×Dic3—31no—
714C2×Dic3—32no—
715C2×Dic3—33no—
716C2×Dic3—36no—
717C2×Dic3—612no—
718D12—312no—
719C4×D3—34no—
720C4×D3—312no—
721C4×D3—312no—
722C4×D3—312no—
723C4×D3—38no—
724C4×D3—612no—
725C4×D3—612no—
726C4×D3—612no—
727Dic6—312no—
728C2×C32—26no—
729C2×C32C23×C4×D311yescharacteristic
730C2×C32C2×D3×#4112yes—
731C3×D3—34no—
732C3×D3—66no—
733C2×C9—26no—
734C2×C9—21no—
735C2×C9—22no—
736C2×C9—46no—
737C2×C9C24×C3×C411yescharacteristic
738C2×C9C22×C3×#4112yes—
739D9—26no—
740D9C3×C4×#4114yescomplemented
741C24—93no—
742#41—98no—
743#41—924no—
744#41—924no—
745#41C4×AGL(1,ℤ/9)18yesdirect product factor
746C2×Q8—98no—
747C2×Q8—93no—
748C2×Q8C22×AGL(1,ℤ/9)11yescharacteristic
749C2×D4—96no—
750C2×D4—924no—
751C2×D4—93no—
752C2×D4C22×AGL(1,ℤ/9)13yes—
753C22×C4—93no—
754C22×C4—91no—
755C22×C4—92no—
756C22×C4—93no—
757C22×C4—93no—
758C22×C4—93no—
759C22×C4—924no—
760C22×C4—96no—
761C22×C4—96no—
762C22×C4—96no—
763C22×C4—96no—
764C22×C4—1824no—
765C22×C4C22×AGL(1,ℤ/9)16yes—
766C22×C4C22×AGL(1,ℤ/9)13yes—
767C4⋊C4—912no—
768C4⋊C4—96no—
769C4⋊C4C22×AGL(1,ℤ/9)16yes—
770C22⋊C4—96no—
771C22⋊C4—912no—
772C22⋊C4C22×AGL(1,ℤ/9)16yes—
773C42—91no—
774C42—92no—
775C42—96no—
776C42—93no—
777C42—96no—
778C42—96no—
779C42—96no—
780C42C22×AGL(1,ℤ/9)13yes—
781C42C22×AGL(1,ℤ/9)16yes—
782C42C22×AGL(1,ℤ/9)11yescharacteristic
783C22×C3—26no—
784C22×C3—61no—
785C22×C3—66no—
786C22×C3—92no—
787C22×C3—94no—
788C22×C3—96no—
789C22×C3—126no—
790C22×C3—186no—
791C22×C3—1824no—
792C22×C3C22×C3×C4×D316yes—
793C22×C3C24×C3×D311yescharacteristic
794C2×D3—32no—
795C2×D3—34no—
796C2×D3—36no—
797C2×D3—624no—
798C2×D3—66no—
799C3×C4—26no—
800C3×C4—62no—
801C3×C4—66no—
802C3×C4—64no—
803C3×C4—92no—
804C3×C4—96no—
805C3×C4—94no—
806C3×C4—126no—
807C3×C4—186no—
808C3×C4C22×C3×C4×D316yes—
809C3×C4C22×C3×C4×D312yes—
810C3×C4C3×D3×#4114yes—
811Dic3—36no—
812Dic3—32no—
813Dic3—34no—
814Dic3—66no—
815C32C4×D3×#4111yescharacteristic
816C9—21no—
817C9C2×C3×C4×#4111yescharacteristic, complemented
818C23—91no—
819C23—93no—
820C23—912no—
821C23—1812no—
822C23C23×AGL(1,ℤ/9)13yes—
823Q8—912no—
824Q8C2×C4×AGL(1,ℤ/9)14yescomplemented
825D4—924no—
826D4—912no—
827D4C2×C4×AGL(1,ℤ/9)112yescomplemented
828C2×C4—212no—
829C2×C4—91no—
830C2×C4—92no—
831C2×C4—93no—
832C2×C4—912no—
833C2×C4—94no—
834C2×C4—912no—
835C2×C4—912no—
836C2×C4—912no—
837C2×C4—98no—
838C2×C4—96no—
839C2×C4—1812no—
840C2×C4—1812no—
841C2×C4—1812no—
842C2×C4—1812no—
843C2×C4C2×C4×AGL(1,ℤ/9)112yescomplemented
844C2×C4C23×AGL(1,ℤ/9)16yes—
845C2×C4C23×AGL(1,ℤ/9)11yescharacteristic
846C2×C4C23×AGL(1,ℤ/9)13yes—
847C2×C4C23×AGL(1,ℤ/9)12yes—
848C2×C3—26no—
849C2×C3—61no—
850C2×C3—62no—
851C2×C3—94no—
852C2×C3—126no—
853C2×C3—186no—
854C2×C3C23×C3×C4×D311yescharacteristic
855C2×C3C2×C3×D3×#4112yes—
856D3—34no—
857D3—66no—
858C22—26no—
859C22—92no—
860C22—94no—
861C22—96no—
862C22—1824no—
863C22—186no—
864C22C22×C4×AGL(1,ℤ/9)16yes—
865C22C24×AGL(1,ℤ/9)11yescharacteristic
866C4—26no—
867C4—92no—
868C4—96no—
869C4—94no—
870C4—186no—
871C4C22×C4×AGL(1,ℤ/9)12yes—
872C4C22×C4×AGL(1,ℤ/9)16yes—
873C4#41×AGL(1,ℤ/9)14yesdirect product factor
874C3—61no—
875C3C3×C4×D3×#4111yescharacteristic
876C2—26no—
877C2—94no—
878C2—186no—
879C2C23×C4×AGL(1,ℤ/9)11yescharacteristic
880C2C2×#41×AGL(1,ℤ/9)12yes—
subgroupG/H
centerC42C22×AGL(1,ℤ/9)
commutatorC2×C9C24×C3×C4
Frattini, socleC22×C3C24×C3×D3
FittingC4×#41×3−1+2C2
prime radicalC2×#41×AGL(1,ℤ/9)C2
cosocleC22×C9C25×C3
hypercenterC4×#41AGL(1,ℤ/9)
hypocenterC9C2×C3×C4×#41
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C4×#41×3−1+2C2semidirect
3. #41×3−1+2⋊C4C2semidirect
4. C4×#88724C2semidirect
5. C4×Q8×AGL(1,ℤ/9)C2semidirect
6. C4×#3699⋊C3C2semidirect
7. C4×D4×AGL(1,ℤ/9)C2semidirect
8. #10589624⋊C3C2semidirect
9. #117×AGL(1,ℤ/9)C2semidirect
10. C4×#3697⋊C3C2semidirect
11. C2×C42×AGL(1,ℤ/9)C2semidirect
13. C4×#41×D9C3semidirect
15. #41×AGL(1,ℤ/9)C4direct (N × H)
23. C4×Q8×3−1+2C22semidirect
24. C4×D4×3−1+2C22semidirect
25. 3−1+2×#117C22semidirect
26. C2×C42×3−1+2C22semidirect
27. Q8×3−1+2⋊C4C22semidirect
28. D4×3−1+2⋊C4C22semidirect
29. C4×#611⋊C3C22semidirect
30. #63488⋊C3C22semidirect
31. C2×C4×3−1+2⋊C4C22semidirect
32. C2×C4×3−1+2⋊C4C22semidirect
33. #63455⋊C3C22semidirect
34. #63454⋊C3C22semidirect
36. #63449⋊C3C22semidirect
37. (#611⋊C3)⋊C4C22semidirect
39. #63439⋊C3C22semidirect
40. C4×C4⋊AGL(1,ℤ/9)C22semidirect
41. #63434⋊C3C22semidirect
45. C42×AGL(1,ℤ/9)C22semidirect
46. C42×AGL(1,ℤ/9)C22semidirect
47. C42×AGL(1,ℤ/9)C22semidirect
48. C4×3−1+2⋊Q8C22semidirect
62. C4×C9×#41C2×C3semidirect
63. #41×Dic9C2×C3semidirect
64. C4×#3701C2×C3semidirect
65. C4×Q8×D9C2×C3semidirect
66. C4×D4×D9C2×C3semidirect
67. C4×#3699C2×C3semidirect
68. #10589624C2×C3semidirect
69. D9×#117C2×C3semidirect
70. C4×#3697C2×C3semidirect
71. C2×C42×D9C2×C3semidirect
73. #41×3−1+2C2×C4semidirect
81. #88724C2×C4semidirect
82. Q8×AGL(1,ℤ/9)C2×C4semidirect
83. #3699⋊C3C2×C4semidirect
84. D4×AGL(1,ℤ/9)C2×C4semidirect
85. #3697⋊C3C2×C4semidirect
88. C2×C4×AGL(1,ℤ/9)C2×C4semidirect
153. #41×D9C3×C4semidirect
162. C4×Q8×C9C22×C3semidirect
164. C4×D4×C9C22×C3semidirect
166. C9×#117C22×C3semidirect
168. C2×C42×C9C22×C3semidirect
169. Q8×Dic9C22×C3semidirect
170. D4×Dic9C22×C3semidirect
171. C4×#611C22×C3semidirect
172. #63488C22×C3semidirect
173. C2×C4×Dic9C22×C3semidirect
174. C2×C4×Dic9C22×C3semidirect
175. #63455C22×C3semidirect
176. #63454C22×C3semidirect
178. #63449C22×C3semidirect
179. #611⋊C4C22×C3semidirect
181. #63439C22×C3semidirect
182. C4×D36C22×C3semidirect
183. #63434C22×C3semidirect
187. C42×D9C22×C3semidirect
188. C42×D9C22×C3semidirect
189. C42×D9C22×C3semidirect
190. C4×Dic18C22×C3semidirect
196. Q8×3−1+2C22×C4semidirect
197. D4×3−1+2C22×C4semidirect
199. C2×C4×3−1+2C22×C4semidirect
204. #611⋊C3C22×C4semidirect
206. C2×3−1+2⋊C4C22×C4semidirect
211. C4⋊AGL(1,ℤ/9)C22×C4semidirect
217. C4×AGL(1,ℤ/9)C22×C4semidirect
218. C4×AGL(1,ℤ/9)C22×C4semidirect
219. C4×AGL(1,ℤ/9)#41direct (N × H)
220. 3−1+2⋊Q8C22×C4semidirect
287. C9×#41C2×C3×C4semidirect
299. #3701C2×C3×C4semidirect
300. Q8×D9C2×C3×C4semidirect
301. #3699C2×C3×C4semidirect
302. D4×D9C2×C3×C4semidirect
303. #3697C2×C3×C4semidirect
306. C2×C4×D9C2×C3×C4semidirect
349. C4×3−1+2C2×#41semidirect
353. 3−1+2⋊C4C2×#41semidirect
461. Q8×C9C22×C3×C4semidirect
463. D4×C9C22×C3×C4semidirect
471. C2×C4×C9C22×C3×C4semidirect
476. #611C22×C3×C4semidirect
478. C2×Dic9C22×C3×C4semidirect
483. D36C22×C3×C4semidirect
489. C4×D9C22×C3×C4semidirect
490. C4×D9C22×C3×C4semidirect
491. C4×D9C3×#41semidirect
492. Dic18C22×C3×C4semidirect
499. C4×#41AGL(1,ℤ/9)direct (N × H)
508. AGL(1,ℤ/9)C4×#41direct (N × H)
627. C4×C9C2×C3×#41semidirect
631. Dic9C2×C3×#41semidirect
644. C4×Q8C2×AGL(1,ℤ/9)semidirect
650. C4×D4C2×AGL(1,ℤ/9)semidirect
655. #117C2×AGL(1,ℤ/9)semidirect
666. C2×C42C2×AGL(1,ℤ/9)semidirect
667. 3−1+2C2×C4×#41semidirect
740. D9C3×C4×#41semidirect
745. #41C4×AGL(1,ℤ/9)direct (N × H)
817. C9C2×C3×C4×#41semidirect
824. Q8C2×C4×AGL(1,ℤ/9)semidirect
827. D4C2×C4×AGL(1,ℤ/9)semidirect
843. C2×C4C2×C4×AGL(1,ℤ/9)semidirect
873. C4#41×AGL(1,ℤ/9)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#41×AGL(1,ℤ/9)2
C4×#41×3−1+22
#41×3−1+2⋊C42
C4×#887242
C4×Q8×AGL(1,ℤ/9)2
C4×#3699⋊C32
C4×D4×AGL(1,ℤ/9)2
#10589624⋊C32
#117×AGL(1,ℤ/9)2
C4×#3697⋊C32
C2×C42×AGL(1,ℤ/9)2
C3×C4×D3×#413
C4×#41×D93