Finite Group Databasebeta

← #72220032

Subgroups — #72220032

Order 5184.

1573 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
13−1+2×#833C211yesmaximal, characteristic, complemented
2#72219967C212yesmaximal, complemented
3#72219947C211yesmaximal, characteristic, complemented
4C3×#63710⋊C3C211yesmaximal, characteristic, complemented
5#72219923C212yesmaximal, complemented
6C3×#10591510—31nomaximal
7#10588427⋊C3—31nomaximal
8#13140391C311yesmaximal, characteristic, complemented
9C2×C3×D4×3−1+2C2211yescharacteristic
10C2×#10619980—22no—
11C2×C4⋊(C3⋊AGL(1,ℤ/9))C2211yescharacteristic, complemented
12C2×C3×#611⋊C3—22no—
13C3×#3699⋊C3—22no—
14C3×D4×AGL(1,ℤ/9)—22no—
15C3×#3697⋊C3C2212yes—
16C4×C3⋊(3−1+2⋊C4)C2211yescharacteristic, complemented
173−1+2×#208C2212yescomplemented
18#88417⋊C3—22no—
19#88416⋊C3—22no—
20C32×#1004—31no—
21C3×#64149—31no—
22C3×#63825—32no—
23#63710⋊C3—21no—
24#63710⋊C3D311yescharacteristic, complemented
25C3×#63710C2×C311yescharacteristic, complemented
26C32×#833D311yescharacteristic
27C3×#63568—32no—
28#11721840C2×C311yescharacteristic, complemented
29#63502⋊C3—31no—
30#63502⋊C3—61no—
31#63470⋊C3—32no—
32#11720873C2×C312yescomplemented
333−1+2×#100—31no—
34C9×#833—21no—
35C9×#833C2×C311yescharacteristic, complemented
36#63384⋊C3—32no—
37#11720291C2×C312yescomplemented
38C23×C3×3−1+2D412yes—
39C22×C3⋊AGL(1,ℤ/9)—21no—
40C22×C3×AGL(1,ℤ/9)—22no—
41C3×D4×3−1+2—22no—
42C2×C3×C4×3−1+2C2311yescharacteristic
43#10619980—44no—
44C2×C3⋊(3−1+2⋊C4)—21no—
45C4⋊(C3⋊AGL(1,ℤ/9))—22no—
46C3×#611⋊C3—24no—
47C3×#611⋊C3—22no—
48C2×C3×3−1+2⋊C4—22no—
49C3×C4⋊AGL(1,ℤ/9)D412yescomplemented
50C3×C4×AGL(1,ℤ/9)—22no—
51C3×3−1+2⋊Q8D412yescomplemented
52C3⋊C8×3−1+2—22no—
53C3×#5241—91no—
54C3×#4747—91no—
55#10591510—31no—
56#10588427—31no—
57C2×C33×D4C2×D311yescharacteristic
58C2×C3×#638—62no—
59C2×C3×C4⋊(C3⋊D3)—31no—
60C2×C32×#67—62no—
61C32×#237—62no—
62C32×D3×D4—62no—
63C32×#235—32no—
64C3×C4×C3⋊Dic3—31no—
65C32×#208C2×D312yes—
66C3×#3717—62no—
67C3×#3714—62no—
68C2×D4×3−1+2—21no—
69C2×D4×3−1+2—21no—
70C2×D4×3−1+2—41no—
71C2×D4×3−1+2C2×D311yescharacteristic
72C2×C3×D4×C9—21no—
73C2×C3×D4×C9C22×C311yescharacteristic
74C2×#6233—22no—
75C2×C4⋊(C3⋊D9)C22×C311yescharacteristic, complemented
76C2×#611⋊C3—24no—
77C2×#611⋊C3—22no—
78C2×#611⋊C3—64no—
79C2×#611⋊C3—62no—
80C2×C3×#611—22no—
81#3699⋊C3—24no—
82#3699⋊C3—22no—
83D4×AGL(1,ℤ/9)—24no—
84D4×AGL(1,ℤ/9)—22no—
85C3×#3699—22no—
86C3×D4×D9—22no—
87#3697⋊C3—22no—
88#3697⋊C3C2×D312yes—
89C2×C4⋊AGL(1,ℤ/9)—31no—
90C2×C4⋊AGL(1,ℤ/9)—61no—
91C3×#3697C22×C312yes—
92M16×3−1+2—32no—
93C4×C3⋊Dic9C22×C311yescharacteristic, complemented
94C4×3−1+2⋊C4—31no—
95C4×3−1+2⋊C4—61no—
96C9×#208—22no—
97C9×#208C22×C312yescomplemented
98D72⋊C3—62no—
99#3664⋊C3—62no—
100#88417—22no—
101#88416—22no—
102C22×C3×3−1+2—22no—
103C22×C3×3−1+2—42no—
104C22×C3×3−1+2C2×D411yescharacteristic
105C2×C3⋊AGL(1,ℤ/9)—42no—
106C2×C3⋊AGL(1,ℤ/9)—41no—
107C2×C3×AGL(1,ℤ/9)—22no—
108C2×C3×AGL(1,ℤ/9)—82no—
109C3×C4×3−1+2C2×D412yes—
110C3⋊(3−1+2⋊C4)—22no—
111C3×3−1+2⋊C4—22no—
112C32×H(5,𝔽2)—91no—
113C3×#1004—31no—
114C3×#1004—31no—
115C3×#1004—61no—
116#64149—31no—
117C3×#949—92no—
118C3×#940—91no—
119C3×#940—91no—
120C3×#940—181no—
121C3×#908—92no—
122#63825—32no—
123#63710C3×D311yescharacteristic, complemented
124C32×#100—31no—
125C3×#837—92no—
126C3×#833—31no—
127C3×#833C3×D311yescharacteristic
128C3×#825—92no—
129#63568—32no—
130#63502—31no—
131#63502—61no—
132#63470—32no—
133C9×#100—31no—
134C9×#100—61no—
135#63384—32no—
136C23×C33D1212yes—
137C22×C3×C3⋊D3—61no—
138C22×C32×D3—62no—
139C33×D4—22no—
140C2×C33×C4C22×D311yescharacteristic
141C3×#638—124no—
142C2×C3×C3⋊Dic3—61no—
143C3×C4⋊(C3⋊D3)—62no—
144C32×#67—64no—
145C32×#67—62no—
146C2×C32×Dic3—62no—
147C32×D12—32no—
148C32×C4×D3—62no—
149C32×Dic6—32no—
150C23×3−1+2—22no—
151C23×3−1+2—22no—
152C23×3−1+2—42no—
153C23×3−1+2#6712yes—
154C23×C3×C9—22no—
155C23×C3×C9C3×D412yes—
156C22×C3⋊D9—21no—
157C22×AGL(1,ℤ/9)—24no—
158C22×AGL(1,ℤ/9)—22no—
159C22×AGL(1,ℤ/9)—62no—
160C22×AGL(1,ℤ/9)—61no—
161C22×C3×D9—22no—
162C32×C3⋊C8—22no—
163D4×3−1+2—24no—
164D4×3−1+2—22no—
165D4×3−1+2—42no—
166D4×3−1+2—44no—
167C3×D4×C9—22no—
168C3×D4×C9—42no—
169C2×C4×3−1+2—21no—
170C2×C4×3−1+2—21no—
171C2×C4×3−1+2—41no—
172C2×C4×3−1+2C22×D311yescharacteristic
173C2×C3×C4×C9—21no—
174C2×C3×C4×C9C23×C311yescharacteristic
175#6233—44no—
176C2×C3⋊Dic9—21no—
177C4⋊(C3⋊D9)—22no—
178#611⋊C3—24no—
179#611⋊C3—28no—
180#611⋊C3—24no—
181#611⋊C3—22no—
182#611⋊C3—124no—
183#611⋊C3—128no—
184C2×3−1+2⋊C4—24no—
185C2×3−1+2⋊C4—22no—
186C2×3−1+2⋊C4—62no—
187C2×3−1+2⋊C4—61no—
188C3×#611—24no—
189C3×#611—22no—
190C2×C3×Dic9—22no—
191C4⋊AGL(1,ℤ/9)—22no—
192C4⋊AGL(1,ℤ/9)—62no—
193C4⋊AGL(1,ℤ/9)—122no—
194C4⋊AGL(1,ℤ/9)#6712yescomplemented
195C4×AGL(1,ℤ/9)—24no—
196C4×AGL(1,ℤ/9)—22no—
1973−1+2⋊Q8—22no—
1983−1+2⋊Q8#6712yescomplemented
199C3×D36C3×D412yescomplemented
200C3×C4×D9—22no—
201C3×Dic18C3×D412yescomplemented
202C8×3−1+2—62no—
203C9×C3⋊C8—22no—
204C9×C3⋊C8—42no—
205C3×#453—271no—
206#5241—91no—
207#4747—91no—
208C2×C3×3−1+2—21no—
209C2×C3×3−1+2—42no—
210C2×C3×3−1+2#12011yescharacteristic
211C3⋊AGL(1,ℤ/9)—81no—
212C3×AGL(1,ℤ/9)—42no—
213C32×#41—92no—
214C32×#41—182no—
215C2×C32×D4—21no—
216C2×C32×D4—31no—
217C2×C32×D4—61no—
218C2×C32×D4—182no—
219C2×C32×D4—182no—
220C2×C32×D4D3211yescharacteristic
221C2×C32×D4C2×C3×D311yescharacteristic
222C2×#638—62no—
223C2×C4⋊(C3⋊D3)—31no—
224C2×C3×#67—64no—
225C2×C3×#67—62no—
226C2×C3×#67—62no—
227C2×C3×#67—182no—
228C2×C3×#67—184no—
229C2×C3×#67—182no—
230C3×#237—62no—
231C3×#237—62no—
232C3×#237—64no—
233C3×D3×D4—62no—
234C3×D3×D4—62no—
235C3×D3×D4—64no—
236C3×#235—32no—
237C3×#235—32no—
238C3×#235—62no—
239C2×C3×D12—91no—
240C2×C3×D12—91no—
241C2×C3×D12—181no—
242C32×M16—32no—
243C4×C3⋊Dic3—31no—
244C3×#215—182no—
245C3×#213—182no—
246C3×C4×Dic3—91no—
247C3×C4×Dic3—91no—
248C3×C4×Dic3—181no—
249C3×#208—32no—
250C3×#208C2×C3×D312yes—
251C3×D24—182no—
252C3×#204—182no—
253#3717—62no—
254#3714—62no—
255C2×D4×C9—21no—
256C2×D4×C9—21no—
257C2×D4×C9—41no—
258C2×D4×C9C2×C3×D311yescharacteristic
259C2×#611—22no—
260C2×#611—64no—
261C2×#611—62no—
262#3699—22no—
263D4×D9—22no—
264#3697C2×C3×D312yes—
265C2×D36—31no—
266C2×D36—61no—
267C9×M16—32no—
268C9×M16—62no—
269C4×Dic9—31no—
270C4×Dic9—61no—
271D72—62no—
272#3664—62no—
273C22×C33—22no—
274C22×C33—42no—
275C22×C33C2×D1211yescharacteristic
276C2×C3×C3⋊D3—122no—
277C2×C3×C3⋊D3—121no—
278C2×C32×D3—62no—
279C2×C32×D3—242no—
280C33×C4D3×D412yes—
281C3×C3⋊Dic3—62no—
282C32×Dic3—62no—
283C22×3−1+2—21no—
284C22×3−1+2—24no—
285C22×3−1+2—21no—
286C22×3−1+2—22no—
287C22×3−1+2—42no—
288C22×3−1+2—42no—
289C22×3−1+2—44no—
290C22×3−1+2—41no—
291C22×3−1+2—44no—
292C22×3−1+2—82no—
293C22×3−1+2—84no—
294C22×3−1+2C2×#6711yescharacteristic
295C22×C3×C9—21no—
296C22×C3×C9—22no—
297C22×C3×C9—42no—
298C22×C3×C9—42no—
299C22×C3×C9—82no—
300C22×C3×C9C2×C3×D411yescharacteristic
301C2×C3⋊D9—42no—
302C2×C3⋊D9—41no—
303C2×AGL(1,ℤ/9)—24no—
304C2×AGL(1,ℤ/9)—22no—
305C2×AGL(1,ℤ/9)—84no—
306C2×AGL(1,ℤ/9)—82no—
307C2×AGL(1,ℤ/9)—122no—
308C2×AGL(1,ℤ/9)—124no—
309C2×AGL(1,ℤ/9)—122no—
310C2×AGL(1,ℤ/9)—121no—
311C2×C3×D9—22no—
312C2×C3×D9—82no—
313C4×3−1+2—22no—
314C4×3−1+2—22no—
315C4×3−1+2—42no—
316C4×3−1+2C2×#6712yes—
317C3×C4×C9—22no—
318C3×C4×C9C2×C3×D412yes—
319C3⋊Dic9—22no—
3203−1+2⋊C4—24no—
3213−1+2⋊C4—22no—
3223−1+2⋊C4—64no—
3233−1+2⋊C4—62no—
324C3×Dic9—22no—
325C3×H(5,𝔽2)—91no—
326C3×H(5,𝔽2)—91no—
327C3×H(5,𝔽2)—181no—
328#1004—31no—
329C3×AGL(1,ℤ/8)—272no—
330C3×#127—271no—
331#949—92no—
332#940—91no—
333#940—91no—
334#940—181no—
335#908—92no—
336C3×#104—272no—
337C3×#100—31no—
338C3×#100—91no—
339#837—92no—
340#833AGL(1,ℤ/9)11yescharacteristic, complemented
341#825—92no—
342C3×3−1+2#45311yescharacteristic, complemented, Sylow
343C23×C32—22no—
344C23×C32—32no—
345C23×C32—62no—
346C23×C32—182no—
347C23×C32#62612yes—
348C23×C32C3×D1212yes—
349C22×C3⋊D3—61no—
350C22×C3×D3—62no—
351C22×C3×D3—64no—
352C22×C3×D3—62no—
353C22×C3×D3—181no—
354C22×C3×D3—182no—
355C22×C3×D3—181no—
356C32×Q8—92no—
357C32×D4—22no—
358C32×D4—24no—
359C32×D4—22no—
360C32×D4—62no—
361C32×D4—92no—
362C32×D4—122no—
363C32×D4—182no—
364C32×D4—184no—
365C2×C32×C4—21no—
366C2×C32×C4—31no—
367C2×C32×C4—61no—
368C2×C32×C4—182no—
369C2×C32×C4—182no—
370C2×C32×C4C2×D3211yescharacteristic
371C2×C32×C4C22×C3×D311yescharacteristic
372#638—124no—
373C2×C3⋊Dic3—61no—
374C4⋊(C3⋊D3)—62no—
375C3×#67—64no—
376C3×#67—64no—
377C3×#67—68no—
378C3×#67—64no—
379C3×#67—62no—
380C3×#67—62no—
381C3×#67—364no—
382C3×#67—364no—
383C3×#67—368no—
384C2×C3×Dic3—62no—
385C2×C3×Dic3—64no—
386C2×C3×Dic3—62no—
387C2×C3×Dic3—181no—
388C2×C3×Dic3—182no—
389C2×C3×Dic3—181no—
390C3×D12—32no—
391C3×D12—32no—
392C3×D12—62no—
393C3×D12—182no—
394C3×D12—182no—
395C3×D12—362no—
396C3×C4×D3—64no—
397C3×C4×D3—62no—
398C3×C4×D3—62no—
399C3×Dic6—32no—
400C3×Dic6—32no—
401C3×Dic6—62no—
402C23×C9—22no—
403C23×C9—22no—
404C23×C9—42no—
405C23×C9C3×#6712yes—
406C22×D9—22no—
407C22×D9—62no—
408C22×D9—61no—
409C32×C8—62no—
410C3×C3⋊C8—22no—
411C3×C3⋊C8—62no—
412D4×C9—22no—
413D4×C9—42no—
414D4×C9—42no—
415D4×C9—44no—
416C2×C4×C9—21no—
417C2×C4×C9—21no—
418C2×C4×C9—41no—
419C2×C4×C9C22×C3×D311yescharacteristic
420#611—24no—
421#611—22no—
422#611—124no—
423#611—128no—
424C2×Dic9—22no—
425C2×Dic9—62no—
426C2×Dic9—61no—
427D36—62no—
428D36—122no—
429D36C3×#6712yescomplemented
430C4×D9—22no—
431Dic18C3×#6712yescomplemented
432C8×C9—62no—
433C8×C9—122no—
434#453—271noSylow
435C2×C33—21no—
436C2×C33—42no—
437C2×C33#88211yescharacteristic
438C3×C3⋊D3—241no—
439C32×D3—122no—
440C2×3−1+2—22no—
441C2×3−1+2—21no—
442C2×3−1+2—21no—
443C2×3−1+2—21no—
444C2×3−1+2—41no—
445C2×3−1+2—41no—
446C2×3−1+2—42no—
447C2×3−1+2—44no—
448C2×3−1+2—42no—
449C2×3−1+2—82no—
450C2×3−1+2—84no—
451C2×3−1+2#95311yescharacteristic
452C2×C3×C9—21no—
453C2×C3×C9—21no—
454C2×C3×C9—41no—
455C2×C3×C9—42no—
456C2×C3×C9—82no—
457C2×C3×C9C3×#12011yescharacteristic
458C3⋊D9—81no—
459AGL(1,ℤ/9)—44no—
460AGL(1,ℤ/9)—42no—
461AGL(1,ℤ/9)—242no—
462AGL(1,ℤ/9)—241no—
463C3×D9—42no—
464C3×#41—92no—
465C3×#41—92no—
466C3×#41—182no—
467C3×#41—182no—
468C3×#41—182no—
469C3×#41—184no—
470C2×C3×D4—21no—
471C2×C3×D4—31no—
472C2×C3×D4—61no—
473C2×C3×D4—182no—
474C2×C3×D4—182no—
475C2×C3×D4—184no—
476C2×C3×D4—182no—
477C2×C3×D4—184no—
478C2×C3×D4—182no—
479C2×C3×D4—271no—
480C2×C3×D4—542no—
481C2×C3×D4C2×AGL(1,ℤ/9)11yescharacteristic
482C2×C3×D4C3×D3211yescharacteristic
483C2×#67—62no—
484C2×#67—184no—
485C2×#67—182no—
486C2×#67—182no—
487#237—62no—
488D3×D4—62no—
489#235—32no—
490C2×D12—91no—
491C2×D12—91no—
492C2×D12—181no—
493C3×SD16—542no—
494C3×D8—542no—
495C3×M16—32no—
496C3×M16—92no—
497C3×C42—271no—
498#215—182no—
499#213—182no—
500C4×Dic3—91no—
501C4×Dic3—91no—
502C4×Dic3—181no—
503#208C2×AGL(1,ℤ/9)12yescomplemented
504D24—182no—
505#204—182no—
506C22×C32—22no—
507C22×C32—24no—
508C22×C32—22no—
509C22×C32—21no—
510C22×C32—31no—
511C22×C32—42no—
512C22×C32—42no—
513C22×C32—61no—
514C22×C32—62no—
515C22×C32—82no—
516C22×C32—122no—
517C22×C32—122no—
518C22×C32—124no—
519C22×C32—182no—
520C22×C32—722no—
521C22×C32C2×#62611yescharacteristic
522C22×C32C2×C3×D1211yescharacteristic
523C2×C3⋊D3—122no—
524C2×C3⋊D3—121no—
525C2×C3×D3—64no—
526C2×C3×D3—62no—
527C2×C3×D3—62no—
528C2×C3×D3—242no—
529C2×C3×D3—244no—
530C2×C3×D3—242no—
531C2×C3×D3—362no—
532C2×C3×D3—361no—
533C2×C3×D3—362no—
534C2×C3×D3—362no—
535C2×C3×D3—364no—
536C2×C3×D3—361no—
537C32×C4—22no—
538C32×C4—32no—
539C32×C4—62no—
540C32×C4—182no—
541C32×C4D3×#6712yes—
542C32×C4C3×D3×D412yes—
543C3⋊Dic3—62no—
544C3×Dic3—64no—
545C3×Dic3—62no—
546C3×Dic3—62no—
547C3×Dic3—182no—
548C3×Dic3—182no—
549C3×Dic3—184no—
550C22×C9—22no—
551C22×C9—21no—
552C22×C9—21no—
553C22×C9—42no—
554C22×C9—42no—
555C22×C9—44no—
556C22×C9—42no—
557C22×C9—44no—
558C22×C9—41no—
559C22×C9—82no—
560C22×C9—84no—
561C22×C9C2×C3×#6711yescharacteristic
562C2×D9—22no—
563C2×D9—82no—
564C2×D9—122no—
565C2×D9—124no—
566C2×D9—122no—
567C2×D9—121no—
568C4×C9—22no—
569C4×C9—22no—
570C4×C9—42no—
571C4×C9C2×C3×#6712yes—
572Dic9—22no—
573Dic9—64no—
574Dic9—62no—
575H(5,𝔽2)—91no—
576AGL(1,ℤ/8)—272no—
577#127—271no—
578#104—272no—
579#100—31no—
580C33#474711yescharacteristic
5813−1+2—21no—
5823−1+2—21no—
5833−1+2—41no—
5843−1+2#524111yescharacteristic, complemented
585C3×C9—21no—
586C3×C9C3×#45311yescharacteristic, complemented
587C23×C3—22no—
588C23×C3—32no—
589C23×C3—62no—
590C23×C3—182no—
591C23×C3—182no—
592C23×C3—184no—
593C23×C3—541no—
594C23×C3C4⋊AGL(1,ℤ/9)12yes—
595C23×C3C3×#62612yes—
596C22×D3—62no—
597C22×D3—182no—
598C22×D3—181no—
599C22×D3—181no—
600C3×Q8—92no—
601C3×Q8—92no—
602C3×Q8—182no—
603C3×D4—22no—
604C3×D4—22no—
605C3×D4—42no—
606C3×D4—62no—
607C3×D4—64no—
608C3×D4—92no—
609C3×D4—92no—
610C3×D4—182no—
611C3×D4—184no—
612C3×D4—182no—
613C3×D4—184no—
614C3×D4—188no—
615C3×D4—184no—
616C3×D4—182no—
617C3×D4—542no—
618C3×D4—1084no—
619C2×C3×C4—21no—
620C2×C3×C4—31no—
621C2×C3×C4—61no—
622C2×C3×C4—182no—
623C2×C3×C4—184no—
624C2×C3×C4—182no—
625C2×C3×C4—182no—
626C2×C3×C4—184no—
627C2×C3×C4—182no—
628C2×C3×C4—541no—
629C2×C3×C4C22×AGL(1,ℤ/9)11yescharacteristic
630C2×C3×C4C2×C3×D3211yescharacteristic
631#67—64no—
632#67—62no—
633#67—364no—
634#67—364no—
635#67—368no—
636C2×Dic3—62no—
637C2×Dic3—182no—
638C2×Dic3—181no—
639C2×Dic3—181no—
640D12—32no—
641D12—182no—
642D12—182no—
643D12—362no—
644C4×D3—62no—
645Dic6—32no—
646C3×C8—62no—
647C3×C8—182no—
648C3⋊C8—22no—
649C2×C32—21no—
650C2×C32—21no—
651C2×C32—21no—
652C2×C32—31no—
653C2×C32—41no—
654C2×C32—42no—
655C2×C32—44no—
656C2×C32—42no—
657C2×C32—61no—
658C2×C32—61no—
659C2×C32—62no—
660C2×C32—122no—
661C2×C32—242no—
662C2×C32—362no—
663C2×C32#6397711yescharacteristic
664C2×C32C3×#88211yescharacteristic
665C3⋊D3—241no—
666C3×D3—124no—
667C3×D3—122no—
668C3×D3—122no—
669C3×D3—721no—
670C3×D3—722no—
671C3×D3—721no—
672C2×C9—22no—
673C2×C9—21no—
674C2×C9—21no—
675C2×C9—21no—
676C2×C9—41no—
677C2×C9—42no—
678C2×C9—42no—
679C2×C9—41no—
680C2×C9—82no—
681C2×C9—82no—
682C2×C9—84no—
683C2×C9C3×#95311yescharacteristic
684D9—42no—
685D9—242no—
686D9—241no—
687#41—92no—
688#41—182no—
689C2×D4—182no—
690C2×D4—182no—
691C2×D4—271no—
692C2×D4—542no—
693C2×D4D3×AGL(1,ℤ/9)11yescharacteristic
694SD16—542no—
695D8—542no—
696M16—32no—
697C42—271no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—21no—
701C22×C3—31no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—44no—
706C22×C3—62no—
707C22×C3—64no—
708C22×C3—61no—
709C22×C3—122no—
710C22×C3—182no—
711C22×C3—184no—
712C22×C3—182no—
713C22×C3—242no—
714C22×C3—722no—
715C22×C3—722no—
716C22×C3—724no—
717C22×C3—1081no—
718C22×C3—1082no—
719C22×C3C2×C4⋊AGL(1,ℤ/9)11yescharacteristic
720C22×C3C2×C3×#62611yescharacteristic
721C2×D3—62no—
722C2×D3—242no—
723C2×D3—362no—
724C2×D3—362no—
725C2×D3—364no—
726C2×D3—362no—
727C2×D3—361no—
728C2×D3—361no—
729C3×C4—22no—
730C3×C4—32no—
731C3×C4—62no—
732C3×C4—182no—
733C3×C4—184no—
734C3×C4—182no—
735C3×C4—542no—
736C3×C4D4×AGL(1,ℤ/9)12yes—
737C3×C4C3×D3×#6712yes—
738Dic3—62no—
739Dic3—182no—
740Dic3—184no—
741Dic3—182no—
742C32—21no—
743C32—31no—
744C32—61no—
745C32#1059151011yescharacteristic
746C32C3×#474711yescharacteristic
747C9—21no—
748C9—21no—
749C9—41no—
750C9C3×#524111yescharacteristic, complemented
751C23—182no—
752C23—541no—
753C23#6192⋊C312yes—
754Q8—92no—
755D4—22no—
756D4—92no—
757D4—184no—
758D4—182no—
759D4—542no—
760D4—1084no—
761C2×C4—182no—
762C2×C4—182no—
763C2×C4—541no—
764C2×C4C2×D3×AGL(1,ℤ/9)11yescharacteristic
765C8—62no—
766C2×C3—22no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—31no—
771C2×C3—42no—
772C2×C3—42no—
773C2×C3—61no—
774C2×C3—61no—
775C2×C3—82no—
776C2×C3—121no—
777C2×C3—122no—
778C2×C3—124no—
779C2×C3—362no—
780C2×C3—364no—
781C2×C3—362no—
782C2×C3—2161no—
783C2×C3#63444⋊C311yescharacteristic
784C2×C3C3×#6397711yescharacteristic
785D3—122no—
786D3—722no—
787D3—721no—
788D3—721no—
789C22—22no—
790C22—42no—
791C22—182no—
792C22—722no—
793C22—1082no—
794C22—1081no—
795C22C2×#6192⋊C311yescharacteristic
796C4—182no—
797C4—542no—
798C4#67×AGL(1,ℤ/9)12yes—
799C3—21no—
800C3—31no—
801C3—61no—
802C3#10588427⋊C311yescharacteristic, complemented
803C3C3×#1059151011yescharacteristic
804C2—21no—
805C2—42no—
806C2—362no—
807C2—2161no—
808C2#7222003111yescharacteristic
subgroupG/H
centerC2#72220031
commutator, cosocleC2×C3×C4×C9C23×C3
FrattiniC2×C3×C4C2×C3×D32
FittingC2×C3×D4×3−1+2C22
socleC2×C32C3×#882
hypercenterC2×D4D3×AGL(1,ℤ/9)
hypocenterC3×C9C3×#453
LCSG ▷ C2×C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. 3−1+2×#833C2semidirect
2. #72219967C2semidirect
3. #72219947C2semidirect
4. C3×#63710⋊C3C2semidirect
5. #72219923C2semidirect
8. #13140391C3semidirect
11. C2×C4⋊(C3⋊AGL(1,ℤ/9))C22semidirect
16. C4×C3⋊(3−1+2⋊C4)C22semidirect
17. 3−1+2×#208C22semidirect
24. #63710⋊C3D3semidirect
25. C3×#63710C2×C3semidirect
28. #11721840C2×C3semidirect
32. #11720873C2×C3semidirect
35. C9×#833C2×C3semidirect
37. #11720291C2×C3semidirect
49. C3×C4⋊AGL(1,ℤ/9)D4semidirect
51. C3×3−1+2⋊Q8D4semidirect
75. C2×C4⋊(C3⋊D9)C22×C3semidirect
93. C4×C3⋊Dic9C22×C3semidirect
97. C9×#208C22×C3semidirect
123. #63710C3×D3semidirect
194. C4⋊AGL(1,ℤ/9)#67semidirect
198. 3−1+2⋊Q8#67semidirect
199. C3×D36C3×D4semidirect
201. C3×Dic18C3×D4semidirect
340. #833AGL(1,ℤ/9)semidirect
342. C3×3−1+2#453semidirect
429. D36C3×#67semidirect
431. Dic18C3×#67semidirect
503. #208C2×AGL(1,ℤ/9)semidirect
584. 3−1+2#5241semidirect
586. C3×C9C3×#453semidirect
750. C9C3×#5241semidirect
802. C3#10588427⋊C3semidirect

Maximal subgroups

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

subgroupindex
3−1+2×#8332
#722199672
#722199472
C3×#63710⋊C32
#722199232
C3×#105915103
#10588427⋊C33
#131403913