Finite Group Databasebeta

← #72220042

Subgroups — #72220042

Order 5184.

1448 conjugacy classes of subgroups.

The subgroup lattice has 1087 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72219981C211yesmaximal, characteristic, complemented
2#72219968C211yesmaximal, characteristic, complemented
3#72219967C211yesmaximal, characteristic, complemented
4#72219953C211yesmaximal, characteristic, complemented
5#72219947C211yesmaximal, characteristic, complemented
63−1+2×#932C211yesmaximal, characteristic, complemented
7C3×#63495⋊C3C211yesmaximal, characteristic, complemented
8C3×#10591522—31nomaximal
9#10588879⋊C3—31nomaximal
10#13140511C311yesmaximal, characteristic, complemented
11C2×C3×D4×3−1+2C2211yescharacteristic, complemented
12C2×#10619980—22no—
13C2×C4⋊(C3⋊AGL(1,ℤ/9))C2211yescharacteristic
143−1+2×#235C2211yescharacteristic
15C3×#3697⋊C3C2211yescharacteristic
16#88668⋊C3—22no—
17D3×C4⋊AGL(1,ℤ/9)—21no—
18D12×AGL(1,ℤ/9)—21no—
19#88642⋊C3—21no—
20#88635⋊C3—21no—
21C4×C3⋊(3−1+2⋊C4)C2211yescharacteristic, complemented
223−1+2×#214—21no—
233−1+2×#213—21no—
24C3×#3673⋊C3—21no—
25C3×#3672⋊C3—21no—
263−1+2×#208C2211yescharacteristic, complemented
27C3×#3667⋊C3C2211yescharacteristic, complemented
28C3×#64308—31no—
29C3×#64149—31no—
30C32×#932—31no—
31C32×#932D311yescharacteristic
32#11722641—31no—
33#11722478C2×C311yescharacteristic, complemented
34C3×#63568—31no—
35C3×#63568—31no—
36C3×#63559—31no—
373−1+2×AGL(1,ℤ/8)—31no—
38#11721840C2×C311yescharacteristic, complemented
39#63502⋊C3—31no—
40#63502⋊C3—61no—
41#63495⋊C3—21no—
42#63495⋊C3D311yescharacteristic, complemented
43C9×#932—21no—
44C9×#932C2×C311yescharacteristic, complemented
45C3×#63495C2×C311yescharacteristic, complemented
46#63396⋊C3—31no—
47#63384⋊C3—31no—
48#63383⋊C3—31no—
49#11720300C2×C311yescharacteristic, complemented
50#11720291C2×C311yescharacteristic, complemented
51#11720288C2×C311yescharacteristic, complemented
52C23×C3×3−1+2—21no—
53C22×C3⋊AGL(1,ℤ/9)D412yes—
54C2×D3×AGL(1,ℤ/9)—22no—
55C3×D4×3−1+2—21no—
56C3×D4×3−1+2—21no—
57C2×C3×C4×3−1+2C2311yescharacteristic
58#10619980—44no—
59C2×C3⋊(3−1+2⋊C4)—21no—
60C4⋊(C3⋊AGL(1,ℤ/9))—21no—
61C4⋊(C3⋊AGL(1,ℤ/9))—21no—
62#67×3−1+2—21no—
63C3×#611⋊C3—21no—
64D12×3−1+2D411yescharacteristic, complemented
65C4×D3×3−1+2—21no—
66C3×C4⋊AGL(1,ℤ/9)D411yescharacteristic, complemented
67C3×C4×AGL(1,ℤ/9)—21no—
68Dic6×3−1+2D411yescharacteristic, complemented
69C3×3−1+2⋊Q8D411yescharacteristic, complemented
70#6195⋊C3—22no—
71#6192⋊C3—22no—
72(C3⋊AGL(1,ℤ/9))⋊C4—22no—
73C3⋊C8×3−1+2—21no—
74C3×3−1+2⋊C8—21no—
75C3×#5198—91no—
76C3×#5198—91no—
77#10591522—31no—
78#10588879—31no—
79C2×C33×D4C2×D311yescharacteristic
80C2×C3×#638—62no—
81C2×C3×C4⋊(C3⋊D3)—31no—
82C32×#235—31no—
83C32×#235C2×D311yescharacteristic
84C3×#3811—62no—
85C3×D3×D12—61no—
86C3×D3×D12—61no—
87C3×#3799—61no—
88C3×#3799—61no—
89C3×C4×C3⋊Dic3—31no—
90C32×#214—21no—
91C32×#214—61no—
92C32×#213—21no—
93C32×#213—61no—
94C32×#208—31no—
95C32×#208C2×D311yescharacteristic
96#41×3−1+2—31no—
97C2×D4×3−1+2—21no—
98C2×D4×3−1+2—21no—
99C2×D4×3−1+2—41no—
100C2×D4×3−1+2C2×D311yescharacteristic, complemented
101C2×C3×D4×C9—21no—
102C2×C3×D4×C9C22×C311yescharacteristic, complemented
103C2×#6233—22no—
104C2×C4⋊(C3⋊D9)C22×C311yescharacteristic
105C2×#611⋊C3—62no—
106C2×#611⋊C3—64no—
107#88724—61no—
108D4×AGL(1,ℤ/9)—61no—
109D4×AGL(1,ℤ/9)—62no—
110#3697⋊C3—21no—
111#3697⋊C3—61no—
112#3697⋊C3C2×D311yescharacteristic
113C2×C4⋊AGL(1,ℤ/9)—31no—
114C2×C4⋊AGL(1,ℤ/9)—61no—
115C2×C4⋊AGL(1,ℤ/9)—61no—
116C9×#235—21no—
117C9×#235C22×C311yescharacteristic
118C3×#3697C22×C311yescharacteristic
119#88668—22no—
120D9×D12—21no—
121D3×D36—21no—
122#88642—21no—
123#88635—21no—
124SD16×3−1+2—61no—
125D8×3−1+2—61no—
126M16×3−1+2—31no—
127C4×C3⋊Dic9C22×C311yescharacteristic, complemented
128#3673⋊C3—22no—
129#3673⋊C3—21no—
130#3672⋊C3—22no—
131#3672⋊C3—21no—
132C9×#214—22no—
133C9×#214—21no—
134C9×#213—22no—
135C9×#213—21no—
136C3×#3673—21no—
137C3×#3672—21no—
138C4×3−1+2⋊C4—31no—
139C4×3−1+2⋊C4—61no—
140#3667⋊C3—21no—
141#3667⋊C3C2×D311yescharacteristic, complemented
142C9×#208—21no—
143C9×#208C22×C311yescharacteristic, complemented
144C3×#3667C22×C311yescharacteristic, complemented
145C22×C3×3−1+2—41no—
146C22×C3×3−1+2—42no—
147C22×C3×3−1+2C2×D411yescharacteristic
148C2×C3⋊AGL(1,ℤ/9)—22no—
149C2×C3⋊AGL(1,ℤ/9)—42no—
150C2×D3×3−1+2—21no—
151C2×C3×AGL(1,ℤ/9)—21no—
152D3×AGL(1,ℤ/9)—82no—
153C3×C4×3−1+2C2×D411yescharacteristic
154C3×C4×3−1+2C2×D411yescharacteristic
155C3⋊(3−1+2⋊C4)—22no—
156Dic3×3−1+2—21no—
157C3×3−1+2⋊C4—21no—
158C3×#1009—91no—
159C3×#1009—91no—
160#64308—31no—
161C32×AGL(1,ℤ/8)—31no—
162C32×AGL(1,ℤ/8)—91no—
163#64149—31no—
164C3×#940—91no—
165C3×#940—91no—
166C3×#940—181no—
167C3×#932—31no—
168C3×#932—31no—
169C3×#932—31no—
170C3×#932—61no—
171C3×#932C3×D311yescharacteristic
172#63715—31no—
173C3×#837—91no—
174C3×#837—91no—
175C3×#825—91no—
176C3×#825—91no—
177C3×#823—91no—
178C3×#823—91no—
179#63568—31no—
180#63568—31no—
181#63559—31no—
182C9×AGL(1,ℤ/8)—31no—
183C9×AGL(1,ℤ/8)—61no—
184#63502—31no—
185#63502—61no—
186#63495C3×D311yescharacteristic, complemented
187#63396—31no—
188#63384—31no—
189#63383—31no—
190C23×C33—21no—
191C22×C3×C3⋊D3—32no—
192C2×C3×D32—62no—
193C33×D4—21no—
194C33×D4—21no—
195C2×C33×C4C22×D311yescharacteristic
196C3×#638—124no—
197C2×C3×C3⋊Dic3—61no—
198C3×C4⋊(C3⋊D3)—61no—
199C3×C4⋊(C3⋊D3)—61no—
200C32×#67—21no—
201C32×#67—61no—
202C32×D12—31no—
203C32×D12#6711yescharacteristic
204C32×C4×D3—21no—
205C32×C4×D3—61no—
206C32×Dic6—31no—
207C32×Dic6#6711yescharacteristic
208C3×#626—62no—
209C3×#626—62no—
210C3×#624—62no—
211C23×3−1+2—22no—
212C23×3−1+2—21no—
213C23×3−1+2—41no—
214C23×3−1+2—42no—
215C23×C3×C9—21no—
216C23×C3×C9—41no—
217C22×C3⋊D9C3×D412yes—
218C22×AGL(1,ℤ/9)—32no—
219C22×AGL(1,ℤ/9)—62no—
220C22×AGL(1,ℤ/9)—62no—
221C2×D3×D9—22no—
222C32×C3⋊C8—21no—
223C32×C3⋊C8—61no—
224Q8×3−1+2—31no—
225D4×3−1+2—22no—
226D4×3−1+2—21no—
227D4×3−1+2—21no—
228D4×3−1+2—31no—
229D4×3−1+2—41no—
230D4×3−1+2—41no—
231D4×3−1+2—41no—
232D4×3−1+2—42no—
233D4×3−1+2—42no—
234D4×3−1+2—61no—
235C3×D4×C9—22no—
236C3×D4×C9—21no—
237C3×D4×C9—21no—
238C3×D4×C9—41no—
239C2×C4×3−1+2—21no—
240C2×C4×3−1+2—21no—
241C2×C4×3−1+2—41no—
242C2×C4×3−1+2—61no—
243C2×C4×3−1+2C22×D311yescharacteristic
244C2×C3×C4×C9—21no—
245C2×C3×C4×C9C23×C311yescharacteristic
246#6233—44no—
247C2×C3⋊Dic9—21no—
248C4⋊(C3⋊D9)—21no—
249C4⋊(C3⋊D9)—21no—
250#611⋊C3—21no—
251#611⋊C3—41no—
252#611⋊C3—62no—
253#611⋊C3—124no—
254#611⋊C3—128no—
255C2×3−1+2⋊C4—62no—
256C2×3−1+2⋊C4—61no—
257C9×#67—21no—
258C9×#67—41no—
259C3×#611—21no—
260C4⋊AGL(1,ℤ/9)—21no—
261C4⋊AGL(1,ℤ/9)—62no—
262C4⋊AGL(1,ℤ/9)—61no—
263C4⋊AGL(1,ℤ/9)—61no—
264C4⋊AGL(1,ℤ/9)—121no—
265C4⋊AGL(1,ℤ/9)—121no—
266C4⋊AGL(1,ℤ/9)#6711yescharacteristic, complemented
267C4×AGL(1,ℤ/9)—21no—
268C4×AGL(1,ℤ/9)—41no—
269C4×AGL(1,ℤ/9)—62no—
2703−1+2⋊Q8—21no—
2713−1+2⋊Q8#6711yescharacteristic, complemented
272C9×D12—21no—
273C9×D12C3×D411yescharacteristic, complemented
274C4×D3×C9—21no—
275C4×D3×C9—41no—
276C3×D36C3×D411yescharacteristic, complemented
277C3×C4×D9—21no—
278C9×Dic6—21no—
279C9×Dic6C3×D411yescharacteristic, complemented
280C3×Dic18C3×D411yescharacteristic, complemented
281#6195—22no—
282#6192—22no—
283(C3⋊D9)⋊C4—22no—
284C8×3−1+2—61no—
2853−1+2⋊C8—22no—
2863−1+2⋊C8—21no—
287C9×C3⋊C8—22no—
288C9×C3⋊C8—21no—
289C3×C9⋊C8—21no—
290C3×#453—271no—
291#5198—91no—
292#5198—91no—
293C2×C3×3−1+2—21no—
294C2×C3×3−1+2—81no—
295C2×C3×3−1+2#12011yescharacteristic
296C3⋊AGL(1,ℤ/9)—42no—
297D3×3−1+2—41no—
298C3×AGL(1,ℤ/9)—41no—
299C32×#41—31no—
300C32×#41—91no—
301C2×C32×D4—21no—
302C2×C32×D4—31no—
303C2×C32×D4—61no—
304C2×C32×D4D3211yescharacteristic
305C2×C32×D4C2×C3×D311yescharacteristic
306C2×#638—62no—
307C2×C4⋊(C3⋊D3)—31no—
308C2×C3×#67—182no—
309C2×C3×#67—182no—
310C2×C3×#67—184no—
311C3×#239—181no—
312C3×#239—181no—
313C3×D3×D4—181no—
314C3×D3×D4—181no—
315C3×D3×D4—182no—
316C3×D3×D4—182no—
317C3×#235—31no—
318C3×#235—31no—
319C3×#235—31no—
320C3×#235—61no—
321C3×#235—181no—
322C3×#235—181no—
323C3×#235C2×C3×D311yescharacteristic
324C2×C3×D12—91no—
325C2×C3×D12—91no—
326C2×C3×D12—181no—
327C2×C3×D12—181no—
328C2×C3×D12—181no—
329#3811—62no—
330D3×D12—61no—
331D3×D12—61no—
332#3799—61no—
333#3799—61no—
334C32×SD16—61no—
335C32×SD16—181no—
336C32×D8—61no—
337C32×D8—181no—
338C32×M16—31no—
339C32×M16—91no—
340C4×C3⋊Dic3—31no—
341C3×#214—21no—
342C3×#214—61no—
343C3×#214—61no—
344C3×#214—61no—
345C3×#214—62no—
346C3×#213—21no—
347C3×#213—61no—
348C3×#213—61no—
349C3×#213—61no—
350C3×#213—62no—
351C3×C4×Dic3—91no—
352C3×C4×Dic3—91no—
353C3×C4×Dic3—181no—
354C3×#208—31no—
355C3×#208—31no—
356C3×#208—31no—
357C3×#208—61no—
358C3×#208C2×C3×D311yescharacteristic
359C9×#41—31no—
360C9×#41—61no—
361C2×D4×C9—21no—
362C2×D4×C9—21no—
363C2×D4×C9—41no—
364C2×D4×C9C2×C3×D311yescharacteristic, complemented
365C2×#611—62no—
366C2×#611—64no—
367#3701—61no—
368D4×D9—61no—
369D4×D9—62no—
370#3697—61no—
371#3697C2×C3×D311yescharacteristic
372C2×D36—31no—
373C2×D36—61no—
374C2×D36—61no—
375C9×SD16—61no—
376C9×SD16—62no—
377C9×D8—61no—
378C9×D8—62no—
379C9×M16—31no—
380C9×M16—61no—
381#3673—21no—
382#3672—21no—
383C4×Dic9—31no—
384C4×Dic9—61no—
385#3667C2×C3×D311yescharacteristic, complemented
386C22×C33—42no—
387C22×C33—41no—
388C22×C33D3×D411yescharacteristic
389C2×C3×C3⋊D3—62no—
390C2×C3×C3⋊D3—122no—
391C2×C32×D3—21no—
392C2×C32×D3—61no—
393C3×D32—242no—
394C33×C4D3×D411yescharacteristic
395C33×C4C2×#6711yescharacteristic
396C3×C3⋊Dic3—62no—
397C32×Dic3—21no—
398C32×Dic3—61no—
399C22×3−1+2—21no—
400C22×3−1+2—21no—
401C22×3−1+2—42no—
402C22×3−1+2—42no—
403C22×3−1+2—44no—
404C22×3−1+2—42no—
405C22×3−1+2—41no—
406C22×3−1+2—44no—
407C22×3−1+2—41no—
408C22×3−1+2—61no—
409C22×3−1+2—82no—
410C22×3−1+2—84no—
411C22×3−1+2D3×D411yescharacteristic
412C22×C3×C9—21no—
413C22×C3×C9—42no—
414C22×C3×C9—42no—
415C22×C3×C9—41no—
416C22×C3×C9—82no—
417C22×C3×C9C2×C3×D411yescharacteristic
418C2×C3⋊D9—22no—
419C2×C3⋊D9—42no—
420C2×AGL(1,ℤ/9)—21no—
421C2×AGL(1,ℤ/9)—41no—
422C2×AGL(1,ℤ/9)—62no—
423C2×AGL(1,ℤ/9)—122no—
424C2×AGL(1,ℤ/9)—122no—
425C2×AGL(1,ℤ/9)—124no—
426C2×AGL(1,ℤ/9)—242no—
427C2×D3×C9—21no—
428C2×D3×C9—41no—
429C2×C3×D9—21no—
430D3×D9—82no—
431C4×3−1+2—21no—
432C4×3−1+2—21no—
433C4×3−1+2—21no—
434C4×3−1+2—21no—
435C4×3−1+2—41no—
436C4×3−1+2—41no—
437C4×3−1+2—61no—
438C4×3−1+2D3×D411yescharacteristic
439C4×3−1+2C2×#6711yescharacteristic
440C3×C4×C9—21no—
441C3×C4×C9—21no—
442C3×C4×C9C2×C3×D411yescharacteristic
443C3×C4×C9C2×C3×D411yescharacteristic
444C3⋊Dic9—22no—
4453−1+2⋊C4—21no—
4463−1+2⋊C4—41no—
4473−1+2⋊C4—64no—
4483−1+2⋊C4—62no—
449C9×Dic3—21no—
450C9×Dic3—41no—
451C3×Dic9—21no—
452C3×H(5,𝔽2)—271no—
453#1009—91no—
454#1009—91no—
455C3×AGL(1,ℤ/8)—31no—
456C3×AGL(1,ℤ/8)—91no—
457C3×AGL(1,ℤ/8)—91no—
458C3×AGL(1,ℤ/8)—91no—
459C3×AGL(1,ℤ/8)—181no—
460C3×#127—271no—
461#940—91no—
462#940—91no—
463#940—181no—
464#932—31no—
465#932AGL(1,ℤ/9)11yescharacteristic, complemented
466C3×#104—271no—
467C3×#104—271no—
468C3×#100—271no—
469#837—91no—
470#837—91no—
471#825—91no—
472#825—91no—
473#823—91no—
474#823—91no—
475C3×3−1+2#45311yescharacteristic, complemented, Sylow
476C23×C32—21no—
477C23×C32—21no—
478C23×C32—41no—
479C23×C32—61no—
480C23×C32—62no—
481C22×C3⋊D3—32no—
482C22×C3×D3—92no—
483C22×C3×D3—92no—
484C22×C3×D3—182no—
485C22×C3×D3—182no—
486C22×C3×D3—182no—
487C2×D32—62no—
488C32×Q8—31no—
489C32×Q8—91no—
490C32×D4—21no—
491C32×D4—21no—
492C32×D4—22no—
493C32×D4—21no—
494C32×D4—21no—
495C32×D4—31no—
496C32×D4—41no—
497C32×D4—61no—
498C32×D4—61no—
499C32×D4—61no—
500C32×D4—91no—
501C32×D4—121no—
502C32×D4—121no—
503C32×D4—181no—
504C2×C32×C4—21no—
505C2×C32×C4—31no—
506C2×C32×C4—61no—
507C2×C32×C4—61no—
508C2×C32×C4—181no—
509C2×C32×C4C2×D3211yescharacteristic
510C2×C32×C4C22×C3×D311yescharacteristic
511#638—124no—
512C2×C3⋊Dic3—61no—
513C4⋊(C3⋊D3)—61no—
514C4⋊(C3⋊D3)—61no—
515C3×#67—21no—
516C3×#67—61no—
517C3×#67—61no—
518C3×#67—61no—
519C3×#67—121no—
520C3×#67—182no—
521C3×#67—182no—
522C3×#67—364no—
523C3×#67—364no—
524C3×#67—368no—
525C2×C3×Dic3—181no—
526C2×C3×Dic3—182no—
527C2×C3×Dic3—181no—
528C3×D12—31no—
529C3×D12—31no—
530C3×D12—31no—
531C3×D12—61no—
532C3×D12—181no—
533C3×D12—181no—
534C3×D12—182no—
535C3×D12—182no—
536C3×D12—181no—
537C3×D12—181no—
538C3×D12—361no—
539C3×D12—361no—
540C3×D12C3×#6711yescharacteristic
541C3×C4×D3—21no—
542C3×C4×D3—61no—
543C3×C4×D3—61no—
544C3×C4×D3—61no—
545C3×C4×D3—121no—
546C3×C4×D3—182no—
547C3×C4×D3—182no—
548C3×Dic6—31no—
549C3×Dic6—31no—
550C3×Dic6—31no—
551C3×Dic6—61no—
552C3×Dic6C3×#6711yescharacteristic
553#626—62no—
554#626—62no—
555#624—62no—
556C23×C9—22no—
557C23×C9—21no—
558C23×C9—41no—
559C23×C9—42no—
560C22×D9—32no—
561C22×D9—62no—
562C22×D9—62no—
563C32×C8—61no—
564C32×C8—181no—
565C3×C3⋊C8—21no—
566C3×C3⋊C8—61no—
567C3×C3⋊C8—62no—
568C3×C3⋊C8—61no—
569C3×C3⋊C8—61no—
570Q8×C9—31no—
571Q8×C9—61no—
572D4×C9—22no—
573D4×C9—21no—
574D4×C9—21no—
575D4×C9—31no—
576D4×C9—41no—
577D4×C9—41no—
578D4×C9—41no—
579D4×C9—42no—
580D4×C9—42no—
581D4×C9—61no—
582D4×C9—61no—
583D4×C9—121no—
584C2×C4×C9—21no—
585C2×C4×C9—21no—
586C2×C4×C9—41no—
587C2×C4×C9—61no—
588C2×C4×C9—121no—
589C2×C4×C9C22×C3×D311yescharacteristic
590#611—21no—
591#611—62no—
592#611—124no—
593#611—128no—
594C2×Dic9—62no—
595C2×Dic9—61no—
596D36—62no—
597D36—61no—
598D36—61no—
599D36—121no—
600D36—121no—
601D36C3×#6711yescharacteristic, complemented
602C4×D9—21no—
603C4×D9—62no—
604Dic18C3×#6711yescharacteristic, complemented
605C8×C9—62no—
606C8×C9—61no—
607C9⋊C8—21no—
608#453—271noSylow
609C2×C33—21no—
610C2×C33—81no—
611C2×C33#93711yescharacteristic
612C3×C3⋊D3—122no—
613C32×D3—41no—
614C32×D3—121no—
615C2×3−1+2—22no—
616C2×3−1+2—21no—
617C2×3−1+2—21no—
618C2×3−1+2—21no—
619C2×3−1+2—41no—
620C2×3−1+2—41no—
621C2×3−1+2—42no—
622C2×3−1+2—82no—
623C2×3−1+2—82no—
624C2×3−1+2—84no—
625C2×3−1+2—81no—
626C2×3−1+2—121no—
627C2×3−1+2#93711yescharacteristic
628C2×C3×C9—21no—
629C2×C3×C9—21no—
630C2×C3×C9—41no—
631C2×C3×C9—82no—
632C2×C3×C9—81no—
633C2×C3×C9C3×#12011yescharacteristic
634C3⋊D9—42no—
635AGL(1,ℤ/9)—41no—
636AGL(1,ℤ/9)—81no—
637AGL(1,ℤ/9)—122no—
638AGL(1,ℤ/9)—242no—
639D3×C9—41no—
640D3×C9—81no—
641C3×D9—41no—
642C3×#41—31no—
643C3×#41—91no—
644C3×#41—91no—
645C3×#41—91no—
646C3×#41—181no—
647C3×#41—541no—
648C3×#41—541no—
649C2×C3×D4—21no—
650C2×C3×D4—31no—
651C2×C3×D4—61no—
652C2×C3×D4—271no—
653C2×C3×D4—541no—
654C2×C3×D4—541no—
655C2×C3×D4—542no—
656C2×C3×D4—542no—
657C2×C3×D4C2×AGL(1,ℤ/9)11yescharacteristic, complemented
658C2×C3×D4C3×D3211yescharacteristic
659C2×#67—182no—
660C2×#67—182no—
661C2×#67—184no—
662#239—181no—
663#239—181no—
664D3×D4—181no—
665D3×D4—181no—
666D3×D4—182no—
667D3×D4—182no—
668#235—31no—
669#235—181no—
670#235—181no—
671#235C2×AGL(1,ℤ/9)11yescharacteristic
672C2×D12—91no—
673C2×D12—91no—
674C2×D12—181no—
675C2×D12—181no—
676C2×D12—181no—
677C3×SD16—61no—
678C3×SD16—181no—
679C3×SD16—181no—
680C3×SD16—181no—
681C3×SD16—182no—
682C3×D8—61no—
683C3×D8—181no—
684C3×D8—181no—
685C3×D8—181no—
686C3×D8—182no—
687C3×M16—31no—
688C3×M16—91no—
689C3×M16—91no—
690C3×M16—91no—
691C3×M16—181no—
692C3×C42—271no—
693#214—21no—
694#214—61no—
695#213—21no—
696#213—61no—
697C4×Dic3—91no—
698C4×Dic3—91no—
699C4×Dic3—181no—
700#208—31no—
701#208C2×AGL(1,ℤ/9)11yescharacteristic, complemented
702C22×C32—21no—
703C22×C32—31no—
704C22×C32—42no—
705C22×C32—41no—
706C22×C32—42no—
707C22×C32—42no—
708C22×C32—41no—
709C22×C32—61no—
710C22×C32—61no—
711C22×C32—82no—
712C22×C32—121no—
713C22×C32—122no—
714C22×C32—122no—
715C22×C32—124no—
716C22×C32—181no—
717C22×C32#381111yescharacteristic
718C22×C32C3×D3×D411yescharacteristic
719C2×C3⋊D3—62no—
720C2×C3⋊D3—122no—
721C2×C3×D3—21no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—121no—
726C2×C3×D3—182no—
727C2×C3×D3—182no—
728C2×C3×D3—362no—
729C2×C3×D3—362no—
730C2×C3×D3—362no—
731C2×C3×D3—364no—
732C2×C3×D3—722no—
733C2×C3×D3—722no—
734D32—242no—
735C32×C4—21no—
736C32×C4—21no—
737C32×C4—31no—
738C32×C4—31no—
739C32×C4—61no—
740C32×C4—61no—
741C32×C4—61no—
742C32×C4—181no—
743C32×C4D3×#6711yescharacteristic
744C32×C4D3×#6711yescharacteristic
745C32×C4C3×D3×D411yescharacteristic
746C32×C4C2×C3×#6711yescharacteristic
747C3⋊Dic3—62no—
748C3×Dic3—21no—
749C3×Dic3—61no—
750C3×Dic3—61no—
751C3×Dic3—61no—
752C3×Dic3—121no—
753C3×Dic3—182no—
754C3×Dic3—182no—
755C3×Dic3—184no—
756C22×C9—21no—
757C22×C9—21no—
758C22×C9—42no—
759C22×C9—42no—
760C22×C9—44no—
761C22×C9—42no—
762C22×C9—44no—
763C22×C9—41no—
764C22×C9—41no—
765C22×C9—61no—
766C22×C9—82no—
767C22×C9—84no—
768C22×C9—121no—
769C22×C9C3×D3×D411yescharacteristic
770C2×D9—21no—
771C2×D9—62no—
772C2×D9—122no—
773C2×D9—122no—
774C2×D9—124no—
775C2×D9—242no—
776C4×C9—21no—
777C4×C9—21no—
778C4×C9—21no—
779C4×C9—21no—
780C4×C9—41no—
781C4×C9—41no—
782C4×C9—61no—
783C4×C9—121no—
784C4×C9C3×D3×D411yescharacteristic
785C4×C9C2×C3×#6711yescharacteristic
786Dic9—21no—
787Dic9—64no—
788Dic9—62no—
789H(5,𝔽2)—271no—
790AGL(1,ℤ/8)—31no—
791AGL(1,ℤ/8)—91no—
792#127—271no—
793#104—271no—
794#104—271no—
795#100—271no—
796C33#519811yescharacteristic
7973−1+2—21no—
7983−1+2—21no—
7993−1+2—41no—
8003−1+2#519811yescharacteristic, complemented
801C3×C9—21no—
802C3×C9C3×#45311yescharacteristic, complemented
803C23×C3—22no—
804C23×C3—21no—
805C23×C3—21no—
806C23×C3—61no—
807C23×C3—121no—
808C23×C3—272no—
809C23×C3—542no—
810C22×D3—92no—
811C22×D3—92no—
812C22×D3—182no—
813C22×D3—182no—
814C22×D3—182no—
815C3×Q8—31no—
816C3×Q8—91no—
817C3×Q8—91no—
818C3×Q8—91no—
819C3×Q8—181no—
820C3×D4—21no—
821C3×D4—21no—
822C3×D4—21no—
823C3×D4—21no—
824C3×D4—31no—
825C3×D4—41no—
826C3×D4—41no—
827C3×D4—61no—
828C3×D4—61no—
829C3×D4—62no—
830C3×D4—61no—
831C3×D4—91no—
832C3×D4—91no—
833C3×D4—91no—
834C3×D4—121no—
835C3×D4—181no—
836C3×D4—181no—
837C3×D4—181no—
838C3×D4—181no—
839C3×D4—361no—
840C3×D4—541no—
841C3×D4—541no—
842C3×D4—542no—
843C3×D4—542no—
844C3×D4—1084no—
845C2×C3×C4—21no—
846C2×C3×C4—31no—
847C2×C3×C4—61no—
848C2×C3×C4—61no—
849C2×C3×C4—181no—
850C2×C3×C4—181no—
851C2×C3×C4—181no—
852C2×C3×C4—361no—
853C2×C3×C4—542no—
854C2×C3×C4—541no—
855C2×C3×C4C22×AGL(1,ℤ/9)11yescharacteristic
856C2×C3×C4C2×C3×D3211yescharacteristic
857#67—21no—
858#67—61no—
859#67—182no—
860#67—182no—
861#67—364no—
862#67—364no—
863#67—368no—
864C2×Dic3—182no—
865C2×Dic3—181no—
866C2×Dic3—181no—
867D12—31no—
868D12—182no—
869D12—182no—
870D12—181no—
871D12—181no—
872D12—181no—
873D12—181no—
874D12—361no—
875D12—361no—
876D12#611⋊C311yescharacteristic, complemented
877C4×D3—21no—
878C4×D3—61no—
879C4×D3—182no—
880C4×D3—182no—
881Dic6—31no—
882Dic6#611⋊C311yescharacteristic, complemented
883C3×C8—61no—
884C3×C8—181no—
885C3×C8—181no—
886C3×C8—182no—
887C3×C8—181no—
888C3⋊C8—21no—
889C3⋊C8—61no—
890C2×C32—21no—
891C2×C32—21no—
892C2×C32—21no—
893C2×C32—31no—
894C2×C32—41no—
895C2×C32—61no—
896C2×C32—61no—
897C2×C32—62no—
898C2×C32—81no—
899C2×C32—82no—
900C2×C32—81no—
901C2×C32—121no—
902C2×C32—241no—
903C2×C32—242no—
904C2×C32—361no—
905C2×C32#6398311yescharacteristic
906C2×C32C3×#93711yescharacteristic
907C3⋊D3—122no—
908C3×D3—41no—
909C3×D3—121no—
910C3×D3—121no—
911C3×D3—121no—
912C3×D3—241no—
913C3×D3—362no—
914C3×D3—362no—
915C3×D3—722no—
916C2×C9—22no—
917C2×C9—21no—
918C2×C9—21no—
919C2×C9—21no—
920C2×C9—41no—
921C2×C9—42no—
922C2×C9—41no—
923C2×C9—82no—
924C2×C9—82no—
925C2×C9—84no—
926C2×C9—81no—
927C2×C9—121no—
928C2×C9—241no—
929C2×C9C3×#93711yescharacteristic
930D9—41no—
931D9—122no—
932D9—242no—
933#41—31no—
934#41—91no—
935#41—541no—
936#41—541no—
937C2×D4—271no—
938C2×D4—541no—
939C2×D4—541no—
940C2×D4—542no—
941C2×D4—542no—
942C2×D4D3×AGL(1,ℤ/9)11yescharacteristic, complemented
943SD16—61no—
944SD16—181no—
945D8—61no—
946D8—181no—
947M16—31no—
948M16—91no—
949C42—271no—
950C22×C3—21no—
951C22×C3—31no—
952C22×C3—42no—
953C22×C3—44no—
954C22×C3—42no—
955C22×C3—42no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—61no—
959C22×C3—61no—
960C22×C3—121no—
961C22×C3—122no—
962C22×C3—122no—
963C22×C3—181no—
964C22×C3—181no—
965C22×C3—181no—
966C22×C3—242no—
967C22×C3—361no—
968C22×C3—542no—
969C22×C3—1082no—
970C22×C3—2162no—
971C22×C3D4×AGL(1,ℤ/9)11yescharacteristic
972C22×C3C3×#381111yescharacteristic
973C2×D3—21no—
974C2×D3—61no—
975C2×D3—182no—
976C2×D3—182no—
977C2×D3—362no—
978C2×D3—362no—
979C2×D3—362no—
980C2×D3—364no—
981C2×D3—722no—
982C2×D3—722no—
983C3×C4—21no—
984C3×C4—21no—
985C3×C4—31no—
986C3×C4—31no—
987C3×C4—61no—
988C3×C4—61no—
989C3×C4—61no—
990C3×C4—181no—
991C3×C4—181no—
992C3×C4—181no—
993C3×C4—361no—
994C3×C4—542no—
995C3×C4D4×AGL(1,ℤ/9)11yescharacteristic
996C3×C4C2×#611⋊C311yescharacteristic
997C3×C4C3×D3×#6711yescharacteristic
998C3×C4C3×D3×#6711yescharacteristic
999Dic3—21no—
1000Dic3—61no—
1001Dic3—182no—
1002Dic3—184no—
1003Dic3—182no—
1004C32—21no—
1005C32—31no—
1006C32—61no—
1007C32#1059152211yescharacteristic
1008C32C3×#519811yescharacteristic
1009C9—21no—
1010C9—21no—
1011C9—41no—
1012C9C3×#519811yescharacteristic, complemented
1013C23—21no—
1014C23—272no—
1015C23—542no—
1016Q8—31no—
1017Q8—91no—
1018D4—21no—
1019D4—21no—
1020D4—31no—
1021D4—61no—
1022D4—91no—
1023D4—181no—
1024D4—542no—
1025D4—542no—
1026D4—541no—
1027D4—541no—
1028D4—1084no—
1029C2×C4—61no—
1030C2×C4—181no—
1031C2×C4—542no—
1032C2×C4—541no—
1033C2×C4C2×D3×AGL(1,ℤ/9)11yescharacteristic
1034C8—61no—
1035C8—181no—
1036C2×C3—22no—
1037C2×C3—21no—
1038C2×C3—21no—
1039C2×C3—21no—
1040C2×C3—31no—
1041C2×C3—61no—
1042C2×C3—61no—
1043C2×C3—82no—
1044C2×C3—81no—
1045C2×C3—81no—
1046C2×C3—121no—
1047C2×C3—121no—
1048C2×C3—241no—
1049C2×C3—242no—
1050C2×C3—361no—
1051C2×C3—361no—
1052C2×C3—361no—
1053C2×C3—721no—
1054C2×C3—1082no—
1055C2×C3#63499⋊C311yescharacteristic
1056C2×C3C3×#6398311yescharacteristic
1057D3—41no—
1058D3—121no—
1059D3—362no—
1060D3—362no—
1061D3—722no—
1062C22—42no—
1063C22—41no—
1064C22—61no—
1065C22—181no—
1066C22—542no—
1067C22—1082no—
1068C22—2162no—
1069C22#88668⋊C311yescharacteristic
1070C4—61no—
1071C4—181no—
1072C4—542no—
1073C4#67×AGL(1,ℤ/9)11yescharacteristic
1074C4D3×#611⋊C311yescharacteristic
1075C3—21no—
1076C3—31no—
1077C3—61no—
1078C3#10588879⋊C311yescharacteristic, complemented
1079C3C3×#1059152211yescharacteristic
1080C2—21no—
1081C2—81no—
1082C2—121no—
1083C2—361no—
1084C2—1082no—
1085C2#7222004111yescharacteristic
subgroupG/H
centerC2#72220041
commutator, cosocleC2×C3×C4×C9C23×C3
FrattiniC2×C3×C4C2×C3×D32
FittingC2×C3×D4×3−1+2C22
socleC2×C32C3×#937
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. #72219981C2semidirect
2. #72219968C2semidirect
3. #72219967C2semidirect
4. #72219953C2semidirect
5. #72219947C2semidirect
6. 3−1+2×#932C2semidirect
7. C3×#63495⋊C3C2semidirect
10. #13140511C3semidirect
11. C2×C3×D4×3−1+2C22semidirect
21. C4×C3⋊(3−1+2⋊C4)C22semidirect
26. 3−1+2×#208C22semidirect
27. C3×#3667⋊C3C22semidirect
33. #11722478C2×C3semidirect
38. #11721840C2×C3semidirect
42. #63495⋊C3D3semidirect
44. C9×#932C2×C3semidirect
45. C3×#63495C2×C3semidirect
49. #11720300C2×C3semidirect
50. #11720291C2×C3semidirect
51. #11720288C2×C3semidirect
64. D12×3−1+2D4semidirect
66. C3×C4⋊AGL(1,ℤ/9)D4semidirect
68. Dic6×3−1+2D4semidirect
69. C3×3−1+2⋊Q8D4semidirect
100. C2×D4×3−1+2C2×D3semidirect
102. C2×C3×D4×C9C22×C3semidirect
127. C4×C3⋊Dic9C22×C3semidirect
141. #3667⋊C3C2×D3semidirect
143. C9×#208C22×C3semidirect
144. C3×#3667C22×C3semidirect
186. #63495C3×D3semidirect
266. C4⋊AGL(1,ℤ/9)#67semidirect
271. 3−1+2⋊Q8#67semidirect
273. C9×D12C3×D4semidirect
276. C3×D36C3×D4semidirect
279. C9×Dic6C3×D4semidirect
280. C3×Dic18C3×D4semidirect
364. C2×D4×C9C2×C3×D3semidirect
385. #3667C2×C3×D3semidirect
465. #932AGL(1,ℤ/9)semidirect
475. C3×3−1+2#453semidirect
601. D36C3×#67semidirect
604. Dic18C3×#67semidirect
657. C2×C3×D4C2×AGL(1,ℤ/9)semidirect
701. #208C2×AGL(1,ℤ/9)semidirect
800. 3−1+2#5198semidirect
802. C3×C9C3×#453semidirect
876. D12#611⋊C3semidirect
882. Dic6#611⋊C3semidirect
942. C2×D4D3×AGL(1,ℤ/9)semidirect
1012. C9C3×#5198semidirect
1078. C3#10588879⋊C3semidirect

Maximal subgroups

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

subgroupindex
#722199812
#722199682
#722199672
#722199532
#722199472
3−1+2×#9322
C3×#63495⋊C32
C3×#105915223
#10588879⋊C33
#131405113