Finite Group Databasebeta

← #72259642

Subgroups — #72259642

Order 3888.

1221 conjugacy classes of subgroups.

The subgroup lattice has 1035 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C3⋊AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
2C2×D3×C3⋊AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
3#10619897⋊C3C211yesmaximal, characteristic, complemented
4#14518697C211yesmaximal, characteristic, complemented
53−1+2×#625C211yesmaximal, characteristic, complemented
6C3×#6195⋊C3C211yesmaximal, characteristic, complemented
7C3×#6195⋊C3C211yesmaximal, characteristic, complemented
8C3×#88954—31nomaximal
9#88668⋊C3—31nomaximal
10#88668⋊C3—31nomaximal
11#13048301C311yesmaximal, characteristic, complemented
12C2×C3⋊(C3⋊AGL(1,ℤ/9))C2211yescharacteristic
13C2×C3×C3⋊AGL(1,ℤ/9)C2211yescharacteristic, complemented
14C2×C3×C3⋊AGL(1,ℤ/9)C2211yescharacteristic, complemented
15C2×C3×D3×3−1+2C2211yescharacteristic, complemented
16C2×C3×D3×3−1+2C2211yescharacteristic, complemented
17D3×C3⋊AGL(1,ℤ/9)—22no—
18D3×C3⋊AGL(1,ℤ/9)—22no—
193−1+2×C3⋊Dic3C2211yescharacteristic, complemented
20C32×3−1+2⋊C4C2211yescharacteristic, complemented
21C2×C3×D3×C3⋊D3—31no—
22C2×C3×D3×C3⋊D3—31no—
23C3×#6295—31no—
24C3×#6289—31no—
25C32×#626—31no—
26C32×#626—31no—
27C32×#625D311yescharacteristic
28C22×C3⋊AGL(1,ℤ/9)—31no—
29C22×C3⋊AGL(1,ℤ/9)—31no—
30C2×D3×C3⋊D9C2×C311yescharacteristic, complemented
31C2×D3×C3⋊D9C2×C311yescharacteristic, complemented
32C2×D3×AGL(1,ℤ/9)—31no—
33C2×D3×AGL(1,ℤ/9)—31no—
34C2×D3×AGL(1,ℤ/9)—61no—
35C2×D3×AGL(1,ℤ/9)—61no—
36#67×3−1+2—31no—
37#67×3−1+2—31no—
38C3×#611⋊C3—31no—
39C3×#611⋊C3—31no—
40#10619897C2×C311yescharacteristic, complemented
41#10619870C2×C311yescharacteristic, complemented
42#6195⋊C3—21no—
43#6195⋊C3—21no—
44#6195⋊C3D311yescharacteristic, complemented
45#6195⋊C3D311yescharacteristic, complemented
46#6192⋊C3—31no—
47#6192⋊C3—31no—
48(C3⋊AGL(1,ℤ/9))⋊C4—31no—
49(C3⋊AGL(1,ℤ/9))⋊C4—31no—
50(C3⋊AGL(1,ℤ/9))⋊C4—61no—
51C9×#625—21no—
52C9×#625C2×C311yescharacteristic, complemented
53C3×#6195C2×C311yescharacteristic, complemented
54C3×#6195C2×C311yescharacteristic, complemented
55C2×C32×3−1+2C2311yescharacteristic
56C3⋊(C3⋊AGL(1,ℤ/9))D412yescomplemented
57C3×C3⋊AGL(1,ℤ/9)—21no—
58C3×C3⋊AGL(1,ℤ/9)—21no—
59C3×D3×3−1+2—21no—
60C3×D3×3−1+2—21no—
61C3×#3811—91no—
62C3×#3811—91no—
63C3×#3802—91no—
64#88954—31no—
65D4×AGL(1,ℤ/9)—91no—
66#88668—31no—
67#88668—31no—
68C2×C3×C3⋊(C3⋊D3)—31no—
69C2×C32×C3⋊D3—31no—
70C2×C32×C3⋊D3—31no—
71C2×C33×D3C2×D311yescharacteristic
72C2×C33×D3C2×D311yescharacteristic
73C3×D3×C3⋊D3—62no—
74C3×D3×C3⋊D3—62no—
75C32×C3⋊Dic3C2×D311yescharacteristic
76C33×Dic3—31no—
77C22×C3×3−1+2—31no—
78C22×C3×3−1+2—31no—
79C2×C3⋊(C3⋊D9)C22×C311yescharacteristic
80C2×C3⋊AGL(1,ℤ/9)—21no—
81C2×C3⋊AGL(1,ℤ/9)—21no—
82C2×C3⋊AGL(1,ℤ/9)—31no—
83C2×C3⋊AGL(1,ℤ/9)—31no—
84C2×C3⋊AGL(1,ℤ/9)—61no—
85C2×C3⋊AGL(1,ℤ/9)—62no—
86C2×C3⋊AGL(1,ℤ/9)—62no—
87C2×C3⋊AGL(1,ℤ/9)—61no—
88C2×C3⋊AGL(1,ℤ/9)—61no—
89C2×C3⋊AGL(1,ℤ/9)—121no—
90C2×C3⋊AGL(1,ℤ/9)C2×D311yescharacteristic, complemented
91C2×C3⋊AGL(1,ℤ/9)C2×D311yescharacteristic, complemented
92C2×C3×C3⋊D9C22×C311yescharacteristic, complemented
93C2×C3×C3⋊D9C22×C311yescharacteristic, complemented
94C2×D3×3−1+2—21no—
95C2×D3×3−1+2—21no—
96C2×D3×3−1+2—21no—
97C2×D3×3−1+2—21no—
98C2×D3×3−1+2—41no—
99C2×D3×3−1+2—41no—
100C2×D3×3−1+2C2×D311yescharacteristic, complemented
101C2×D3×3−1+2C2×D311yescharacteristic, complemented
102C2×C3×AGL(1,ℤ/9)—31no—
103C2×C3×AGL(1,ℤ/9)—31no—
104C2×C3×AGL(1,ℤ/9)—61no—
105C2×C3×AGL(1,ℤ/9)—61no—
106C2×C3×D3×C9—21no—
107C2×C3×D3×C9—21no—
108C2×C3×D3×C9C22×C311yescharacteristic, complemented
109C2×C3×D3×C9C22×C311yescharacteristic, complemented
110D3×C3⋊D9—22no—
111D3×C3⋊D9—22no—
112D3×AGL(1,ℤ/9)—62no—
113D3×AGL(1,ℤ/9)—62no—
114D3×AGL(1,ℤ/9)—64no—
115D3×AGL(1,ℤ/9)—64no—
116C9×C3⋊Dic3—21no—
117C9×C3⋊Dic3C22×C311yescharacteristic, complemented
118Dic3×3−1+2—31no—
119Dic3×3−1+2—31no—
120Dic3×3−1+2—61no—
121C3×3−1+2⋊C4—21no—
122C3×3−1+2⋊C4—21no—
123C3×3−1+2⋊C4—21no—
124C3×3−1+2⋊C4—41no—
125C3×3−1+2⋊C4C2×D311yescharacteristic, complemented
126C3×3−1+2⋊C4C2×D311yescharacteristic, complemented
127C32×Dic9C22×C311yescharacteristic, complemented
128C32×3−1+2C2×D411yescharacteristic, complemented, Sylow
129C22×C3×C3⋊D3—91no—
130C22×C3×C3⋊D3—91no—
131C2×D3×C3⋊D3—31no—
132C2×D3×C3⋊D3—31no—
133C2×C3×D32—91no—
134C2×C3×D32—91no—
135C2×C3×D32—91no—
136C2×C3×D32—91no—
137C2×C3×D32—181no—
138C2×C3×D32—181no—
139C3×C4×C3⋊D3—91no—
140C32×#67—31no—
141C32×#67—31no—
142C32×#67—91no—
143C32×#67—91no—
144C32×D12—91no—
145C32×D12—91no—
146#6295—31no—
147#6289—31no—
148C3×#626—31no—
149C3×#626—31no—
150C3×#626—31no—
151C3×#626—31no—
152C3×#626—61no—
153C3×#626—61no—
154C3×#626—91no—
155C3×#626—91no—
156C3×#625—61no—
157C3×#625—91no—
158C3×#625C3×D311yescharacteristic
159C3×#624—91no—
160C3×#624—91no—
161C3×#624—181no—
162C22×C3⋊D9—31no—
163C22×C3⋊D9—31no—
164C22×AGL(1,ℤ/9)—91no—
165C22×AGL(1,ℤ/9)—91no—
166C22×AGL(1,ℤ/9)—181no—
167C22×AGL(1,ℤ/9)—181no—
168C2×D3×D9—31no—
169C2×D3×D9—31no—
170C2×D3×D9—61no—
171C2×D3×D9—61no—
172D4×3−1+2—91no—
173#611⋊C3—31no—
174#611⋊C3—31no—
175#611⋊C3—61no—
176#611⋊C3—61no—
177C9×#67—31no—
178C9×#67—31no—
179C9×#67—61no—
180C9×#67—61no—
181C3×#611—31no—
182C3×#611—31no—
183C4⋊AGL(1,ℤ/9)—91no—
184C4×AGL(1,ℤ/9)—91no—
185#6195C3×D311yescharacteristic, complemented
186#6195C3×D311yescharacteristic, complemented
187#6192—31no—
188#6192—31no—
189(C3⋊D9)⋊C4—31no—
190(C3⋊D9)⋊C4—31no—
191(C3⋊D9)⋊C4—61no—
192C2×C34C22×D311yescharacteristic
193C3×C3⋊(C3⋊D3)—32no—
194C32×C3⋊D3—61no—
195C32×C3⋊D3—61no—
196C33×D3—21no—
197C33×D3—21no—
198C2×C3×3−1+2—21no—
199C2×C3×3−1+2—21no—
200C2×C3×3−1+2—21no—
201C2×C3×3−1+2—21no—
202C2×C3×3−1+2—21no—
203C2×C3×3−1+2—41no—
204C2×C3×3−1+2—41no—
205C2×C3×3−1+2—41no—
206C2×C3×3−1+2—41no—
207C2×C3×3−1+2—61no—
208C2×C3×3−1+2—61no—
209C2×C3×3−1+2—81no—
210C2×C3×3−1+2C22×D311yescharacteristic
211C2×C3×3−1+2C22×D311yescharacteristic
212C2×C32×C9—21no—
213C2×C32×C9C23×C311yescharacteristic
214C3⋊(C3⋊D9)C3×D412yescomplemented
215C3⋊AGL(1,ℤ/9)—21no—
216C3⋊AGL(1,ℤ/9)—21no—
217C3⋊AGL(1,ℤ/9)—32no—
218C3⋊AGL(1,ℤ/9)—32no—
219C3⋊AGL(1,ℤ/9)—41no—
220C3⋊AGL(1,ℤ/9)—41no—
221C3⋊AGL(1,ℤ/9)—62no—
222C3⋊AGL(1,ℤ/9)—62no—
223C3⋊AGL(1,ℤ/9)—62no—
224C3⋊AGL(1,ℤ/9)—122no—
225C3×C3⋊D9—21no—
226C3×C3⋊D9—21no—
227D3×3−1+2—22no—
228D3×3−1+2—22no—
229D3×3−1+2—21no—
230D3×3−1+2—21no—
231D3×3−1+2—41no—
232D3×3−1+2—41no—
233D3×3−1+2—42no—
234D3×3−1+2—42no—
235C3×AGL(1,ℤ/9)—62no—
236C3×AGL(1,ℤ/9)—62no—
237C3×AGL(1,ℤ/9)—61no—
238C3×AGL(1,ℤ/9)—61no—
239C3×D3×C9—21no—
240C3×D3×C9—21no—
241C3×D3×C9—41no—
242C3×D3×C9—41no—
243C3×D3×D4—271no—
244C3×D3×D4—271no—
245C3×D3×D4—271no—
246#3811—91no—
247#3811—91no—
248#3802—91no—
249D4×D9—91no—
250C22×C33—31no—
251C22×C33—31no—
252C2×C3⋊(C3⋊D3)—31no—
253C2×C3×C3⋊D3—31no—
254C2×C3×C3⋊D3—31no—
255C2×C3×C3⋊D3—31no—
256C2×C3×C3⋊D3—31no—
257C2×C3×C3⋊D3—61no—
258C2×C3×C3⋊D3—61no—
259C2×C3×C3⋊D3—91no—
260C2×C3×C3⋊D3—91no—
261C2×C3×C3⋊D3—91no—
262C2×C3×C3⋊D3—182no—
263C2×C3×C3⋊D3—182no—
264C2×C3×C3⋊D3—181no—
265C2×C3×C3⋊D3—181no—
266C2×C3×C3⋊D3—181no—
267C2×C3×C3⋊D3—361no—
268C2×C32×D3—21no—
269C2×C32×D3—21no—
270C2×C32×D3—61no—
271C2×C32×D3—61no—
272C2×C32×D3—61no—
273C2×C32×D3—91no—
274C2×C32×D3—91no—
275C2×C32×D3—91no—
276C2×C32×D3—91no—
277C2×C32×D3—121no—
278C2×C32×D3—181no—
279C2×C32×D3—181no—
280C2×C32×D3D3211yescharacteristic
281C2×C32×D3D3211yescharacteristic
282C2×C32×D3C2×C3×D311yescharacteristic
283C2×C32×D3C2×C3×D311yescharacteristic
284D3×C3⋊D3—62no—
285D3×C3⋊D3—62no—
286C3×D32—182no—
287C3×D32—182no—
288C3×D32—182no—
289C3×D32—182no—
290C3×D32—182no—
291C3×D32—184no—
292C3×D32—182no—
293C33×C4—91no—
294C3×C3⋊Dic3—61no—
295C3×C3⋊Dic3C2×C3×D311yescharacteristic
296C32×Dic3—31no—
297C32×Dic3—31no—
298C32×Dic3—31no—
299C32×Dic3—31no—
300C32×Dic3—31no—
301C32×Dic3—61no—
302C32×Dic3—61no—
303C32×Dic3—61no—
304C32×Dic3—61no—
305C32×Dic3—121no—
306C22×3−1+2—31no—
307C22×3−1+2—31no—
308C22×3−1+2—61no—
309C22×3−1+2—61no—
310C22×3−1+2—61no—
311C22×3−1+2—61no—
312C22×3−1+2—121no—
313C22×3−1+2—121no—
314C22×C3×C9—31no—
315C22×C3×C9—31no—
316C22×C3×C9—61no—
317C22×C3×C9—61no—
318C2×C3⋊D9—31no—
319C2×C3⋊D9—31no—
320C2×C3⋊D9—62no—
321C2×C3⋊D9—62no—
322C2×C3⋊D9—61no—
323C2×C3⋊D9—61no—
324C2×C3⋊D9—61no—
325C2×C3⋊D9—121no—
326C2×C3⋊D9C2×C3×D311yescharacteristic, complemented
327C2×C3⋊D9C2×C3×D311yescharacteristic, complemented
328C2×AGL(1,ℤ/9)—31no—
329C2×AGL(1,ℤ/9)—31no—
330C2×AGL(1,ℤ/9)—61no—
331C2×AGL(1,ℤ/9)—61no—
332C2×AGL(1,ℤ/9)—61no—
333C2×AGL(1,ℤ/9)—61no—
334C2×AGL(1,ℤ/9)—91no—
335C2×AGL(1,ℤ/9)—121no—
336C2×AGL(1,ℤ/9)—121no—
337C2×AGL(1,ℤ/9)—182no—
338C2×AGL(1,ℤ/9)—182no—
339C2×AGL(1,ℤ/9)—184no—
340C2×AGL(1,ℤ/9)—184no—
341C2×AGL(1,ℤ/9)—181no—
342C2×AGL(1,ℤ/9)—181no—
343C2×AGL(1,ℤ/9)—361no—
344C2×D3×C9—21no—
345C2×D3×C9—21no—
346C2×D3×C9—21no—
347C2×D3×C9—21no—
348C2×D3×C9—41no—
349C2×D3×C9—41no—
350C2×D3×C9C2×C3×D311yescharacteristic, complemented
351C2×D3×C9C2×C3×D311yescharacteristic, complemented
352C2×C3×D9—31no—
353C2×C3×D9—31no—
354C2×C3×D9—61no—
355C2×C3×D9—61no—
356D3×D9—62no—
357D3×D9—62no—
358D3×D9—64no—
359D3×D9—64no—
360C4×3−1+2—91no—
3613−1+2⋊C4—21no—
3623−1+2⋊C4—21no—
3633−1+2⋊C4—41no—
3643−1+2⋊C4D3211yescharacteristic, complemented
365C9×Dic3—31no—
366C9×Dic3—31no—
367C9×Dic3—61no—
368C9×Dic3—61no—
369C9×Dic3—61no—
370C9×Dic3—121no—
371C3×Dic9—21no—
372C3×Dic9C2×C3×D311yescharacteristic, complemented
373C3×Dic9C2×C3×D311yescharacteristic, complemented
374C34D3×D411yescharacteristic
375C3×3−1+2—21no—
376C3×3−1+2—21no—
377C3×3−1+2—21no—
378C3×3−1+2—21no—
379C3×3−1+2—21no—
380C3×3−1+2—41no—
381C3×3−1+2—41no—
382C3×3−1+2—41no—
383C3×3−1+2—41no—
384C3×3−1+2—81no—
385C3×3−1+2D3×D411yescharacteristic, complemented
386C3×3−1+2D3×D411yescharacteristic, complemented
387C32×C9—21no—
388C32×C9C2×C3×D411yescharacteristic, complemented
389C22×C3⋊D3—91no—
390C22×C3⋊D3—91no—
391C22×C3×D3—271no—
392C22×C3×D3—271no—
393C22×C3×D3—271no—
394C22×C3×D3—271no—
395C22×C3×D3—271no—
396C22×C3×D3—271no—
397C22×C3×D3—541no—
398C22×C3×D3—541no—
399C2×D32—91no—
400C2×D32—91no—
401C2×D32—91no—
402C2×D32—91no—
403C2×D32—181no—
404C2×D32—181no—
405C32×D4—91no—
406C32×D4—271no—
407C32×D4—271no—
408C4×C3⋊D3—91no—
409C3×#67—31no—
410C3×#67—31no—
411C3×#67—91no—
412C3×#67—91no—
413C3×#67—91no—
414C3×#67—91no—
415C3×#67—91no—
416C3×#67—181no—
417C3×#67—181no—
418C3×#67—181no—
419C3×#67—271no—
420C3×#67—271no—
421C3×D12—91no—
422C3×D12—91no—
423C3×D12—91no—
424C3×D12—91no—
425C3×D12—181no—
426C3×D12—181no—
427C3×D12—271no—
428C3×C4×D3—271no—
429C3×C4×D3—271no—
430C3×C4×D3—271no—
431C3×C4×D3—541no—
432#626—31no—
433#626—31no—
434#626—91no—
435#626—91no—
436#625—91no—
437#625AGL(1,ℤ/9)11yescharacteristic, complemented
438#624—91no—
439#624—91no—
440#624—181no—
441C22×D9—91no—
442C22×D9—91no—
443C22×D9—181no—
444C22×D9—181no—
445D4×C9—91no—
446D4×C9—181no—
447#611—31no—
448#611—31no—
449D36—91no—
450C4×D9—91no—
451C2×C33—21no—
452C2×C33—21no—
453C2×C33—21no—
454C2×C33—41no—
455C2×C33—61no—
456C2×C33—61no—
457C2×C33—61no—
458C2×C33—61no—
459C2×C33—121no—
460C2×C33—241no—
461C2×C33C2×D3211yescharacteristic
462C2×C33C2×D3211yescharacteristic
463C2×C33C22×C3×D311yescharacteristic
464C3⋊(C3⋊D3)—32no—
465C3×C3⋊D3—61no—
466C3×C3⋊D3—61no—
467C3×C3⋊D3—61no—
468C3×C3⋊D3—61no—
469C3×C3⋊D3—92no—
470C3×C3⋊D3—92no—
471C3×C3⋊D3—92no—
472C3×C3⋊D3—121no—
473C3×C3⋊D3—121no—
474C3×C3⋊D3—182no—
475C3×C3⋊D3—182no—
476C3×C3⋊D3—182no—
477C3×C3⋊D3—362no—
478C32×D3—21no—
479C32×D3—21no—
480C32×D3—21no—
481C32×D3—21no—
482C32×D3—41no—
483C32×D3—41no—
484C32×D3—61no—
485C32×D3—121no—
486C32×D3—122no—
487C32×D3—121no—
488C32×D3—121no—
489C32×D3—181no—
490C32×D3—181no—
491C32×D3—182no—
492C32×D3—182no—
493C32×D3—181no—
494C32×D3—181no—
495C2×3−1+2—21no—
496C2×3−1+2—21no—
497C2×3−1+2—21no—
498C2×3−1+2—21no—
499C2×3−1+2—41no—
500C2×3−1+2—41no—
501C2×3−1+2—41no—
502C2×3−1+2—41no—
503C2×3−1+2—41no—
504C2×3−1+2—41no—
505C2×3−1+2—62no—
506C2×3−1+2—62no—
507C2×3−1+2—61no—
508C2×3−1+2—61no—
509C2×3−1+2—81no—
510C2×3−1+2—81no—
511C2×3−1+2—81no—
512C2×3−1+2—81no—
513C2×3−1+2—81no—
514C2×3−1+2—81no—
515C2×3−1+2—121no—
516C2×3−1+2—121no—
517C2×3−1+2—122no—
518C2×3−1+2—122no—
519C2×3−1+2C2×D3211yescharacteristic
520C2×C3×C9—21no—
521C2×C3×C9—21no—
522C2×C3×C9—21no—
523C2×C3×C9—21no—
524C2×C3×C9—21no—
525C2×C3×C9—41no—
526C2×C3×C9—41no—
527C2×C3×C9—41no—
528C2×C3×C9—41no—
529C2×C3×C9—61no—
530C2×C3×C9—61no—
531C2×C3×C9—81no—
532C2×C3×C9—121no—
533C2×C3×C9—121no—
534C2×C3×C9C22×C3×D311yescharacteristic
535C2×C3×C9C22×C3×D311yescharacteristic
536C3⋊D9—21no—
537C3⋊D9—21no—
538C3⋊D9—32no—
539C3⋊D9—32no—
540C3⋊D9—62no—
541C3⋊D9—62no—
542C3⋊D9—62no—
543C3⋊D9—122no—
544AGL(1,ℤ/9)—62no—
545AGL(1,ℤ/9)—62no—
546AGL(1,ℤ/9)—61no—
547AGL(1,ℤ/9)—61no—
548AGL(1,ℤ/9)—92no—
549AGL(1,ℤ/9)—121no—
550AGL(1,ℤ/9)—121no—
551AGL(1,ℤ/9)—122no—
552AGL(1,ℤ/9)—122no—
553AGL(1,ℤ/9)—182no—
554AGL(1,ℤ/9)—182no—
555AGL(1,ℤ/9)—362no—
556D3×C9—22no—
557D3×C9—22no—
558D3×C9—21no—
559D3×C9—21no—
560D3×C9—41no—
561D3×C9—41no—
562D3×C9—42no—
563D3×C9—42no—
564C3×D9—62no—
565C3×D9—62no—
566C3×D9—61no—
567C3×D9—61no—
568C2×C3×D4—811no—
569D3×D4—271no—
570D3×D4—271no—
571D3×D4—271no—
572C22×C32—31no—
573C22×C32—31no—
574C22×C32—31no—
575C22×C32—31no—
576C22×C32—61no—
577C22×C32—61no—
578C22×C32—91no—
579C22×C32—181no—
580C22×C32—271no—
581C22×C32—271no—
582C22×C32—361no—
583C22×C32—361no—
584C2×C3⋊D3—31no—
585C2×C3⋊D3—31no—
586C2×C3⋊D3—91no—
587C2×C3⋊D3—91no—
588C2×C3⋊D3—91no—
589C2×C3⋊D3—181no—
590C2×C3⋊D3—181no—
591C2×C3⋊D3—181no—
592C2×C3⋊D3—182no—
593C2×C3⋊D3—182no—
594C2×C3⋊D3—361no—
595C2×C3×D3—21no—
596C2×C3×D3—21no—
597C2×C3×D3—31no—
598C2×C3×D3—61no—
599C2×C3×D3—91no—
600C2×C3×D3—91no—
601C2×C3×D3—91no—
602C2×C3×D3—91no—
603C2×C3×D3—91no—
604C2×C3×D3—91no—
605C2×C3×D3—91no—
606C2×C3×D3—91no—
607C2×C3×D3—121no—
608C2×C3×D3—121no—
609C2×C3×D3—181no—
610C2×C3×D3—181no—
611C2×C3×D3—181no—
612C2×C3×D3—181no—
613C2×C3×D3—181no—
614C2×C3×D3—181no—
615C2×C3×D3—181no—
616C2×C3×D3—181no—
617C2×C3×D3—271no—
618C2×C3×D3—271no—
619C2×C3×D3—271no—
620C2×C3×D3—361no—
621C2×C3×D3—361no—
622C2×C3×D3—541no—
623C2×C3×D3—541no—
624C2×C3×D3—541no—
625C2×C3×D3—542no—
626C2×C3×D3—542no—
627C2×C3×D3—542no—
628C2×C3×D3—542no—
629C2×C3×D3—542no—
630C2×C3×D3—542no—
631C2×C3×D3—542no—
632C2×C3×D3—544no—
633C2×C3×D3—542no—
634C2×C3×D3—1081no—
635C2×C3×D3C2×AGL(1,ℤ/9)11yescharacteristic, complemented
636C2×C3×D3C2×AGL(1,ℤ/9)11yescharacteristic, complemented
637C2×C3×D3C3×D3211yescharacteristic
638C2×C3×D3C3×D3211yescharacteristic
639D32—182no—
640D32—182no—
641D32—182no—
642D32—182no—
643D32—182no—
644D32—184no—
645D32—182no—
646C32×C4—91no—
647C32×C4—91no—
648C32×C4—91no—
649C32×C4—91no—
650C32×C4—181no—
651C32×C4—181no—
652C32×C4—181no—
653C32×C4—361no—
654C3⋊Dic3C2×AGL(1,ℤ/9)11yescharacteristic, complemented
655C3×Dic3—31no—
656C3×Dic3—31no—
657C3×Dic3—31no—
658C3×Dic3—31no—
659C3×Dic3—31no—
660C3×Dic3—61no—
661C3×Dic3—61no—
662C3×Dic3—61no—
663C3×Dic3—61no—
664C3×Dic3—91no—
665C3×Dic3—121no—
666C3×Dic3—181no—
667C3×Dic3—361no—
668C22×C9—31no—
669C22×C9—31no—
670C22×C9—61no—
671C22×C9—61no—
672C22×C9—61no—
673C22×C9—61no—
674C22×C9—121no—
675C22×C9—121no—
676C2×D9—31no—
677C2×D9—31no—
678C2×D9—61no—
679C2×D9—61no—
680C2×D9—91no—
681C2×D9—181no—
682C2×D9—181no—
683C2×D9—182no—
684C2×D9—182no—
685C2×D9—184no—
686C2×D9—184no—
687C2×D9—361no—
688C4×C9—91no—
689C4×C9—181no—
690Dic9C3×D3211yescharacteristic, complemented
691C33—21no—
692C33—21no—
693C33—21no—
694C33—41no—
695C33—61no—
696C33—61no—
697C33—121no—
698C33—241no—
699C33#381111yescharacteristic
700C33#381111yescharacteristic
701C33C3×D3×D411yescharacteristic
7023−1+2—21no—
7033−1+2—21no—
7043−1+2—21no—
7053−1+2—21no—
7063−1+2—41no—
7073−1+2—41no—
7083−1+2—41no—
7093−1+2—41no—
7103−1+2—41no—
7113−1+2—41no—
7123−1+2—81no—
7133−1+2—81no—
7143−1+2—81no—
7153−1+2—81no—
7163−1+2—81no—
7173−1+2—81no—
7183−1+2#380211yescharacteristic, complemented
719C3×C9—21no—
720C3×C9—21no—
721C3×C9—21no—
722C3×C9—21no—
723C3×C9—21no—
724C3×C9—41no—
725C3×C9—41no—
726C3×C9—41no—
727C3×C9—41no—
728C3×C9—81no—
729C3×C9C3×D3×D411yescharacteristic, complemented
730C3×C9C3×D3×D411yescharacteristic, complemented
731C23×C3—811no—
732C23×C3—811no—
733C22×D3—271no—
734C22×D3—271no—
735C22×D3—271no—
736C22×D3—271no—
737C22×D3—271no—
738C22×D3—271no—
739C22×D3—541no—
740C22×D3—541no—
741C3×D4—91no—
742C3×D4—271no—
743C3×D4—271no—
744C3×D4—271no—
745C3×D4—271no—
746C3×D4—541no—
747C3×D4—541no—
748C3×D4—541no—
749C3×D4—811no—
750C2×C3×C4—811no—
751#67—31no—
752#67—31no—
753#67—91no—
754#67—91no—
755#67—271no—
756#67—271no—
757D12—91no—
758D12—91no—
759D12—271no—
760C4×D3—271no—
761C4×D3—271no—
762C4×D3—271no—
763C4×D3—541no—
764C2×C32—21no—
765C2×C32—21no—
766C2×C32—21no—
767C2×C32—21no—
768C2×C32—21no—
769C2×C32—31no—
770C2×C32—41no—
771C2×C32—41no—
772C2×C32—61no—
773C2×C32—61no—
774C2×C32—61no—
775C2×C32—61no—
776C2×C32—61no—
777C2×C32—121no—
778C2×C32—121no—
779C2×C32—121no—
780C2×C32—121no—
781C2×C32—121no—
782C2×C32—121no—
783C2×C32—121no—
784C2×C32—121no—
785C2×C32—121no—
786C2×C32—181no—
787C2×C32—241no—
788C2×C32—241no—
789C2×C32—241no—
790C2×C32—361no—
791C2×C32—361no—
792C2×C32—362no—
793C2×C32—361no—
794C2×C32—541no—
795C2×C32—541no—
796C2×C32C22×AGL(1,ℤ/9)11yescharacteristic
797C2×C32D3311yescharacteristic
798C2×C32C2×C3×D3211yescharacteristic
799C2×C32C2×C3×D3211yescharacteristic
800C3⋊D3—61no—
801C3⋊D3—61no—
802C3⋊D3—92no—
803C3⋊D3—92no—
804C3⋊D3—92no—
805C3⋊D3—182no—
806C3⋊D3—182no—
807C3⋊D3—182no—
808C3⋊D3—362no—
809C3×D3—21no—
810C3×D3—22no—
811C3×D3—21no—
812C3×D3—21no—
813C3×D3—21no—
814C3×D3—21no—
815C3×D3—21no—
816C3×D3—61no—
817C3×D3—121no—
818C3×D3—121no—
819C3×D3—121no—
820C3×D3—182no—
821C3×D3—182no—
822C3×D3—181no—
823C3×D3—181no—
824C3×D3—182no—
825C3×D3—182no—
826C3×D3—181no—
827C3×D3—181no—
828C3×D3—181no—
829C3×D3—181no—
830C3×D3—181no—
831C3×D3—181no—
832C3×D3—272no—
833C3×D3—272no—
834C3×D3—272no—
835C3×D3—361no—
836C3×D3—361no—
837C3×D3—361no—
838C3×D3—361no—
839C3×D3—362no—
840C3×D3—362no—
841C3×D3—542no—
842C3×D3—542no—
843C3×D3—542no—
844C3×D3—1082no—
845C2×C9—21no—
846C2×C9—21no—
847C2×C9—21no—
848C2×C9—41no—
849C2×C9—41no—
850C2×C9—41no—
851C2×C9—62no—
852C2×C9—62no—
853C2×C9—61no—
854C2×C9—61no—
855C2×C9—81no—
856C2×C9—121no—
857C2×C9—121no—
858C2×C9—122no—
859C2×C9—122no—
860C2×C9C2×C3×D3211yescharacteristic
861D9—62no—
862D9—62no—
863D9—61no—
864D9—61no—
865D9—92no—
866D9—182no—
867D9—182no—
868D9—362no—
869C2×D4—811noSylow
870C22×C3—31no—
871C22×C3—31no—
872C22×C3—31no—
873C22×C3—31no—
874C22×C3—61no—
875C22×C3—61no—
876C22×C3—181no—
877C22×C3—181no—
878C22×C3—271no—
879C22×C3—271no—
880C22×C3—271no—
881C22×C3—271no—
882C22×C3—361no—
883C22×C3—361no—
884C22×C3—541no—
885C22×C3—541no—
886C22×C3—811no—
887C22×C3—1622no—
888C22×C3—1622no—
889C2×D3—91no—
890C2×D3—91no—
891C2×D3—91no—
892C2×D3—91no—
893C2×D3—181no—
894C2×D3—181no—
895C2×D3—271no—
896C2×D3—271no—
897C2×D3—271no—
898C2×D3—541no—
899C2×D3—541no—
900C2×D3—541no—
901C2×D3—542no—
902C2×D3—542no—
903C2×D3—542no—
904C2×D3—542no—
905C2×D3—542no—
906C2×D3—542no—
907C2×D3—542no—
908C2×D3—544no—
909C2×D3—542no—
910C2×D3—1081no—
911C2×D3D3×AGL(1,ℤ/9)11yescharacteristic, complemented
912C2×D3D3×AGL(1,ℤ/9)11yescharacteristic, complemented
913C3×C4—91no—
914C3×C4—91no—
915C3×C4—91no—
916C3×C4—91no—
917C3×C4—181no—
918C3×C4—181no—
919C3×C4—181no—
920C3×C4—361no—
921C3×C4—541no—
922Dic3—31no—
923Dic3—31no—
924Dic3—31no—
925Dic3—61no—
926C32—21no—
927C32—21no—
928C32—21no—
929C32—21no—
930C32—21no—
931C32—31no—
932C32—41no—
933C32—41no—
934C32—61no—
935C32—121no—
936C32—121no—
937C32—121no—
938C32—121no—
939C32—121no—
940C32—121no—
941C32—121no—
942C32—241no—
943C32—241no—
944C32—241no—
945C32D4×AGL(1,ℤ/9)11yescharacteristic, complemented
946C32#8895411yescharacteristic
947C32C3×#381111yescharacteristic
948C32C3×#381111yescharacteristic
949C9—21no—
950C9—21no—
951C9—21no—
952C9—41no—
953C9—41no—
954C9—41no—
955C9—81no—
956C9C3×#380211yescharacteristic, complemented
957C23—811no—
958C23—811no—
959D4—91no—
960D4—271no—
961D4—271no—
962D4—811no—
963C2×C4—811no—
964C2×C3—21no—
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—41no—
968C2×C3—61no—
969C2×C3—62no—
970C2×C3—61no—
971C2×C3—61no—
972C2×C3—61no—
973C2×C3—61no—
974C2×C3—61no—
975C2×C3—61no—
976C2×C3—121no—
977C2×C3—121no—
978C2×C3—121no—
979C2×C3—361no—
980C2×C3—361no—
981C2×C3—361no—
982C2×C3—361no—
983C2×C3—541no—
984C2×C3—541no—
985C2×C3—541no—
986C2×C3—541no—
987C2×C3—812no—
988C2×C3—1081no—
989C2×C3—1081no—
990C2×C3C2×D3×AGL(1,ℤ/9)11yescharacteristic
991C2×C3C2×D3×AGL(1,ℤ/9)11yescharacteristic
992C2×C3C3×D3311yescharacteristic
993D3—21no—
994D3—21no—
995D3—182no—
996D3—182no—
997D3—181no—
998D3—181no—
999D3—181no—
1000D3—181no—
1001D3—272no—
1002D3—272no—
1003D3—272no—
1004D3—542no—
1005D3—542no—
1006D3—542no—
1007D3—1082no—
1008C22—31no—
1009C22—31no—
1010C22—271no—
1011C22—271no—
1012C22—811no—
1013C22—1622no—
1014C22—1622no—
1015C4—91no—
1016C4—91no—
1017C3—21no—
1018C3—21no—
1019C3—21no—
1020C3—41no—
1021C3—61no—
1022C3—121no—
1023C3—121no—
1024C3—121no—
1025C3#88668⋊C311yescharacteristic, complemented
1026C3#88668⋊C311yescharacteristic, complemented
1027C3C3×#8895411yescharacteristic
1028C2—61no—
1029C2—61no—
1030C2—541no—
1031C2—541no—
1032C2—812no—
1033C2D32×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC2D32×AGL(1,ℤ/9)
commutator, cosocleC2×C32×C9C23×C3
FrattiniC2×C3C3×D33
FittingC2×C32×3−1+2C23
socleC2×C33C22×C3×D3
hypocenterC32×C9C2×C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×D3×C3⋊AGL(1,ℤ/9)C2semidirect
2. C2×D3×C3⋊AGL(1,ℤ/9)C2semidirect
3. #10619897⋊C3C2semidirect
4. #14518697C2semidirect
5. 3−1+2×#625C2semidirect
6. C3×#6195⋊C3C2semidirect
7. C3×#6195⋊C3C2semidirect
11. #13048301C3semidirect
13. C2×C3×C3⋊AGL(1,ℤ/9)C22semidirect
14. C2×C3×C3⋊AGL(1,ℤ/9)C22semidirect
15. C2×C3×D3×3−1+2C22semidirect
16. C2×C3×D3×3−1+2C22semidirect
19. 3−1+2×C3⋊Dic3C22semidirect
20. C32×3−1+2⋊C4C22semidirect
30. C2×D3×C3⋊D9C2×C3semidirect
31. C2×D3×C3⋊D9C2×C3semidirect
40. #10619897C2×C3semidirect
41. #10619870C2×C3semidirect
44. #6195⋊C3D3semidirect
45. #6195⋊C3D3semidirect
52. C9×#625C2×C3semidirect
53. C3×#6195C2×C3semidirect
54. C3×#6195C2×C3semidirect
56. C3⋊(C3⋊AGL(1,ℤ/9))D4semidirect
90. C2×C3⋊AGL(1,ℤ/9)C2×D3semidirect
91. C2×C3⋊AGL(1,ℤ/9)C2×D3semidirect
92. C2×C3×C3⋊D9C22×C3semidirect
93. C2×C3×C3⋊D9C22×C3semidirect
100. C2×D3×3−1+2C2×D3semidirect
101. C2×D3×3−1+2C2×D3semidirect
108. C2×C3×D3×C9C22×C3semidirect
109. C2×C3×D3×C9C22×C3semidirect
117. C9×C3⋊Dic3C22×C3semidirect
125. C3×3−1+2⋊C4C2×D3semidirect
126. C3×3−1+2⋊C4C2×D3semidirect
127. C32×Dic9C22×C3semidirect
128. C32×3−1+2C2×D4semidirect
185. #6195C3×D3semidirect
186. #6195C3×D3semidirect
214. C3⋊(C3⋊D9)C3×D4semidirect
326. C2×C3⋊D9C2×C3×D3semidirect
327. C2×C3⋊D9C2×C3×D3semidirect
350. C2×D3×C9C2×C3×D3semidirect
351. C2×D3×C9C2×C3×D3semidirect
364. 3−1+2⋊C4D32semidirect
372. C3×Dic9C2×C3×D3semidirect
373. C3×Dic9C2×C3×D3semidirect
385. C3×3−1+2D3×D4semidirect
386. C3×3−1+2D3×D4semidirect
388. C32×C9C2×C3×D4semidirect
437. #625AGL(1,ℤ/9)semidirect
635. C2×C3×D3C2×AGL(1,ℤ/9)semidirect
636. C2×C3×D3C2×AGL(1,ℤ/9)semidirect
654. C3⋊Dic3C2×AGL(1,ℤ/9)semidirect
690. Dic9C3×D32semidirect
718. 3−1+2#3802semidirect
729. C3×C9C3×D3×D4semidirect
730. C3×C9C3×D3×D4semidirect
911. C2×D3D3×AGL(1,ℤ/9)semidirect
912. C2×D3D3×AGL(1,ℤ/9)semidirect
945. C32D4×AGL(1,ℤ/9)semidirect
956. C9C3×#3802semidirect
1025. C3#88668⋊C3semidirect
1026. C3#88668⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C3⋊AGL(1,ℤ/9)2
#10619897⋊C32
#145186972
3−1+2×#6252
C3×#6195⋊C32
C3×#889543
#88668⋊C33
#130483013