Finite Group Databasebeta

← #72220051

Subgroups — #72220051

Order 5184.

1757 conjugacy classes of subgroups.

The subgroup lattice has 871 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72219981C212yesmaximal, complemented
23−1+2×#833C211yesmaximal, characteristic, complemented
3C3×#63391⋊C3C211yesmaximal, characteristic, complemented
4#72219893C212yesmaximal, complemented
5C2×D4×C3⋊AGL(1,ℤ/9)C211yesmaximal, characteristic
6C3×#10591503—31nomaximal
7#100×AGL(1,ℤ/9)—31nomaximal
8#13140387C311yesmaximal, characteristic, complemented
9C23×C3⋊AGL(1,ℤ/9)C412yes—
10C2×C3×D4×3−1+2C2211yescharacteristic
11C2×#10619980C412yes—
12D4×C3⋊AGL(1,ℤ/9)—22no—
13D4×C3⋊AGL(1,ℤ/9)—22no—
14C2×C4⋊(C3⋊AGL(1,ℤ/9))C2211yescharacteristic
15C2×C4×C3⋊AGL(1,ℤ/9)C2211yescharacteristic
163−1+2×#208C2212yescomplemented
17C3×#3667⋊C3C2212yescomplemented
18#88414⋊C3—22no—
19(C3⋊AGL(1,ℤ/9))⋊C8—22no—
20C2×C3×D4×C3⋊D3—31no—
21C3×#63818—32no—
22C2×D4×C3⋊D9C2×C311yescharacteristic
23C2×D4×AGL(1,ℤ/9)—31no—
24C2×D4×AGL(1,ℤ/9)—61no—
25C32×#833—31no—
26C32×#833D311yescharacteristic
27C3×#63559—32no—
28M16×AGL(1,ℤ/9)—32no—
29#11720863C2×C312yescomplemented
303−1+2×#100—31no—
31#63391⋊C3—21no—
32#63391⋊C3D311yescharacteristic, complemented
33C9×#833—21no—
34C9×#833C2×C311yescharacteristic, complemented
35C3×#63391C2×C311yescharacteristic, complemented
36#63383⋊C3—32no—
37#11720288C2×C312yescomplemented
38C23×C3×3−1+2C2×C412yes—
39C22×C3⋊AGL(1,ℤ/9)—22no—
40C22×C3⋊AGL(1,ℤ/9)—22no—
41C22×C3⋊AGL(1,ℤ/9)—44no—
42C22×C3⋊AGL(1,ℤ/9)C2×C411yescharacteristic
43C22×C3⋊AGL(1,ℤ/9)C2×C412yes—
44C3×D4×3−1+2—22no—
45C2×C3×C4×3−1+2C2311yescharacteristic
46#10619980—24no—
47C2×C3⋊(3−1+2⋊C4)C2×C411yescharacteristic
48C4⋊(C3⋊AGL(1,ℤ/9))—22no—
49C4×C3⋊AGL(1,ℤ/9)D412yes—
50C4×C3⋊AGL(1,ℤ/9)D412yes—
51C3⋊C8×3−1+2—22no—
52C3×3−1+2⋊C8—22no—
53C3×D3×#100—91no—
54C3×D3×#100—91no—
55#10591503—31no—
56D9×#100—31no—
57C23×C3×C3⋊D3—32no—
58C2×C33×D4C2×D311yescharacteristic
59C2×C3×#638—32no—
60C3×D4×C3⋊D3—62no—
61C3×D4×C3⋊D3—62no—
62C2×C3×C4⋊(C3⋊D3)—31no—
63C2×C3×C4×C3⋊D3—31no—
64C23×C3⋊D9C3×C412yes—
65C23×AGL(1,ℤ/9)—32no—
66C23×AGL(1,ℤ/9)—62no—
67C32×#208—32no—
68C32×#208C2×D312yes—
69C3×#3712—62no—
70C3×#3710—62no—
71C2×D4×3−1+2—21no—
72C2×D4×3−1+2—21no—
73C2×D4×3−1+2—41no—
74C2×D4×3−1+2C2×D311yescharacteristic
75C2×C3×D4×C9—21no—
76C2×C3×D4×C9C22×C311yescharacteristic
77C2×#6233C3×C412yes—
78D4×C3⋊D9—22no—
79D4×C3⋊D9—22no—
80C2×C4⋊(C3⋊D9)C22×C311yescharacteristic
81C2×C4×C3⋊D9C22×C311yescharacteristic
82C2×#611⋊C3—32no—
83C2×#611⋊C3—62no—
84D4×AGL(1,ℤ/9)—62no—
85D4×AGL(1,ℤ/9)—62no—
86D4×AGL(1,ℤ/9)—64no—
87D4×AGL(1,ℤ/9)—64no—
88C2×C4⋊AGL(1,ℤ/9)—31no—
89C2×C4⋊AGL(1,ℤ/9)—61no—
90C2×C4×AGL(1,ℤ/9)—31no—
91C2×C4×AGL(1,ℤ/9)—61no—
92M16×3−1+2—32no—
93#3667⋊C3—22no—
94#3667⋊C3C2×D312yescomplemented
95C9×#208—22no—
96C9×#208C22×C312yescomplemented
97C3×#3667C22×C312yescomplemented
98#3663⋊C3—62no—
99C8×AGL(1,ℤ/9)—62no—
100#88414—22no—
101(C3⋊D9)⋊C8—22no—
102C22×C3×3−1+2—22no—
103C22×C3×3−1+2—42no—
104C22×C3×3−1+2C22×C411yescharacteristic
105C2×C3⋊AGL(1,ℤ/9)—22no—
106C2×C3⋊AGL(1,ℤ/9)—22no—
107C2×C3⋊AGL(1,ℤ/9)—44no—
108C2×C3⋊AGL(1,ℤ/9)—44no—
109C2×C3⋊AGL(1,ℤ/9)—42no—
110C2×C3⋊AGL(1,ℤ/9)C22⋊C411yescharacteristic
111C2×C3⋊AGL(1,ℤ/9)C22⋊C411yescharacteristic
112C3×C4×3−1+2C2×D412yes—
113C3⋊(3−1+2⋊C4)C22⋊C412yes—
114C2×D4×C3⋊D3—31no—
115C2×C3×D3×D4—91no—
116C2×C3×D3×D4—91no—
117C2×C3×D3×D4—181no—
118C3×D3×M16—92no—
119C3×D3×M16—92no—
120#63818—32no—
121C2×D4×D9—31no—
122C2×D4×D9—61no—
123C32×#100—31no—
124C32×#100—91no—
125C3×#833—31no—
126C3×#833—31no—
127C3×#833—31no—
128C3×#833—61no—
129C3×#833C3×D311yescharacteristic
130C3×#823—92no—
131C3×#823—92no—
132#63559—32no—
133M16×D9—32no—
134C9×#100—31no—
135C9×#100—61no—
136#63391C3×D311yescharacteristic, complemented
137#63383—32no—
138C23×C33C4×D312yes—
139C22×C3×C3⋊D3—31no—
140C22×C3×C3⋊D3—32no—
141C22×C3×C3⋊D3—62no—
142C22×C3×C3⋊D3—62no—
143C22×C3×C3⋊D3—124no—
144C33×D4—22no—
145C2×C33×C4C22×D311yescharacteristic
146C3×#638—64no—
147C2×C3×C3⋊Dic3—31no—
148C3×C4⋊(C3⋊D3)—62no—
149C3×C4×C3⋊D3—32no—
150C3×C4×C3⋊D3—32no—
151C23×3−1+2—22no—
152C23×3−1+2—22no—
153C23×3−1+2—42no—
154C23×3−1+2C4×D312yes—
155C23×C3×C9—22no—
156C23×C3×C9C2×C3×C412yes—
157C22×C3⋊D9—22no—
158C22×C3⋊D9—22no—
159C22×C3⋊D9—44no—
160C22×C3⋊D9C2×C3×C411yescharacteristic
161C22×C3⋊D9C2×C3×C412yes—
162C22×AGL(1,ℤ/9)—31no—
163C22×AGL(1,ℤ/9)—32no—
164C22×AGL(1,ℤ/9)—62no—
165C22×AGL(1,ℤ/9)—62no—
166C22×AGL(1,ℤ/9)—61no—
167C22×AGL(1,ℤ/9)—62no—
168C22×AGL(1,ℤ/9)—64no—
169C22×AGL(1,ℤ/9)—64no—
170C22×AGL(1,ℤ/9)—128no—
171C22×AGL(1,ℤ/9)—124no—
172C32×C3⋊C8—22no—
173C32×C3⋊C8—62no—
174D4×3−1+2—24no—
175D4×3−1+2—22no—
176D4×3−1+2—42no—
177D4×3−1+2—44no—
178C3×D4×C9—22no—
179C3×D4×C9—42no—
180C2×C4×3−1+2—21no—
181C2×C4×3−1+2—21no—
182C2×C4×3−1+2—41no—
183C2×C4×3−1+2C22×D311yescharacteristic
184C2×C3×C4×C9—21no—
185C2×C3×C4×C9C23×C311yescharacteristic
186#6233—24no—
187C2×C3⋊Dic9C2×C3×C411yescharacteristic
188C4⋊(C3⋊D9)—22no—
189C4×C3⋊D9C3×D412yes—
190C4×C3⋊D9C3×D412yes—
191#611⋊C3—64no—
192#611⋊C3—68no—
193C2×3−1+2⋊C4—31no—
194C2×3−1+2⋊C4—61no—
195C4⋊AGL(1,ℤ/9)—64no—
196C4⋊AGL(1,ℤ/9)—62no—
197C4×AGL(1,ℤ/9)—32no—
198C4×AGL(1,ℤ/9)—32no—
199C4×AGL(1,ℤ/9)—62no—
200C4×AGL(1,ℤ/9)—62no—
201C8×3−1+2—62no—
2023−1+2⋊C8—22no—
2033−1+2⋊C8—42no—
204C9×C3⋊C8—22no—
205C9×C3⋊C8—42no—
206C3×C9⋊C8—22no—
207C2×C3×#100—271no—
208D3×#100—91no—
209D3×#100—91no—
210C2×C3×3−1+2—21no—
211C2×C3×3−1+2—42no—
212C2×C3×3−1+2C2×C22⋊C411yescharacteristic
213C3⋊AGL(1,ℤ/9)—21no—
214C3⋊AGL(1,ℤ/9)—42no—
215C3⋊AGL(1,ℤ/9)#10012yescomplemented
216C23×C3⋊D3—32no—
217C23×C3×D3—92no—
218C23×C3×D3—92no—
219C23×C3×D3—182no—
220C2×C32×D4—21no—
221C2×C32×D4—31no—
222C2×C32×D4—61no—
223C2×C32×D4D3211yescharacteristic
224C2×C32×D4C2×C3×D311yescharacteristic
225C2×#638—32no—
226D4×C3⋊D3—62no—
227D4×C3⋊D3—62no—
228C2×C4⋊(C3⋊D3)—31no—
229C2×C4×C3⋊D3—31no—
230C2×C3×#67—92no—
231C2×C3×#67—92no—
232C2×C3×#67—182no—
233C3×D3×D4—182no—
234C3×D3×D4—182no—
235C3×D3×D4—182no—
236C3×D3×D4—182no—
237C3×D3×D4—184no—
238C3×D3×D4—184no—
239C2×C3×D12—91no—
240C2×C3×D12—91no—
241C2×C3×D12—181no—
242C2×C3×C4×D3—91no—
243C2×C3×C4×D3—91no—
244C2×C3×C4×D3—181no—
245C23×D9—32no—
246C23×D9—62no—
247C32×M16—32no—
248C32×M16—92no—
249C3×#208—32no—
250C3×#208—32no—
251C3×#208—32no—
252C3×#208—62no—
253C3×#208C2×C3×D312yes—
254C3×ΓL(1,𝔽25)—182no—
255C3×ΓL(1,𝔽25)—182no—
256C3×D3×C8—182no—
257C3×D3×C8—182no—
258#3712—62no—
259#3710—62no—
260C2×D4×C9—21no—
261C2×D4×C9—21no—
262C2×D4×C9—41no—
263C2×D4×C9C2×C3×D311yescharacteristic
264C2×#611—32no—
265C2×#611—62no—
266D4×D9—62no—
267D4×D9—62no—
268D4×D9—64no—
269D4×D9—64no—
270C2×D36—31no—
271C2×D36—61no—
272C2×C4×D9—31no—
273C2×C4×D9—61no—
274C9×M16—32no—
275C9×M16—62no—
276#3667C2×C3×D312yescomplemented
277#3663—62no—
278C8×D9—62no—
279C22×C33—22no—
280C22×C33—42no—
281C22×C33C2×C4×D311yescharacteristic
282C2×C3×C3⋊D3—31no—
283C2×C3×C3⋊D3—31no—
284C2×C3×C3⋊D3—62no—
285C2×C3×C3⋊D3—62no—
286C2×C3×C3⋊D3—124no—
287C2×C3×C3⋊D3—124no—
288C2×C3×C3⋊D3—122no—
289C33×C4D3×D412yes—
290C3×C3⋊Dic3—32no—
291C22×3−1+2—21no—
292C22×3−1+2—24no—
293C22×3−1+2—21no—
294C22×3−1+2—22no—
295C22×3−1+2—44no—
296C22×3−1+2—42no—
297C22×3−1+2—42no—
298C22×3−1+2—41no—
299C22×3−1+2—44no—
300C22×3−1+2—84no—
301C22×3−1+2—82no—
302C22×3−1+2C2×C4×D311yescharacteristic
303C22×C3×C9—21no—
304C22×C3×C9—22no—
305C22×C3×C9—42no—
306C22×C3×C9—42no—
307C22×C3×C9—82no—
308C22×C3×C9C22×C3×C411yescharacteristic
309C2×C3⋊D9—22no—
310C2×C3⋊D9—22no—
311C2×C3⋊D9—44no—
312C2×C3⋊D9—44no—
313C2×C3⋊D9—42no—
314C2×C3⋊D9C3×C22⋊C411yescharacteristic
315C2×C3⋊D9C3×C22⋊C411yescharacteristic
316C2×AGL(1,ℤ/9)—31no—
317C2×AGL(1,ℤ/9)—31no—
318C2×AGL(1,ℤ/9)—62no—
319C2×AGL(1,ℤ/9)—61no—
320C2×AGL(1,ℤ/9)—61no—
321C2×AGL(1,ℤ/9)—64no—
322C2×AGL(1,ℤ/9)—64no—
323C2×AGL(1,ℤ/9)—62no—
324C2×AGL(1,ℤ/9)—124no—
325C2×AGL(1,ℤ/9)—128no—
326C2×AGL(1,ℤ/9)—128no—
327C2×AGL(1,ℤ/9)—124no—
328C2×AGL(1,ℤ/9)—124no—
329C2×AGL(1,ℤ/9)—122no—
330C4×3−1+2—22no—
331C4×3−1+2—22no—
332C4×3−1+2—42no—
333C4×3−1+2D3×D412yes—
334C3×C4×C9—22no—
335C3×C4×C9C2×C3×D412yes—
336C3⋊Dic9C3×C22⋊C412yes—
3373−1+2⋊C4—32no—
3383−1+2⋊C4—62no—
339C22×C3×D4—271no—
340C2×D3×D4—91no—
341C2×D3×D4—91no—
342C2×D3×D4—181no—
343C2×C3×M16—272no—
344D3×M16—92no—
345D3×M16—92no—
346C3×#100—31no—
347C3×#100—91no—
348C3×#100—91no—
349C3×#100—91no—
350C3×#100—181no—
351C3×#100—272no—
352#833—31no—
353#833AGL(1,ℤ/9)11yescharacteristic, complemented
354#823—92no—
355#823—92no—
356C3×3−1+2C2×#10011yescharacteristic, complemented, Sylow
357C23×C32—22no—
358C23×C32—32no—
359C23×C32—62no—
360C23×C32#62412yes—
361C23×C32C3×C4×D312yes—
362C22×C3⋊D3—31no—
363C22×C3⋊D3—32no—
364C22×C3⋊D3—62no—
365C22×C3⋊D3—62no—
366C22×C3⋊D3—124no—
367C22×C3×D3—91no—
368C22×C3×D3—91no—
369C22×C3×D3—92no—
370C22×C3×D3—92no—
371C22×C3×D3—181no—
372C22×C3×D3—182no—
373C22×C3×D3—182no—
374C22×C3×D3—182no—
375C22×C3×D3—182no—
376C22×C3×D3—182no—
377C22×C3×D3—184no—
378C22×C3×D3—184no—
379C22×C3×D3—368no—
380C22×C3×D3—364no—
381C22×C3×D3—364no—
382C32×D4—22no—
383C32×D4—22no—
384C32×D4—42no—
385C32×D4—62no—
386C32×D4—64no—
387C2×C32×C4—21no—
388C2×C32×C4—31no—
389C2×C32×C4—61no—
390C2×C32×C4C2×D3211yescharacteristic
391C2×C32×C4C22×C3×D311yescharacteristic
392#638—64no—
393C2×C3⋊Dic3—31no—
394C4⋊(C3⋊D3)—62no—
395C4×C3⋊D3—32no—
396C4×C3⋊D3—32no—
397C3×#67—184no—
398C3×#67—184no—
399C3×#67—188no—
400C2×C3×Dic3—91no—
401C2×C3×Dic3—91no—
402C2×C3×Dic3—181no—
403C3×D12—182no—
404C3×D12—184no—
405C3×D12—182no—
406C3×C4×D3—92no—
407C3×C4×D3—92no—
408C3×C4×D3—92no—
409C3×C4×D3—92no—
410C3×C4×D3—182no—
411C3×C4×D3—182no—
412C23×C9—22no—
413C23×C9—22no—
414C23×C9—42no—
415C23×C9C3×C4×D312yes—
416C22×D9—31no—
417C22×D9—32no—
418C22×D9—61no—
419C22×D9—62no—
420C22×D9—62no—
421C22×D9—62no—
422C22×D9—64no—
423C22×D9—64no—
424C22×D9—128no—
425C22×D9—124no—
426C32×C8—62no—
427C32×C8—182no—
428C3×C3⋊C8—22no—
429C3×C3⋊C8—62no—
430C3×C3⋊C8—62no—
431C3×C3⋊C8—62no—
432C3×C3⋊C8—122no—
433D4×C9—24no—
434D4×C9—22no—
435D4×C9—42no—
436D4×C9—44no—
437C2×C4×C9—21no—
438C2×C4×C9—21no—
439C2×C4×C9—41no—
440C2×C4×C9C22×C3×D311yescharacteristic
441#611—64no—
442#611—68no—
443C2×Dic9—31no—
444C2×Dic9—61no—
445D36—64no—
446D36—62no—
447C4×D9—32no—
448C4×D9—32no—
449C4×D9—62no—
450C4×D9—62no—
451C8×C9—62no—
452C8×C9—122no—
453C9⋊C8—22no—
454C2×#100—271noSylow
455C2×C33—21no—
456C2×C33—42no—
457C2×C33D3×C22⋊C411yescharacteristic
458C3×C3⋊D3—32no—
459C3×C3⋊D3—61no—
460C3×C3⋊D3—122no—
461C2×3−1+2—22no—
462C2×3−1+2—21no—
463C2×3−1+2—21no—
464C2×3−1+2—21no—
465C2×3−1+2—41no—
466C2×3−1+2—41no—
467C2×3−1+2—42no—
468C2×3−1+2—44no—
469C2×3−1+2—42no—
470C2×3−1+2—82no—
471C2×3−1+2—84no—
472C2×3−1+2D3×C22⋊C411yescharacteristic
473C2×C3×C9—21no—
474C2×C3×C9—21no—
475C2×C3×C9—41no—
476C2×C3×C9—42no—
477C2×C3×C9—82no—
478C2×C3×C9C2×C3×C22⋊C411yescharacteristic
479C3⋊D9—21no—
480C3⋊D9—42no—
481C3⋊D9C3×#10012yescomplemented
482AGL(1,ℤ/9)—32no—
483AGL(1,ℤ/9)—62no—
484AGL(1,ℤ/9)—62no—
485AGL(1,ℤ/9)—61no—
486AGL(1,ℤ/9)—124no—
487AGL(1,ℤ/9)—122no—
488C24×C3—272no—
489C23×D3—92no—
490C23×D3—92no—
491C23×D3—182no—
492C2×C3×D4—21no—
493C2×C3×D4—31no—
494C2×C3×D4—61no—
495C2×C3×D4—271no—
496C2×C3×D4—272no—
497C2×C3×D4—542no—
498C2×C3×D4—542no—
499C2×C3×D4C2×AGL(1,ℤ/9)11yescharacteristic
500C2×C3×D4C3×D3211yescharacteristic
501C22×C3×C4—271no—
502C2×#67—92no—
503C2×#67—92no—
504C2×#67—182no—
505D3×D4—182no—
506D3×D4—182no—
507D3×D4—182no—
508D3×D4—182no—
509D3×D4—184no—
510D3×D4—184no—
511C2×D12—91no—
512C2×D12—91no—
513C2×D12—181no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—181no—
517C3×M16—32no—
518C3×M16—92no—
519C3×M16—92no—
520C3×M16—92no—
521C3×M16—182no—
522C3×M16—542no—
523C2×C3×C8—542no—
524#208—32no—
525#208C2×AGL(1,ℤ/9)12yescomplemented
526ΓL(1,𝔽25)—182no—
527ΓL(1,𝔽25)—182no—
528D3×C8—182no—
529D3×C8—182no—
530C22×C32—22no—
531C22×C32—22no—
532C22×C32—21no—
533C22×C32—31no—
534C22×C32—42no—
535C22×C32—42no—
536C22×C32—42no—
537C22×C32—61no—
538C22×C32—62no—
539C22×C32—64no—
540C22×C32—82no—
541C22×C32—122no—
542C22×C32—124no—
543C22×C32C2×#62411yescharacteristic
544C22×C32C2×C3×C4×D311yescharacteristic
545C2×C3⋊D3—31no—
546C2×C3⋊D3—31no—
547C2×C3⋊D3—62no—
548C2×C3⋊D3—62no—
549C2×C3⋊D3—124no—
550C2×C3⋊D3—124no—
551C2×C3⋊D3—122no—
552C2×C3×D3—91no—
553C2×C3×D3—91no—
554C2×C3×D3—91no—
555C2×C3×D3—91no—
556C2×C3×D3—181no—
557C2×C3×D3—181no—
558C2×C3×D3—182no—
559C2×C3×D3—182no—
560C2×C3×D3—184no—
561C2×C3×D3—182no—
562C2×C3×D3—184no—
563C2×C3×D3—182no—
564C2×C3×D3—364no—
565C2×C3×D3—364no—
566C2×C3×D3—364no—
567C2×C3×D3—368no—
568C2×C3×D3—364no—
569C2×C3×D3—368no—
570C2×C3×D3—364no—
571C2×C3×D3—362no—
572C2×C3×D3—362no—
573C32×C4—22no—
574C32×C4—32no—
575C32×C4—62no—
576C32×C4#381112yes—
577C32×C4C3×D3×D412yes—
578C3⋊Dic3—32no—
579C3×Dic3—92no—
580C3×Dic3—92no—
581C3×Dic3—182no—
582C22×C9—24no—
583C22×C9—22no—
584C22×C9—21no—
585C22×C9—21no—
586C22×C9—42no—
587C22×C9—44no—
588C22×C9—42no—
589C22×C9—44no—
590C22×C9—41no—
591C22×C9—82no—
592C22×C9—84no—
593C22×C9C2×C3×C4×D311yescharacteristic
594C2×D9—31no—
595C2×D9—31no—
596C2×D9—61no—
597C2×D9—61no—
598C2×D9—62no—
599C2×D9—64no—
600C2×D9—64no—
601C2×D9—62no—
602C2×D9—124no—
603C2×D9—128no—
604C2×D9—128no—
605C2×D9—124no—
606C2×D9—124no—
607C2×D9—122no—
608C4×C9—22no—
609C4×C9—22no—
610C4×C9—42no—
611C4×C9C3×D3×D412yes—
612Dic9—32no—
613Dic9—62no—
614C22×D4—271no—
615C2×M16—272no—
616#100—31no—
617#100—91no—
618#100—272no—
619C33D3×#10011yescharacteristic
6203−1+2—21no—
6213−1+2—21no—
6223−1+2—41no—
6233−1+2D3×#10011yescharacteristic, complemented
624C3×C9—21no—
625C3×C9C2×C3×#10011yescharacteristic, complemented
626C23×C3—22no—
627C23×C3—32no—
628C23×C3—62no—
629C23×C3—271no—
630C23×C3—272no—
631C23×C3—542no—
632C23×C3—542no—
633C23×C3—1084no—
634C23×C3C4×AGL(1,ℤ/9)12yes—
635C23×C3C3×#62412yes—
636C22×D3—91no—
637C22×D3—91no—
638C22×D3—92no—
639C22×D3—92no—
640C22×D3—181no—
641C22×D3—182no—
642C22×D3—182no—
643C22×D3—182no—
644C22×D3—182no—
645C22×D3—182no—
646C22×D3—184no—
647C22×D3—184no—
648C22×D3—368no—
649C22×D3—364no—
650C22×D3—364no—
651C3×D4—24no—
652C3×D4—22no—
653C3×D4—22no—
654C3×D4—62no—
655C3×D4—122no—
656C3×D4—542no—
657C3×D4—544no—
658C2×C3×C4—21no—
659C2×C3×C4—31no—
660C2×C3×C4—61no—
661C2×C3×C4—272no—
662C2×C3×C4—272no—
663C2×C3×C4—271no—
664C2×C3×C4C22×AGL(1,ℤ/9)11yescharacteristic
665C2×C3×C4C2×C3×D3211yescharacteristic
666#67—184no—
667#67—184no—
668#67—188no—
669C2×Dic3—91no—
670C2×Dic3—91no—
671C2×Dic3—181no—
672D12—184no—
673D12—182no—
674D12—182no—
675C4×D3—92no—
676C4×D3—92no—
677C4×D3—92no—
678C4×D3—92no—
679C4×D3—182no—
680C4×D3—182no—
681C3×C8—62no—
682C3×C8—182no—
683C3×C8—182no—
684C3×C8—182no—
685C3×C8—362no—
686C3⋊C8—22no—
687C3⋊C8—62no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—31no—
692C2×C32—41no—
693C2×C32—42no—
694C2×C32—42no—
695C2×C32—61no—
696C2×C32—61no—
697C2×C32—62no—
698C2×C32—82no—
699C2×C32—122no—
700C2×C32—124no—
701C2×C32#6397411yescharacteristic
702C2×C32C3×D3×C22⋊C411yescharacteristic
703C3⋊D3—32no—
704C3⋊D3—61no—
705C3⋊D3—122no—
706C3×D3—92no—
707C3×D3—92no—
708C3×D3—182no—
709C3×D3—181no—
710C3×D3—182no—
711C3×D3—181no—
712C3×D3—362no—
713C3×D3—364no—
714C3×D3—362no—
715C2×C9—22no—
716C2×C9—21no—
717C2×C9—21no—
718C2×C9—21no—
719C2×C9—41no—
720C2×C9—42no—
721C2×C9—44no—
722C2×C9—42no—
723C2×C9—41no—
724C2×C9—82no—
725C2×C9—84no—
726C2×C9C3×D3×C22⋊C411yescharacteristic
727D9—32no—
728D9—62no—
729D9—62no—
730D9—61no—
731D9—124no—
732D9—122no—
733C24—272no—
734C2×D4—272no—
735C2×D4—271no—
736C2×D4—542no—
737C2×D4—542no—
738C2×D4D3×AGL(1,ℤ/9)11yescharacteristic
739C22×C4—271no—
740M16—32no—
741M16—92no—
742M16—542no—
743C2×C8—542no—
744C22×C3—24no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—21no—
748C22×C3—31no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—44no—
752C22×C3—62no—
753C22×C3—61no—
754C22×C3—122no—
755C22×C3—122no—
756C22×C3—242no—
757C22×C3—271no—
758C22×C3—271no—
759C22×C3—542no—
760C22×C3—542no—
761C22×C3—1082no—
762C22×C3—1084no—
763C22×C3—1084no—
764C22×C3C2×C4×AGL(1,ℤ/9)11yescharacteristic
765C22×C3C2×C3×#62411yescharacteristic
766C2×D3—91no—
767C2×D3—91no—
768C2×D3—91no—
769C2×D3—91no—
770C2×D3—181no—
771C2×D3—181no—
772C2×D3—182no—
773C2×D3—182no—
774C2×D3—184no—
775C2×D3—184no—
776C2×D3—182no—
777C2×D3—182no—
778C2×D3—364no—
779C2×D3—364no—
780C2×D3—364no—
781C2×D3—368no—
782C2×D3—368no—
783C2×D3—364no—
784C2×D3—364no—
785C2×D3—362no—
786C2×D3—362no—
787C3×C4—22no—
788C3×C4—32no—
789C3×C4—62no—
790C3×C4—272no—
791C3×C4D4×AGL(1,ℤ/9)12yes—
792C3×C4C3×#381112yes—
793Dic3—92no—
794Dic3—92no—
795Dic3—182no—
796C32—21no—
797C32—31no—
798C32—61no—
799C32#1059150311yescharacteristic
800C32C3×D3×#10011yescharacteristic
801C9—21no—
802C9—21no—
803C9—41no—
804C9C3×D3×#10011yescharacteristic, complemented
805C23—271no—
806C23—272no—
807C23—542no—
808C23—542no—
809C23—1084no—
810C23(C3⋊AGL(1,ℤ/9))⋊C412yes—
811D4—22no—
812D4—544no—
813D4—542no—
814C2×C4—271no—
815C2×C4—272no—
816C2×C4—272no—
817C2×C4C2×D3×AGL(1,ℤ/9)11yescharacteristic
818C8—62no—
819C8—182no—
820C2×C3—22no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—31no—
825C2×C3—44no—
826C2×C3—42no—
827C2×C3—42no—
828C2×C3—61no—
829C2×C3—61no—
830C2×C3—121no—
831C2×C3—122no—
832C2×C3—242no—
833C2×C3—272no—
834C2×C3—541no—
835C2×C3—1082no—
836C2×C3C22⋊C4×AGL(1,ℤ/9)11yescharacteristic
837C2×C3C3×#6397411yescharacteristic
838D3—92no—
839D3—92no—
840D3—182no—
841D3—182no—
842D3—181no—
843D3—181no—
844D3—364no—
845D3—362no—
846D3—362no—
847C22—22no—
848C22—42no—
849C22—271no—
850C22—271no—
851C22—542no—
852C22—542no—
853C22—1082no—
854C22—1084no—
855C22—1084no—
856C22C2×(C3⋊AGL(1,ℤ/9))⋊C411yescharacteristic
857C4—272no—
858C4#88668⋊C312yes—
859C3—21no—
860C3—31no—
861C3—61no—
862C3#100×AGL(1,ℤ/9)11yescharacteristic, complemented
863C3C3×#1059150311yescharacteristic
864C2—21no—
865C2—42no—
866C2—272no—
867C2—541no—
868C2—1082no—
869C2#7222005011yescharacteristic
subgroupG/H
centerC2#72220050
commutatorC22×C3×C9C22×C3×C4
FrattiniC2×C3×C4C2×C3×D32
FittingC2×C3×D4×3−1+2C22
socleC2×C32C3×D3×C22⋊C4
prime radicalC2×D4×C3⋊AGL(1,ℤ/9)C2
cosocleC2×C3×C4×C9C23×C3
hypercenterC2×D4D3×AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×#100
LCSG ▷ C22×C3×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. 3−1+2×#833C2semidirect
3. C3×#63391⋊C3C2semidirect
4. #72219893C2semidirect
8. #13140387C3semidirect
16. 3−1+2×#208C22semidirect
17. C3×#3667⋊C3C22semidirect
29. #11720863C2×C3semidirect
32. #63391⋊C3D3semidirect
34. C9×#833C2×C3semidirect
35. C3×#63391C2×C3semidirect
37. #11720288C2×C3semidirect
94. #3667⋊C3C2×D3semidirect
96. C9×#208C22×C3semidirect
97. C3×#3667C22×C3semidirect
136. #63391C3×D3semidirect
215. C3⋊AGL(1,ℤ/9)#100semidirect
276. #3667C2×C3×D3semidirect
353. #833AGL(1,ℤ/9)semidirect
356. C3×3−1+2C2×#100semidirect
481. C3⋊D9C3×#100semidirect
525. #208C2×AGL(1,ℤ/9)semidirect
623. 3−1+2D3×#100semidirect
625. C3×C9C2×C3×#100semidirect
804. C9C3×D3×#100semidirect
862. C3#100×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
#722199812
3−1+2×#8332
C3×#63391⋊C32
#722198932
C2×D4×C3⋊AGL(1,ℤ/9)2
C3×#105915033
#100×AGL(1,ℤ/9)3
#131403873