Finite Group Databasebeta

← #72220002

Subgroups — #72220002

Order 5184.

1376 conjugacy classes of subgroups.

The subgroup lattice has 1173 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72219968C211yesmaximal, characteristic, complemented
2#72219967C211yesmaximal, characteristic, complemented
33−1+2×#805C211yesmaximal, characteristic, complemented
4C3×#63364⋊C3C211yesmaximal, characteristic, complemented
5#72219929C211yesmaximal, characteristic
6C42×C3⋊AGL(1,ℤ/9)C211yesmaximal, characteristic, complemented
7#72219893C211yesmaximal, characteristic, complemented
8C3×#10590393—31nomaximal
9#104×AGL(1,ℤ/9)—31nomaximal
10#13137291C311yesmaximal, characteristic, complemented
11C2×C4×C3⋊AGL(1,ℤ/9)—21no—
12C2×C4×C3⋊AGL(1,ℤ/9)C2211yescharacteristic
133−1+2×#235C2211yescharacteristic
14C3×#3697⋊C3C2211yescharacteristic
15#88668⋊C3—21no—
16#88663⋊C3—21no—
17#88646⋊C3C411yescharacteristic, complemented
18C4×D3×AGL(1,ℤ/9)—21no—
19#88640⋊C3—21no—
20#88639⋊C3C411yescharacteristic, complemented
21(C3⋊AGL(1,ℤ/9))⋊Q8C411yescharacteristic, complemented
22#88634⋊C3C411yescharacteristic, complemented
23C3×C42×3−1+2C2211yescharacteristic, complemented
24C4×C3⋊(3−1+2⋊C4)—21no—
25C4×C3⋊(3−1+2⋊C4)C2211yescharacteristic, complemented
263−1+2×#208C2211yescharacteristic, complemented
27C3×#3667⋊C3C2211yescharacteristic, complemented
28#88414⋊C3—21no—
29(C3⋊AGL(1,ℤ/9))⋊C8—21no—
30C3×#64306—31no—
31C3×C42×C3⋊D3—31no—
32C3×#63818—31no—
33#41×AGL(1,ℤ/9)—31no—
34#11722475C2×C311yescharacteristic
35C32×#805—31no—
36C32×#805D311yescharacteristic
37C3×#63568—31no—
38C3×#63568—31no—
39C42×C3⋊D9C2×C311yescharacteristic, complemented
40M16×AGL(1,ℤ/9)—31no—
41C42×AGL(1,ℤ/9)—31no—
42C42×AGL(1,ℤ/9)—61no—
43#11720863C2×C311yescharacteristic, complemented
443−1+2×#104—31no—
45#63396⋊C3—31no—
46#63384⋊C3—31no—
47#63364⋊C3—21no—
48#63364⋊C3D311yescharacteristic, complemented
49C9×#805—21no—
50C9×#805C2×C311yescharacteristic, complemented
51C3×#63364C2×C311yescharacteristic, complemented
52#11720300C2×C311yescharacteristic, complemented
53#11720291C2×C311yescharacteristic, complemented
54C22×C3⋊AGL(1,ℤ/9)D411yescharacteristic
55C2×D3×AGL(1,ℤ/9)—21no—
56C2×C3×C4×3−1+2—21no—
57C2×C3×C4×3−1+2C2311yescharacteristic
58C2×C3⋊(3−1+2⋊C4)—21no—
59C2×C3⋊(3−1+2⋊C4)D411yescharacteristic
60C4×C3⋊AGL(1,ℤ/9)—24no—
61C4×C3⋊AGL(1,ℤ/9)C2×C411yescharacteristic
62C4×C3⋊AGL(1,ℤ/9)C2×C411yescharacteristic
63C4×C3⋊AGL(1,ℤ/9)D411yescharacteristic
64C4×C3⋊AGL(1,ℤ/9)D411yescharacteristic
65#67×3−1+2—21no—
66C3×#611⋊C3—21no—
67D12×3−1+2C2×C411yescharacteristic, complemented
68C4×D3×3−1+2—21no—
69C3×C4⋊AGL(1,ℤ/9)C2×C411yescharacteristic, complemented
70C3×C4×AGL(1,ℤ/9)—21no—
71Dic6×3−1+2C2×C411yescharacteristic, complemented
72C3×3−1+2⋊Q8C2×C411yescharacteristic, complemented
73#6195⋊C3—21no—
74#6194⋊C3—21no—
75D3×3−1+2⋊C4—21no—
76#6192⋊C3—21no—
77(C3⋊AGL(1,ℤ/9))⋊C4—21no—
78Dic3×AGL(1,ℤ/9)—21no—
79#6189⋊C3—21no—
80C3⋊C8×3−1+2—21no—
81C3×3−1+2⋊C8—21no—
82C3×D3×#104—91no—
83C3×D3×#104—91no—
84#10590393—31no—
85D9×#104—31no—
86C2×C3×C4×C3⋊D3—31no—
87C2×C3×C4×C3⋊D3—61no—
88C32×#235—31no—
89C32×#235C2×D311yescharacteristic
90C3×#3811—61no—
91C3×#3805—61no—
92C3×#3802—31no—
93C3×C4×D32—61no—
94C3×#3798—61no—
95C3×#3797—31no—
96C3×#3796—31no—
97C3×#3796—31no—
98C33×C42C2×D311yescharacteristic
99C3×C4×C3⋊Dic3—31no—
100C3×C4×C3⋊Dic3—61no—
101C32×#208—31no—
102C32×#208C2×D311yescharacteristic
103C3×#3712—61no—
104C3×#3710—61no—
105#41×3−1+2—31no—
106C2×C4×C3⋊D9—21no—
107C2×C4×C3⋊D9C22×C311yescharacteristic
108#88724—31no—
109Q8×AGL(1,ℤ/9)—31no—
110#3699⋊C3—31no—
111#3699⋊C3—61no—
112D4×AGL(1,ℤ/9)—31no—
113D4×AGL(1,ℤ/9)—61no—
114#3697⋊C3—21no—
115#3697⋊C3—61no—
116#3697⋊C3C2×D311yescharacteristic
117C2×C4×AGL(1,ℤ/9)—31no—
118C2×C4×AGL(1,ℤ/9)—61no—
119C2×C4×AGL(1,ℤ/9)—61no—
120C2×C4×AGL(1,ℤ/9)—61no—
121C2×C4×AGL(1,ℤ/9)—62no—
122C9×#235—21no—
123C9×#235C22×C311yescharacteristic
124C3×#3697C22×C311yescharacteristic
125#88668—21no—
126#88663—21no—
127#88646C3×C411yescharacteristic, complemented
128C4×D3×D9—21no—
129#88640—21no—
130#88639C3×C411yescharacteristic, complemented
131(C3⋊D9)⋊Q8C3×C411yescharacteristic, complemented
132#88634C3×C411yescharacteristic, complemented
133M16×3−1+2—31no—
134C42×3−1+2—21no—
135C42×3−1+2—21no—
136C42×3−1+2—41no—
137C42×3−1+2C2×D311yescharacteristic, complemented
138C3×C42×C9—21no—
139C3×C42×C9C22×C311yescharacteristic, complemented
140C4×C3⋊Dic9—21no—
141C4×C3⋊Dic9C22×C311yescharacteristic, complemented
142C4×3−1+2⋊C4—31no—
143C4×3−1+2⋊C4—61no—
144C4×3−1+2⋊C4—61no—
145C4×3−1+2⋊C4—62no—
146#3667⋊C3—21no—
147#3667⋊C3C2×D311yescharacteristic, complemented
148C9×#208—21no—
149C9×#208C22×C311yescharacteristic, complemented
150C3×#3667C22×C311yescharacteristic, complemented
151#3663⋊C3—61no—
152C8×AGL(1,ℤ/9)—61no—
153#88414—21no—
154(C3⋊D9)⋊C8—21no—
155C22×C3×3−1+2C2×D411yescharacteristic
156C2×C3⋊AGL(1,ℤ/9)—22no—
157C2×C3⋊AGL(1,ℤ/9)C22⋊C411yescharacteristic
158C2×C3⋊AGL(1,ℤ/9)C22⋊C411yescharacteristic
159C2×D3×3−1+2—21no—
160C2×C3×AGL(1,ℤ/9)—21no—
161D3×AGL(1,ℤ/9)—42no—
162C3×C4×3−1+2—22no—
163C3×C4×3−1+2C22×C411yescharacteristic
164C3×C4×3−1+2C2×D411yescharacteristic
165C3⋊(3−1+2⋊C4)—22no—
166C3⋊(3−1+2⋊C4)C22⋊C411yescharacteristic
167C3⋊(3−1+2⋊C4)C22⋊C411yescharacteristic
168Dic3×3−1+2—21no—
169C3×3−1+2⋊C4—21no—
170C3×D3×#41—91no—
171C3×D3×#41—91no—
172#64306—31no—
173C42×C3⋊D3—31no—
174C3×D3×M16—91no—
175C3×D3×M16—91no—
176C3×C42×D3—91no—
177C3×C42×D3—91no—
178C3×C42×D3—181no—
179#63818—31no—
180#41×D9—31no—
181C32×#104—31no—
182C32×#104—91no—
183C3×#837—91no—
184C3×#837—91no—
185C3×#825—91no—
186C3×#825—91no—
187C3×#805—31no—
188C3×#805—31no—
189C3×#805—31no—
190C3×#805—61no—
191C3×#805C3×D311yescharacteristic
192#63568—31no—
193#63568—31no—
194M16×D9—31no—
195C42×D9—31no—
196C42×D9—61no—
197C9×#104—31no—
198C9×#104—61no—
199#63396—31no—
200#63384—31no—
201#63364C3×D311yescharacteristic, complemented
202C22×C3×C3⋊D3—31no—
203C2×C3×D32—61no—
204C2×C33×C4—21no—
205C2×C33×C4C22×D311yescharacteristic
206C2×C3×C3⋊Dic3—31no—
207C2×C3×C3⋊Dic3—61no—
208C3×C4×C3⋊D3—31no—
209C3×C4×C3⋊D3—31no—
210C3×C4×C3⋊D3—31no—
211C3×C4×C3⋊D3—31no—
212C3×C4×C3⋊D3—64no—
213C32×#67—21no—
214C32×#67—61no—
215C32×D12—31no—
216C32×D12C4×D311yescharacteristic
217C32×C4×D3—21no—
218C32×C4×D3—61no—
219C32×Dic6—31no—
220C32×Dic6C4×D311yescharacteristic
221C3×#627—61no—
222C3×#626—61no—
223C3×#626—61no—
224C3×#625—61no—
225C3×#624—61no—
226C3×D3×Dic3—61no—
227C3×D3×Dic3—61no—
228C22×C3⋊D9C3×D411yescharacteristic
229C22×AGL(1,ℤ/9)—31no—
230C22×AGL(1,ℤ/9)—61no—
231C22×AGL(1,ℤ/9)—61no—
232C2×D3×D9—21no—
233C32×C3⋊C8—21no—
234C32×C3⋊C8—61no—
235Q8×3−1+2—31no—
236D4×3−1+2—31no—
237D4×3−1+2—61no—
238C2×C4×3−1+2—22no—
239C2×C4×3−1+2—21no—
240C2×C4×3−1+2—21no—
241C2×C4×3−1+2—21no—
242C2×C4×3−1+2—41no—
243C2×C4×3−1+2—41no—
244C2×C4×3−1+2—42no—
245C2×C4×3−1+2—61no—
246C2×C4×3−1+2C22×D311yescharacteristic
247C2×C3×C4×C9—21no—
248C2×C3×C4×C9—21no—
249C2×C3×C4×C9—41no—
250C2×C3×C4×C9C23×C311yescharacteristic
251C2×C3⋊Dic9—21no—
252C2×C3⋊Dic9C3×D411yescharacteristic
253C4×C3⋊D9—24no—
254C4×C3⋊D9C2×C3×C411yescharacteristic
255C4×C3⋊D9C2×C3×C411yescharacteristic
256C4×C3⋊D9C3×D411yescharacteristic
257C4×C3⋊D9C3×D411yescharacteristic
258#611⋊C3—21no—
259#611⋊C3—41no—
260#611⋊C3—61no—
261#611⋊C3—61no—
262C2×3−1+2⋊C4—31no—
263C2×3−1+2⋊C4—61no—
264C2×3−1+2⋊C4—61no—
265C2×3−1+2⋊C4—62no—
266C2×3−1+2⋊C4—61no—
267C9×#67—21no—
268C9×#67—41no—
269C3×#611—21no—
270C4⋊AGL(1,ℤ/9)—21no—
271C4⋊AGL(1,ℤ/9)—61no—
272C4⋊AGL(1,ℤ/9)C4×D311yescharacteristic, complemented
273C4×AGL(1,ℤ/9)—21no—
274C4×AGL(1,ℤ/9)—31no—
275C4×AGL(1,ℤ/9)—31no—
276C4×AGL(1,ℤ/9)—31no—
277C4×AGL(1,ℤ/9)—31no—
278C4×AGL(1,ℤ/9)—41no—
279C4×AGL(1,ℤ/9)—61no—
280C4×AGL(1,ℤ/9)—61no—
281C4×AGL(1,ℤ/9)—61no—
282C4×AGL(1,ℤ/9)—61no—
283C4×AGL(1,ℤ/9)—61no—
284C4×AGL(1,ℤ/9)—61no—
285C4×AGL(1,ℤ/9)—64no—
286C4×AGL(1,ℤ/9)—68no—
2873−1+2⋊Q8—21no—
2883−1+2⋊Q8—61no—
2893−1+2⋊Q8C4×D311yescharacteristic, complemented
290C9×D12—21no—
291C9×D12C2×C3×C411yescharacteristic, complemented
292C4×D3×C9—21no—
293C4×D3×C9—41no—
294C3×D36C2×C3×C411yescharacteristic, complemented
295C3×C4×D9—21no—
296C9×Dic6—21no—
297C9×Dic6C2×C3×C411yescharacteristic, complemented
298C3×Dic18C2×C3×C411yescharacteristic, complemented
299#6195—21no—
300#6194—21no—
301D3×Dic9—21no—
302#6192—21no—
303(C3⋊D9)⋊C4—21no—
304Dic3×D9—21no—
305#6189—21no—
306C8×3−1+2—61no—
3073−1+2⋊C8—21no—
3083−1+2⋊C8—41no—
309C9×C3⋊C8—21no—
310C9×C3⋊C8—41no—
311C3×C9⋊C8—21no—
312C2×C3×#104—271no—
313D3×#104—91no—
314D3×#104—91no—
315C2×C3×3−1+2—21no—
316C2×C3×3−1+2C2×C22⋊C411yescharacteristic
317C3⋊AGL(1,ℤ/9)—21no—
318C3⋊AGL(1,ℤ/9)#10412yescomplemented
319D3×3−1+2—41no—
320C3×AGL(1,ℤ/9)—41no—
321C32×#41—31no—
322C32×#41—91no—
323C2×C4×C3⋊D3—31no—
324C2×C4×C3⋊D3—61no—
325C3×#239—91no—
326C3×#239—91no—
327C3×D3×Q8—91no—
328C3×D3×Q8—91no—
329C3×#237—91no—
330C3×#237—91no—
331C3×#237—181no—
332C3×#237—181no—
333C3×D3×D4—91no—
334C3×D3×D4—91no—
335C3×D3×D4—181no—
336C3×D3×D4—181no—
337C3×#235—31no—
338C3×#235—31no—
339C3×#235—31no—
340C3×#235—61no—
341C3×#235—181no—
342C3×#235—181no—
343C3×#235C2×C3×D311yescharacteristic
344C2×C3×C4×D3—91no—
345C2×C3×C4×D3—91no—
346C2×C3×C4×D3—181no—
347C2×C3×C4×D3—181no—
348C2×C3×C4×D3—181no—
349C2×C3×C4×D3—181no—
350C2×C3×C4×D3—181no—
351C2×C3×C4×D3—182no—
352#3811—61no—
353#3805—61no—
354#3802—31no—
355C4×D32—61no—
356#3798—61no—
357#3797—31no—
358#3796—31no—
359#3796—31no—
360C32×M16—31no—
361C32×M16—91no—
362C32×C42—21no—
363C32×C42—31no—
364C32×C42—61no—
365C32×C42D3211yescharacteristic
366C32×C42C2×C3×D311yescharacteristic
367C4×C3⋊Dic3—31no—
368C4×C3⋊Dic3—61no—
369C3×C4×Dic3—91no—
370C3×C4×Dic3—91no—
371C3×C4×Dic3—181no—
372C3×C4×Dic3—181no—
373C3×C4×Dic3—181no—
374C3×C4×Dic3—182no—
375C3×#208—31no—
376C3×#208—31no—
377C3×#208—31no—
378C3×#208—61no—
379C3×#208C2×C3×D311yescharacteristic
380C3×ΓL(1,𝔽25)—181no—
381C3×ΓL(1,𝔽25)—181no—
382C3×D3×C8—181no—
383C3×D3×C8—181no—
384#3712—61no—
385#3710—61no—
386C9×#41—31no—
387C9×#41—61no—
388#3701—31no—
389Q8×D9—31no—
390#3699—31no—
391#3699—61no—
392D4×D9—31no—
393D4×D9—61no—
394#3697—61no—
395#3697C2×C3×D311yescharacteristic
396C2×C4×D9—31no—
397C2×C4×D9—61no—
398C2×C4×D9—61no—
399C2×C4×D9—61no—
400C2×C4×D9—62no—
401C9×M16—31no—
402C9×M16—61no—
403C42×C9—21no—
404C42×C9—21no—
405C42×C9—41no—
406C42×C9C2×C3×D311yescharacteristic, complemented
407C4×Dic9—31no—
408C4×Dic9—61no—
409C4×Dic9—61no—
410C4×Dic9—62no—
411#3667C2×C3×D311yescharacteristic, complemented
412#3663—61no—
413C8×D9—61no—
414C22×C33D3×D411yescharacteristic
415C2×C3×C3⋊D3—31no—
416C2×C3×C3⋊D3—31no—
417C2×C3×C3⋊D3—62no—
418C2×C32×D3—21no—
419C2×C32×D3—61no—
420C3×D32—122no—
421C33×C4—22no—
422C33×C4C2×C4×D311yescharacteristic
423C33×C4D3×D411yescharacteristic
424C3×C3⋊Dic3—31no—
425C3×C3⋊Dic3—31no—
426C3×C3⋊Dic3—62no—
427C32×Dic3—21no—
428C32×Dic3—61no—
429C22×3−1+2—21no—
430C22×3−1+2—21no—
431C22×3−1+2—41no—
432C22×3−1+2—61no—
433C22×3−1+2D3×D411yescharacteristic
434C22×C3×C9—21no—
435C22×C3×C9C2×C3×D411yescharacteristic
436C2×C3⋊D9—22no—
437C2×C3⋊D9C3×C22⋊C411yescharacteristic
438C2×C3⋊D9C3×C22⋊C411yescharacteristic
439C2×AGL(1,ℤ/9)—21no—
440C2×AGL(1,ℤ/9)—31no—
441C2×AGL(1,ℤ/9)—31no—
442C2×AGL(1,ℤ/9)—41no—
443C2×AGL(1,ℤ/9)—62no—
444C2×AGL(1,ℤ/9)—61no—
445C2×AGL(1,ℤ/9)—61no—
446C2×AGL(1,ℤ/9)—64no—
447C2×AGL(1,ℤ/9)—122no—
448C2×D3×C9—21no—
449C2×D3×C9—41no—
450C2×C3×D9—21no—
451D3×D9—42no—
452C4×3−1+2—24no—
453C4×3−1+2—22no—
454C4×3−1+2—21no—
455C4×3−1+2—21no—
456C4×3−1+2—21no—
457C4×3−1+2—21no—
458C4×3−1+2—41no—
459C4×3−1+2—41no—
460C4×3−1+2—42no—
461C4×3−1+2—44no—
462C4×3−1+2—61no—
463C4×3−1+2C2×C4×D311yescharacteristic
464C4×3−1+2D3×D411yescharacteristic
465C3×C4×C9—22no—
466C3×C4×C9—21no—
467C3×C4×C9—21no—
468C3×C4×C9—42no—
469C3×C4×C9C22×C3×C411yescharacteristic
470C3×C4×C9C2×C3×D411yescharacteristic
471C3⋊Dic9—22no—
472C3⋊Dic9C3×C22⋊C411yescharacteristic
473C3⋊Dic9C3×C22⋊C411yescharacteristic
4743−1+2⋊C4—21no—
4753−1+2⋊C4—31no—
4763−1+2⋊C4—31no—
4773−1+2⋊C4—41no—
4783−1+2⋊C4—61no—
4793−1+2⋊C4—61no—
4803−1+2⋊C4—64no—
4813−1+2⋊C4—62no—
482C9×Dic3—21no—
483C9×Dic3—41no—
484C3×Dic9—21no—
485C2×C3×#41—271no—
486D3×#41—91no—
487D3×#41—91no—
488C2×C3×M16—271no—
489C2×C3×C42—271no—
490D3×M16—91no—
491D3×M16—91no—
492C42×D3—91no—
493C42×D3—91no—
494C42×D3—181no—
495C3×#104—31no—
496C3×#104—91no—
497C3×#104—91no—
498C3×#104—91no—
499C3×#104—181no—
500C3×#104—271no—
501C3×#104—271no—
502#837—91no—
503#837—91no—
504#825—91no—
505#825—91no—
506#805—31no—
507#805AGL(1,ℤ/9)11yescharacteristic, complemented
508C3×3−1+2C2×#10411yescharacteristic, complemented, Sylow
509C22×C3⋊D3—31no—
510C22×C3×D3—91no—
511C22×C3×D3—91no—
512C22×C3×D3—181no—
513C22×C3×D3—181no—
514C22×C3×D3—181no—
515C2×D32—61no—
516C32×Q8—31no—
517C32×Q8—91no—
518C32×D4—31no—
519C32×D4—61no—
520C32×D4—91no—
521C32×D4—181no—
522C2×C32×C4—21no—
523C2×C32×C4—21no—
524C2×C32×C4—21no—
525C2×C32×C4—31no—
526C2×C32×C4—41no—
527C2×C32×C4—61no—
528C2×C32×C4—61no—
529C2×C32×C4—62no—
530C2×C32×C4—61no—
531C2×C32×C4—181no—
532C2×C32×C4C2×D3211yescharacteristic
533C2×C32×C4C22×C3×D311yescharacteristic
534C2×C3⋊Dic3—31no—
535C2×C3⋊Dic3—61no—
536C4×C3⋊D3—31no—
537C4×C3⋊D3—31no—
538C4×C3⋊D3—31no—
539C4×C3⋊D3—31no—
540C4×C3⋊D3—64no—
541C3×#67—21no—
542C3×#67—61no—
543C3×#67—61no—
544C3×#67—61no—
545C3×#67—121no—
546C3×#67—181no—
547C3×#67—181no—
548C3×#67—181no—
549C3×#67—181no—
550C2×C3×Dic3—91no—
551C2×C3×Dic3—91no—
552C2×C3×Dic3—181no—
553C2×C3×Dic3—181no—
554C2×C3×Dic3—181no—
555C2×C3×Dic3—181no—
556C2×C3×Dic3—182no—
557C2×C3×Dic3—181no—
558C3×D12—31no—
559C3×D12—31no—
560C3×D12—31no—
561C3×D12—61no—
562C3×D12—181no—
563C3×D12—181no—
564C3×D12C3×C4×D311yescharacteristic
565C3×C4×D3—21no—
566C3×C4×D3—61no—
567C3×C4×D3—61no—
568C3×C4×D3—61no—
569C3×C4×D3—91no—
570C3×C4×D3—91no—
571C3×C4×D3—91no—
572C3×C4×D3—91no—
573C3×C4×D3—91no—
574C3×C4×D3—91no—
575C3×C4×D3—91no—
576C3×C4×D3—91no—
577C3×C4×D3—121no—
578C3×C4×D3—181no—
579C3×C4×D3—181no—
580C3×C4×D3—181no—
581C3×C4×D3—181no—
582C3×C4×D3—181no—
583C3×C4×D3—181no—
584C3×C4×D3—181no—
585C3×C4×D3—181no—
586C3×C4×D3—184no—
587C3×C4×D3—184no—
588C3×C4×D3—188no—
589C3×Dic6—31no—
590C3×Dic6—31no—
591C3×Dic6—31no—
592C3×Dic6—61no—
593C3×Dic6—181no—
594C3×Dic6—181no—
595C3×Dic6C3×C4×D311yescharacteristic
596#627—61no—
597#626—61no—
598#626—61no—
599#625—61no—
600#624—61no—
601D3×Dic3—61no—
602D3×Dic3—61no—
603C22×D9—31no—
604C22×D9—61no—
605C22×D9—61no—
606C32×C8—61no—
607C32×C8—181no—
608C3×C3⋊C8—21no—
609C3×C3⋊C8—61no—
610C3×C3⋊C8—61no—
611C3×C3⋊C8—61no—
612C3×C3⋊C8—121no—
613Q8×C9—31no—
614Q8×C9—61no—
615D4×C9—31no—
616D4×C9—61no—
617D4×C9—61no—
618D4×C9—121no—
619C2×C4×C9—22no—
620C2×C4×C9—21no—
621C2×C4×C9—21no—
622C2×C4×C9—21no—
623C2×C4×C9—41no—
624C2×C4×C9—42no—
625C2×C4×C9—41no—
626C2×C4×C9—61no—
627C2×C4×C9—121no—
628C2×C4×C9C22×C3×D311yescharacteristic
629#611—21no—
630#611—61no—
631#611—61no—
632C2×Dic9—31no—
633C2×Dic9—61no—
634C2×Dic9—61no—
635C2×Dic9—62no—
636C2×Dic9—61no—
637D36—61no—
638D36C3×C4×D311yescharacteristic, complemented
639C4×D9—21no—
640C4×D9—31no—
641C4×D9—31no—
642C4×D9—31no—
643C4×D9—31no—
644C4×D9—61no—
645C4×D9—61no—
646C4×D9—61no—
647C4×D9—61no—
648C4×D9—61no—
649C4×D9—61no—
650C4×D9—64no—
651C4×D9—68no—
652Dic18—61no—
653Dic18C3×C4×D311yescharacteristic, complemented
654C8×C9—61no—
655C8×C9—121no—
656C9⋊C8—21no—
657C2×#104—271noSylow
658C2×C33—21no—
659C2×C33D3×C22⋊C411yescharacteristic
660C3×C3⋊D3—32no—
661C3×C3⋊D3—61no—
662C32×D3—41no—
663C32×D3—121no—
664C2×3−1+2—22no—
665C2×3−1+2—21no—
666C2×3−1+2—21no—
667C2×3−1+2—21no—
668C2×3−1+2—41no—
669C2×3−1+2—41no—
670C2×3−1+2—42no—
671C2×3−1+2—121no—
672C2×3−1+2D3×C22⋊C411yescharacteristic
673C2×C3×C9—21no—
674C2×C3×C9—21no—
675C2×C3×C9—41no—
676C2×C3×C9C2×C3×C22⋊C411yescharacteristic
677C3⋊D9—21no—
678C3⋊D9C3×#10412yescomplemented
679AGL(1,ℤ/9)—32no—
680AGL(1,ℤ/9)—41no—
681AGL(1,ℤ/9)—62no—
682AGL(1,ℤ/9)—62no—
683AGL(1,ℤ/9)—61no—
684AGL(1,ℤ/9)—81no—
685D3×C9—41no—
686D3×C9—81no—
687C3×D9—41no—
688C3×#41—31no—
689C3×#41—91no—
690C3×#41—91no—
691C3×#41—91no—
692C3×#41—181no—
693C3×#41—271no—
694C3×#41—271no—
695C3×#41—541no—
696C3×#41—541no—
697C2×C3×Q8—271no—
698C2×C3×D4—271no—
699C2×C3×D4—541no—
700C22×C3×C4—271no—
701C22×C3×C4—541no—
702C22×C3×C4—541no—
703#239—91no—
704#239—91no—
705D3×Q8—91no—
706D3×Q8—91no—
707#237—91no—
708#237—91no—
709#237—181no—
710#237—181no—
711D3×D4—91no—
712D3×D4—91no—
713D3×D4—181no—
714D3×D4—181no—
715#235—31no—
716#235—181no—
717#235—181no—
718#235C2×AGL(1,ℤ/9)11yescharacteristic
719C2×C4×D3—91no—
720C2×C4×D3—91no—
721C2×C4×D3—181no—
722C2×C4×D3—181no—
723C2×C4×D3—181no—
724C2×C4×D3—181no—
725C2×C4×D3—181no—
726C2×C4×D3—182no—
727C3×M16—31no—
728C3×M16—91no—
729C3×M16—91no—
730C3×M16—91no—
731C3×M16—181no—
732C3×M16—541no—
733C2×C3×C8—541no—
734C3×C42—21no—
735C3×C42—31no—
736C3×C42—61no—
737C3×C42—271no—
738C3×C42—541no—
739C3×C42C2×AGL(1,ℤ/9)11yescharacteristic, complemented
740C3×C42C3×D3211yescharacteristic
741C4×Dic3—91no—
742C4×Dic3—91no—
743C4×Dic3—181no—
744C4×Dic3—181no—
745C4×Dic3—181no—
746C4×Dic3—182no—
747#208—31no—
748#208C2×AGL(1,ℤ/9)11yescharacteristic, complemented
749ΓL(1,𝔽25)—181no—
750ΓL(1,𝔽25)—181no—
751D3×C8—181no—
752D3×C8—181no—
753C22×C32—21no—
754C22×C32—31no—
755C22×C32—61no—
756C22×C32—61no—
757C22×C32—181no—
758C22×C32#381111yescharacteristic
759C22×C32C3×D3×D411yescharacteristic
760C2×C3⋊D3—31no—
761C2×C3⋊D3—31no—
762C2×C3⋊D3—62no—
763C2×C3×D3—21no—
764C2×C3×D3—61no—
765C2×C3×D3—61no—
766C2×C3×D3—61no—
767C2×C3×D3—91no—
768C2×C3×D3—91no—
769C2×C3×D3—91no—
770C2×C3×D3—91no—
771C2×C3×D3—121no—
772C2×C3×D3—181no—
773C2×C3×D3—181no—
774C2×C3×D3—182no—
775C2×C3×D3—182no—
776C2×C3×D3—184no—
777C2×C3×D3—362no—
778C2×C3×D3—362no—
779D32—122no—
780C32×C4—22no—
781C32×C4—22no—
782C32×C4—21no—
783C32×C4—21no—
784C32×C4—31no—
785C32×C4—31no—
786C32×C4—42no—
787C32×C4—61no—
788C32×C4—61no—
789C32×C4—62no—
790C32×C4—64no—
791C32×C4—61no—
792C32×C4—181no—
793C32×C4C4×D3211yescharacteristic
794C32×C4#380211yescharacteristic
795C32×C4C2×C3×C4×D311yescharacteristic
796C32×C4C3×D3×D411yescharacteristic
797C3⋊Dic3—31no—
798C3⋊Dic3—31no—
799C3⋊Dic3—62no—
800C3×Dic3—21no—
801C3×Dic3—61no—
802C3×Dic3—61no—
803C3×Dic3—61no—
804C3×Dic3—91no—
805C3×Dic3—91no—
806C3×Dic3—91no—
807C3×Dic3—91no—
808C3×Dic3—121no—
809C3×Dic3—181no—
810C3×Dic3—181no—
811C3×Dic3—182no—
812C3×Dic3—182no—
813C3×Dic3—184no—
814C22×C9—21no—
815C22×C9—21no—
816C22×C9—41no—
817C22×C9—61no—
818C22×C9—121no—
819C22×C9C3×D3×D411yescharacteristic
820C2×D9—21no—
821C2×D9—31no—
822C2×D9—31no—
823C2×D9—61no—
824C2×D9—61no—
825C2×D9—62no—
826C2×D9—64no—
827C2×D9—122no—
828C4×C9—24no—
829C4×C9—22no—
830C4×C9—21no—
831C4×C9—21no—
832C4×C9—21no—
833C4×C9—21no—
834C4×C9—42no—
835C4×C9—44no—
836C4×C9—41no—
837C4×C9—41no—
838C4×C9—61no—
839C4×C9—121no—
840C4×C9C2×C3×C4×D311yescharacteristic
841C4×C9C3×D3×D411yescharacteristic
842Dic9—21no—
843Dic9—31no—
844Dic9—31no—
845Dic9—61no—
846Dic9—61no—
847Dic9—64no—
848Dic9—62no—
849C2×#41—271no—
850C2×M16—271no—
851C2×C42—271no—
852#104—31no—
853#104—91no—
854#104—271no—
855#104—271no—
856C33D3×#10411yescharacteristic
8573−1+2—21no—
8583−1+2—21no—
8593−1+2—41no—
8603−1+2D3×#10411yescharacteristic, complemented
861C3×C9—21no—
862C3×C9C2×C3×#10411yescharacteristic, complemented
863C23×C3—271no—
864C23×C3—541no—
865C22×D3—91no—
866C22×D3—91no—
867C22×D3—181no—
868C22×D3—181no—
869C22×D3—181no—
870C3×Q8—31no—
871C3×Q8—91no—
872C3×Q8—91no—
873C3×Q8—91no—
874C3×Q8—181no—
875C3×Q8—541no—
876C3×D4—31no—
877C3×D4—61no—
878C3×D4—91no—
879C3×D4—91no—
880C3×D4—91no—
881C3×D4—181no—
882C3×D4—181no—
883C3×D4—181no—
884C3×D4—181no—
885C3×D4—361no—
886C3×D4—541no—
887C3×D4—541no—
888C3×D4—541no—
889C2×C3×C4—22no—
890C2×C3×C4—21no—
891C2×C3×C4—21no—
892C2×C3×C4—21no—
893C2×C3×C4—31no—
894C2×C3×C4—61no—
895C2×C3×C4—61no—
896C2×C3×C4—61no—
897C2×C3×C4—121no—
898C2×C3×C4—181no—
899C2×C3×C4—181no—
900C2×C3×C4—181no—
901C2×C3×C4—271no—
902C2×C3×C4—271no—
903C2×C3×C4—271no—
904C2×C3×C4—271no—
905C2×C3×C4—271no—
906C2×C3×C4—361no—
907C2×C3×C4—544no—
908C2×C3×C4—541no—
909C2×C3×C4—541no—
910C2×C3×C4—541no—
911C2×C3×C4—541no—
912C2×C3×C4C22×AGL(1,ℤ/9)11yescharacteristic
913C2×C3×C4C2×C3×D3211yescharacteristic
914#67—21no—
915#67—61no—
916#67—181no—
917#67—181no—
918#67—181no—
919#67—181no—
920C2×Dic3—91no—
921C2×Dic3—91no—
922C2×Dic3—181no—
923C2×Dic3—181no—
924C2×Dic3—181no—
925C2×Dic3—182no—
926C2×Dic3—181no—
927C2×Dic3—181no—
928D12—31no—
929D12—181no—
930D12—181no—
931D12C4×AGL(1,ℤ/9)11yescharacteristic, complemented
932C4×D3—21no—
933C4×D3—61no—
934C4×D3—91no—
935C4×D3—91no—
936C4×D3—91no—
937C4×D3—91no—
938C4×D3—91no—
939C4×D3—91no—
940C4×D3—91no—
941C4×D3—91no—
942C4×D3—181no—
943C4×D3—181no—
944C4×D3—181no—
945C4×D3—181no—
946C4×D3—181no—
947C4×D3—181no—
948C4×D3—181no—
949C4×D3—181no—
950C4×D3—184no—
951C4×D3—184no—
952C4×D3—188no—
953Dic6—31no—
954Dic6—181no—
955Dic6—181no—
956Dic6C4×AGL(1,ℤ/9)11yescharacteristic, complemented
957C3×C8—61no—
958C3×C8—181no—
959C3×C8—181no—
960C3×C8—181no—
961C3×C8—361no—
962C3⋊C8—21no—
963C3⋊C8—61no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—21no—
967C2×C32—31no—
968C2×C32—41no—
969C2×C32—61no—
970C2×C32—61no—
971C2×C32—62no—
972C2×C32—121no—
973C2×C32—361no—
974C2×C32#6392111yescharacteristic
975C2×C32C3×D3×C22⋊C411yescharacteristic
976C3⋊D3—32no—
977C3⋊D3—61no—
978C3×D3—41no—
979C3×D3—92no—
980C3×D3—92no—
981C3×D3—121no—
982C3×D3—121no—
983C3×D3—121no—
984C3×D3—182no—
985C3×D3—181no—
986C3×D3—182no—
987C3×D3—181no—
988C3×D3—241no—
989C2×C9—22no—
990C2×C9—21no—
991C2×C9—21no—
992C2×C9—21no—
993C2×C9—41no—
994C2×C9—42no—
995C2×C9—41no—
996C2×C9—121no—
997C2×C9—241no—
998C2×C9C3×D3×C22⋊C411yescharacteristic
999D9—32no—
1000D9—41no—
1001D9—62no—
1002D9—62no—
1003D9—61no—
1004#41—31no—
1005#41—91no—
1006#41—271no—
1007#41—271no—
1008#41—541no—
1009#41—541no—
1010C2×Q8—271no—
1011C2×D4—271no—
1012C2×D4—541no—
1013C22×C4—271no—
1014C22×C4—541no—
1015C22×C4—541no—
1016M16—31no—
1017M16—91no—
1018M16—541no—
1019C2×C8—541no—
1020C42—271no—
1021C42—541no—
1022C42D3×AGL(1,ℤ/9)11yescharacteristic, complemented
1023C22×C3—21no—
1024C22×C3—31no—
1025C22×C3—61no—
1026C22×C3—61no—
1027C22×C3—181no—
1028C22×C3—181no—
1029C22×C3—181no—
1030C22×C3—271no—
1031C22×C3—271no—
1032C22×C3—361no—
1033C22×C3—542no—
1034C22×C3—1082no—
1035C22×C3D4×AGL(1,ℤ/9)11yescharacteristic
1036C22×C3C3×#381111yescharacteristic
1037C2×D3—21no—
1038C2×D3—61no—
1039C2×D3—91no—
1040C2×D3—91no—
1041C2×D3—91no—
1042C2×D3—91no—
1043C2×D3—181no—
1044C2×D3—181no—
1045C2×D3—182no—
1046C2×D3—182no—
1047C2×D3—184no—
1048C2×D3—362no—
1049C2×D3—362no—
1050C3×C4—22no—
1051C3×C4—24no—
1052C3×C4—22no—
1053C3×C4—21no—
1054C3×C4—21no—
1055C3×C4—31no—
1056C3×C4—31no—
1057C3×C4—62no—
1058C3×C4—61no—
1059C3×C4—61no—
1060C3×C4—61no—
1061C3×C4—122no—
1062C3×C4—181no—
1063C3×C4—181no—
1064C3×C4—181no—
1065C3×C4—271no—
1066C3×C4—271no—
1067C3×C4—361no—
1068C3×C4—542no—
1069C3×C4C2×C4×AGL(1,ℤ/9)11yescharacteristic
1070C3×C4D4×AGL(1,ℤ/9)11yescharacteristic
1071C3×C4C3×C4×D3211yescharacteristic
1072C3×C4C3×#380211yescharacteristic
1073Dic3—21no—
1074Dic3—61no—
1075Dic3—91no—
1076Dic3—91no—
1077Dic3—91no—
1078Dic3—91no—
1079Dic3—181no—
1080Dic3—181no—
1081Dic3—182no—
1082Dic3—184no—
1083Dic3—182no—
1084C32—21no—
1085C32—31no—
1086C32—61no—
1087C32#1059039311yescharacteristic
1088C32C3×D3×#10411yescharacteristic
1089C9—21no—
1090C9—21no—
1091C9—41no—
1092C9C3×D3×#10411yescharacteristic, complemented
1093C23—271no—
1094C23—541no—
1095Q8—31no—
1096Q8—91no—
1097Q8—541no—
1098D4—31no—
1099D4—61no—
1100D4—91no—
1101D4—181no—
1102D4—541no—
1103D4—541no—
1104D4—541no—
1105C2×C4—21no—
1106C2×C4—61no—
1107C2×C4—181no—
1108C2×C4—271no—
1109C2×C4—271no—
1110C2×C4—271no—
1111C2×C4—271no—
1112C2×C4—271no—
1113C2×C4—544no—
1114C2×C4—541no—
1115C2×C4—541no—
1116C2×C4—541no—
1117C2×C4—541no—
1118C2×C4C2×D3×AGL(1,ℤ/9)11yescharacteristic
1119C8—61no—
1120C8—181no—
1121C2×C3—22no—
1122C2×C3—21no—
1123C2×C3—21no—
1124C2×C3—21no—
1125C2×C3—31no—
1126C2×C3—61no—
1127C2×C3—61no—
1128C2×C3—121no—
1129C2×C3—121no—
1130C2×C3—272no—
1131C2×C3—361no—
1132C2×C3—361no—
1133C2×C3—361no—
1134C2×C3—541no—
1135C2×C3—721no—
1136C2×C3C22⋊C4×AGL(1,ℤ/9)11yescharacteristic
1137C2×C3C3×#6392111yescharacteristic
1138D3—41no—
1139D3—92no—
1140D3—92no—
1141D3—121no—
1142D3—182no—
1143D3—182no—
1144D3—181no—
1145D3—181no—
1146C22—61no—
1147C22—181no—
1148C22—271no—
1149C22—271no—
1150C22—542no—
1151C22—1082no—
1152C22#88668⋊C311yescharacteristic
1153C4—22no—
1154C4—61no—
1155C4—181no—
1156C4—271no—
1157C4—271no—
1158C4—542no—
1159C4C4×D3×AGL(1,ℤ/9)11yescharacteristic
1160C4#88646⋊C311yescharacteristic
1161C3—21no—
1162C3—31no—
1163C3—61no—
1164C3#104×AGL(1,ℤ/9)11yescharacteristic, complemented
1165C3C3×#1059039311yescharacteristic
1166C2—21no—
1167C2—121no—
1168C2—272no—
1169C2—361no—
1170C2—541no—
1171C2#7222000111yescharacteristic
subgroupG/H
centerC4#88646⋊C3
commutatorC3×C4×C9C22×C3×C4
FrattiniC2×C3×C4C2×C3×D32
FittingC3×C42×3−1+2C22
socleC2×C32C3×D3×C22⋊C4
prime radical#72219929C2
cosocleC2×C3×C4×C9C23×C3
hypercenterC42D3×AGL(1,ℤ/9)
hypocenterC3×C9C2×C3×#104
LCSG ▷ C3×C4×C9 ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C4 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #72219968C2semidirect
2. #72219967C2semidirect
3. 3−1+2×#805C2semidirect
4. C3×#63364⋊C3C2semidirect
6. C42×C3⋊AGL(1,ℤ/9)C2semidirect
7. #72219893C2semidirect
10. #13137291C3semidirect
17. #88646⋊C3C4semidirect
20. #88639⋊C3C4semidirect
21. (C3⋊AGL(1,ℤ/9))⋊Q8C4semidirect
22. #88634⋊C3C4semidirect
23. C3×C42×3−1+2C22semidirect
25. C4×C3⋊(3−1+2⋊C4)C22semidirect
26. 3−1+2×#208C22semidirect
27. C3×#3667⋊C3C22semidirect
39. C42×C3⋊D9C2×C3semidirect
43. #11720863C2×C3semidirect
48. #63364⋊C3D3semidirect
50. C9×#805C2×C3semidirect
51. C3×#63364C2×C3semidirect
52. #11720300C2×C3semidirect
53. #11720291C2×C3semidirect
67. D12×3−1+2C2×C4semidirect
69. C3×C4⋊AGL(1,ℤ/9)C2×C4semidirect
71. Dic6×3−1+2C2×C4semidirect
72. C3×3−1+2⋊Q8C2×C4semidirect
127. #88646C3×C4semidirect
130. #88639C3×C4semidirect
131. (C3⋊D9)⋊Q8C3×C4semidirect
132. #88634C3×C4semidirect
137. C42×3−1+2C2×D3semidirect
139. C3×C42×C9C22×C3semidirect
141. C4×C3⋊Dic9C22×C3semidirect
147. #3667⋊C3C2×D3semidirect
149. C9×#208C22×C3semidirect
150. C3×#3667C22×C3semidirect
201. #63364C3×D3semidirect
272. C4⋊AGL(1,ℤ/9)C4×D3semidirect
289. 3−1+2⋊Q8C4×D3semidirect
291. C9×D12C2×C3×C4semidirect
294. C3×D36C2×C3×C4semidirect
297. C9×Dic6C2×C3×C4semidirect
298. C3×Dic18C2×C3×C4semidirect
318. C3⋊AGL(1,ℤ/9)#104semidirect
406. C42×C9C2×C3×D3semidirect
411. #3667C2×C3×D3semidirect
507. #805AGL(1,ℤ/9)semidirect
508. C3×3−1+2C2×#104semidirect
638. D36C3×C4×D3semidirect
653. Dic18C3×C4×D3semidirect
678. C3⋊D9C3×#104semidirect
739. C3×C42C2×AGL(1,ℤ/9)semidirect
748. #208C2×AGL(1,ℤ/9)semidirect
860. 3−1+2D3×#104semidirect
862. C3×C9C2×C3×#104semidirect
931. D12C4×AGL(1,ℤ/9)semidirect
956. Dic6C4×AGL(1,ℤ/9)semidirect
1022. C42D3×AGL(1,ℤ/9)semidirect
1092. C9C3×D3×#104semidirect
1164. C3#104×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
#722199682
#722199672
3−1+2×#8052
C3×#63364⋊C32
#722199292
C42×C3⋊AGL(1,ℤ/9)2
#722198932
C3×#105903933
#104×AGL(1,ℤ/9)3
#131372913