Finite Group Databasebeta

← D3×#92264 #72243316

Subgroups — D3×#92264 #72243316

Order 2916.

466 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#6896C211yesmaximal, characteristic, complemented
2C3⋊#92264C211yesmaximal, characteristic, complemented
3C3×#92264C211yesmaximal, characteristic, complemented
4D32×3−1+2—31nomaximal
5C3×D3×AGL(1,ℤ/9)C311yesmaximal, characteristic
6C2×#92264—31nomaximal
7D3×D9⋊C9C311yesmaximal, characteristic, complemented
8D3×D9⋊C9C311yesmaximal, characteristic, complemented
9D3×C9×D9C311yesmaximal, characteristic, complemented
10C3×#6896C2211yescharacteristic, complemented, Sylow
11C3⋊D3×3−1+2—31no—
12C3×C3⋊AGL(1,ℤ/9)C2×C311yescharacteristic
13C3×D3×3−1+2—31no—
14C3×D3×3−1+2D311yescharacteristic
15C3×D3×3−1+2C2×C311yescharacteristic
16C32×AGL(1,ℤ/9)C2×C311yescharacteristic
17C2×#6896—31no—
18C3⋊(D9⋊C9)C2×C311yescharacteristic, complemented
19C3⋊(D9⋊C9)C2×C311yescharacteristic, complemented
20C9×C3⋊D9C2×C311yescharacteristic, complemented
21#92264—21no—
22#92264—21no—
23#92264—21no—
24#92264—21no—
25#92264—31no—
26#92264—61no—
27#92264D311yescharacteristic, direct product factor
28D3×C9⋊C9—21no—
29D3×C9⋊C9—21no—
30D3×C9⋊C9—21no—
31D3×C9⋊C9C2×C311yescharacteristic, complemented
32D3×C9⋊C9C2×C311yescharacteristic, complemented
33C3×D9⋊C9C2×C311yescharacteristic, complemented
34C3×D9⋊C9C2×C311yescharacteristic, complemented
35D3×C32⋊C9—21no—
36D3×C92C2×C311yescharacteristic, complemented
37C3×C9×D9C2×C311yescharacteristic, complemented
38C32×D32—31no—
39C2×D3×3−1+2—91no—
40C2×D3×3−1+2—91no—
41C2×C3×AGL(1,ℤ/9)—31no—
42D3×AGL(1,ℤ/9)—31no—
43D32×C9—31no—
44D32×C9—31no—
45D32×C9—31no—
46C3×D3×D9C3211yescharacteristic
47C2×D9⋊C9—31no—
48C2×D9⋊C9—31no—
49C2×C9×D9—31no—
50C32×3−1+2C2×D311yescharacteristic
51C32×3−1+2C22×C311yescharacteristic
52#6896—21no—
53#6896—21no—
54#6896—21no—
55#6896—21no—
56#6896—21no—
57#6896—41no—
58#6896—41no—
59#6896—41no—
60#6896—41no—
61#6896C2×D311yescharacteristic, complemented
62C3×C9⋊C9—21no—
63C3×C9⋊C9—21no—
64C3×C9⋊C9—21no—
65C3×C9⋊C9C22×C311yescharacteristic, complemented
66C3×C9⋊C9C22×C311yescharacteristic, complemented
67C3×C32⋊C9—21no—
68C3×C92C22×C311yescharacteristic, complemented
69C32×C3⋊D3—31no—
70C33×D3—31no—
71C33×D3C3×D311yescharacteristic
72C2×C3×3−1+2—31no—
73C2×C3×3−1+2—31no—
74C2×C3×3−1+2—91no—
75C3⋊AGL(1,ℤ/9)—31no—
76C9×C3⋊D3—31no—
77C9×C3⋊D3—31no—
78C9×C3⋊D3—31no—
79C3×C3⋊D9C2×C3211yescharacteristic
80D3×3−1+2—31no—
81D3×3−1+2—31no—
82D3×3−1+2—61no—
83D3×3−1+2—61no—
84D3×3−1+2—61no—
85D3×3−1+2—61no—
86D3×3−1+2—61no—
87D3×3−1+2—61no—
88D3×3−1+2—61no—
89D3×3−1+2—91no—
90D3×3−1+2—91no—
91D3×3−1+2—181no—
92C3×AGL(1,ℤ/9)—21no—
93C3×AGL(1,ℤ/9)—31no—
94C3×AGL(1,ℤ/9)—31no—
95C3×AGL(1,ℤ/9)—61no—
96C3×AGL(1,ℤ/9)—61no—
97C3×AGL(1,ℤ/9)C3×D311yescharacteristic
98C3×D3×C9—21no—
99C3×D3×C9—21no—
100C3×D3×C9—21no—
101C3×D3×C9—21no—
102C3×D3×C9—31no—
103C3×D3×C9—31no—
104C3×D3×C9—31no—
105C3×D3×C9C3×D311yescharacteristic
106C3×D3×C9C3×D311yescharacteristic
107C3×D3×C9C3×D311yescharacteristic
108C3×D3×C9C2×C3211yescharacteristic
109C32×D9C2×C3211yescharacteristic
110C2×C9⋊C9—31no—
111C2×C9⋊C9—31no—
112C2×C9⋊C9—61no—
113C2×C9⋊C9—61no—
114C2×C9⋊C9—61no—
115C2×C32⋊C9—61no—
116C2×C92—31no—
117D9⋊C9—21no—
118D9⋊C9—21no—
119D9⋊C9—31no—
120D9⋊C9—31no—
121D9⋊C9—61no—
122D9⋊C9—61no—
123D9⋊C9C3×D311yescharacteristic, complemented
124D9⋊C9C3×D311yescharacteristic, complemented
125C9×D9—21no—
126C9×D9—31no—
127C9×D9—61no—
128C9×D9C3×D311yescharacteristic, complemented
129C2×C32×D3—91no—
130C2×C32×D3—91no—
131C3×D32—31no—
132C3×D32—91no—
133C22×3−1+2—271no—
134C2×AGL(1,ℤ/9)—91no—
135C2×D3×C9—91no—
136C2×D3×C9—91no—
137C2×D3×C9—91no—
138C2×D3×C9—91no—
139C2×D3×C9—91no—
140C2×D3×C9—91no—
141C2×C3×D9—31no—
142D3×D93−1+211yescharacteristic, complemented
143C34C2×C3×D311yescharacteristic
144C3×3−1+2—21no—
145C3×3−1+2—21no—
146C3×3−1+2—21no—
147C3×3−1+2—21no—
148C3×3−1+2—21no—
149C3×3−1+2—21no—
150C3×3−1+2—31no—
151C3×3−1+2—41no—
152C3×3−1+2—61no—
153C3×3−1+2—61no—
154C3×3−1+2—61no—
155C3×3−1+2—61no—
156C3×3−1+2—121no—
157C3×3−1+2—121no—
158C3×3−1+2—121no—
159C3×3−1+2D3211yescharacteristic
160C3×3−1+2C2×C3×D311yescharacteristic
161C32×C9—21no—
162C32×C9—21no—
163C32×C9—21no—
164C32×C9—21no—
165C32×C9C2×C3×D311yescharacteristic
166C32×C9C2×C3×D311yescharacteristic
167C32×C9C2×C3×D311yescharacteristic
168C32×C9C22×C3211yescharacteristic
169C9⋊C9—21no—
170C9⋊C9—21no—
171C9⋊C9—21no—
172C9⋊C9—21no—
173C9⋊C9—21no—
174C9⋊C9—21no—
175C9⋊C9—21no—
176C9⋊C9—41no—
177C9⋊C9—41no—
178C9⋊C9—41no—
179C9⋊C9—41no—
180C9⋊C9—41no—
181C9⋊C9—41no—
182C9⋊C9—41no—
183C9⋊C9—41no—
184C9⋊C9—41no—
185C9⋊C9—41no—
186C9⋊C9—41no—
187C9⋊C9—41no—
188C9⋊C9—41no—
189C9⋊C9—41no—
190C9⋊C9C2×C3×D311yescharacteristic, complemented
191C9⋊C9C2×C3×D311yescharacteristic, complemented
192C32⋊C9—21no—
193C32⋊C9—41no—
194C32⋊C9—41no—
195C32⋊C9—41no—
196C32⋊C9—41no—
197C92—21no—
198C92—21no—
199C92—41no—
200C92C2×C3×D311yescharacteristic, complemented
201C2×C33—31no—
202C2×C33—91no—
203C3×C3⋊D3—31no—
204C3×C3⋊D3—91no—
205C32×D3—31no—
206C32×D3—31no—
207C32×D3—31no—
208C32×D3—61no—
209C32×D3—61no—
210C32×D3—61no—
211C32×D3—91no—
212C32×D3—91no—
213C32×D3—91no—
214C32×D3—181no—
215C32×D3—181no—
216C32×D3C32×D311yescharacteristic
217C2×3−1+2—91no—
218C2×3−1+2—91no—
219C2×3−1+2—91no—
220C2×3−1+2—181no—
221C2×3−1+2—181no—
222C2×3−1+2—181no—
223C2×3−1+2—181no—
224C2×3−1+2—181no—
225C2×3−1+2—181no—
226C2×3−1+2—271no—
227C2×C3×C9—31no—
228C2×C3×C9—31no—
229C2×C3×C9—31no—
230C2×C3×C9—31no—
231C2×C3×C9—61no—
232C2×C3×C9—61no—
233C2×C3×C9—61no—
234C2×C3×C9—61no—
235C2×C3×C9—91no—
236C2×C3×C9—91no—
237C2×C3×C9—91no—
238C3⋊D9C2×3−1+211yescharacteristic, complemented
239AGL(1,ℤ/9)—31no—
240AGL(1,ℤ/9)—61no—
241AGL(1,ℤ/9)—91no—
242AGL(1,ℤ/9)—181no—
243D3×C9—21no—
244D3×C9—21no—
245D3×C9—31no—
246D3×C9—31no—
247D3×C9—31no—
248D3×C9—31no—
249D3×C9—61no—
250D3×C9—61no—
251D3×C9—61no—
252D3×C9—61no—
253D3×C9—61no—
254D3×C9—61no—
255D3×C9—61no—
256D3×C9—61no—
257D3×C9—91no—
258D3×C9—91no—
259D3×C9—91no—
260D3×C9—91no—
261D3×C9—91no—
262D3×C9—91no—
263D3×C9—181no—
264D3×C9—181no—
265D3×C9—181no—
266D3×C9AGL(1,ℤ/9)11yescharacteristic, complemented
267D3×C9C2×3−1+211yescharacteristic, complemented
268C3×D9—21no—
269C3×D9—31no—
270C3×D9—61no—
271C3×D9C2×3−1+211yescharacteristic, complemented
272C3×D9C32×D311yescharacteristic
273C22×C32—271no—
274C2×C3×D3—91no—
275C2×C3×D3—91no—
276C2×C3×D3—271no—
277C2×C3×D3—271no—
278D32—31no—
279C22×C9—271no—
280C22×C9—271no—
281C22×C9—271no—
282C2×D9—31no—
283C33—21no—
284C33—31no—
285C33—61no—
286C33—61no—
287C33—61no—
288C33—121no—
289C33—121no—
290C33C3×D3211yescharacteristic
291C33C2×C32×D311yescharacteristic
2923−1+2—31no—
2933−1+2—31no—
2943−1+2—61no—
2953−1+2—61no—
2963−1+2—61no—
2973−1+2—61no—
2983−1+2—61no—
2993−1+2—121no—
3003−1+2—121no—
3013−1+2—121no—
3023−1+2—121no—
3033−1+2—121no—
3043−1+2—121no—
3053−1+2—121no—
3063−1+2—122no—
3073−1+2—121no—
3083−1+2—121no—
3093−1+2—121no—
310C3×C9—21no—
311C3×C9—21no—
312C3×C9—21no—
313C3×C9—21no—
314C3×C9—21no—
315C3×C9—21no—
316C3×C9—21no—
317C3×C9—21no—
318C3×C9—21no—
319C3×C9—21no—
320C3×C9—21no—
321C3×C9—21no—
322C3×C9—31no—
323C3×C9—41no—
324C3×C9—41no—
325C3×C9—41no—
326C3×C9—41no—
327C3×C9—41no—
328C3×C9—41no—
329C3×C9—61no—
330C3×C9—61no—
331C3×C9—61no—
332C3×C9—61no—
333C3×C9—61no—
334C3×C9—61no—
335C3×C9—121no—
336C3×C9—121no—
337C3×C9—121no—
338C3×C9—121no—
339C3×C9—121no—
340C3×C9C2×AGL(1,ℤ/9)11yescharacteristic, complemented
341C3×C9C22×3−1+211yescharacteristic, complemented
342C3×C9C3×D3211yescharacteristic
343C3×C9C3×D3211yescharacteristic
344C3×C9C3×D3211yescharacteristic
345C3×C9C2×C32×D311yescharacteristic
346C2×C32—31no—
347C2×C32—91no—
348C2×C32—91no—
349C2×C32—91no—
350C2×C32—91no—
351C2×C32—181no—
352C2×C32—181no—
353C2×C32—271no—
354C2×C32—271no—
355C2×C32—541no—
356C3⋊D3—31no—
357C3×D3—21no—
358C3×D3—31no—
359C3×D3—31no—
360C3×D3—61no—
361C3×D3—91no—
362C3×D3—91no—
363C3×D3—91no—
364C3×D3—181no—
365C3×D3—181no—
366C3×D3—181no—
367C3×D3—271no—
368C3×D3—271no—
369C3×D3—541no—
370C3×D3C3×AGL(1,ℤ/9)11yescharacteristic
371C3×D3D3×3−1+211yescharacteristic
372C2×C9—31no—
373C2×C9—31no—
374C2×C9—61no—
375C2×C9—61no—
376C2×C9—91no—
377C2×C9—91no—
378C2×C9—91no—
379C2×C9—91no—
380C2×C9—181no—
381C2×C9—181no—
382C2×C9—181no—
383C2×C9—181no—
384C2×C9—181no—
385C2×C9—181no—
386C2×C9—181no—
387C2×C9—181no—
388C2×C9—271no—
389C2×C9—271no—
390C2×C9—271no—
391D9—31no—
392D9—61no—
393D9D3×3−1+211yescharacteristic, complemented
394C22×C3—271no—
395C22×C3—811no—
396C2×D3—91no—
397C2×D3—91no—
398C32—21no—
399C32—21no—
400C32—21no—
401C32—31no—
402C32—31no—
403C32—41no—
404C32—61no—
405C32—61no—
406C32—61no—
407C32—121no—
408C32—181no—
409C32—181no—
410C32—181no—
411C32—361no—
412C32C2×C3×AGL(1,ℤ/9)11yescharacteristic
413C32C2×D3×3−1+211yescharacteristic
414C32C32×D3211yescharacteristic
415C9—21no—
416C9—21no—
417C9—21no—
418C9—21no—
419C9—31no—
420C9—41no—
421C9—41no—
422C9—61no—
423C9—61no—
424C9—61no—
425C9—61no—
426C9—61no—
427C9—121no—
428C9—121no—
429C9—121no—
430C9—121no—
431C9—121no—
432C9—121no—
433C9D3×AGL(1,ℤ/9)11yescharacteristic, complemented
434C9C2×D3×3−1+211yescharacteristic, complemented
435C2×C3—31no—
436C2×C3—31no—
437C2×C3—61no—
438C2×C3—91no—
439C2×C3—91no—
440C2×C3—181no—
441C2×C3—271no—
442C2×C3—271no—
443C2×C3—541no—
444C2×C3—541no—
445C2×C3—811no—
446D3—31no—
447D3—91no—
448D3—91no—
449D3—181no—
450D3#9226411yescharacteristic, direct product factor
451C22—271noSylow
452C3—21no—
453C3—21no—
454C3—21no—
455C3—41no—
456C3—181no—
457C3—181no—
458C3C2×#9226411yescharacteristic, complemented
459C3C3×D3×AGL(1,ℤ/9)11yescharacteristic
460C3D32×3−1+211yescharacteristic
461C2—31no—
462C2—91no—
463C2—271no—
subgroupG/H
centerC3C3×D3×AGL(1,ℤ/9)
commutator, cosocleC32×C9C22×C32
FrattiniC32C32×D32
FittingC3×#6896C22
socleC33C2×C32×D3
prime radicalC3×D3×AGL(1,ℤ/9)C3
hypercenterC9D3×AGL(1,ℤ/9)
hypocenterC3×C9C22×3−1+2
LCSG ▷ C32×C9 ▷ C3×C9
UCSC1 ◁ C3 ◁ C9

Complements

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

NH ≅ G/Ntype
1. D3×#6896C2semidirect
2. C3⋊#92264C2semidirect
3. C3×#92264C2semidirect
7. D3×D9⋊C9C3semidirect
8. D3×D9⋊C9C3semidirect
9. D3×C9×D9C3semidirect
10. C3×#6896C22semidirect
18. C3⋊(D9⋊C9)C2×C3semidirect
19. C3⋊(D9⋊C9)C2×C3semidirect
20. C9×C3⋊D9C2×C3semidirect
27. #92264D3direct (N × H)
31. D3×C9⋊C9C2×C3semidirect
32. D3×C9⋊C9C2×C3semidirect
33. C3×D9⋊C9C2×C3semidirect
34. C3×D9⋊C9C2×C3semidirect
36. D3×C92C2×C3semidirect
37. C3×C9×D9C2×C3semidirect
61. #6896C2×D3semidirect
65. C3×C9⋊C9C22×C3semidirect
66. C3×C9⋊C9C22×C3semidirect
68. C3×C92C22×C3semidirect
123. D9⋊C9C3×D3semidirect
124. D9⋊C9C3×D3semidirect
128. C9×D9C3×D3semidirect
142. D3×D93−1+2semidirect
190. C9⋊C9C2×C3×D3semidirect
191. C9⋊C9C2×C3×D3semidirect
200. C92C2×C3×D3semidirect
238. C3⋊D9C2×3−1+2semidirect
266. D3×C9AGL(1,ℤ/9)semidirect
267. D3×C9C2×3−1+2semidirect
271. C3×D9C2×3−1+2semidirect
340. C3×C9C2×AGL(1,ℤ/9)semidirect
341. C3×C9C22×3−1+2semidirect
393. D9D3×3−1+2semidirect
433. C9D3×AGL(1,ℤ/9)semidirect
434. C9C2×D3×3−1+2semidirect
450. D3#92264direct (N × H)
458. C3C2×#92264semidirect

Maximal subgroups

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

subgroupindex
D3×#68962
C3⋊#922642
C3×#922642
D32×3−1+23
C3×D3×AGL(1,ℤ/9)3
C2×#922643
D3×D9⋊C93
D3×C9×D93