Finite Group Databasebeta

← D3×#4177⋊C3 #72243927

Subgroups — D3×#4177⋊C3 #72243927

Order 2916.

552 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C3⋊(#4177⋊C3)C211yesmaximal, characteristic, complemented
2C3×#4177⋊C3C211yesmaximal, characteristic, complemented
3D3×#6910C211yesmaximal, characteristic, complemented
4D3×C3⋊AGL(1,ℤ/9)C311yesmaximal, characteristic, complemented
5C3×D3×(C3⋊D3)⋊C3—31nomaximal
6C2×#4177⋊C3—31nomaximal
7D3×#4177C311yesmaximal, characteristic, complemented
8D3×#4177C311yesmaximal, characteristic, complemented
9D3×#4177C311yesmaximal, characteristic, complemented
10C3×#6910C2211yescharacteristic, complemented, Sylow
11C3⋊(C3⋊AGL(1,ℤ/9))C2×C311yescharacteristic, complemented
12C3×C3⋊AGL(1,ℤ/9)C2×C311yescharacteristic, complemented
13C3×C3⋊((C3⋊D3)⋊C3)—31no—
14C3×D3×3−1+2—21no—
15C3×D3×3−1+2C2×C311yescharacteristic, complemented
16C3×D3×H(3,𝔽3)D311yescharacteristic
17C32×(C3⋊D3)⋊C3—31no—
18C2×#6910—31no—
19C3⋊#4177C2×C311yescharacteristic, complemented
20C3⋊#4177C2×C311yescharacteristic, complemented
21C3⋊#4177C2×C311yescharacteristic, complemented
22#4177⋊C3—21no—
23#4177⋊C3—21no—
24#4177⋊C3—21no—
25#4177⋊C3—21no—
26#4177⋊C3—31no—
27#4177⋊C3—61no—
28#4177⋊C3D311yescharacteristic, direct product factor
29D3×#731—21no—
30D3×#731—21no—
31D3×#731—21no—
32D3×#731C2×C311yescharacteristic, complemented
33D3×#731C2×C311yescharacteristic, complemented
34D3×#731C2×C311yescharacteristic, complemented
35C3×#4177C2×C311yescharacteristic, complemented
36C3×#4177C2×C311yescharacteristic, complemented
37C3×#4177C2×C311yescharacteristic, complemented
38C3×D3×C3⋊D3—31no—
39C32×D32—91no—
40C2×C3⋊AGL(1,ℤ/9)—31no—
41C2×C3×(C3⋊D3)⋊C3—91no—
42D3×C3⋊D9C3211yescharacteristic, complemented
43D3×AGL(1,ℤ/9)—91no—
44D3×(C3⋊D3)⋊C3—31no—
45D3×(C3⋊D3)⋊C3—31no—
46D3×(C3⋊D3)⋊C3—31no—
47C2×#4177—31no—
48C2×#4177—31no—
49C2×#4177—31no—
50C32×3−1+2—21no—
51C32×3−1+2C22×C311yescharacteristic, complemented
52C32×H(3,𝔽3)C2×D311yescharacteristic
53#6910—21no—
54#6910—21no—
55#6910—21no—
56#6910—21no—
57#6910—21no—
58#6910—41no—
59#6910—41no—
60#6910—41no—
61#6910—41no—
62#6910C2×D311yescharacteristic, complemented
63C3×#731—21no—
64C3×#731—21no—
65C3×#731—21no—
66C3×#731C22×C311yescharacteristic, complemented
67C3×#731C22×C311yescharacteristic, complemented
68C3×#731C22×C311yescharacteristic, complemented
69C3×C3⋊(C3⋊D3)—31no—
70C32×C3⋊D3—31no—
71C32×C3⋊D3—91no—
72C33×D3—31no—
73C33×D3—91no—
74C33×D3C3×D311yescharacteristic
75C2×C3×3−1+2—31no—
76C2×C3×3−1+2—61no—
77C2×C3×H(3,𝔽3)—31no—
78C3⋊(C3⋊D9)C2×C3211yescharacteristic, complemented
79C3⋊AGL(1,ℤ/9)—21no—
80C3⋊AGL(1,ℤ/9)—31no—
81C3⋊AGL(1,ℤ/9)—61no—
82C3⋊AGL(1,ℤ/9)—91no—
83C3⋊AGL(1,ℤ/9)—181no—
84C3⋊AGL(1,ℤ/9)C3×D311yescharacteristic, complemented
85C3⋊((C3⋊D3)⋊C3)—31no—
86C3⋊((C3⋊D3)⋊C3)—31no—
87C3⋊((C3⋊D3)⋊C3)—31no—
88C3×C3⋊D9C2×C3211yescharacteristic, complemented
89D3×3−1+2—21no—
90D3×3−1+2—21no—
91D3×3−1+2—21no—
92D3×3−1+2—31no—
93D3×3−1+2—61no—
94D3×3−1+2—61no—
95D3×3−1+2—61no—
96C3×AGL(1,ℤ/9)—91no—
97D3×H(3,𝔽3)—61no—
98D3×H(3,𝔽3)C3×D311yescharacteristic
99D3×H(3,𝔽3)C3×D311yescharacteristic
100D3×H(3,𝔽3)C3×D311yescharacteristic
101C3×(C3⋊D3)⋊C3—31no—
102C3×(C3⋊D3)⋊C3—31no—
103C3×(C3⋊D3)⋊C3—31no—
104C3×(C3⋊D3)⋊C3—31no—
105C3×(C3⋊D3)⋊C3—61no—
106C3×(C3⋊D3)⋊C3—61no—
107C3×(C3⋊D3)⋊C3—61no—
108C3×(C3⋊D3)⋊C3—61no—
109C3×(C3⋊D3)⋊C3—91no—
110C3×(C3⋊D3)⋊C3—181no—
111C3×D3×C9—21no—
112C3×D3×C9—61no—
113C3×D3×C9C2×C3211yescharacteristic, complemented
114C2×#731—31no—
115C2×#731—31no—
116C2×#731—31no—
117C2×#731—61no—
118C2×#731—61no—
119C2×#731—61no—
120#4177—21no—
121#4177—21no—
122#4177—21no—
123#4177—31no—
124#4177—31no—
125#4177—31no—
126#4177—61no—
127#4177—61no—
128#4177—61no—
129#4177C3×D311yescharacteristic, complemented
130#4177C3×D311yescharacteristic, complemented
131#4177C3×D311yescharacteristic, complemented
132C2×C3×C3⋊D3—91no—
133C2×C32×D3—271no—
134C2×C32×D3—271no—
135D3×C3⋊D3—31no—
136C3×D32—91no—
137C3×D32—91no—
138C3×D32—91no—
139C3×D32—91no—
140C3×D32—271no—
141C2×C3⋊D9—31no—
142C2×AGL(1,ℤ/9)—271no—
143C2×(C3⋊D3)⋊C3—91no—
144C2×(C3⋊D3)⋊C3—91no—
145C2×(C3⋊D3)⋊C3—91no—
146D3×D9—91no—
147C34—31no—
148C34C2×C3×D311yescharacteristic
149C3×3−1+2—21no—
150C3×3−1+2—21no—
151C3×3−1+2—21no—
152C3×3−1+2—21no—
153C3×3−1+2—21no—
154C3×3−1+2—21no—
155C3×3−1+2—31no—
156C3×3−1+2—41no—
157C3×3−1+2—41no—
158C3×3−1+2—41no—
159C3×3−1+2—41no—
160C3×3−1+2—41no—
161C3×3−1+2—61no—
162C3×3−1+2—61no—
163C3×3−1+2—61no—
164C3×3−1+2—61no—
165C3×3−1+2—121no—
166C3×3−1+2—121no—
167C3×3−1+2—121no—
168C3×3−1+2—121no—
169C3×3−1+2C2×C3×D311yescharacteristic, complemented
170C3×H(3,𝔽3)—21no—
171C3×H(3,𝔽3)—21no—
172C3×H(3,𝔽3)—21no—
173C3×H(3,𝔽3)—21no—
174C3×H(3,𝔽3)—61no—
175C3×H(3,𝔽3)—121no—
176C3×H(3,𝔽3)—121no—
177C3×H(3,𝔽3)D3211yescharacteristic
178C3×H(3,𝔽3)C2×C3×D311yescharacteristic
179C3×H(3,𝔽3)C2×C3×D311yescharacteristic
180C3×H(3,𝔽3)C2×C3×D311yescharacteristic
181C32×C9—21no—
182C32×C9—61no—
183C32×C9C22×C3211yescharacteristic, complemented
184#731—21no—
185#731—21no—
186#731—21no—
187#731—21no—
188#731—21no—
189#731—21no—
190#731—21no—
191#731—21no—
192#731—21no—
193#731—41no—
194#731—41no—
195#731—41no—
196#731—41no—
197#731—41no—
198#731—41no—
199#731—41no—
200#731—41no—
201#731—41no—
202#731—41no—
203#731—41no—
204#731—41no—
205#731—41no—
206#731—41no—
207#731—41no—
208#731C2×C3×D311yescharacteristic, complemented
209#731C2×C3×D311yescharacteristic, complemented
210#731C2×C3×D311yescharacteristic, complemented
211C2×C33—31no—
212C2×C33—91no—
213C2×C33—271no—
214C3⋊(C3⋊D3)—31no—
215C3×C3⋊D3—31no—
216C3×C3⋊D3—31no—
217C3×C3⋊D3—61no—
218C3×C3⋊D3—91no—
219C3×C3⋊D3—91no—
220C3×C3⋊D3—91no—
221C3×C3⋊D3—91no—
222C3×C3⋊D3—91no—
223C3×C3⋊D3—181no—
224C3×C3⋊D3—271no—
225C3×C3⋊D3—541no—
226C32×D3—21no—
227C32×D3—31no—
228C32×D3—31no—
229C32×D3—61no—
230C32×D3—91no—
231C32×D3—91no—
232C32×D3—91no—
233C32×D3—91no—
234C32×D3—91no—
235C32×D3—91no—
236C32×D3—181no—
237C32×D3—181no—
238C32×D3—181no—
239C32×D3—181no—
240C32×D3—181no—
241C32×D3—181no—
242C32×D3—271no—
243C32×D3—271no—
244C32×D3—271no—
245C32×D3—541no—
246C32×D3(C3⋊D3)⋊C311yescharacteristic
247C32×D3C32×D311yescharacteristic
248C2×3−1+2—61no—
249C2×3−1+2—61no—
250C2×3−1+2—61no—
251C2×3−1+2—91no—
252C2×3−1+2—181no—
253C2×3−1+2—181no—
254C2×3−1+2—181no—
255C2×H(3,𝔽3)—31no—
256C2×H(3,𝔽3)—31no—
257C2×H(3,𝔽3)—31no—
258C2×H(3,𝔽3)—181no—
259C2×C3×C9—31no—
260C2×C3×C9—61no—
261C2×C3×C9—181no—
262C3⋊D9—31no—
263C3⋊D9—61no—
264C3⋊D9—91no—
265C3⋊D9—181no—
266C3⋊D9C32×D311yescharacteristic, complemented
267AGL(1,ℤ/9)—91no—
268AGL(1,ℤ/9)—181no—
269AGL(1,ℤ/9)—271no—
270AGL(1,ℤ/9)—541no—
271(C3⋊D3)⋊C3—31no—
272(C3⋊D3)⋊C3—31no—
273(C3⋊D3)⋊C3—31no—
274(C3⋊D3)⋊C3—61no—
275(C3⋊D3)⋊C3—61no—
276(C3⋊D3)⋊C3—61no—
277(C3⋊D3)⋊C3—91no—
278(C3⋊D3)⋊C3—91no—
279(C3⋊D3)⋊C3—91no—
280(C3⋊D3)⋊C3—181no—
281(C3⋊D3)⋊C3—181no—
282(C3⋊D3)⋊C3—181no—
283D3×C9—31no—
284D3×C9—61no—
285D3×C9—61no—
286D3×C9—61no—
287D3×C9—61no—
288C3×D9—91no—
289C22×C32—811no—
290C2×C3⋊D3—91no—
291C2×C3×D3—271no—
292C2×C3×D3—271no—
293C2×C3×D3—271no—
294C2×C3×D3—271no—
295C2×C3×D3—271no—
296C2×C3×D3—271no—
297C2×C3×D3—271no—
298C2×C3×D3—271no—
299C2×C3×D3—811no—
300D32—91no—
301D32—271no—
302C2×D9—271no—
303C33—21no—
304C33—21no—
305C33—21no—
306C33—31no—
307C33—31no—
308C33—31no—
309C33—41no—
310C33—61no—
311C33—61no—
312C33—91no—
313C33—121no—
314C33—121no—
315C33—121no—
316C33—181no—
317C33—181no—
318C33—361no—
319C33—361no—
320C33—361no—
321C33C2×(C3⋊D3)⋊C311yescharacteristic
322C33C3×D3211yescharacteristic
323C33C2×C32×D311yescharacteristic
3243−1+2—21no—
3253−1+2—21no—
3263−1+2—21no—
3273−1+2—31no—
3283−1+2—41no—
3293−1+2—41no—
3303−1+2—41no—
3313−1+2—61no—
3323−1+2—61no—
3333−1+2—61no—
3343−1+2—61no—
3353−1+2—61no—
3363−1+2—121no—
3373−1+2—121no—
3383−1+2—122no—
3393−1+2—121no—
3403−1+2—121no—
3413−1+2—121no—
3423−1+2—121no—
3433−1+2—121no—
3443−1+2—121no—
3453−1+2—121no—
3463−1+2—121no—
3473−1+2—121no—
3483−1+2—121no—
3493−1+2—121no—
3503−1+2—121no—
351H(3,𝔽3)—21no—
352H(3,𝔽3)—21no—
353H(3,𝔽3)—21no—
354H(3,𝔽3)—61no—
355H(3,𝔽3)—61no—
356H(3,𝔽3)—61no—
357H(3,𝔽3)—121no—
358H(3,𝔽3)—121no—
359H(3,𝔽3)—121no—
360H(3,𝔽3)—121no—
361H(3,𝔽3)—121no—
362H(3,𝔽3)C3×D3211yescharacteristic
363H(3,𝔽3)C3×D3211yescharacteristic
364H(3,𝔽3)C3×D3211yescharacteristic
365C3×C9—21no—
366C3×C9—21no—
367C3×C9—31no—
368C3×C9—41no—
369C3×C9—61no—
370C3×C9—61no—
371C3×C9—61no—
372C3×C9—61no—
373C3×C9—61no—
374C3×C9—61no—
375C3×C9—121no—
376C3×C9—121no—
377C3×C9—121no—
378C3×C9—121no—
379C3×C9—121no—
380C3×C9C2×C32×D311yescharacteristic, complemented
381C2×C32—31no—
382C2×C32—31no—
383C2×C32—61no—
384C2×C32—181no—
385C2×C32—181no—
386C2×C32—181no—
387C2×C32—271no—
388C2×C32—271no—
389C2×C32—271no—
390C2×C32—271no—
391C2×C32—271no—
392C2×C32—271no—
393C2×C32—541no—
394C2×C32—541no—
395C2×C32—541no—
396C2×C32—541no—
397C2×C32—541no—
398C2×C32—541no—
399C2×C32—811no—
400C3⋊D3—31no—
401C3⋊D3—91no—
402C3⋊D3—91no—
403C3⋊D3—181no—
404C3⋊D3—271no—
405C3⋊D3—541no—
406C3×D3—31no—
407C3×D3—61no—
408C3×D3—61no—
409C3×D3—91no—
410C3×D3—91no—
411C3×D3—91no—
412C3×D3—91no—
413C3×D3—91no—
414C3×D3—181no—
415C3×D3—181no—
416C3×D3—181no—
417C3×D3—181no—
418C3×D3—181no—
419C3×D3—181no—
420C3×D3—181no—
421C3×D3—271no—
422C3×D3—271no—
423C3×D3—271no—
424C3×D3—271no—
425C3×D3—271no—
426C3×D3—271no—
427C3×D3—271no—
428C3×D3—271no—
429C3×D3—271no—
430C3×D3—271no—
431C3×D3—541no—
432C3×D3—541no—
433C3×D3—541no—
434C3×D3—541no—
435C3×D3—541no—
436C3×D3—811no—
437C3×D3—1621no—
438C3×D3C3×(C3⋊D3)⋊C311yescharacteristic
439C2×C9—91no—
440C2×C9—181no—
441C2×C9—181no—
442C2×C9—181no—
443C2×C9—181no—
444D9—91no—
445D9—271no—
446D9—541no—
447C22×C3—811no—
448C22×C3—811no—
449C22×C3—811no—
450C22×C3—811no—
451C2×D3—271no—
452C2×D3—271no—
453C2×D3—811no—
454C32—21no—
455C32—21no—
456C32—21no—
457C32—31no—
458C32—41no—
459C32—61no—
460C32—61no—
461C32—61no—
462C32—61no—
463C32—61no—
464C32—61no—
465C32—61no—
466C32—91no—
467C32—121no—
468C32—121no—
469C32—121no—
470C32—121no—
471C32—181no—
472C32—181no—
473C32—181no—
474C32—181no—
475C32—181no—
476C32—181no—
477C32—361no—
478C32—361no—
479C32—361no—
480C32—361no—
481C32—361no—
482C32—361no—
483C32—361no—
484C32—361no—
485C32—361no—
486C32—361no—
487C32—361no—
488C32—361no—
489C32—361no—
490C32D3×(C3⋊D3)⋊C311yescharacteristic
491C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
492C32C32×D3211yescharacteristic
493C9—31no—
494C9—61no—
495C9—61no—
496C9—61no—
497C9—61no—
498C9—61no—
499C9—121no—
500C9—121no—
501C9—121no—
502C9—121no—
503C2×C3—31no—
504C2×C3—91no—
505C2×C3—181no—
506C2×C3—181no—
507C2×C3—271no—
508C2×C3—271no—
509C2×C3—271no—
510C2×C3—271no—
511C2×C3—271no—
512C2×C3—271no—
513C2×C3—541no—
514C2×C3—541no—
515C2×C3—541no—
516C2×C3—541no—
517C2×C3—541no—
518C2×C3—541no—
519C2×C3—811no—
520C2×C3—811no—
521C2×C3—811no—
522C2×C3—811no—
523D3—91no—
524D3—271no—
525D3—271no—
526D3—271no—
527D3—541no—
528D3—811no—
529D3—1621no—
530D3#4177⋊C311yescharacteristic, direct product factor
531C22—811noSylow
532C3—21no—
533C3—31no—
534C3—61no—
535C3—61no—
536C3—61no—
537C3—61no—
538C3—91no—
539C3—121no—
540C3—181no—
541C3—181no—
542C3—181no—
543C3—361no—
544C3—361no—
545C3C2×#4177⋊C311yescharacteristic, complemented
546C3C3×D3×(C3⋊D3)⋊C311yescharacteristic
547C2—31no—
548C2—271no—
549C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC32×C9C22×C32
FrattiniC32C32×D32
FittingC3×#6910C22
socleC32C2×C3×(C3⋊D3)⋊C3
LCSG ▷ C32×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(#4177⋊C3)C2semidirect
2. C3×#4177⋊C3C2semidirect
3. D3×#6910C2semidirect
4. D3×C3⋊AGL(1,ℤ/9)C3semidirect
7. D3×#4177C3semidirect
8. D3×#4177C3semidirect
9. D3×#4177C3semidirect
10. C3×#6910C22semidirect
11. C3⋊(C3⋊AGL(1,ℤ/9))C2×C3semidirect
12. C3×C3⋊AGL(1,ℤ/9)C2×C3semidirect
15. C3×D3×3−1+2C2×C3semidirect
19. C3⋊#4177C2×C3semidirect
20. C3⋊#4177C2×C3semidirect
21. C3⋊#4177C2×C3semidirect
28. #4177⋊C3D3direct (N × H)
32. D3×#731C2×C3semidirect
33. D3×#731C2×C3semidirect
34. D3×#731C2×C3semidirect
35. C3×#4177C2×C3semidirect
36. C3×#4177C2×C3semidirect
37. C3×#4177C2×C3semidirect
42. D3×C3⋊D9C32semidirect
51. C32×3−1+2C22×C3semidirect
62. #6910C2×D3semidirect
66. C3×#731C22×C3semidirect
67. C3×#731C22×C3semidirect
68. C3×#731C22×C3semidirect
78. C3⋊(C3⋊D9)C2×C32semidirect
84. C3⋊AGL(1,ℤ/9)C3×D3semidirect
88. C3×C3⋊D9C2×C32semidirect
113. C3×D3×C9C2×C32semidirect
129. #4177C3×D3semidirect
130. #4177C3×D3semidirect
131. #4177C3×D3semidirect
169. C3×3−1+2C2×C3×D3semidirect
183. C32×C9C22×C32semidirect
208. #731C2×C3×D3semidirect
209. #731C2×C3×D3semidirect
210. #731C2×C3×D3semidirect
266. C3⋊D9C32×D3semidirect
380. C3×C9C2×C32×D3semidirect
530. D3#4177⋊C3direct (N × H)
545. C3C2×#4177⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(#4177⋊C3)2
C3×#4177⋊C32
D3×#69102
D3×C3⋊AGL(1,ℤ/9)3
C3×D3×(C3⋊D3)⋊C33
C2×#4177⋊C33
D3×#41773