Finite Group Databasebeta

← D3×#638⋊C3 #13048612

Subgroups — D3×#638⋊C3 #13048612

Order 1296.

534 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×D3×H(3,𝔽3)C211yesmaximal, characteristic, complemented
2C2×D3×(C3⋊D3)⋊C3C211yesmaximal, characteristic, complemented
3#10619977C211yesmaximal, characteristic, complemented
4C3×#638⋊C3C211yesmaximal, characteristic, complemented
5#6291⋊C3C211yesmaximal, characteristic, complemented
6#6290⋊C3C211yesmaximal, characteristic, complemented
7D3×(C3⋊Dic3)⋊C3C211yesmaximal, characteristic, complemented
8D3×#638C311yesmaximal, characteristic, complemented
9C3×D3×#67—31nomaximal
10C2×#638⋊C3—31nomaximal
11C22×C3×H(3,𝔽3)C2211yescharacteristic, complemented
12C2×C3⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
13C2×D3×H(3,𝔽3)—22no—
14C2×D3×H(3,𝔽3)C2211yescharacteristic
15C2×D3×H(3,𝔽3)C2211yescharacteristic, complemented
16C2×C3×(C3⋊D3)⋊C3C2211yescharacteristic, complemented
17D3×(C3⋊D3)⋊C3—22no—
18C3⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
19C3×(C3⋊Dic3)⋊C3C2211yescharacteristic, complemented
20C22×C32×D3—21no—
21C22×C32×D3D311yescharacteristic, complemented
22C22×C32×D3C2×C311yescharacteristic, complemented
23C2×D3×C3⋊D3C2×C311yescharacteristic, complemented
24C2×C3×D32—31no—
25#6312C2×C311yescharacteristic, complemented
26C3×#638—31no—
27C3×#638C2×C311yescharacteristic, complemented
28C32×#67—31no—
29#6291C2×C311yescharacteristic, complemented
30#6290C2×C311yescharacteristic, complemented
31D3×C3⋊Dic3C2×C311yescharacteristic, complemented
32C3×#626—31no—
33C3×#625—31no—
34C3×D3×Dic3—31no—
35C23×H(3,𝔽3)—31no—
36C22×(C3⋊D3)⋊C3—31no—
37#638⋊C3—21no—
38#638⋊C3—31no—
39#638⋊C3—31no—
40#638⋊C3—31no—
41#638⋊C3—61no—
42#638⋊C3D311yescharacteristic, direct product factor
43C2×(C3⋊Dic3)⋊C3—31no—
44C2×C3×H(3,𝔽3)—21no—
45C2×C3×H(3,𝔽3)C2311yescharacteristic
46C3⋊((C3⋊D3)⋊C3)—21no—
47D3×H(3,𝔽3)—21no—
48D3×H(3,𝔽3)D412yescomplemented
49C3×(C3⋊D3)⋊C3—21no—
50C2×#638—31no—
51C2×C3×#67—91no—
52C3×D3×D4—91no—
53D3×#67—31no—
54D3×#67—91no—
55C22×C33—21no—
56C22×C33C2×D311yescharacteristic, complemented
57C22×C33C22×C311yescharacteristic, complemented
58C2×C3⋊(C3⋊D3)C22×C311yescharacteristic, complemented
59C2×C3×C3⋊D3—31no—
60C2×C3×C3⋊D3C22×C311yescharacteristic, complemented
61C2×C32×D3—24no—
62C2×C32×D3—21no—
63C2×C32×D3—21no—
64C2×C32×D3—22no—
65C2×C32×D3—22no—
66C2×C32×D3—31no—
67C2×C32×D3C2×D311yescharacteristic
68C2×C32×D3C2×D311yescharacteristic, complemented
69C2×C32×D3C22×C311yescharacteristic
70C2×C32×D3C22×C311yescharacteristic, complemented
71D3×C3⋊D3—22no—
72C3×D32—62no—
73C3⋊(C3⋊Dic3)C22×C311yescharacteristic, complemented
74C3×C3⋊Dic3—31no—
75C3×C3⋊Dic3C22×C311yescharacteristic, complemented
76C32×Dic3—31no—
77C22×H(3,𝔽3)—21no—
78C22×H(3,𝔽3)—21no—
79C22×H(3,𝔽3)—31no—
80C22×H(3,𝔽3)—31no—
81C22×H(3,𝔽3)—41no—
82C22×H(3,𝔽3)—62no—
83C22×H(3,𝔽3)C2×D311yescharacteristic, complemented
84C2×(C3⋊D3)⋊C3—21no—
85C2×(C3⋊D3)⋊C3—31no—
86C2×(C3⋊D3)⋊C3—62no—
87C2×(C3⋊D3)⋊C3—61no—
88C2×(C3⋊D3)⋊C3C2×D311yescharacteristic, complemented
89(C3⋊Dic3)⋊C3—21no—
90(C3⋊Dic3)⋊C3—31no—
91(C3⋊Dic3)⋊C3—61no—
92(C3⋊Dic3)⋊C3C2×D311yescharacteristic, complemented
93C3×H(3,𝔽3)C2×D411yescharacteristic, complemented, Sylow
94C23×C32—31no—
95C23×C32—31no—
96C23×C32—61no—
97C22×C3⋊D3—31no—
98C22×C3×D3—31no—
99C22×C3×D3—31no—
100C22×C3×D3—61no—
101C22×C3×D3—91no—
102C22×C3×D3—91no—
103C22×C3×D3C3×D311yescharacteristic
104C2×D32—31no—
105C2×D32—91no—
106C32×D4—91no—
107#638—31no—
108#638—31no—
109#638—31no—
110#638—31no—
111#638—61no—
112#638—91no—
113#638—181no—
114#638C3×D311yescharacteristic, complemented
115C2×C3⋊Dic3—31no—
116C3×#67—31no—
117C3×#67—31no—
118C3×#67—61no—
119C3×#67—91no—
120C3×#67—91no—
121C3×#67—91no—
122C3×#67—91no—
123C3×#67—91no—
124C3×#67—91no—
125C3×#67—181no—
126C2×C3×Dic3—91no—
127C3×D12—91no—
128C3×C4×D3—91no—
129#626—31no—
130#626—91no—
131#625—31no—
132#625—91no—
133D3×Dic3—31no—
134D3×Dic3—91no—
135C2×C33—22no—
136C2×C33—21no—
137C2×C33—21no—
138C2×C33—21no—
139C2×C33C22×D311yescharacteristic
140C2×C33C23×C311yescharacteristic
141C3⋊(C3⋊D3)—21no—
142C3×C3⋊D3—21no—
143C3×C3⋊D3—61no—
144C32×D3—22no—
145C32×D3—21no—
146C32×D3—21no—
147C32×D3—22no—
148C32×D3—61no—
149C32×D3#6712yescomplemented
150C32×D3C3×D412yescomplemented
151C2×H(3,𝔽3)—21no—
152C2×H(3,𝔽3)—21no—
153C2×H(3,𝔽3)—21no—
154C2×H(3,𝔽3)—32no—
155C2×H(3,𝔽3)—41no—
156C2×H(3,𝔽3)—41no—
157C2×H(3,𝔽3)—41no—
158C2×H(3,𝔽3)—42no—
159C2×H(3,𝔽3)—61no—
160C2×H(3,𝔽3)C22×D311yescharacteristic
161(C3⋊D3)⋊C3—21no—
162(C3⋊D3)⋊C3—41no—
163(C3⋊D3)⋊C3—61no—
164(C3⋊D3)⋊C3—121no—
165C2×C3×D4—271no—
166C2×#67—91no—
167C2×#67—271no—
168D3×D4—91no—
169C22×C32—21no—
170C22×C32—21no—
171C22×C32—21no—
172C22×C32—31no—
173C22×C32—31no—
174C22×C32—31no—
175C22×C32—31no—
176C22×C32—31no—
177C22×C32—31no—
178C22×C32—41no—
179C22×C32—61no—
180C22×C32—61no—
181C22×C32—61no—
182C22×C32—61no—
183C22×C32—61no—
184C22×C32—62no—
185C22×C32—62no—
186C22×C32—64no—
187C22×C32—91no—
188C22×C32—121no—
189C22×C32D3211yescharacteristic, complemented
190C22×C32C2×C3×D311yescharacteristic
191C22×C32C2×C3×D311yescharacteristic, complemented
192C2×C3⋊D3—31no—
193C2×C3⋊D3—31no—
194C2×C3⋊D3—61no—
195C2×C3⋊D3—62no—
196C2×C3⋊D3—91no—
197C2×C3⋊D3—181no—
198C2×C3⋊D3C2×C3×D311yescharacteristic, complemented
199C2×C3×D3—22no—
200C2×C3×D3—31no—
201C2×C3×D3—31no—
202C2×C3×D3—31no—
203C2×C3×D3—31no—
204C2×C3×D3—31no—
205C2×C3×D3—31no—
206C2×C3×D3—62no—
207C2×C3×D3—62no—
208C2×C3×D3—64no—
209C2×C3×D3—61no—
210C2×C3×D3—61no—
211C2×C3×D3—61no—
212C2×C3×D3—91no—
213C2×C3×D3—91no—
214C2×C3×D3—91no—
215C2×C3×D3—181no—
216C2×C3×D3—182no—
217C2×C3×D3—182no—
218C2×C3×D3C2×C3×D311yescharacteristic
219C2×C3×D3C2×C3×D311yescharacteristic
220D32—62no—
221D32—182no—
222C32×C4—91no—
223C3⋊Dic3—31no—
224C3⋊Dic3—31no—
225C3⋊Dic3—61no—
226C3⋊Dic3—91no—
227C3⋊Dic3—181no—
228C3⋊Dic3C2×C3×D311yescharacteristic, complemented
229C3×Dic3—31no—
230C3×Dic3—31no—
231C3×Dic3—61no—
232C3×Dic3—91no—
233C3×Dic3—91no—
234C3×Dic3—91no—
235C3×Dic3—181no—
236C33—21no—
237C33C2×#6711yescharacteristic, complemented
238C33C2×C3×D411yescharacteristic, complemented
239H(3,𝔽3)—21no—
240H(3,𝔽3)—21no—
241H(3,𝔽3)—41no—
242H(3,𝔽3)D3×D411yescharacteristic, complemented
243C23×C3—31no—
244C23×C3—91no—
245C23×C3—91no—
246C23×C3—181no—
247C23×C3—271no—
248C22×D3—91no—
249C22×D3—91no—
250C22×D3—271no—
251C22×D3(C3⋊D3)⋊C311yescharacteristic, complemented
252C3×D4—91no—
253C3×D4—91no—
254C3×D4—181no—
255C3×D4—271no—
256C3×D4—271no—
257C3×D4—271no—
258C2×C3×C4—271no—
259#67—31no—
260#67—91no—
261#67—91no—
262#67—91no—
263#67—91no—
264#67—91no—
265#67—91no—
266#67—181no—
267#67—271no—
268#67—271no—
269#67—271no—
270#67—541no—
271C2×Dic3—91no—
272C2×Dic3—271no—
273D12—91no—
274C4×D3—91no—
275C2×C32—21no—
276C2×C32—22no—
277C2×C32—21no—
278C2×C32—21no—
279C2×C32—21no—
280C2×C32—21no—
281C2×C32—21no—
282C2×C32—31no—
283C2×C32—31no—
284C2×C32—32no—
285C2×C32—32no—
286C2×C32—41no—
287C2×C32—41no—
288C2×C32—42no—
289C2×C32—41no—
290C2×C32—61no—
291C2×C32—61no—
292C2×C32—61no—
293C2×C32—61no—
294C2×C32—62no—
295C2×C32—62no—
296C2×C32—61no—
297C2×C32—62no—
298C2×C32—61no—
299C2×C32—61no—
300C2×C32—121no—
301C2×C32—121no—
302C2×C32—121no—
303C2×C32—122no—
304C2×C32—181no—
305C2×C32C2×D3211yescharacteristic
306C2×C32C22×C3×D311yescharacteristic
307C2×C32C22×C3×D311yescharacteristic
308C3⋊D3—21no—
309C3⋊D3—61no—
310C3⋊D3—61no—
311C3⋊D3—121no—
312C3⋊D3—181no—
313C3⋊D3—361no—
314C3×D3—21no—
315C3×D3—32no—
316C3×D3—32no—
317C3×D3—61no—
318C3×D3—61no—
319C3×D3—62no—
320C3×D3—61no—
321C3×D3—61no—
322C3×D3—62no—
323C3×D3—121no—
324C3×D3—181no—
325C3×D3—181no—
326C3×D3—181no—
327C3×D3—361no—
328C3×D3C3×#6712yes—
329C2×D4—271noSylow
330C22×C3—21no—
331C22×C3—31no—
332C22×C3—31no—
333C22×C3—31no—
334C22×C3—31no—
335C22×C3—62no—
336C22×C3—61no—
337C22×C3—61no—
338C22×C3—61no—
339C22×C3—91no—
340C22×C3—91no—
341C22×C3—91no—
342C22×C3—91no—
343C22×C3—91no—
344C22×C3—91no—
345C22×C3—121no—
346C22×C3—181no—
347C22×C3—181no—
348C22×C3—182no—
349C22×C3—182no—
350C22×C3—184no—
351C22×C3—181no—
352C22×C3—271no—
353C22×C3—542no—
354C22×C3C2×(C3⋊D3)⋊C311yescharacteristic, complemented
355C22×C3C3×D3211yescharacteristic
356C2×D3—22no—
357C2×D3—31no—
358C2×D3—91no—
359C2×D3—91no—
360C2×D3—91no—
361C2×D3—181no—
362C2×D3—182no—
363C2×D3—182no—
364C2×D3—271no—
365C2×D3—541no—
366C2×D3—542no—
367C2×D3C2×(C3⋊D3)⋊C311yescharacteristic
368C2×D3C2×(C3⋊D3)⋊C311yescharacteristic, complemented
369C3×C4—91no—
370C3×C4—91no—
371C3×C4—181no—
372C3×C4—271no—
373Dic3—31no—
374Dic3—91no—
375Dic3—91no—
376Dic3—91no—
377Dic3—181no—
378Dic3—271no—
379Dic3—541no—
380C32—21no—
381C32—21no—
382C32—21no—
383C32—31no—
384C32—31no—
385C32—41no—
386C32—61no—
387C32—61no—
388C32—61no—
389C32—121no—
390C32D3×#6711yescharacteristic, complemented
391C32C3×D3×D411yescharacteristic, complemented
392C32C2×C3×#6711yescharacteristic
393C23—31no—
394C23—271no—
395D4—91no—
396D4—271no—
397D4—271no—
398D4—271no—
399C2×C4—271no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—32no—
404C2×C3—31no—
405C2×C3—31no—
406C2×C3—41no—
407C2×C3—61no—
408C2×C3—61no—
409C2×C3—62no—
410C2×C3—61no—
411C2×C3—61no—
412C2×C3—61no—
413C2×C3—61no—
414C2×C3—92no—
415C2×C3—92no—
416C2×C3—121no—
417C2×C3—121no—
418C2×C3—122no—
419C2×C3—121no—
420C2×C3—182no—
421C2×C3—181no—
422C2×C3—181no—
423C2×C3—182no—
424C2×C3—181no—
425C2×C3—181no—
426C2×C3—361no—
427C2×C3—541no—
428C2×C3C22×(C3⋊D3)⋊C311yescharacteristic
429C2×C3C2×C3×D3211yescharacteristic
430D3—21no—
431D3—61no—
432D3—181no—
433D3—181no—
434D3—181no—
435D3—361no—
436D3—541no—
437D3—1081no—
438D3#638⋊C312yesdirect product factor
439C22—31no—
440C22—31no—
441C22—62no—
442C22—91no—
443C22—271no—
444C22—542no—
445C22D3×(C3⋊D3)⋊C311yescharacteristic, complemented
446C4—91no—
447C4—271no—
448C3—21no—
449C3—31no—
450C3—31no—
451C3—61no—
452C3—61no—
453C3—61no—
454C3—121no—
455C3C2×#638⋊C311yescharacteristic, complemented
456C3C3×D3×#6711yescharacteristic
457C2—21no—
458C2—32no—
459C2—61no—
460C2—181no—
461C2—541no—
462C2C2×D3×(C3⋊D3)⋊C311yescharacteristic
subgroupG/H
centerC2C2×D3×(C3⋊D3)⋊C3
commutator, cosocleC2×C33C23×C3
FrattiniC2×C3C2×C3×D32
FittingC22×C3×H(3,𝔽3)C22
socleC2×C32C22×C3×D3
hypercenterC22D3×(C3⋊D3)⋊C3
hypocenterC33C2×C3×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×D3×H(3,𝔽3)C2semidirect
2. C2×D3×(C3⋊D3)⋊C3C2semidirect
3. #10619977C2semidirect
4. C3×#638⋊C3C2semidirect
5. #6291⋊C3C2semidirect
6. #6290⋊C3C2semidirect
7. D3×(C3⋊Dic3)⋊C3C2semidirect
8. D3×#638C3semidirect
11. C22×C3×H(3,𝔽3)C22semidirect
12. C2×C3⋊((C3⋊D3)⋊C3)C22semidirect
15. C2×D3×H(3,𝔽3)C22semidirect
16. C2×C3×(C3⋊D3)⋊C3C22semidirect
18. C3⋊((C3⋊Dic3)⋊C3)C22semidirect
19. C3×(C3⋊Dic3)⋊C3C22semidirect
21. C22×C32×D3D3semidirect
22. C22×C32×D3C2×C3semidirect
23. C2×D3×C3⋊D3C2×C3semidirect
25. #6312C2×C3semidirect
27. C3×#638C2×C3semidirect
29. #6291C2×C3semidirect
30. #6290C2×C3semidirect
31. D3×C3⋊Dic3C2×C3semidirect
42. #638⋊C3D3direct (N × H)
48. D3×H(3,𝔽3)D4semidirect
56. C22×C33C2×D3semidirect
57. C22×C33C22×C3semidirect
58. C2×C3⋊(C3⋊D3)C22×C3semidirect
60. C2×C3×C3⋊D3C22×C3semidirect
68. C2×C32×D3C2×D3semidirect
70. C2×C32×D3C22×C3semidirect
73. C3⋊(C3⋊Dic3)C22×C3semidirect
75. C3×C3⋊Dic3C22×C3semidirect
83. C22×H(3,𝔽3)C2×D3semidirect
88. C2×(C3⋊D3)⋊C3C2×D3semidirect
92. (C3⋊Dic3)⋊C3C2×D3semidirect
93. C3×H(3,𝔽3)C2×D4semidirect
114. #638C3×D3semidirect
149. C32×D3#67semidirect
150. C32×D3C3×D4semidirect
189. C22×C32D32semidirect
191. C22×C32C2×C3×D3semidirect
198. C2×C3⋊D3C2×C3×D3semidirect
228. C3⋊Dic3C2×C3×D3semidirect
237. C33C2×#67semidirect
238. C33C2×C3×D4semidirect
242. H(3,𝔽3)D3×D4semidirect
251. C22×D3(C3⋊D3)⋊C3semidirect
354. C22×C3C2×(C3⋊D3)⋊C3semidirect
368. C2×D3C2×(C3⋊D3)⋊C3semidirect
390. C32D3×#67semidirect
391. C32C3×D3×D4semidirect
438. D3#638⋊C3direct (N × H)
445. C22D3×(C3⋊D3)⋊C3semidirect
455. C3C2×#638⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×D3×H(3,𝔽3)2
C2×D3×(C3⋊D3)⋊C32
#106199772
C3×#638⋊C32
#6291⋊C32
#6290⋊C32
D3×(C3⋊Dic3)⋊C32
D3×#6383
C3×D3×#673
C2×#638⋊C33