Finite Group Databasebeta

← D3×#6233 #13048707

Subgroups — D3×#6233 #13048707

Order 1296.

660 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 124 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×C3×D3×C9C211yesmaximal, characteristic, complemented
2C2×D3×C3⋊D9C211yesmaximal, characteristic, complemented
3#10619992C211yesmaximal, characteristic, complemented
4C3×#6233C211yesmaximal, characteristic, complemented
5#10619880C211yesmaximal, characteristic, complemented
6#10619879C211yesmaximal, characteristic, complemented
7D3×C3⋊Dic9C211yesmaximal, characteristic, complemented
8D3×#638—31nomaximal
9C2×#6233—31nomaximal
10D3×#611—33nomaximal
11C22×C32×C9C2211yescharacteristic, complemented
12C2×C3⋊(C3⋊D9)C2211yescharacteristic, complemented
13C2×C3×C3⋊D9C2211yescharacteristic, complemented
14C2×C3×D3×C9—22no—
15C2×C3×D3×C9C2211yescharacteristic
16C2×C3×D3×C9C2211yescharacteristic, complemented
17D3×C3⋊D9—22no—
18C3⋊(C3⋊Dic9)C2211yescharacteristic, complemented
19C3×C3⋊Dic9C2211yescharacteristic, complemented
20C22×C32×D3D311yescharacteristic
21C2×D3×C3⋊D3—31no—
22#6312—31no—
23C3×#638—31no—
24#6291—31no—
25#6290—31no—
26D3×C3⋊Dic3—31no—
27C23×C3×C9—31no—
28C22×C3⋊D9—31no—
29C22×D3×C9D313yescomplemented
30C2×D3×D9—33no—
31#6233—31no—
32#6233—33no—
33#6233—31no—
34#6233—31no—
35#6233—63no—
36#6233—61no—
37#6233D311yescharacteristic, direct product factor
38C2×C3⋊Dic9—31no—
39C3×#611—33no—
40#6195—33no—
41#6194—33no—
42D3×Dic9—33no—
43C2×C32×C9—21no—
44C2×C32×C9C2311yescharacteristic
45C3⋊(C3⋊D9)—21no—
46C3×C3⋊D9—21no—
47C3×D3×C9—21no—
48C3×D3×C9D412yescomplemented
49C2×#638—91no—
50D3×#67—93no—
51D3×#67—91no—
52C2×#611—93no—
53C22×C33C2×D311yescharacteristic
54C2×C3⋊(C3⋊D3)—31no—
55C2×C3×C3⋊D3—31no—
56C2×C32×D3—22no—
57C2×C32×D3C2×D311yescharacteristic
58C2×C32×D3C2×D311yescharacteristic
59D3×C3⋊D3—62no—
60C3⋊(C3⋊Dic3)—31no—
61C3×C3⋊Dic3—31no—
62C22×C3×C9—21no—
63C22×C3×C9—23no—
64C22×C3×C9—31no—
65C22×C3×C9—31no—
66C22×C3×C9—62no—
67C22×C3×C9C2×D313yescomplemented
68C22×C3×C9C2×D311yescharacteristic, complemented
69C2×C3⋊D9—31no—
70C2×C3⋊D9—33no—
71C2×C3⋊D9—62no—
72C2×C3⋊D9—63no—
73C2×C3⋊D9—61no—
74C2×C3⋊D9C2×D311yescharacteristic, complemented
75C2×D3×C9—26no—
76C2×D3×C9C2×D313yes—
77C2×D3×C9C2×D313yescomplemented
78C2×C3×D9—33no—
79D3×D9—66no—
80C3⋊Dic9—31no—
81C3⋊Dic9—33no—
82C3⋊Dic9—63no—
83C3⋊Dic9—61no—
84C3⋊Dic9C2×D311yescharacteristic, complemented
85C3×Dic9—33no—
86C32×C9C2×D411yescharacteristic, complemented, Sylow
87C23×C32—31no—
88C22×C3⋊D3—91no—
89C22×C3×D3D913yescomplemented
90C22×C3×D3C3⋊D311yescharacteristic
91C2×D32—93no—
92C2×D32—91no—
93#638—31no—
94#638—91no—
95#638—91no—
96#638—91no—
97#638—93no—
98#638—91no—
99#638—181no—
100#638—183no—
101C2×C3⋊Dic3—91no—
102C3×#67—93no—
103C3×#67—91no—
104#626—93no—
105#626—91no—
106#625—93no—
107#625—91no—
108D3×Dic3—93no—
109D3×Dic3—91no—
110C23×C9—33no—
111C22×D9—93no—
112#611—33no—
113#611—93no—
114#611—93no—
115#611—93no—
116#611—183no—
117C2×Dic9—93no—
118C2×C33—21no—
119C2×C33C22×D311yescharacteristic
120C3⋊(C3⋊D3)—61no—
121C3×C3⋊D3—61no—
122C32×D3—21no—
123C32×D3#6712yes—
124C2×C3×C9—21no—
125C2×C3×C9—21no—
126C2×C3×C9—23no—
127C2×C3×C9—23no—
128C2×C3×C9—32no—
129C2×C3×C9—43no—
130C2×C3×C9—41no—
131C2×C3×C9—61no—
132C2×C3×C9C22×D313yes—
133C2×C3×C9C22×D311yescharacteristic
134C3⋊D9—21no—
135C3⋊D9—61no—
136C3⋊D9—63no—
137C3⋊D9—123no—
138C3⋊D9—121no—
139D3×C9—23no—
140D3×C9#6716yescomplemented
141C3×D9—63no—
142C2×#67—271no—
143C2×#67—273no—
144D3×D4—271no—
145C22×C32—23no—
146C22×C32—21no—
147C22×C32—31no—
148C22×C32—31no—
149C22×C32—62no—
150C22×C32C2×D913yescomplemented
151C22×C32D3211yescharacteristic
152C22×C32C2×C3⋊D311yescharacteristic
153C2×C3⋊D3—31no—
154C2×C3⋊D3—91no—
155C2×C3⋊D3—93no—
156C2×C3⋊D3—91no—
157C2×C3⋊D3—181no—
158C2×C3⋊D3—183no—
159C2×C3⋊D3—182no—
160C2×C3×D3—26no—
161C2×C3×D3—22no—
162C2×C3×D3—93no—
163C2×C3×D3—91no—
164C2×C3×D3C2×D913yes—
165C2×C3×D3C2×D913yescomplemented
166C2×C3×D3C2×C3⋊D311yescharacteristic
167C2×C3×D3C2×C3⋊D311yescharacteristic
168D32—186no—
169D32—182no—
170C3⋊Dic3—31no—
171C3⋊Dic3—91no—
172C3⋊Dic3—93no—
173C3⋊Dic3—91no—
174C3⋊Dic3—181no—
175C3⋊Dic3—183no—
176C3×Dic3—93no—
177C3×Dic3—91no—
178C22×C9—23no—
179C22×C9—33no—
180C22×C9—33no—
181C22×C9—66no—
182C22×C9D3213yescomplemented
183C2×D9—33no—
184C2×D9—93no—
185C2×D9—183no—
186C2×D9—186no—
187Dic9—33no—
188Dic9—93no—
189Dic9—183no—
190C33C2×#6711yescharacteristic
191C3×C9—21no—
192C3×C9—23no—
193C3×C9D3×D411yescharacteristic, complemented
194C3×C9C2×#6713yescomplemented
195C23×C3—33no—
196C23×C3—31no—
197C22×D3—271no—
198C22×D3—273no—
199C22×D3—271no—
200C22×D3C3⋊D911yescharacteristic, complemented
201C3×D4—271no—
202#67—93no—
203#67—91no—
204#67—271no—
205#67—273no—
206#67—271no—
207#67—273no—
208#67—273no—
209#67—271no—
210#67—271no—
211#67—271no—
212#67—543no—
213#67—541no—
214C2×Dic3—271no—
215C2×Dic3—273no—
216D12—271no—
217C4×D3—271no—
218C2×C32—21no—
219C2×C32—23no—
220C2×C32—21no—
221C2×C32—23no—
222C2×C32—21no—
223C2×C32—32no—
224C2×C32—41no—
225C2×C32—43no—
226C2×C32—61no—
227C2×C32C22×D913yes—
228C2×C32C2×D3211yescharacteristic
229C2×C32C22×C3⋊D311yescharacteristic
230C3⋊D3—61no—
231C3⋊D3—181no—
232C3⋊D3—183no—
233C3⋊D3—181no—
234C3⋊D3—361no—
235C3⋊D3—363no—
236C3×D3—23no—
237C3×D3—21no—
238C3×D3—183no—
239C3×D3—181no—
240C3×D3#61116yescomplemented
241C3×D3#63812yes—
242C2×C9—23no—
243C2×C9—23no—
244C2×C9—36no—
245C2×C9—43no—
246C2×C9—63no—
247C2×C9C2×D3213yes—
248D9—63no—
249D9—183no—
250D9—363no—
251C2×D4—811noSylow
252C22×C3—23no—
253C22×C3—21no—
254C22×C3—33no—
255C22×C3—31no—
256C22×C3—33no—
257C22×C3—31no—
258C22×C3—62no—
259C22×C3—66no—
260C22×C3—271no—
261C22×C3D3×D913yescomplemented
262C22×C3C2×C3⋊D911yescharacteristic, complemented
263C22×C3D3×C3⋊D311yescharacteristic
264C2×D3—22no—
265C2×D3—93no—
266C2×D3—91no—
267C2×D3—273no—
268C2×D3—271no—
269C2×D3—271no—
270C2×D3—543no—
271C2×D3—541no—
272C2×D3—542no—
273C2×D3—546no—
274C2×D3—542no—
275C2×D3C2×C3⋊D911yescharacteristic
276C2×D3C2×C3⋊D911yescharacteristic, complemented
277C3×C4—271no—
278Dic3—93no—
279Dic3—91no—
280Dic3—273no—
281Dic3—271no—
282Dic3—271no—
283Dic3—543no—
284Dic3—541no—
285C32—23no—
286C32—21no—
287C32C2×#61113yescomplemented
288C32D3×#6711yescharacteristic
289C32C2×#63811yescharacteristic
290C9—23no—
291C9D3×#6713yescomplemented
292C23—31no—
293C23—811no—
294D4—271no—
295D4—811no—
296D4—811no—
297D4—811no—
298C2×C4—811no—
299C2×C3—23no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—23no—
303C2×C3—21no—
304C2×C3—36no—
305C2×C3—32no—
306C2×C3—43no—
307C2×C3—41no—
308C2×C3—63no—
309C2×C3—61no—
310C2×C3—541no—
311C2×C3C2×D3×D913yes—
312C2×C3C22×C3⋊D911yescharacteristic
313C2×C3C2×D3×C3⋊D311yescharacteristic
314D3—21no—
315D3—183no—
316D3—181no—
317D3—543no—
318D3—541no—
319D3—541no—
320D3—1083no—
321D3—1081no—
322D3#623312yesdirect product factor
323C22—31no—
324C22—31no—
325C22—62no—
326C22—271no—
327C22—811no—
328C22—1622no—
329C22D3×C3⋊D911yescharacteristic, complemented
330C4—271no—
331C4—811no—
332C3—23no—
333C3—21no—
334C3D3×#61113yescomplemented
335C3C2×#623311yescharacteristic, complemented
336C3D3×#63811yescharacteristic
337C2—21no—
338C2—32no—
339C2—61no—
340C2—541no—
341C2—1621no—
342C2C2×D3×C3⋊D911yescharacteristic
subgroupG/H
centerC2C2×D3×C3⋊D9
commutator, cosocleC2×C32×C9C23
FrattiniC2×C3C2×D3×C3⋊D3
FittingC22×C32×C9C22
socleC2×C33C22×D3
hypercenterC22D3×C3⋊D9
hypocenterC32×C9C2×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×C9C2semidirect
2. C2×D3×C3⋊D9C2semidirect
3. #10619992C2semidirect
4. C3×#6233C2semidirect
5. #10619880C2semidirect
6. #10619879C2semidirect
7. D3×C3⋊Dic9C2semidirect
11. C22×C32×C9C22semidirect
12. C2×C3⋊(C3⋊D9)C22semidirect
13. C2×C3×C3⋊D9C22semidirect
16. C2×C3×D3×C9C22semidirect
18. C3⋊(C3⋊Dic9)C22semidirect
19. C3×C3⋊Dic9C22semidirect
29. C22×D3×C9D3semidirect
37. #6233D3direct (N × H)
48. C3×D3×C9D4semidirect
67. C22×C3×C9C2×D3semidirect
68. C22×C3×C9C2×D3semidirect
74. C2×C3⋊D9C2×D3semidirect
77. C2×D3×C9C2×D3semidirect
84. C3⋊Dic9C2×D3semidirect
86. C32×C9C2×D4semidirect
89. C22×C3×D3D9semidirect
140. D3×C9#67semidirect
150. C22×C32C2×D9semidirect
165. C2×C3×D3C2×D9semidirect
182. C22×C9D32semidirect
193. C3×C9D3×D4semidirect
194. C3×C9C2×#67semidirect
200. C22×D3C3⋊D9semidirect
240. C3×D3#611semidirect
261. C22×C3D3×D9semidirect
262. C22×C3C2×C3⋊D9semidirect
276. C2×D3C2×C3⋊D9semidirect
287. C32C2×#611semidirect
291. C9D3×#67semidirect
322. D3#6233direct (N × H)
329. C22D3×C3⋊D9semidirect
334. C3D3×#611semidirect
335. C3C2×#6233semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C92
C2×D3×C3⋊D92
#106199922
C3×#62332
#106198802
#106198792
D3×C3⋊Dic92
D3×#6383
C2×#62333
D3×#6113