Finite Group Databasebeta

← #14518705

Subgroups — #14518705

Order 1944.

656 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C2×C3⋊(C3⋊AGL(1,ℤ/9))C211yesmaximal, characteristic, complemented
2C2×C3×D3×3−1+2C211yesmaximal, characteristic, complemented
3C3×C3⋊(3−1+2⋊C4)C211yesmaximal, characteristic, complemented
4C3×#6291—31nomaximal
5#10619980—31nomaximal
6#10619880C311yesmaximal, characteristic, complemented
7#6195⋊C3—33nomaximal
8C2×C32×3−1+2C2211yescharacteristic
9C3⋊(C3⋊AGL(1,ℤ/9))—21no—
10C3×D3×3−1+2—21no—
11C2×C3×C3⋊(C3⋊D3)—31no—
12C2×C33×D3D311yescharacteristic
13C32×C3⋊Dic3—31no—
14C22×C3×3−1+2—31no—
15C2×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
16C2×C3⋊AGL(1,ℤ/9)—31no—
17C2×C3⋊AGL(1,ℤ/9)—33no—
18C2×C3⋊AGL(1,ℤ/9)—63no—
19C2×C3⋊AGL(1,ℤ/9)—61no—
20C2×D3×3−1+2—23no—
21C2×D3×3−1+2D313yescomplemented
22C2×C3×D3×C9—21no—
23C2×C3×D3×C9C2×C311yescharacteristic, complemented
24C3⋊(3−1+2⋊C4)—21no—
25C3⋊(3−1+2⋊C4)D311yescharacteristic, complemented
26C3×C3⋊Dic9C2×C311yescharacteristic, complemented
27C3×3−1+2⋊C4—33no—
28C32×3−1+2D411yescharacteristic, complemented, Sylow
29C3×#638—91no—
30#6291—31no—
31C3×#626—93no—
32C3×#626—91no—
33#6233—31no—
34#611⋊C3—93no—
35#6195—33no—
36C2×C34C2×D311yescharacteristic
37C3×C3⋊(C3⋊D3)—61no—
38C33×D3—21no—
39C2×C3×3−1+2—23no—
40C2×C3×3−1+2—21no—
41C2×C3×3−1+2—23no—
42C2×C3×3−1+2—21no—
43C2×C3×3−1+2—41no—
44C2×C3×3−1+2—43no—
45C2×C3×3−1+2—61no—
46C2×C3×3−1+2C2×D311yescharacteristic
47C2×C3×3−1+2C2×D313yes—
48C2×C32×C9—21no—
49C2×C32×C9C22×C311yescharacteristic
50C3⋊(C3⋊D9)—21no—
51C3⋊AGL(1,ℤ/9)—62no—
52C3⋊AGL(1,ℤ/9)—66no—
53C3⋊AGL(1,ℤ/9)—61no—
54C3⋊AGL(1,ℤ/9)—63no—
55D3×3−1+2—26no—
56D3×3−1+2—23no—
57C3×D3×C9—22no—
58C3×D3×C9—21no—
59C22×C33—31no—
60C2×C3⋊(C3⋊D3)—31no—
61C2×C3×C3⋊D3—93no—
62C2×C3×C3⋊D3—91no—
63C2×C3×C3⋊D3—91no—
64C2×C3×C3⋊D3—181no—
65C2×C3×C3⋊D3—183no—
66C2×C32×D3—21no—
67C2×C32×D3—33no—
68C2×C32×D3C3×D311yescharacteristic
69C2×C32×D3C3⋊D311yescharacteristic
70C3×C3⋊Dic3—31no—
71C3×C3⋊Dic3—31no—
72C3×C3⋊Dic3—61no—
73C32×Dic3—93no—
74C32×Dic3—91no—
75C22×3−1+2—33no—
76C22×3−1+2—63no—
77C22×C3×C9—31no—
78C22×C3×C9—61no—
79C2×C3⋊D9—31no—
80C2×C3⋊D9—33no—
81C2×C3⋊D9—63no—
82C2×C3⋊D9—61no—
83C2×AGL(1,ℤ/9)—93no—
84C2×AGL(1,ℤ/9)—183no—
85C2×D3×C9—23no—
86C2×D3×C9C3×D313yescomplemented
87C3⋊Dic9C3×D311yescharacteristic, complemented
883−1+2⋊C4—33no—
893−1+2⋊C4—63no—
90C3×Dic9—33no—
91C34#6711yescharacteristic
92C3×3−1+2—23no—
93C3×3−1+2—21no—
94C3×3−1+2—23no—
95C3×3−1+2—21no—
96C3×3−1+2—41no—
97C3×3−1+2—43no—
98C3×3−1+2D1211yescharacteristic, complemented
99C3×3−1+2#6713yescomplemented
100C32×C9—21no—
101C32×C9C3×D411yescharacteristic, complemented
102#638—91no—
103C3×#67—271no—
104C3×#67—273no—
105C3×D12—271no—
106#626—93no—
107#626—91no—
108#611—93no—
109C2×C33—21no—
110C2×C33—21no—
111C2×C33—21no—
112C2×C33—33no—
113C2×C33—41no—
114C2×C33—63no—
115C2×C33—61no—
116C2×C33D3211yescharacteristic
117C2×C33C2×C3×D311yescharacteristic
118C2×C33C2×C3⋊D311yescharacteristic
119C3⋊(C3⋊D3)—61no—
120C3×C3⋊D3—182no—
121C3×C3⋊D3—183no—
122C3×C3⋊D3—186no—
123C3×C3⋊D3—181no—
124C3×C3⋊D3—181no—
125C32×D3—21no—
126C32×D3—22no—
127C32×D3—21no—
128C32×D3—63no—
129C2×3−1+2—23no—
130C2×3−1+2—23no—
131C2×3−1+2—23no—
132C2×3−1+2—43no—
133C2×3−1+2—46no—
134C2×3−1+2—43no—
135C2×3−1+2—43no—
136C2×3−1+2—66no—
137C2×3−1+2—63no—
138C2×3−1+2D3213yes—
139C2×C3×C9—21no—
140C2×C3×C9—21no—
141C2×C3×C9—23no—
142C2×C3×C9—23no—
143C2×C3×C9—43no—
144C2×C3×C9—41no—
145C2×C3×C9—62no—
146C2×C3×C9—61no—
147C2×C3×C9C2×C3×D313yes—
148C2×C3×C9C2×C3×D311yescharacteristic
149C3⋊D9—62no—
150C3⋊D9—66no—
151C3⋊D9—61no—
152C3⋊D9—63no—
153AGL(1,ℤ/9)—186no—
154AGL(1,ℤ/9)—183no—
155D3×C9—26no—
156D3×C9—23no—
157C22×C32—31no—
158C22×C32—31no—
159C22×C32—61no—
160C22×C32—93no—
161C2×C3⋊D3—91no—
162C2×C3⋊D3—93no—
163C2×C3⋊D3—91no—
164C2×C3⋊D3—181no—
165C2×C3⋊D3—183no—
166C2×C3×D3—31no—
167C2×C3×D3—61no—
168C2×C3×D3—271no—
169C2×C3×D3—273no—
170C2×C3×D3—271no—
171C2×C3×D3—541no—
172C2×C3×D3—543no—
173C2×C3×D3AGL(1,ℤ/9)13yescomplemented
174C2×C3×D3C3×C3⋊D311yescharacteristic
175C32×C4—271no—
176C3⋊Dic3—31no—
177C3×Dic3—93no—
178C3×Dic3—93no—
179C3×Dic3—91no—
180C3×Dic3—91no—
181C3×Dic3—181no—
182C3×Dic3—183no—
183C22×C9—33no—
184C22×C9—63no—
185C2×D9—93no—
186C2×D9—183no—
187Dic9—33no—
188C33—21no—
189C33—21no—
190C33—21no—
191C33—33no—
192C33—41no—
193C33—63no—
194C33#62611yescharacteristic
195C33C3×#6711yescharacteristic
196C33#63811yescharacteristic
1973−1+2—23no—
1983−1+2—23no—
1993−1+2—23no—
2003−1+2—43no—
2013−1+2—46no—
2023−1+2—43no—
2033−1+2—43no—
2043−1+2#62613yescomplemented
205C3×C9—21no—
206C3×C9—21no—
207C3×C9—23no—
208C3×C9—23no—
209C3×C9—43no—
210C3×C9—41no—
211C3×C9C3×D1211yescharacteristic, complemented
212C3×C9C3×#6713yescomplemented
213C3×D4—811no—
214#67—271no—
215#67—273no—
216D12—271no—
217C2×C32—23no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32—21no—
221C2×C32—33no—
222C2×C32—31no—
223C2×C32—41no—
224C2×C32—61no—
225C2×C32—63no—
226C2×C32—61no—
227C2×C32—63no—
228C2×C32—61no—
229C2×C32—62no—
230C2×C32—61no—
231C2×C32—123no—
232C2×C32—121no—
233C2×C32—183no—
234C2×C32C2×AGL(1,ℤ/9)13yes—
235C2×C32C3×D3211yescharacteristic
236C2×C32D3×C3⋊D311yescharacteristic
237C2×C32C2×C3×C3⋊D311yescharacteristic
238C3⋊D3—182no—
239C3⋊D3—186no—
240C3⋊D3—183no—
241C3⋊D3—181no—
242C3⋊D3—181no—
243C3×D3—23no—
244C3×D3—21no—
245C3×D3—61no—
246C3×D3—62no—
247C3×D3—541no—
248C3×D3—543no—
249C3×D3—542no—
250C3×D3—546no—
251C3×D3—541no—
252C2×C9—23no—
253C2×C9—23no—
254C2×C9—43no—
255C2×C9—66no—
256C2×C9—63no—
257C2×C9C3×D3213yes—
258D9—186no—
259D9—183no—
260C22×C3—33no—
261C22×C3—31no—
262C22×C3—91no—
263C22×C3—181no—
264C22×C3—811no—
265C2×D3—273no—
266C2×D3—271no—
267C2×D3—271no—
268C2×D3—543no—
269C2×D3—541no—
270C2×D3C3⋊AGL(1,ℤ/9)11yescharacteristic, complemented
271C3×C4—271no—
272C3×C4—271no—
273C3×C4—541no—
274Dic3—93no—
275Dic3—91no—
276C32—23no—
277C32—21no—
278C32—21no—
279C32—21no—
280C32—31no—
281C32—33no—
282C32—41no—
283C32—61no—
284C32—63no—
285C32—61no—
286C32—63no—
287C32—123no—
288C32—121no—
289C32#611⋊C313yescomplemented
290C32C3×#62611yescharacteristic
291C32#629111yescharacteristic
292C32C3×#63811yescharacteristic
293C9—23no—
294C9—23no—
295C9—43no—
296C9C3×#62613yescomplemented
297D4—811noSylow
298C2×C3—23no—
299C2×C3—21no—
300C2×C3—31no—
301C2×C3—63no—
302C2×C3—61no—
303C2×C3—61no—
304C2×C3—61no—
305C2×C3—121no—
306C2×C3—181no—
307C2×C3—182no—
308C2×C3—1621no—
309C2×C3D3×AGL(1,ℤ/9)13yes—
310C2×C3C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
311C2×C3C3×D3×C3⋊D311yescharacteristic
312D3—21no—
313D3—546no—
314D3—542no—
315D3—541no—
316D3—543no—
317D3—541no—
318C22—31no—
319C22—811no—
320C4—271no—
321C3—23no—
322C3—21no—
323C3—31no—
324C3—61no—
325C3—61no—
326C3—121no—
327C3#6195⋊C313yescomplemented
328C3#1061998011yescharacteristic, complemented
329C3C3×#629111yescharacteristic
330C2—61no—
331C2—1621no—
332C2D3×C3⋊AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC2D3×C3⋊AGL(1,ℤ/9)
commutator, cosocleC2×C32×C9C22×C3
FrattiniC2×C3C3×D3×C3⋊D3
FittingC2×C32×3−1+2C22
socleC2×C33C2×C3×D3
hypocenterC32×C9C3×D4
LCSG ▷ C2×C32×C9 ▷ C32×C9
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊(C3⋊AGL(1,ℤ/9))C2semidirect
2. C2×C3×D3×3−1+2C2semidirect
3. C3×C3⋊(3−1+2⋊C4)C2semidirect
6. #10619880C3semidirect
15. C2×C3⋊(C3⋊D9)C2×C3semidirect
21. C2×D3×3−1+2D3semidirect
23. C2×C3×D3×C9C2×C3semidirect
25. C3⋊(3−1+2⋊C4)D3semidirect
26. C3×C3⋊Dic9C2×C3semidirect
28. C32×3−1+2D4semidirect
86. C2×D3×C9C3×D3semidirect
87. C3⋊Dic9C3×D3semidirect
98. C3×3−1+2D12semidirect
99. C3×3−1+2#67semidirect
101. C32×C9C3×D4semidirect
173. C2×C3×D3AGL(1,ℤ/9)semidirect
204. 3−1+2#626semidirect
211. C3×C9C3×D12semidirect
212. C3×C9C3×#67semidirect
270. C2×D3C3⋊AGL(1,ℤ/9)semidirect
289. C32#611⋊C3semidirect
296. C9C3×#626semidirect
327. C3#6195⋊C3semidirect
328. C3#10619980semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊(C3⋊AGL(1,ℤ/9))2
C2×C3×D3×3−1+22
C3×C3⋊(3−1+2⋊C4)2
C3×#62913
#106199803
#106198803
#6195⋊C33