Finite Group Databasebeta

← C3×#10619983 #14518962

Subgroups — C3×#10619983 #14518962

Order 1944.

842 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 132 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×#737C211yesmaximal, characteristic, complemented
2C2×C3×#4207C211yesmaximal, characteristic, complemented
3C3×#66409C211yesmaximal, characteristic, complemented
4#10619983C313yesmaximal, direct product factor
5C3×#6233C311yesmaximal, characteristic, complemented
6C3×#611⋊C3—32nomaximal
7C3×#638⋊C3—31nomaximal
8C32×#611—31nomaximal
9C2×C3×#737—21no—
10C2×C3×#737C2211yescharacteristic
11C3×#4207—21no—
12C22×#737—26no—
13C22×#737—23no—
14C22×#737—23no—
15C22×#737C2×C313yescomplemented
16C22×C3×3−1+2—21no—
17C22×C3×3−1+2—22no—
18C22×C3×3−1+2D312yescomplemented
19C22×C3×H(3,𝔽3)D311yescharacteristic
20C22×C32×C9—21no—
21C22×C32×C9D311yescharacteristic, complemented
22C22×C32×C9C2×C311yescharacteristic, complemented
23C2×#4207C2×C313yescomplemented
24C2×C3×C3⋊D9C2×C311yescharacteristic, complemented
25C2×C3×AGL(1,ℤ/9)—32no—
26C2×C3×(C3⋊D3)⋊C3—31no—
27C2×C32×D9—31no—
28#66409C2×C313yescomplemented
29C3×C3⋊Dic9C2×C311yescharacteristic, complemented
30C3×3−1+2⋊C4—32no—
31C3×(C3⋊Dic3)⋊C3—31no—
32C32×Dic9—31no—
33C3×#737D411yescharacteristic, complemented, Sylow
34C3×#638—31no—
35C32×#67—91no—
36#6233C3211yescharacteristic, complemented
37#611⋊C3—36no—
38#638⋊C3—33no—
39C3×#611—31no—
40C3×#611—32no—
41C3×#611—33no—
42C2×#737—212no—
43C2×#737—26no—
44C2×#737—26no—
45C2×#737—23no—
46C2×#737—26no—
47C2×#737—23no—
48C2×#737—23no—
49C2×#737C22×C313yes—
50C2×C3×3−1+2—22no—
51C2×C3×3−1+2—24no—
52C2×C3×3−1+2—22no—
53C2×C3×3−1+2—21no—
54C2×C3×3−1+2—22no—
55C2×C3×3−1+2C2×D312yes—
56C2×C3×H(3,𝔽3)—21no—
57C2×C3×H(3,𝔽3)C2×D311yescharacteristic
58C2×C32×C9—22no—
59C2×C32×C9—21no—
60C2×C32×C9—21no—
61C2×C32×C9—21no—
62C2×C32×C9C2×D311yescharacteristic
63C2×C32×C9C22×C311yescharacteristic
64#4207—23no—
65C3×C3⋊D9—21no—
66C3×AGL(1,ℤ/9)—62no—
67C3×(C3⋊D3)⋊C3—61no—
68C32×D9—61no—
69C22×C33—21no—
70C22×C33C3×D311yescharacteristic
71C22×C33C3⋊D311yescharacteristic
72C2×C3×C3⋊D3—31no—
73C2×C32×D3—91no—
74C3×C3⋊Dic3—31no—
75C32×Dic3—91no—
76C22×3−1+2—26no—
77C22×3−1+2—212no—
78C22×3−1+2—23no—
79C22×3−1+2—26no—
80C22×3−1+2—26no—
81C22×3−1+2C3×D316yescomplemented
82C22×H(3,𝔽3)—23no—
83C22×H(3,𝔽3)C3×D313yes—
84C22×C3×C9—26no—
85C22×C3×C9—21no—
86C22×C3×C9—22no—
87C22×C3×C9—21no—
88C22×C3×C9—23no—
89C22×C3×C9—23no—
90C22×C3×C9—22no—
91C22×C3×C9—21no—
92C22×C3×C9C3×D311yescharacteristic
93C22×C3×C9C3×D312yes—
94C22×C3×C9C3×D313yescomplemented
95C22×C3×C9C2×C3211yescharacteristic, complemented
96C2×C3⋊D9C2×C3211yescharacteristic, complemented
97C2×AGL(1,ℤ/9)—36no—
98C2×(C3⋊D3)⋊C3—33no—
99C2×C3×D9—31no—
100C2×C3×D9—33no—
101C2×C3×D9—32no—
102C3⋊Dic9C2×C3211yescharacteristic, complemented
1033−1+2⋊C4—36no—
104(C3⋊Dic3)⋊C3—33no—
105C3×Dic9—31no—
106C3×Dic9—33no—
107C3×Dic9—32no—
108#737—26no—
109#737—23no—
110#737—23no—
111#737C3×D413yescomplemented
112C3×3−1+2—21no—
113C3×3−1+2—22no—
114C3×3−1+2#6712yescomplemented
115C3×H(3,𝔽3)#6711yescharacteristic
116C32×C9—21no—
117C32×C9#6711yescharacteristic, complemented
118C32×C9C3×D411yescharacteristic, complemented
119C32×D4—271no—
120#638—31no—
121C3×#67—91no—
122C3×#67—93no—
123C3×#67—271no—
124#611—31no—
125#611—32no—
126C2×C33—22no—
127C2×C33—21no—
128C2×C33—21no—
129C2×C33—21no—
130C2×C33C2×C3×D311yescharacteristic
131C2×C33C2×C3⋊D311yescharacteristic
132C3×C3⋊D3—61no—
133C32×D3—181no—
134C2×3−1+2—212no—
135C2×3−1+2—224no—
136C2×3−1+2—26no—
137C2×3−1+2—212no—
138C2×3−1+2—212no—
139C2×3−1+2—26no—
140C2×3−1+2—212no—
141C2×3−1+2—26no—
142C2×3−1+2—23no—
143C2×3−1+2—26no—
144C2×3−1+2—26no—
145C2×3−1+2C2×C3×D316yes—
146C2×H(3,𝔽3)—26no—
147C2×H(3,𝔽3)—23no—
148C2×H(3,𝔽3)—23no—
149C2×H(3,𝔽3)C2×C3×D313yes—
150C2×C3×C9—24no—
151C2×C3×C9—22no—
152C2×C3×C9—212no—
153C2×C3×C9—22no—
154C2×C3×C9—26no—
155C2×C3×C9—24no—
156C2×C3×C9—26no—
157C2×C3×C9—22no—
158C2×C3×C9—26no—
159C2×C3×C9—21no—
160C2×C3×C9—22no—
161C2×C3×C9—23no—
162C2×C3×C9—21no—
163C2×C3×C9—21no—
164C2×C3×C9—22no—
165C2×C3×C9—21no—
166C2×C3×C9—23no—
167C2×C3×C9—23no—
168C2×C3×C9—22no—
169C2×C3×C9—21no—
170C2×C3×C9C2×C3×D311yescharacteristic
171C2×C3×C9C2×C3×D312yes—
172C2×C3×C9C2×C3×D313yes—
173C2×C3×C9C22×C3211yescharacteristic
174C3⋊D9—21no—
175AGL(1,ℤ/9)—66no—
176(C3⋊D3)⋊C3—63no—
177C3×D9—61no—
178C3×D9—62no—
179C3×D9—63no—
180C22×C32—21no—
181C22×C32—23no—
182C22×C32—31no—
183C22×C32—31no—
184C22×C32—61no—
185C22×C32—61no—
186C22×C32—62no—
187C22×C32—61no—
188C22×C32—271no—
189C22×C32C32×D311yescharacteristic
190C22×C32C3×C3⋊D311yescharacteristic
191C22×C32C3×C3⋊D313yes—
192C2×C3⋊D3—31no—
193C2×C3×D3—91no—
194C2×C3×D3—93no—
195C2×C3×D3—271no—
196C32×C4—271no—
197C3⋊Dic3—31no—
198C3×Dic3—91no—
199C3×Dic3—93no—
200C3×Dic3—271no—
201C22×C9—21no—
202C22×C9—26no—
203C22×C9—22no—
204C22×C9—23no—
205C22×C9C32×D311yescharacteristic
206C22×C9C32×D312yes—
207C2×D9—31no—
208C2×D9—32no—
209Dic9—31no—
210Dic9—32no—
211C33—21no—
212C33C3×#6711yescharacteristic
213C33#63811yescharacteristic
2143−1+2—26no—
2153−1+2—212no—
2163−1+2—23no—
2173−1+2—26no—
2183−1+2—26no—
2193−1+2C3×#6716yescomplemented
220H(3,𝔽3)—23no—
221H(3,𝔽3)C3×#6713yes—
222C3×C9—26no—
223C3×C9—21no—
224C3×C9—22no—
225C3×C9—21no—
226C3×C9—23no—
227C3×C9—23no—
228C3×C9—22no—
229C3×C9—21no—
230C3×C9C3×#6711yescharacteristic
231C3×C9C3×#6712yes—
232C3×C9C3×#6713yescomplemented
233C3×C9C32×D411yescharacteristic, complemented
234C3×D4—273no—
235C3×D4—271no—
236#67—91no—
237#67—271no—
238C2×C32—21no—
239C2×C32—22no—
240C2×C32—26no—
241C2×C32—21no—
242C2×C32—23no—
243C2×C32—21no—
244C2×C32—23no—
245C2×C32—31no—
246C2×C32—31no—
247C2×C32—61no—
248C2×C32—61no—
249C2×C32—61no—
250C2×C32—61no—
251C2×C32—62no—
252C2×C32—62no—
253C2×C32—64no—
254C2×C32—62no—
255C2×C32—62no—
256C2×C32—61no—
257C2×C32—541no—
258C2×C32C2×C32×D311yescharacteristic
259C2×C32C2×C3×C3⋊D311yescharacteristic
260C2×C32C2×C3×C3⋊D313yes—
261C3⋊D3—61no—
262C3×D3—181no—
263C3×D3—183no—
264C3×D3—541no—
265C2×C9—22no—
266C2×C9—212no—
267C2×C9—24no—
268C2×C9—26no—
269C2×C9—21no—
270C2×C9—22no—
271C2×C9—21no—
272C2×C9—26no—
273C2×C9—22no—
274C2×C9—23no—
275C2×C9C2×C32×D311yescharacteristic
276C2×C9C2×C32×D312yes—
277D9—61no—
278D9—62no—
279C22×C3—21no—
280C22×C3—31no—
281C22×C3—33no—
282C22×C3—61no—
283C22×C3—63no—
284C22×C3—273no—
285C22×C3—271no—
286C22×C3#420711yescharacteristic, complemented
287C22×C3C32×C3⋊D311yescharacteristic
288C2×D3—91no—
289C2×D3—271no—
290C3×C4—273no—
291C3×C4—271no—
292Dic3—91no—
293Dic3—271no—
294C32—21no—
295C32—23no—
296C32—31no—
297C32—31no—
298C32—61no—
299C32—61no—
300C32—62no—
301C32—61no—
302C32C32×#6711yescharacteristic
303C32C3×#63811yescharacteristic
304C32C3×#63813yes—
305C9—21no—
306C9—26no—
307C9—22no—
308C9—23no—
309C9C32×#6711yescharacteristic
310C9C32×#6712yes—
311D4—271noSylow
312C2×C3—22no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—31no—
317C2×C3—33no—
318C2×C3—61no—
319C2×C3—63no—
320C2×C3—62no—
321C2×C3—66no—
322C2×C3—61no—
323C2×C3—63no—
324C2×C3—543no—
325C2×C3—541no—
326C2×C3C2×#420711yescharacteristic
327C2×C3C2×C32×C3⋊D311yescharacteristic
328D3—181no—
329D3—541no—
330C22—271no—
331C22C3×#420711yescharacteristic, complemented
332C4—271no—
333C3—21no—
334C3—31no—
335C3—33no—
336C3—61no—
337C3—63no—
338C3#1061998311yescharacteristic, direct product factor
339C3C32×#63811yescharacteristic
340C2—21no—
341C2—541no—
342C2C2×C3×#420711yescharacteristic
subgroupG/H
centerC2×C3C2×#4207
commutator, cosocleC2×C3×C9C22×C32
FrattiniC2×C3C2×C32×C3⋊D3
FittingC22×C3×#737C2
socleC2×C32C2×C3×C3⋊D3
hypercenterC22×C3#4207
hypocenterC3×C9C32×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×#737C2semidirect
2. C2×C3×#4207C2semidirect
3. C3×#66409C2semidirect
4. #10619983C3direct (N × H)
5. C3×#6233C3semidirect
15. C22×#737C2×C3semidirect
18. C22×C3×3−1+2D3semidirect
21. C22×C32×C9D3semidirect
22. C22×C32×C9C2×C3semidirect
23. C2×#4207C2×C3semidirect
24. C2×C3×C3⋊D9C2×C3semidirect
28. #66409C2×C3semidirect
29. C3×C3⋊Dic9C2×C3semidirect
33. C3×#737D4semidirect
36. #6233C32semidirect
81. C22×3−1+2C3×D3semidirect
94. C22×C3×C9C3×D3semidirect
95. C22×C3×C9C2×C32semidirect
96. C2×C3⋊D9C2×C32semidirect
102. C3⋊Dic9C2×C32semidirect
111. #737C3×D4semidirect
114. C3×3−1+2#67semidirect
117. C32×C9#67semidirect
118. C32×C9C3×D4semidirect
219. 3−1+2C3×#67semidirect
232. C3×C9C3×#67semidirect
233. C3×C9C32×D4semidirect
286. C22×C3#4207semidirect
331. C22C3×#4207semidirect
338. C3#10619983direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7372
C2×C3×#42072
C3×#664092
#106199833
C3×#62333
C3×#611⋊C33
C3×#638⋊C33
C32×#6113