Finite Group Databasebeta

← C2×#92184⋊C3 #72244069

Subgroups — C2×#92184⋊C3 #72244069

Order 2916.

364 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 72 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
1#92184⋊C3C212yesmaximal, direct product factor
2C2×#10624704C211yesmaximal, characteristic, complemented
3C2×C3×#4207—31nomaximal
4C2×C3⋊(D27⋊C3)C311yesmaximal, characteristic, complemented
5C2×#92184C311yesmaximal, characteristic, complemented
6C2×#92184C311yesmaximal, characteristic, complemented
7C2×#92184C311yesmaximal, characteristic, complemented
8#10624704C2211yescharacteristic, complemented, Sylow
9C2×C3×#737D311yescharacteristic
10C3×#4207—32no—
11C2×C3×C27⋊C3—21no—
12C2×C3×C27⋊C3C2×C311yescharacteristic, complemented
13C3⋊(D27⋊C3)C2×C312yescomplemented
14C2×#6873—21no—
15C2×#6873—21no—
16C2×#6873—21no—
17C2×#6873C2×C311yescharacteristic, complemented
18C2×#6873C2×C311yescharacteristic, complemented
19C2×#6873C2×C311yescharacteristic, complemented
20#92184C2×C312yescomplemented
21#92184C2×C312yescomplemented
22#92184C2×C312yescomplemented
23C2×#4207—31no—
24C2×#4207—31no—
25C2×#4207—31no—
26C2×C3×C3⋊D9—31no—
27C2×C3×AGL(1,ℤ/9)—91no—
28C2×C3×AGL(1,ℤ/9)—91no—
29C2×C3×(C3⋊D3)⋊C3—91no—
30C2×C32×D9—91no—
31C2×C3⋊D27C3211yescharacteristic, complemented
32C2×D27⋊C3—91no—
33C3×#737C2×D311yescharacteristic
34C3×C27⋊C3—21no—
35C3×C27⋊C3C22×C311yescharacteristic, complemented
36#6873—21no—
37#6873—21no—
38#6873—21no—
39#6873C22×C311yescharacteristic, complemented
40#6873C22×C311yescharacteristic, complemented
41#6873C22×C311yescharacteristic, complemented
42C2×#737—21no—
43C2×#737—21no—
44C2×#737—21no—
45C2×#737—61no—
46C2×#737—61no—
47C2×#737—61no—
48C2×#737C3×D311yescharacteristic
49C2×#737C3×D311yescharacteristic
50C2×#737C3×D311yescharacteristic
51C2×C3×3−1+2—21no—
52C2×C3×3−1+2—31no—
53C2×C3×3−1+2—61no—
54C2×C3×H(3,𝔽3)D911yescharacteristic
55C2×C32×C9—61no—
56C2×C32×C9C3×D311yescharacteristic
57#4207—32no—
58#4207—32no—
59#4207—32no—
60C3×C3⋊D9—32no—
61C3×AGL(1,ℤ/9)—92no—
62C3×AGL(1,ℤ/9)—92no—
63C3×(C3⋊D3)⋊C3—92no—
64C32×D9—92no—
65C2×C27⋊C3—21no—
66C2×C27⋊C3—21no—
67C2×C27⋊C3—21no—
68C2×C27⋊C3—31no—
69C2×C27⋊C3—61no—
70C2×C27⋊C3—61no—
71C2×C27⋊C3—61no—
72C2×C3×C27—21no—
73C2×C3×C27—61no—
74C2×C3×C27C2×C3211yescharacteristic, complemented
75C3⋊D27C2×C3212yescomplemented
76D27⋊C3—92no—
77C2×C3×C3⋊D3—91no—
78C2×C32×D3—271no—
79C2×C3⋊D9—31no—
80C2×AGL(1,ℤ/9)—91no—
81C2×AGL(1,ℤ/9)—91no—
82C2×AGL(1,ℤ/9)—91no—
83C2×AGL(1,ℤ/9)—91no—
84C2×AGL(1,ℤ/9)—91no—
85C2×AGL(1,ℤ/9)—91no—
86C2×(C3⋊D3)⋊C3—91no—
87C2×(C3⋊D3)⋊C3—91no—
88C2×(C3⋊D3)⋊C3—91no—
89C2×C3×D9—91no—
90C2×C3×D9—91no—
91C2×C3×D9—91no—
92C2×C3×D9—91no—
93C2×C3×D9—91no—
94C2×C3×D9—91no—
95C2×D27—91no—
96#737—21no—
97#737—21no—
98#737—21no—
99#737—61no—
100#737—61no—
101#737—61no—
102#737C2×C3×D311yescharacteristic
103#737C2×C3×D311yescharacteristic
104#737C2×C3×D311yescharacteristic
105C3×3−1+2—21no—
106C3×3−1+2—31no—
107C3×3−1+2—61no—
108C3×H(3,𝔽3)C2×D911yescharacteristic
109C32×C9—61no—
110C32×C9C2×C3×D311yescharacteristic
111C27⋊C3—21no—
112C27⋊C3—21no—
113C27⋊C3—21no—
114C27⋊C3—31no—
115C27⋊C3—61no—
116C27⋊C3—61no—
117C27⋊C3—61no—
118C3×C27—21no—
119C3×C27—61no—
120C3×C27C22×C3211yescharacteristic, complemented
121C2×C33—61no—
122C2×C33C3×D911yescharacteristic
123C3×C3⋊D3—92no—
124C32×D3—272no—
125C2×3−1+2—21no—
126C2×3−1+2—21no—
127C2×3−1+2—21no—
128C2×3−1+2—31no—
129C2×3−1+2—31no—
130C2×3−1+2—61no—
131C2×3−1+2—61no—
132C2×3−1+2—61no—
133C2×3−1+2—61no—
134C2×3−1+2—61no—
135C2×3−1+2—61no—
136C2×3−1+2—62no—
137C2×3−1+2—61no—
138C2×3−1+2—61no—
139C2×3−1+2—61no—
140C2×3−1+2—61no—
141C2×H(3,𝔽3)—61no—
142C2×H(3,𝔽3)C3×D911yescharacteristic
143C2×H(3,𝔽3)C3×D911yescharacteristic
144C2×H(3,𝔽3)C3×D911yescharacteristic
145C2×C3×C9—21no—
146C2×C3×C9—21no—
147C2×C3×C9—21no—
148C2×C3×C9—21no—
149C2×C3×C9—61no—
150C2×C3×C9—61no—
151C2×C3×C9—61no—
152C2×C3×C9—61no—
153C2×C3×C9—61no—
154C2×C3×C9—61no—
155C2×C3×C9—61no—
156C2×C3×C9(C3⋊D3)⋊C311yescharacteristic
157C2×C3×C9AGL(1,ℤ/9)11yescharacteristic
158C2×C3×C9AGL(1,ℤ/9)11yescharacteristic
159C2×C3×C9C32×D311yescharacteristic
160C3⋊D9—32no—
161AGL(1,ℤ/9)—92no—
162AGL(1,ℤ/9)—92no—
163AGL(1,ℤ/9)—92no—
164AGL(1,ℤ/9)—92no—
165AGL(1,ℤ/9)—92no—
166AGL(1,ℤ/9)—92no—
167(C3⋊D3)⋊C3—92no—
168(C3⋊D3)⋊C3—92no—
169(C3⋊D3)⋊C3—92no—
170C3×D9—92no—
171C3×D9—92no—
172C3×D9—92no—
173C3×D9—92no—
174C3×D9—92no—
175C3×D9—92no—
176C2×C27—31no—
177C2×C27—61no—
178C2×C27—61no—
179C2×C27—61no—
180C2×C27—61no—
181D27—92no—
182C22×C32—811no—
183C2×C3⋊D3—91no—
184C2×C3×D3—271no—
185C2×C3×D3—271no—
186C2×C3×D3—271no—
187C2×C3×D3—271no—
188C2×C3×D3—811no—
189C2×D9—91no—
190C2×D9—91no—
191C2×D9—91no—
192C33—61no—
193C33C2×C3×D911yescharacteristic
1943−1+2—21no—
1953−1+2—21no—
1963−1+2—21no—
1973−1+2—31no—
1983−1+2—31no—
1993−1+2—61no—
2003−1+2—61no—
2013−1+2—61no—
2023−1+2—61no—
2033−1+2—61no—
2043−1+2—61no—
2053−1+2—62no—
2063−1+2—61no—
2073−1+2—61no—
2083−1+2—61no—
2093−1+2—61no—
210H(3,𝔽3)—61no—
211H(3,𝔽3)C2×C3×D911yescharacteristic
212H(3,𝔽3)C2×C3×D911yescharacteristic
213H(3,𝔽3)C2×C3×D911yescharacteristic
214C3×C9—21no—
215C3×C9—21no—
216C3×C9—21no—
217C3×C9—21no—
218C3×C9—61no—
219C3×C9—61no—
220C3×C9—61no—
221C3×C9—61no—
222C3×C9—61no—
223C3×C9—61no—
224C3×C9—61no—
225C3×C9C2×(C3⋊D3)⋊C311yescharacteristic
226C3×C9C2×AGL(1,ℤ/9)11yescharacteristic
227C3×C9C2×AGL(1,ℤ/9)11yescharacteristic
228C3×C9C2×C32×D311yescharacteristic
229C27—31no—
230C27—61no—
231C27—61no—
232C27—61no—
233C27—61no—
234C2×C32—21no—
235C2×C32—31no—
236C2×C32—31no—
237C2×C32—61no—
238C2×C32—91no—
239C2×C32—181no—
240C2×C32—181no—
241C2×C32—812no—
242C2×C32#416911yescharacteristic
243C2×C32C32×D911yescharacteristic
244C3⋊D3—92no—
245C3×D3—272no—
246C3×D3—272no—
247C3×D3—272no—
248C3×D3—272no—
249C3×D3—812no—
250C2×C9—21no—
251C2×C9—21no—
252C2×C9—21no—
253C2×C9—61no—
254C2×C9—61no—
255C2×C9—61no—
256C2×C9C3×(C3⋊D3)⋊C311yescharacteristic
257C2×C9C3×AGL(1,ℤ/9)11yescharacteristic
258C2×C9C3×AGL(1,ℤ/9)11yescharacteristic
259D9—92no—
260D9—92no—
261D9—92no—
262C22×C3—811no—
263C22×C3—811no—
264C22×C3—811no—
265C22×C3—811no—
266C2×D3—271no—
267C2×D3—811no—
268C32—21no—
269C32—31no—
270C32—31no—
271C32—61no—
272C32—91no—
273C32—181no—
274C32—181no—
275C32C2×#416911yescharacteristic
276C32C2×C32×D911yescharacteristic
277C9—21no—
278C9—21no—
279C9—21no—
280C9—61no—
281C9—61no—
282C9—61no—
283C9C2×C3×(C3⋊D3)⋊C311yescharacteristic
284C9C2×C3×AGL(1,ℤ/9)11yescharacteristic
285C9C2×C3×AGL(1,ℤ/9)11yescharacteristic
286C2×C3—31no—
287C2×C3—61no—
288C2×C3—61no—
289C2×C3—91no—
290C2×C3—181no—
291C2×C3—181no—
292C2×C3—812no—
293C2×C3—812no—
294C2×C3—812no—
295C2×C3—812no—
296C2×C3C3×#416911yescharacteristic
297D3—272no—
298D3—812no—
299C22—811noSylow
300C3—31no—
301C3—61no—
302C3—61no—
303C3—91no—
304C3—181no—
305C3—181no—
306C3C2×C3×#416911yescharacteristic
307C2—812no—
308C2#92184⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#92184⋊C3
commutator, cosocle, hypocenterC3×C27C22×C32
FrattiniC3×C9C2×C32×D3
FittingC2×#10624704C2
socleC2×C3C3×#4169
LCSG ▷ C3×C27
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #92184⋊C3C2direct (N × H)
2. C2×#10624704C2semidirect
4. C2×C3⋊(D27⋊C3)C3semidirect
5. C2×#92184C3semidirect
6. C2×#92184C3semidirect
7. C2×#92184C3semidirect
8. #10624704C22semidirect
12. C2×C3×C27⋊C3C2×C3semidirect
13. C3⋊(D27⋊C3)C2×C3semidirect
17. C2×#6873C2×C3semidirect
18. C2×#6873C2×C3semidirect
19. C2×#6873C2×C3semidirect
20. #92184C2×C3semidirect
21. #92184C2×C3semidirect
22. #92184C2×C3semidirect
31. C2×C3⋊D27C32semidirect
35. C3×C27⋊C3C22×C3semidirect
39. #6873C22×C3semidirect
40. #6873C22×C3semidirect
41. #6873C22×C3semidirect
74. C2×C3×C27C2×C32semidirect
75. C3⋊D27C2×C32semidirect
120. C3×C27C22×C32semidirect
308. C2#92184⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
#92184⋊C32
C2×#106247042
C2×C3×#42073
C2×C3⋊(D27⋊C3)3
C2×#921843