Finite Group Databasebeta

← C2×#92214⋊C3 #72243903

Subgroups — C2×#92214⋊C3 #72243903

Order 2916.

412 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 64 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#92214⋊C3C212yesmaximal, direct product factor
2C2×#10624704C211yesmaximal, characteristic, complemented
3C2×C3×#4207—31nomaximal
4C2×C3×D27⋊C3—31nomaximal
5C2×C3×D27⋊C3—31nomaximal
6C2×C3×D27⋊C3—31nomaximal
7C2×#92214C311yesmaximal, characteristic, complemented
8#10624704C2211yescharacteristic, complemented, Sylow
9C2×C3×#737D311yescharacteristic
10C3×#4207—32no—
11C2×C3×C27⋊C3D311yescharacteristic, complemented
12C2×C3×C27⋊C3D311yescharacteristic, complemented
13C2×C3×C27⋊C3D311yescharacteristic, complemented
14C3×D27⋊C3—32no—
15C3×D27⋊C3—32no—
16C3×D27⋊C3—32no—
17C2×#6873—21no—
18C2×#6873—21no—
19C2×#6873—21no—
20C2×#6873—21no—
21C2×#6873C2×C311yescharacteristic, complemented
22#92214C2×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×D27⋊C3—31no—
32C2×D27⋊C3—31no—
33C2×D27⋊C3—31no—
34C2×D27⋊C3—31no—
35C2×D27⋊C3—31no—
36C2×D27⋊C3—31no—
37C2×D27⋊C3—31no—
38C2×D27⋊C3—31no—
39C2×D27⋊C3—31no—
40C2×C3×D27—31no—
41C2×C3×D27—31no—
42C2×C3×D27—31no—
43C3×#737C2×D311yescharacteristic
44C3×C27⋊C3C2×D311yescharacteristic, complemented
45C3×C27⋊C3C2×D311yescharacteristic, complemented
46C3×C27⋊C3C2×D311yescharacteristic, complemented
47#6873—21no—
48#6873—21no—
49#6873—21no—
50#6873—21no—
51#6873C22×C311yescharacteristic, complemented
52C2×#737—21no—
53C2×#737—21no—
54C2×#737—21no—
55C2×#737—21no—
56C2×#737—31no—
57C2×#737—61no—
58C2×#737—61no—
59C2×#737—61no—
60C2×#737C3×D311yescharacteristic
61C2×C3×3−1+2—61no—
62C2×C3×3−1+2D911yescharacteristic
63C2×C3×3−1+2D911yescharacteristic
64C2×C3×H(3,𝔽3)D911yescharacteristic
65C2×C32×C9—61no—
66C2×C32×C9C3⋊D311yescharacteristic
67#4207—32no—
68#4207—32no—
69#4207—32no—
70C3×C3⋊D9—32no—
71C3×AGL(1,ℤ/9)—92no—
72C3×AGL(1,ℤ/9)—92no—
73C3×(C3⋊D3)⋊C3—92no—
74C32×D9—92no—
75C2×C27⋊C3—21no—
76C2×C27⋊C3—21no—
77C2×C27⋊C3—31no—
78C2×C27⋊C3—61no—
79C2×C27⋊C3—61no—
80C2×C27⋊C3—61no—
81C2×C27⋊C3—61no—
82C2×C27⋊C3—61no—
83C2×C27⋊C3—61no—
84C2×C27⋊C3C3×D311yescharacteristic, complemented
85C2×C27⋊C3C3×D311yescharacteristic, complemented
86C2×C3×C27—21no—
87C2×C3×C27—31no—
88C2×C3×C27—61no—
89C2×C3×C27C3×D311yescharacteristic, complemented
90D27⋊C3—32no—
91D27⋊C3—32no—
92D27⋊C3—32no—
93D27⋊C3—32no—
94D27⋊C3—32no—
95D27⋊C3—32no—
96D27⋊C3—32no—
97D27⋊C3—32no—
98D27⋊C3—32no—
99C3×D27—32no—
100C3×D27—32no—
101C3×D27—32no—
102C2×C3×C3⋊D3—91no—
103C2×C32×D3—271no—
104C2×C3⋊D9—31no—
105C2×AGL(1,ℤ/9)—91no—
106C2×AGL(1,ℤ/9)—91no—
107C2×AGL(1,ℤ/9)—91no—
108C2×AGL(1,ℤ/9)—91no—
109C2×AGL(1,ℤ/9)—91no—
110C2×AGL(1,ℤ/9)—91no—
111C2×(C3⋊D3)⋊C3—91no—
112C2×(C3⋊D3)⋊C3—91no—
113C2×(C3⋊D3)⋊C3—91no—
114C2×C3×D9—91no—
115C2×C3×D9—91no—
116C2×C3×D9—91no—
117C2×C3×D9—91no—
118C2×C3×D9—91no—
119C2×C3×D9—91no—
120C2×D27—31no—
121C2×D27—31no—
122C2×D27—31no—
123#737—21no—
124#737—21no—
125#737—21no—
126#737—21no—
127#737—31no—
128#737—61no—
129#737—61no—
130#737—61no—
131#737C2×C3×D311yescharacteristic
132C3×3−1+2—61no—
133C3×3−1+2C2×D911yescharacteristic
134C3×3−1+2C2×D911yescharacteristic
135C3×H(3,𝔽3)C2×D911yescharacteristic
136C32×C9—61no—
137C32×C9C2×C3⋊D311yescharacteristic
138C27⋊C3—21no—
139C27⋊C3—21no—
140C27⋊C3—31no—
141C27⋊C3—61no—
142C27⋊C3—61no—
143C27⋊C3—61no—
144C27⋊C3—61no—
145C27⋊C3—61no—
146C27⋊C3—61no—
147C27⋊C3C2×C3×D311yescharacteristic, complemented
148C27⋊C3C2×C3×D311yescharacteristic, complemented
149C3×C27—21no—
150C3×C27—31no—
151C3×C27—61no—
152C3×C27C2×C3×D311yescharacteristic, complemented
153C2×C33—61no—
154C2×C33C3⋊D911yescharacteristic
155C3×C3⋊D3—92no—
156C32×D3—272no—
157C2×3−1+2—21no—
158C2×3−1+2—21no—
159C2×3−1+2—31no—
160C2×3−1+2—31no—
161C2×3−1+2—61no—
162C2×3−1+2—61no—
163C2×3−1+2—61no—
164C2×3−1+2—61no—
165C2×3−1+2—61no—
166C2×3−1+2—61no—
167C2×3−1+2—62no—
168C2×3−1+2—61no—
169C2×3−1+2—61no—
170C2×3−1+2—61no—
171C2×3−1+2C3×D911yescharacteristic
172C2×3−1+2C3×D911yescharacteristic
173C2×H(3,𝔽3)—21no—
174C2×H(3,𝔽3)—31no—
175C2×H(3,𝔽3)—61no—
176C2×H(3,𝔽3)C3×D911yescharacteristic
177C2×C3×C9—21no—
178C2×C3×C9—21no—
179C2×C3×C9—21no—
180C2×C3×C9—21no—
181C2×C3×C9—31no—
182C2×C3×C9—31no—
183C2×C3×C9—61no—
184C2×C3×C9—61no—
185C2×C3×C9—61no—
186C2×C3×C9—61no—
187C2×C3×C9—61no—
188C2×C3×C9#27211yescharacteristic
189C2×C3×C9#27211yescharacteristic
190C2×C3×C9#27211yescharacteristic
191C2×C3×C9C3×C3⋊D311yescharacteristic
192C3⋊D9—32no—
193AGL(1,ℤ/9)—92no—
194AGL(1,ℤ/9)—92no—
195AGL(1,ℤ/9)—92no—
196AGL(1,ℤ/9)—92no—
197AGL(1,ℤ/9)—92no—
198AGL(1,ℤ/9)—92no—
199(C3⋊D3)⋊C3—92no—
200(C3⋊D3)⋊C3—92no—
201(C3⋊D3)⋊C3—92no—
202C3×D9—92no—
203C3×D9—92no—
204C3×D9—92no—
205C3×D9—92no—
206C3×D9—92no—
207C3×D9—92no—
208C2×C27—31no—
209C2×C27—31no—
210C2×C27—61no—
211C2×C27—61no—
212C2×C27—61no—
213C2×C27—61no—
214D27—32no—
215D27—32no—
216D27—32no—
217C22×C32—811no—
218C2×C3⋊D3—91no—
219C2×C3×D3—271no—
220C2×C3×D3—271no—
221C2×C3×D3—271no—
222C2×C3×D3—271no—
223C2×C3×D3—811no—
224C2×D9—91no—
225C2×D9—91no—
226C2×D9—91no—
227C33—61no—
228C33C2×C3⋊D911yescharacteristic
2293−1+2—21no—
2303−1+2—21no—
2313−1+2—31no—
2323−1+2—31no—
2333−1+2—61no—
2343−1+2—61no—
2353−1+2—61no—
2363−1+2—61no—
2373−1+2—61no—
2383−1+2—61no—
2393−1+2—62no—
2403−1+2—61no—
2413−1+2—61no—
2423−1+2—61no—
2433−1+2C2×C3×D911yescharacteristic
2443−1+2C2×C3×D911yescharacteristic
245H(3,𝔽3)—21no—
246H(3,𝔽3)—31no—
247H(3,𝔽3)—61no—
248H(3,𝔽3)C2×C3×D911yescharacteristic
249C3×C9—21no—
250C3×C9—21no—
251C3×C9—21no—
252C3×C9—21no—
253C3×C9—31no—
254C3×C9—31no—
255C3×C9—61no—
256C3×C9—61no—
257C3×C9—61no—
258C3×C9—61no—
259C3×C9—61no—
260C3×C9C2×#27211yescharacteristic
261C3×C9C2×#27211yescharacteristic
262C3×C9C2×#27211yescharacteristic
263C3×C9C2×C3×C3⋊D311yescharacteristic
264C27—31no—
265C27—31no—
266C27—61no—
267C27—61no—
268C27—61no—
269C27—61no—
270C2×C32—61no—
271C2×C32—61no—
272C2×C32—91no—
273C2×C32—181no—
274C2×C32—181no—
275C2×C32—812no—
276C2×C32#418111yescharacteristic
277C2×C32#418111yescharacteristic
278C2×C32#418111yescharacteristic
279C2×C32C3×C3⋊D911yescharacteristic
280C3⋊D3—92no—
281C3×D3—272no—
282C3×D3—272no—
283C3×D3—272no—
284C3×D3—272no—
285C3×D3—812no—
286C2×C9—21no—
287C2×C9—21no—
288C2×C9—21no—
289C2×C9—21no—
290C2×C9—61no—
291C2×C9—61no—
292C2×C9—61no—
293C2×C9—61no—
294C2×C9C3×#27211yescharacteristic
295D9—92no—
296D9—92no—
297D9—92no—
298C22×C3—811no—
299C22×C3—811no—
300C22×C3—811no—
301C22×C3—811no—
302C2×D3—271no—
303C2×D3—811no—
304C32—61no—
305C32—61no—
306C32—91no—
307C32—181no—
308C32—181no—
309C32C2×#418111yescharacteristic
310C32C2×#418111yescharacteristic
311C32C2×#418111yescharacteristic
312C32C2×C3×C3⋊D911yescharacteristic
313C9—21no—
314C9—21no—
315C9—21no—
316C9—21no—
317C9—61no—
318C9—61no—
319C9—61no—
320C9—61no—
321C9C2×C3×#27211yescharacteristic
322C2×C3—31no—
323C2×C3—31no—
324C2×C3—61no—
325C2×C3—61no—
326C2×C3—91no—
327C2×C3—181no—
328C2×C3—812no—
329C2×C3—812no—
330C2×C3—812no—
331C2×C3—812no—
332C2×C3C3×#418111yescharacteristic
333D3—272no—
334D3—812no—
335C22—811noSylow
336C3—31no—
337C3—31no—
338C3—61no—
339C3—61no—
340C3—91no—
341C3—181no—
342C3C2×C3×#418111yescharacteristic
343C2—812no—
344C2#92214⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#92214⋊C3
commutator, cosocle, hypocenter#6873C22×C3
FrattiniC3×C9C2×C3×C3⋊D3
FittingC2×#10624704C2
socleC2×C3C3×#4181
LCSG ▷ #6873
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #92214⋊C3C2direct (N × H)
2. C2×#10624704C2semidirect
7. C2×#92214C3semidirect
8. #10624704C22semidirect
11. C2×C3×C27⋊C3D3semidirect
12. C2×C3×C27⋊C3D3semidirect
13. C2×C3×C27⋊C3D3semidirect
21. C2×#6873C2×C3semidirect
22. #92214C2×C3semidirect
44. C3×C27⋊C3C2×D3semidirect
45. C3×C27⋊C3C2×D3semidirect
46. C3×C27⋊C3C2×D3semidirect
51. #6873C22×C3semidirect
84. C2×C27⋊C3C3×D3semidirect
85. C2×C27⋊C3C3×D3semidirect
89. C2×C3×C27C3×D3semidirect
147. C27⋊C3C2×C3×D3semidirect
148. C27⋊C3C2×C3×D3semidirect
152. C3×C27C2×C3×D3semidirect
344. C2#92214⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
#92214⋊C32
C2×#106247042
C2×C3×#42073
C2×C3×D27⋊C33
C2×#922143