Finite Group Databasebeta

← C2×#92318⋊C3 #72243900

Subgroups — C2×#92318⋊C3 #72243900

Order 2916.

686 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 140 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#92318⋊C3C212yesmaximal, direct product factor
2C2×#10624918C211yesmaximal, characteristic, complemented
3C2×C3×#4207—31nomaximal
4C2×#92318C312yesmaximal, complemented
5C2×#92318C311yesmaximal, characteristic, complemented
6C2×C3⋊(D27⋊C3)C311yesmaximal, characteristic, complemented
7C2×C3×D27⋊C3—32nomaximal
8C2×C3×D27⋊C3—31nomaximal
9#10624918C2211yescharacteristic, complemented, Sylow
10C2×C3×#737D311yescharacteristic
11C3×#4207—32no—
12C2×#6903—22no—
13C2×#6903—21no—
14C2×#6903—22no—
15C2×#6903—22no—
16C2×#6903—22no—
17C2×#6903—22no—
18C2×#6903—21no—
19C2×#6903C2×C312yescomplemented
20C2×#6903C2×C311yescharacteristic, complemented
21C2×C3×C27⋊C3—21no—
22C2×C3×C27⋊C3—22no—
23C2×C3×C27⋊C3—21no—
24C2×C3×C27⋊C3D312yescomplemented
25C2×C3×C27⋊C3D311yescharacteristic, complemented
26C2×C3×C27⋊C3C2×C311yescharacteristic, complemented
27#92318C2×C314yescomplemented
28#92318C2×C312yescomplemented
29C3⋊(D27⋊C3)C2×C312yescomplemented
30C3×D27⋊C3—34no—
31C3×D27⋊C3—32no—
32C2×#4207—32no—
33C2×#4207—31no—
34C2×C3×C3⋊D9—31no—
35C2×C3×AGL(1,ℤ/9)—92no—
36C2×C3×(C3⋊D3)⋊C3—91no—
37C2×C32×D9—91no—
38C2×C3⋊D27C3211yescharacteristic, complemented
39C2×D27⋊C3—32no—
40C2×D27⋊C3—31no—
41C2×D27⋊C3—32no—
42C2×D27⋊C3—32no—
43C2×D27⋊C3—32no—
44C2×C3×D27—32no—
45C2×C3×D27—31no—
46C3×#737C2×D311yescharacteristic
47#6903—22no—
48#6903—21no—
49#6903—22no—
50#6903—22no—
51#6903—22no—
52#6903—22no—
53#6903—21no—
54#6903C22×C312yescomplemented
55#6903C22×C311yescharacteristic, complemented
56C3×C27⋊C3—21no—
57C3×C27⋊C3—22no—
58C3×C27⋊C3—21no—
59C3×C27⋊C3C2×D312yescomplemented
60C3×C27⋊C3C2×D311yescharacteristic, complemented
61C3×C27⋊C3C22×C311yescharacteristic, complemented
62C2×#737—24no—
63C2×#737—22no—
64C2×#737—22no—
65C2×#737—21no—
66C2×#737—22no—
67C2×#737—21no—
68C2×#737C3×D312yes—
69C2×#737C3×D311yescharacteristic
70C2×C3×3−1+2—21no—
71C2×C3×3−1+2—22no—
72C2×C3×3−1+2D912yes—
73C2×C3×H(3,𝔽3)D911yescharacteristic
74C2×C32×C9—21no—
75C2×C32×C9C3×D311yescharacteristic
76C2×C32×C9C3⋊D311yescharacteristic
77#4207—34no—
78#4207—32no—
79C3×C3⋊D9—32no—
80C3×AGL(1,ℤ/9)—94no—
81C3×(C3⋊D3)⋊C3—92no—
82C32×D9—92no—
83C2×C27⋊C3—22no—
84C2×C27⋊C3—22no—
85C2×C27⋊C3—22no—
86C2×C27⋊C3—22no—
87C2×C27⋊C3—22no—
88C2×C27⋊C3—22no—
89C2×C27⋊C3—22no—
90C2×C27⋊C3—21no—
91C2×C27⋊C3—21no—
92C2×C27⋊C3—22no—
93C2×C27⋊C3—22no—
94C2×C27⋊C3—21no—
95C2×C27⋊C3—22no—
96C2×C27⋊C3—22no—
97C2×C27⋊C3—22no—
98C2×C27⋊C3—22no—
99C2×C27⋊C3—22no—
100C2×C27⋊C3—22no—
101C2×C27⋊C3—21no—
102C2×C27⋊C3—22no—
103C2×C27⋊C3C3×D312yes—
104C2×C27⋊C3C3×D311yescharacteristic
105C2×C27⋊C3C3×D312yescomplemented
106C2×C27⋊C3C3×D312yescomplemented
107C2×C27⋊C3C3×D312yescomplemented
108C2×C3×C27—22no—
109C2×C3×C27—21no—
110C2×C3×C27—22no—
111C2×C3×C27—21no—
112C2×C3×C27—22no—
113C2×C3×C27—21no—
114C2×C3×C27—21no—
115C2×C3×C27—22no—
116C2×C3×C27—21no—
117C2×C3×C27—21no—
118C2×C3×C27—22no—
119C2×C3×C27C3×D312yescomplemented
120C2×C3×C27C3×D311yescharacteristic, complemented
121C2×C3×C27C2×C3211yescharacteristic, complemented
122C3⋊D27C2×C3212yescomplemented
123D27⋊C3—34no—
124D27⋊C3—32no—
125D27⋊C3—34no—
126D27⋊C3—34no—
127D27⋊C3—34no—
128C3×D27—34no—
129C3×D27—32no—
130C2×C3×C3⋊D3—91no—
131C2×C32×D3—271no—
132C2×C3⋊D9—31no—
133C2×AGL(1,ℤ/9)—94no—
134C2×AGL(1,ℤ/9)—92no—
135C2×(C3⋊D3)⋊C3—92no—
136C2×(C3⋊D3)⋊C3—91no—
137C2×C3×D9—92no—
138C2×C3×D9—92no—
139C2×C3×D9—91no—
140C2×C3×D9—91no—
141C2×D27—32no—
142C2×D27—31no—
143#737—24no—
144#737—22no—
145#737—22no—
146#737—21no—
147#737—22no—
148#737—21no—
149#737C2×C3×D312yes—
150#737C2×C3×D311yescharacteristic
151C3×3−1+2—21no—
152C3×3−1+2—22no—
153C3×3−1+2C2×D912yes—
154C3×H(3,𝔽3)C2×D911yescharacteristic
155C32×C9—21no—
156C32×C9C2×C3×D311yescharacteristic
157C32×C9C2×C3⋊D311yescharacteristic
158C27⋊C3—22no—
159C27⋊C3—22no—
160C27⋊C3—22no—
161C27⋊C3—22no—
162C27⋊C3—22no—
163C27⋊C3—22no—
164C27⋊C3—22no—
165C27⋊C3—21no—
166C27⋊C3—21no—
167C27⋊C3—22no—
168C27⋊C3—22no—
169C27⋊C3—21no—
170C27⋊C3—22no—
171C27⋊C3—22no—
172C27⋊C3—22no—
173C27⋊C3—22no—
174C27⋊C3—22no—
175C27⋊C3—22no—
176C27⋊C3—21no—
177C27⋊C3—22no—
178C27⋊C3C2×C3×D312yes—
179C27⋊C3C2×C3×D311yescharacteristic
180C27⋊C3C2×C3×D312yescomplemented
181C27⋊C3C2×C3×D312yescomplemented
182C27⋊C3C2×C3×D312yescomplemented
183C3×C27—22no—
184C3×C27—21no—
185C3×C27—22no—
186C3×C27—21no—
187C3×C27—22no—
188C3×C27—21no—
189C3×C27—21no—
190C3×C27—22no—
191C3×C27—21no—
192C3×C27—21no—
193C3×C27—22no—
194C3×C27C2×C3×D312yescomplemented
195C3×C27C2×C3×D311yescharacteristic, complemented
196C3×C27C22×C3211yescharacteristic, complemented
197C2×C33—21no—
198C2×C33C3×D911yescharacteristic
199C2×C33C3⋊D911yescharacteristic
200C3×C3⋊D3—92no—
201C32×D3—272no—
202C2×3−1+2—24no—
203C2×3−1+2—22no—
204C2×3−1+2—24no—
205C2×3−1+2—24no—
206C2×3−1+2—24no—
207C2×3−1+2—21no—
208C2×3−1+2—22no—
209C2×3−1+2—24no—
210C2×3−1+2—22no—
211C2×3−1+2—22no—
212C2×3−1+2—24no—
213C2×3−1+2C3×D914yes—
214C2×3−1+2C3×D912yes—
215C2×H(3,𝔽3)—22no—
216C2×H(3,𝔽3)—21no—
217C2×H(3,𝔽3)C3×D912yes—
218C2×H(3,𝔽3)C3×D911yescharacteristic
219C2×C3×C9—24no—
220C2×C3×C9—22no—
221C2×C3×C9—21no—
222C2×C3×C9—22no—
223C2×C3×C9—21no—
224C2×C3×C9—22no—
225C2×C3×C9—21no—
226C2×C3×C9—22no—
227C2×C3×C9—21no—
228C2×C3×C9—22no—
229C2×C3×C9—21no—
230C2×C3×C9C3×D912yes—
231C2×C3×C9C32×D311yescharacteristic
232C2×C3×C9C3×C3⋊D312yes—
233C2×C3×C9C3×C3⋊D311yescharacteristic
234C2×C3×C9C3×C3⋊D311yescharacteristic
235C3⋊D9—32no—
236AGL(1,ℤ/9)—98no—
237AGL(1,ℤ/9)—94no—
238(C3⋊D3)⋊C3—94no—
239(C3⋊D3)⋊C3—92no—
240C3×D9—94no—
241C3×D9—94no—
242C3×D9—92no—
243C3×D9—92no—
244C2×C27—22no—
245C2×C27—21no—
246C2×C27—22no—
247C2×C27—22no—
248C2×C27—22no—
249C2×C27—22no—
250C2×C27—21no—
251C2×C27C32×D312yes—
252C2×C27C32×D311yescharacteristic
253D27—34no—
254D27—32no—
255C22×C32—811no—
256C2×C3⋊D3—91no—
257C2×C3×D3—271no—
258C2×C3×D3—272no—
259C2×C3×D3—271no—
260C2×C3×D3—811no—
261C2×D9—92no—
262C2×D9—91no—
263C33—21no—
264C33C2×C3×D911yescharacteristic
265C33C2×C3⋊D911yescharacteristic
2663−1+2—24no—
2673−1+2—22no—
2683−1+2—24no—
2693−1+2—24no—
2703−1+2—24no—
2713−1+2—21no—
2723−1+2—22no—
2733−1+2—24no—
2743−1+2—22no—
2753−1+2—22no—
2763−1+2—24no—
2773−1+2C2×C3×D914yes—
2783−1+2C2×C3×D912yes—
279H(3,𝔽3)—22no—
280H(3,𝔽3)—21no—
281H(3,𝔽3)C2×C3×D912yes—
282H(3,𝔽3)C2×C3×D911yescharacteristic
283C3×C9—24no—
284C3×C9—22no—
285C3×C9—21no—
286C3×C9—22no—
287C3×C9—21no—
288C3×C9—22no—
289C3×C9—21no—
290C3×C9—22no—
291C3×C9—21no—
292C3×C9—22no—
293C3×C9—21no—
294C3×C9C2×C3×D912yes—
295C3×C9C2×C32×D311yescharacteristic
296C3×C9C2×C3×C3⋊D312yes—
297C3×C9C2×C3×C3⋊D311yescharacteristic
298C3×C9C2×C3×C3⋊D311yescharacteristic
299C27—22no—
300C27—21no—
301C27—22no—
302C27—22no—
303C27—22no—
304C27—22no—
305C27—21no—
306C27C2×C32×D312yes—
307C27C2×C32×D311yescharacteristic
308C2×C32—21no—
309C2×C32—21no—
310C2×C32—22no—
311C2×C32—91no—
312C2×C32—181no—
313C2×C32—181no—
314C2×C32—812no—
315C2×C32C32×D911yescharacteristic
316C2×C32C3×C3⋊D911yescharacteristic
317C2×C32C3×C3⋊D912yes—
318C2×C32C3×C3⋊D911yescharacteristic
319C3⋊D3—92no—
320C3×D3—272no—
321C3×D3—274no—
322C3×D3—272no—
323C3×D3—812no—
324C2×C9—21no—
325C2×C9—22no—
326C2×C9—24no—
327C2×C9—22no—
328C2×C9—21no—
329C2×C9—22no—
330C2×C9C32×D912yes—
331C2×C9C32×C3⋊D311yescharacteristic
332D9—94no—
333D9—92no—
334C22×C3—811no—
335C22×C3—812no—
336C22×C3—811no—
337C2×D3—271no—
338C2×D3—811no—
339C32—21no—
340C32—21no—
341C32—22no—
342C32—91no—
343C32—181no—
344C32—181no—
345C32C2×C32×D911yescharacteristic
346C32C2×C3×C3⋊D911yescharacteristic
347C32C2×C3×C3⋊D912yes—
348C32C2×C3×C3⋊D911yescharacteristic
349C9—21no—
350C9—22no—
351C9—24no—
352C9—22no—
353C9—21no—
354C9—22no—
355C9C2×C32×D912yes—
356C9C2×C32×C3⋊D311yescharacteristic
357C2×C3—31no—
358C2×C3—31no—
359C2×C3—32no—
360C2×C3—61no—
361C2×C3—61no—
362C2×C3—61no—
363C2×C3—62no—
364C2×C3—812no—
365C2×C3—814no—
366C2×C3—812no—
367C2×C3C32×C3⋊D911yescharacteristic
368D3—272no—
369D3—812no—
370C22—811noSylow
371C3—31no—
372C3—31no—
373C3—32no—
374C3—61no—
375C3—61no—
376C3—61no—
377C3—62no—
378C3C2×C32×C3⋊D911yescharacteristic
379C2—812no—
380C2#92318⋊C311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2#92318⋊C3
commutator, cosocle, hypocenterC3×C27C22×C32
FrattiniC9C2×C32×C3⋊D3
FittingC2×#10624918C2
socleC2×C3C32×C3⋊D9
LCSG ▷ C3×C27
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. #92318⋊C3C2direct (N × H)
2. C2×#10624918C2semidirect
4. C2×#92318C3semidirect
5. C2×#92318C3semidirect
6. C2×C3⋊(D27⋊C3)C3semidirect
9. #10624918C22semidirect
19. C2×#6903C2×C3semidirect
20. C2×#6903C2×C3semidirect
24. C2×C3×C27⋊C3D3semidirect
25. C2×C3×C27⋊C3D3semidirect
26. C2×C3×C27⋊C3C2×C3semidirect
27. #92318C2×C3semidirect
28. #92318C2×C3semidirect
29. C3⋊(D27⋊C3)C2×C3semidirect
38. C2×C3⋊D27C32semidirect
54. #6903C22×C3semidirect
55. #6903C22×C3semidirect
59. C3×C27⋊C3C2×D3semidirect
60. C3×C27⋊C3C2×D3semidirect
61. C3×C27⋊C3C22×C3semidirect
105. C2×C27⋊C3C3×D3semidirect
106. C2×C27⋊C3C3×D3semidirect
107. C2×C27⋊C3C3×D3semidirect
119. C2×C3×C27C3×D3semidirect
120. C2×C3×C27C3×D3semidirect
121. C2×C3×C27C2×C32semidirect
122. C3⋊D27C2×C32semidirect
180. C27⋊C3C2×C3×D3semidirect
181. C27⋊C3C2×C3×D3semidirect
182. C27⋊C3C2×C3×D3semidirect
194. C3×C27C2×C3×D3semidirect
195. C3×C27C2×C3×D3semidirect
196. C3×C27C22×C32semidirect
380. C2#92318⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
#92318⋊C32
C2×#106249182
C2×C3×#42073
C2×#923183
C2×C3⋊(D27⋊C3)3
C2×C3×D27⋊C33