Finite Group Databasebeta

← C2×#92299⋊C4 #72276124

Subgroups — C2×#92299⋊C4 #72276124

Order 3888.

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

normal subgroups only

This group has 727 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
1C22×#92299C211yesmaximal, characteristic
2C2×3−1+2×Dic9C211yesmaximal, characteristic, complemented
3C2×C9×3−1+2⋊C4C211yesmaximal, characteristic, complemented
4#92299⋊C4C214yesmaximal, direct product factor
5C2×(C3⋊AGL(1,ℤ/9))⋊C4—31nomaximal
6C2×C3×(C3⋊D9)⋊C4—31nomaximal
7C2×#10619528C311yesmaximal, characteristic, complemented
8C22×C9×3−1+2C2211yescharacteristic
9C2×#92299C414yescomplemented
10C2×#92299C2212yes—
113−1+2×Dic9C2212yescomplemented
12C9×3−1+2⋊C4C2212yescomplemented
13C22×C3⋊AGL(1,ℤ/9)—31no—
14C22×C3×C3⋊D9—31no—
15C2×Dic3×3−1+2—31no—
16C2×C3×3−1+2⋊C4D311yescharacteristic
17C2×C3×C9×Dic3—31no—
18C2×C32×Dic9D311yescharacteristic
19(C3⋊AGL(1,ℤ/9))⋊C4—34no—
20C3×(C3⋊D9)⋊C4—34no—
21C22×C9⋊D9C2×C311yescharacteristic
22C22×#4169—61no—
23C2×Dic9⋊C9—21no—
24C2×C9×Dic9—21no—
25C2×C9×Dic9C2×C311yescharacteristic, complemented
26C2×C9×Dic9C2×C311yescharacteristic, complemented
27#10619528C2×C314yescomplemented
28C2×C9×3−1+2C2×C412yescomplemented
29C2×C9×3−1+2C2311yescharacteristic
30#92299C2×C414yescomplemented
31C2×C3×#624—91no—
32C2×C4×AGL(1,ℤ/9)—91no—
33C2×C3×C4×D9—91no—
34C2×(C3⋊D9)⋊C4—31no—
35C2×(C3⋊D9)⋊C4—31no—
36C22×C3×3−1+2C2×D311yescharacteristic
37C22×C32×C9C2×D311yescharacteristic
38C2×C3⋊AGL(1,ℤ/9)—34no—
39C2×C3⋊AGL(1,ℤ/9)—32no—
40C2×C3×C3⋊D9—34no—
41C2×C3×C3⋊D9—32no—
42Dic3×3−1+2—32no—
43C3×3−1+2⋊C4C2×D312yes—
44C3×C9×Dic3—32no—
45C32×Dic9C2×D312yes—
46C22×C9⋊C9—21no—
47C22×C9⋊C9—41no—
48C22×C32⋊C9—21no—
49C22×C92—21no—
50C22×C92C22×C311yescharacteristic
51C2×C9⋊D9C3×C414yescomplemented
52C2×C9⋊D9C22×C312yes—
53C2×#4169—64no—
54C2×#4169—62no—
55Dic9⋊C9—22no—
56C9×Dic9—22no—
57C9×Dic9C22×C312yescomplemented
58C9×Dic9C22×C312yescomplemented
59C9×3−1+2C22×C411yescharacteristic, complemented, Sylow
60C22×C3×C3⋊D3—91no—
61C2×C32×Dic3—31no—
62C2×C32×Dic3—31no—
63C3×#624—94no—
64C22×C3⋊D9—31no—
65C22×C3⋊D9—31no—
66C22×C3⋊D9—61no—
67C22×AGL(1,ℤ/9)—91no—
68C22×AGL(1,ℤ/9)—181no—
69C22×C3×D9—91no—
70C22×C3×D9—181no—
71C2×C4×3−1+2—91no—
72C2×C3×C4×C9—91no—
73C2×3−1+2⋊C4—21no—
74C2×3−1+2⋊C4D911yescharacteristic, complemented
75C2×C9×Dic3—31no—
76C2×C9×Dic3—31no—
77C2×C9×Dic3—61no—
78C2×C9×Dic3—61no—
79C2×C3×Dic9—31no—
80C2×C3×Dic9C3×D311yescharacteristic
81C2×C3×Dic9C3×D311yescharacteristic
82C4×AGL(1,ℤ/9)—94no—
83C3×C4×D9—94no—
84(C3⋊D9)⋊C4—34no—
85(C3⋊D9)⋊C4—34no—
86C2×C3×3−1+2C4×D312yes—
87C2×C3×3−1+2C22×D311yescharacteristic
88C2×C32×C9C4×D312yes—
89C2×C32×C9C22×D311yescharacteristic
90C3⋊AGL(1,ℤ/9)—34no—
91C3×C3⋊D9—34no—
92C2×C9⋊C9—22no—
93C2×C9⋊C9—21no—
94C2×C9⋊C9—42no—
95C2×C9⋊C9—41no—
96C2×C32⋊C9—22no—
97C2×C32⋊C9—21no—
98C2×C92—22no—
99C2×C92—21no—
100C2×C92C2×C3×C412yescomplemented
101C2×C92C23×C311yescharacteristic
102C9⋊D9C2×C3×C414yescomplemented
103#4169—64no—
104C2×C3×C4×D3—271no—
105C2×C3×C4×D3—271no—
106C2×#624—91no—
107C2×C4×D9—91no—
108C2×C4×D9—91no—
109C22×C33D3211yescharacteristic
110C2×C3×C3⋊D3—94no—
111C2×C3×C3⋊D3—92no—
112C32×Dic3—32no—
113C32×Dic3—32no—
114C22×3−1+2—21no—
115C22×3−1+2—21no—
116C22×3−1+2—41no—
117C22×3−1+2C2×D911yescharacteristic
118C22×C3×C9—21no—
119C22×C3×C9—21no—
120C22×C3×C9—21no—
121C22×C3×C9—31no—
122C22×C3×C9—41no—
123C22×C3×C9—61no—
124C22×C3×C9C2×C3×D311yescharacteristic
125C22×C3×C9C2×C3×D311yescharacteristic
126C2×C3⋊D9—34no—
127C2×C3⋊D9—34no—
128C2×C3⋊D9—32no—
129C2×C3⋊D9—32no—
130C2×C3⋊D9—64no—
131C2×C3⋊D9—62no—
132C2×AGL(1,ℤ/9)—94no—
133C2×AGL(1,ℤ/9)—92no—
134C2×AGL(1,ℤ/9)—184no—
135C2×AGL(1,ℤ/9)—182no—
136C2×C3×D9—92no—
137C2×C3×D9—94no—
138C2×C3×D9—184no—
139C2×C3×D9—182no—
140C4×3−1+2—92no—
141C3×C4×C9—92no—
1423−1+2⋊C4—22no—
1433−1+2⋊C4C2×D912yescomplemented
144C9×Dic3—32no—
145C9×Dic3—32no—
146C9×Dic3—62no—
147C9×Dic3—62no—
148C3×Dic9—32no—
149C3×Dic9C2×C3×D312yes—
150C3×Dic9C2×C3×D312yes—
151C3×3−1+2C2×C4×D311yescharacteristic
152C32×C9C2×C4×D311yescharacteristic
153C9⋊C9—21no—
154C9⋊C9—41no—
155C32⋊C9—21no—
156C92—21no—
157C92C22×C3×C411yescharacteristic, complemented
158C22×C3⋊D3—91no—
159C22×C3×D3—271no—
160C22×C3×D3—271no—
161C22×C3×D3—541no—
162C2×C32×C4—91no—
163C2×C32×C4—91no—
164C2×C3×Dic3—31no—
165C2×C3×Dic3—31no—
166C2×C3×Dic3—31no—
167C2×C3×Dic3—61no—
168C2×C3×Dic3—91no—
169C3×C4×D3—274no—
170C3×C4×D3—274no—
171#624—94no—
172C22×D9—91no—
173C22×D9—91no—
174C22×D9—181no—
175C22×D9—181no—
176C22×D9—541no—
177C2×C4×C9—91no—
178C2×C4×C9—91no—
179C2×C4×C9—181no—
180C2×C4×C9—181no—
181C2×Dic9C3×D911yescharacteristic, complemented
182C2×Dic9AGL(1,ℤ/9)11yescharacteristic, complemented
183C4×D9—94no—
184C4×D9—94no—
185C2×C33#62412yes—
186C2×C33C2×D3211yescharacteristic
187C3×C3⋊D3—94no—
188C2×3−1+2—22no—
189C2×3−1+2—21no—
190C2×3−1+2—22no—
191C2×3−1+2—21no—
192C2×3−1+2—42no—
193C2×3−1+2—41no—
194C2×3−1+2C4×D912yescomplemented
195C2×3−1+2C22×D911yescharacteristic
196C2×C3×C9—22no—
197C2×C3×C9—21no—
198C2×C3×C9—22no—
199C2×C3×C9—22no—
200C2×C3×C9—21no—
201C2×C3×C9—21no—
202C2×C3×C9—32no—
203C2×C3×C9—31no—
204C2×C3×C9—42no—
205C2×C3×C9—41no—
206C2×C3×C9—62no—
207C2×C3×C9—61no—
208C2×C3×C9C3×C4×D312yes—
209C2×C3×C9C3×C4×D312yes—
210C2×C3×C9C22×C3×D311yescharacteristic
211C2×C3×C9C22×C3×D311yescharacteristic
212C3⋊D9—34no—
213C3⋊D9—34no—
214C3⋊D9—64no—
215AGL(1,ℤ/9)—94no—
216AGL(1,ℤ/9)—184no—
217C3×D9—94no—
218C3×D9—184no—
219C22×C3×C4—811no—
220C2×C4×D3—271no—
221C2×C4×D3—271no—
222C22×C32—21no—
223C22×C32—31no—
224C22×C32—61no—
225C22×C32D3×D911yescharacteristic
226C22×C32C3×D3211yescharacteristic
227C2×C3⋊D3—94no—
228C2×C3⋊D3—92no—
229C2×C3×D3—272no—
230C2×C3×D3—274no—
231C2×C3×D3—274no—
232C2×C3×D3—272no—
233C2×C3×D3—542no—
234C2×C3×D3—544no—
235C32×C4—92no—
236C32×C4—92no—
237C3×Dic3—32no—
238C3×Dic3—32no—
239C3×Dic3—32no—
240C3×Dic3—62no—
241C3×Dic3—92no—
242C22×C9—21no—
243C22×C9—21no—
244C22×C9—21no—
245C22×C9—41no—
246C22×C9—61no—
247C22×C9—61no—
248C22×C9—121no—
249C22×C9C2×C3×D911yescharacteristic
250C22×C9C2×AGL(1,ℤ/9)11yescharacteristic
251C2×D9—94no—
252C2×D9—94no—
253C2×D9—92no—
254C2×D9—92no—
255C2×D9—182no—
256C2×D9—184no—
257C2×D9—182no—
258C2×D9—184no—
259C2×D9—544no—
260C2×D9—542no—
261C4×C9—92no—
262C4×C9—92no—
263C4×C9—182no—
264C4×C9—182no—
265Dic9C2×C3×D912yescomplemented
266Dic9C2×AGL(1,ℤ/9)12yescomplemented
267C33C2×#62411yescharacteristic
2683−1+2—21no—
2693−1+2—21no—
2703−1+2—41no—
2713−1+2C2×C4×D911yescharacteristic, complemented
272C3×C9—21no—
273C3×C9—21no—
274C3×C9—21no—
275C3×C9—31no—
276C3×C9—41no—
277C3×C9—61no—
278C3×C9C2×C3×C4×D311yescharacteristic
279C3×C9C2×C3×C4×D311yescharacteristic
280C23×C3—811no—
281C22×D3—271no—
282C22×D3—271no—
283C22×D3—541no—
284C2×C3×C4—91no—
285C2×C3×C4—91no—
286C2×C3×C4—91no—
287C2×C3×C4—181no—
288C2×C3×C4—271no—
289C2×C3×C4—814no—
290C2×Dic3—31no—
291C2×Dic3—31no—
292C4×D3—274no—
293C4×D3—274no—
294C2×C32—21no—
295C2×C32—22no—
296C2×C32—31no—
297C2×C32—32no—
298C2×C32—62no—
299C2×C32—61no—
300C2×C32(C3⋊D9)⋊C412yes—
301C2×C32C2×D3×D911yescharacteristic
302C2×C32C3×#62412yes—
303C2×C32C2×C3×D3211yescharacteristic
304C3⋊D3—94no—
305C3×D3—274no—
306C3×D3—274no—
307C3×D3—544no—
308C2×C9—21no—
309C2×C9—21no—
310C2×C9—21no—
311C2×C9—22no—
312C2×C9—22no—
313C2×C9—22no—
314C2×C9—41no—
315C2×C9—42no—
316C2×C9—61no—
317C2×C9—62no—
318C2×C9—61no—
319C2×C9—62no—
320C2×C9—121no—
321C2×C9—122no—
322C2×C9C3×C4×D912yescomplemented
323C2×C9C4×AGL(1,ℤ/9)12yescomplemented
324C2×C9C22×C3×D911yescharacteristic
325C2×C9C22×AGL(1,ℤ/9)11yescharacteristic
326D9—94no—
327D9—94no—
328D9—184no—
329D9—184no—
330D9—544no—
331C22×C4—811noSylow
332C22×C3—21no—
333C22×C3—31no—
334C22×C3—61no—
335C22×C3—812no—
336C22×C3—814no—
337C22×C3C3×D3×D911yescharacteristic
338C22×C3D3×AGL(1,ℤ/9)11yescharacteristic
339C2×D3—272no—
340C2×D3—272no—
341C2×D3—274no—
342C2×D3—274no—
343C2×D3—542no—
344C2×D3—544no—
345C3×C4—92no—
346C3×C4—92no—
347C3×C4—92no—
348C3×C4—182no—
349C3×C4—272no—
350Dic3—32no—
351Dic3—32no—
352C32—21no—
353C32—31no—
354C32—61no—
355C32C2×(C3⋊D9)⋊C411yescharacteristic
356C32C2×C3×#62411yescharacteristic
357C9—21no—
358C9—21no—
359C9—21no—
360C9—41no—
361C9—61no—
362C9—61no—
363C9—121no—
364C9C2×C3×C4×D911yescharacteristic, complemented
365C9C2×C4×AGL(1,ℤ/9)11yescharacteristic, complemented
366C23—811no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—814no—
370C2×C3—21no—
371C2×C3—22no—
372C2×C3—31no—
373C2×C3—32no—
374C2×C3—61no—
375C2×C3—62no—
376C2×C3—814no—
377C2×C3C3×(C3⋊D9)⋊C412yes—
378C2×C3(C3⋊AGL(1,ℤ/9))⋊C412yes—
379C2×C3C2×C3×D3×D911yescharacteristic
380C2×C3C2×D3×AGL(1,ℤ/9)11yescharacteristic
381D3—274no—
382D3—274no—
383D3—544no—
384C22—812no—
385C22—814no—
386C22D9×AGL(1,ℤ/9)11yescharacteristic
387C4—92no—
388C4—92no—
389C3—21no—
390C3—31no—
391C3—61no—
392C3C2×C3×(C3⋊D9)⋊C411yescharacteristic
393C3C2×(C3⋊AGL(1,ℤ/9))⋊C411yescharacteristic
394C2—814no—
395C2#92299⋊C412yesdirect product factor
396C2C2×D9×AGL(1,ℤ/9)11yescharacteristic
subgroupG/H
center, hypercenterC22D9×AGL(1,ℤ/9)
commutator, hypocenterC92C22×C3×C4
FrattiniC2×C32C2×C3×D32
FittingC22×C9×3−1+2C22
socleC22×C32C3×D32
prime radicalC22×#92299C2
cosocleC2×C92C23×C3
LCSG ▷ C92
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×3−1+2×Dic9C2semidirect
3. C2×C9×3−1+2⋊C4C2semidirect
4. #92299⋊C4C2direct (N × H)
7. C2×#10619528C3semidirect
9. C2×#92299C4semidirect
11. 3−1+2×Dic9C22semidirect
12. C9×3−1+2⋊C4C22semidirect
25. C2×C9×Dic9C2×C3semidirect
26. C2×C9×Dic9C2×C3semidirect
27. #10619528C2×C3semidirect
28. C2×C9×3−1+2C2×C4semidirect
30. #92299C2×C4semidirect
51. C2×C9⋊D9C3×C4semidirect
57. C9×Dic9C22×C3semidirect
58. C9×Dic9C22×C3semidirect
59. C9×3−1+2C22×C4semidirect
74. C2×3−1+2⋊C4D9semidirect
100. C2×C92C2×C3×C4semidirect
102. C9⋊D9C2×C3×C4semidirect
143. 3−1+2⋊C4C2×D9semidirect
157. C92C22×C3×C4semidirect
181. C2×Dic9C3×D9semidirect
182. C2×Dic9AGL(1,ℤ/9)semidirect
194. C2×3−1+2C4×D9semidirect
265. Dic9C2×C3×D9semidirect
266. Dic9C2×AGL(1,ℤ/9)semidirect
271. 3−1+2C2×C4×D9semidirect
322. C2×C9C3×C4×D9semidirect
323. C2×C9C4×AGL(1,ℤ/9)semidirect
364. C9C2×C3×C4×D9semidirect
365. C9C2×C4×AGL(1,ℤ/9)semidirect
395. C2#92299⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#922992
C2×3−1+2×Dic92
C2×C9×3−1+2⋊C42
#92299⋊C42
C2×(C3⋊AGL(1,ℤ/9))⋊C43
C2×C3×(C3⋊D9)⋊C43
C2×#106195283