Finite Group Databasebeta

← C2×#10588671 #11808142

Subgroups — C2×#10588671 #11808142

Order 1152.

1878 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D36C211yesmaximal, characteristic
2C22×C9×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×(C2×D9)⋊C4C212yesmaximal, complemented
4C22×(C2×D9)⋊C4C212yesmaximal, complemented
5C2×C9⋊#95C211yesmaximal, characteristic, complemented
6#10588671C218yesmaximal, direct product factor
7C2×#4991—31nomaximal
8C24×D9C2212yes—
9C23×C4×C9C2211yescharacteristic
10C23×C4×C9C2211yescharacteristic
11C23×C4×C9C2211yescharacteristic
12C23×Dic9C2212yes—
13C22×D36—28no—
14C22×D36—24no—
15C22×D36C2214yes—
16C2×C9×C4⋊C4—24no—
17C2×C9×C4⋊C4C2214yescomplemented
18C2×(C2×D9)⋊C4—28no—
19C2×(C2×D9)⋊C4—28no—
20C2×(C2×D9)⋊C4C2218yescomplemented
21C2×(C2×D9)⋊C4C2218yescomplemented
22C9⋊#95C2214yescomplemented
23C23×D12—31no—
24C22×C3×C4⋊C4D311yescharacteristic
25C22×(C2×D3)⋊C4—32no—
26C22×(C2×D3)⋊C4—32no—
27C2×C3⋊#95—31no—
28#4991—38no—
29C24×C9C2311yescharacteristic
30C23×D9—24no—
31C23×D9—24no—
32C23×D9—24no—
33C23×D9—24no—
34C23×D9—24no—
35C23×D9—24no—
36C23×D9D418yes—
37C23×D9C2314yes—
38C22×C4×C9—22no—
39C22×C4×C9—24no—
40C22×C4×C9—22no—
41C22×C4×C9—24no—
42C22×C4×C9—22no—
43C22×C4×C9D414yes—
44C22×C4×C9D414yescomplemented
45C22×C4×C9C2312yes—
46C22×C4×C9C2312yes—
47C22×C4×C9C2312yes—
48C22×Dic9—24no—
49C22×Dic9—24no—
50C22×Dic9—24no—
51C22×Dic9C2314yes—
52C2×D36—232no—
53C2×D36—216no—
54C2×D36—28no—
55C9×C4⋊C4—28no—
56(C2×D9)⋊C4—216no—
57(C2×D9)⋊C4—216no—
58C2×#394—91noSylow
59C24×D3—32no—
60C23×C3×C4C2×D311yescharacteristic
61C23×C3×C4C2×D311yescharacteristic
62C23×C3×C4C2×D311yescharacteristic
63C23×Dic3—32no—
64C22×D12—34no—
65C22×D12—68no—
66C22×D12—64no—
67C2×C3×C4⋊C4—24no—
68C2×C3×C4⋊C4C2×D314yes—
69C2×(C2×D3)⋊C4—38no—
70C2×(C2×D3)⋊C4—38no—
71C2×(C2×D3)⋊C4—68no—
72C2×(C2×D3)⋊C4—68no—
73C3⋊#95—34no—
74C23×C9C2×D412yes—
75C23×C9C2×D414yes—
76C23×C9C2×D412yes—
77C23×C9#4112yes—
78C23×C9#4114yes—
79C23×C9C2411yescharacteristic
80C22×D9—216no—
81C22×D9—216no—
82C22×D9—216no—
83C22×D9—24no—
84C22×D9—24no—
85C22×D9—24no—
86C22×D9—24no—
87C22×D9—24no—
88C22×D9—24no—
89C22×D9—48no—
90C22×D9—48no—
91C22×D9—48no—
92C22×D9—48no—
93C22×D9C2×D418yes—
94C2×C4×C9—28no—
95C2×C4×C9—28no—
96C2×C4×C9—22no—
97C2×C4×C9—24no—
98C2×C4×C9—22no—
99C2×C4×C9—24no—
100C2×C4×C9—22no—
101C2×C4×C9—44no—
102C2×C4×C9C2×D414yes—
103C2×C4×C9C2×D414yescomplemented
104C2×Dic9—24no—
105C2×Dic9—24no—
106C2×Dic9—24no—
107C2×Dic9—48no—
108D36—232no—
109C23×D4—91no—
110C22×C4⋊C4D911yescharacteristic, complemented
111C22×C22⋊C4—92no—
112C22×C22⋊C4—92no—
113#394—98no—
114C2×#95—91no—
115C24×C3C22×D311yescharacteristic
116C23×D3—38no—
117C23×D3—34no—
118C23×D3—64no—
119C23×D3—64no—
120C23×D3—64no—
121C23×D3—64no—
122C23×D3—64no—
123C23×D3—64no—
124C22×C3×C4—22no—
125C22×C3×C4—24no—
126C22×C3×C4—22no—
127C22×C3×C4—24no—
128C22×C3×C4—22no—
129C22×C3×C4D1214yes—
130C22×C3×C4#6714yes—
131C22×C3×C4C22×D312yes—
132C22×C3×C4C22×D312yes—
133C22×C3×C4C22×D312yes—
134C22×Dic3—34no—
135C22×Dic3—64no—
136C22×Dic3—64no—
137C22×Dic3—64no—
138C2×D12—616no—
139C2×D12—632no—
140C2×D12—68no—
141C3×C4⋊C4—28no—
142(C2×D3)⋊C4—616no—
143(C2×D3)⋊C4—616no—
144C22×C9#12014yes—
145C22×C9#12118yes—
146C22×C9#12114yes—
147C22×C9#12318yes—
148C22×C9#12414yes—
149C22×C9C22×D411yescharacteristic
150C22×C9C22×D412yes—
151C22×C9C22×D411yescharacteristic
152C22×C9C2×#4111yescharacteristic
153C22×C9C2×#4112yes—
154C2×D9—28no—
155C2×D9—28no—
156C2×D9—28no—
157C2×D9—44no—
158C2×D9—44no—
159C2×D9—44no—
160C2×D9—44no—
161C2×D9—432no—
162C4×C9—24no—
163C4×C9—24no—
164C4×C9—42no—
165Dic9—44no—
166C25—92no—
167C22×D4—94no—
168C22×D4—188no—
169C22×D4—184no—
170C23×C4—92no—
171C23×C4C2×D911yescharacteristic
172C23×C4C2×D911yescharacteristic
173C23×C4C2×D911yescharacteristic
174C2×C4⋊C4—24no—
175C2×C4⋊C4C2×D914yescomplemented
176C2×C22⋊C4—98no—
177C2×C22⋊C4—98no—
178C2×C22⋊C4—188no—
179C2×C22⋊C4—188no—
180#95—94no—
181C23×C3C2×D1212yes—
182C23×C3#23512yes—
183C23×C3D3×D414yes—
184C23×C3#23914yes—
185C23×C3C2×#6712yes—
186C23×C3C23×D311yescharacteristic
187C22×D3—38no—
188C22×D3—616no—
189C22×D3—616no—
190C22×D3—616no—
191C22×D3—64no—
192C22×D3—64no—
193C22×D3—64no—
194C22×D3—64no—
195C22×D3—64no—
196C22×D3—64no—
197C22×D3—128no—
198C22×D3—128no—
199C22×D3—128no—
200C22×D3—128no—
201C2×C3×C4—28no—
202C2×C3×C4—28no—
203C2×C3×C4—22no—
204C2×C3×C4—24no—
205C2×C3×C4—22no—
206C2×C3×C4—24no—
207C2×C3×C4—22no—
208C2×C3×C4—44no—
209C2×C3×C4C2×D1214yes—
210C2×C3×C4C2×#6714yes—
211C2×Dic3—64no—
212C2×Dic3—64no—
213C2×Dic3—64no—
214C2×Dic3—128no—
215D12—632no—
216C2×C9#39418yescomplemented
217C2×C9C2×#12011yescharacteristic
218C2×C9C2×#12112yes—
219C2×C9C2×#12111yescharacteristic
220C2×C9C2×#12312yes—
221C2×C9C2×#12411yescharacteristic
222D9—48no—
223C24—98no—
224C24—94no—
225C24—184no—
226C24—184no—
227C24—184no—
228C24—184no—
229C24—184no—
230C24—184no—
231C24C22×D911yescharacteristic
232C2×D4—1816no—
233C2×D4—1832no—
234C2×D4—188no—
235C22×C4—22no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—94no—
241C22×C4—184no—
242C22×C4—184no—
243C22×C4—184no—
244C22×C4D3614yescomplemented
245C22×C4#61114yes—
246C22×C4C22×D912yes—
247C22×C4C22×D912yes—
248C22×C4C22×D912yes—
249C4⋊C4—28no—
250C22⋊C4—1816no—
251C22⋊C4—1816no—
252C22×C3#89418yes—
253C22×C3#89518yes—
254C22×C3#93014yes—
255C22×C3#93714yes—
256C22×C3#94714yes—
257C22×C3C22×D1211yescharacteristic
258C22×C3C2×#23511yescharacteristic
259C22×C3C2×D3×D412yes—
260C22×C3C2×#23912yes—
261C22×C3C22×#6711yescharacteristic
262C2×D3—68no—
263C2×D3—68no—
264C2×D3—68no—
265C2×D3—1232no—
266C2×D3—124no—
267C2×D3—124no—
268C2×D3—124no—
269C2×D3—124no—
270C3×C4—24no—
271C3×C4—24no—
272C3×C4—42no—
273Dic3—124no—
274C9C2×#39411yescharacteristic, complemented, Sylow
275C23—98no—
276C23—1816no—
277C23—184no—
278C23—184no—
279C23—184no—
280C23—1816no—
281C23—184no—
282C23—184no—
283C23—1816no—
284C23—184no—
285C23—368no—
286C23—368no—
287C23—368no—
288C23—368no—
289C23C2×D3612yes—
290C23#369712yes—
291C23D4×D914yes—
292C23#370114yes—
293C23C2×#61112yes—
294C23C23×D911yescharacteristic
295D4—1832no—
296C2×C4—28no—
297C2×C4—28no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—44no—
304C2×C4—184no—
305C2×C4—184no—
306C2×C4—184no—
307C2×C4—368no—
308C2×C4C2×D3614yescomplemented
309C2×C4C2×#61114yes—
310C2×C3#499118yes—
311C2×C3C2×#89412yes—
312C2×C3C2×#89512yes—
313C2×C3C2×#93011yescharacteristic
314C2×C3C2×#93711yescharacteristic
315C2×C3C2×#94711yescharacteristic
316D3—128no—
317C22—188no—
318C22—188no—
319C22—188no—
320C22—364no—
321C22—364no—
322C22—364no—
323C22—364no—
324C22—3632no—
325C22#6345618yes—
326C22#6345718yes—
327C22#6349214yes—
328C22#6349914yes—
329C22#6350914yes—
330C22C22×D3611yescharacteristic
331C22C2×#369711yescharacteristic
332C22C2×D4×D912yes—
333C22C2×#370112yes—
334C22C22×#61111yescharacteristic
335C4—24no—
336C4—24no—
337C4—42no—
338C4—364no—
339C3C2×#499111yescharacteristic
340C2—368no—
341C2#1058867118yesdirect product factor
342C2C2×#6345612yes—
343C2C2×#6345712yes—
344C2C2×#6349211yescharacteristic
345C2C2×#6349911yescharacteristic
346C2C2×#6350911yescharacteristic
subgroupG/H
centerC24C22×D9
commutator, cosocleC23×C9C24
FrattiniC23×C3C23×D3
FittingC22×C9×C4⋊C4C2
socleC24×C3C22×D3
prime radicalC23×D36C2
hypercenterC22×C4⋊C4D9
hypocenterC9C2×#394
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C9×C4⋊C4C2semidirect
3. C22×(C2×D9)⋊C4C2semidirect
4. C22×(C2×D9)⋊C4C2semidirect
5. C2×C9⋊#95C2semidirect
6. #10588671C2direct (N × H)
17. C2×C9×C4⋊C4C22semidirect
20. C2×(C2×D9)⋊C4C22semidirect
21. C2×(C2×D9)⋊C4C22semidirect
22. C9⋊#95C22semidirect
44. C22×C4×C9D4semidirect
103. C2×C4×C9C2×D4semidirect
110. C22×C4⋊C4D9semidirect
175. C2×C4⋊C4C2×D9semidirect
216. C2×C9#394semidirect
244. C22×C4D36semidirect
274. C9C2×#394semidirect
308. C2×C4C2×D36semidirect
341. C2#10588671direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D362
C22×C9×C4⋊C42
C22×(C2×D9)⋊C42
C2×C9⋊#952
#105886712
C2×#49913