Finite Group Databasebeta

← C2×#10589624 #11899948

Subgroups — C2×#10589624 #11899948

Order 1152.

2592 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3697C211yesmaximal, characteristic
2C2×C9×#117C211yesmaximal, characteristic, complemented
3C22×C4×Dic9C211yesmaximal, characteristic, complemented
4#10589624C2116yesmaximal, direct product factor
5C2×#63455C212yesmaximal, complemented
6C2×#63449C212yesmaximal, complemented
7C2×#611⋊C4C214yesmaximal, complemented
8C2×#63434C212yesmaximal, complemented
9C2×C42×D9C212yesmaximal, complemented
10C2×#5522—31nomaximal
11C23×C4×C9C2211yescharacteristic
12C22×#611C2212yes—
13C23×Dic9C2212yes—
14C2×#3697C4116yescomplemented
15C2×#3697C2218yes—
16C22×D36C2211yescharacteristic
17C22×C4×D9C2214yes—
18C22×C4×D9C2212yes—
19C22×Dic18C2211yescharacteristic
20C9×#117C2218yescomplemented
21C2×C9×C4⋊C4C2212yes—
22C2×C9×C22⋊C4C2212yes—
23C2×C42×C9C2212yes—
24C2×(C2×D9)⋊C4C2214yes—
25C2×Dic9⋊C4C2214yes—
26C2×C4×Dic9C2211yescharacteristic
27C2×C4×Dic9C2214yes—
28C2×C4×Dic9C2211yescharacteristic
29C2×C4×Dic9C2212yes—
30C2×C4×Dic9C2218yescomplemented
31#63455C22116yescomplemented
32#63449C22116yescomplemented
33#611⋊C4C22132yescomplemented
34#63434C22116yescomplemented
35C42×D9C22116yescomplemented
36C22×#235—31no—
37C2×C3×#117D311yescharacteristic
38C22×C4×Dic3—31no—
39#5522—316no—
40C2×#893—32no—
41C2×#887—32no—
42C2×#67⋊C4—34no—
43C2×#872—32no—
44C2×C42×D3—32no—
45C24×C9C2311yescharacteristic
46C23×D9C2312yes—
47C22×C4×C9C2×C418yescomplemented
48C22×C4×C9C2314yes—
49C22×C4×C9C2311yescharacteristic
50C22×C4×C9C2311yescharacteristic
51C22×C4×C9C2314yes—
52C2×#611C2×C4116yescomplemented
53C2×#611C2318yes—
54C22×Dic9—28no—
55C22×Dic9C2312yes—
56C22×Dic9C2318yes—
57C22×Dic9C2312yes—
58C22×Dic9C2312yes—
59#3697C2×C4164yescomplemented
60C2×D36C2×C418yescomplemented
61C2×D36C2314yes—
62C2×C4×D9—216no—
63C2×C4×D9C2×C4116yescomplemented
64C2×C4×D9C23116yes—
65C2×C4×D9C2318yes—
66C2×Dic18C2×C418yescomplemented
67C2×Dic18C2314yes—
68C9×C4⋊C4C2318yes—
69C9×C22⋊C4C2318yes—
70C42×C9C2318yes—
71(C2×D9)⋊C4C23116yes—
72Dic9⋊C4C23116yes—
73C4×Dic9C2314yes—
74C4×Dic9C23116yes—
75C4×Dic9C2314yes—
76C4×Dic9C2318yes—
77C2×C4×#41—91noSylow
78C23×C3×C4C2×D311yescharacteristic
79C22×#67—32no—
80C23×Dic3—32no—
81C2×#235—316no—
82C2×#235—38no—
83C22×D12—31no—
84C22×C4×D3—32no—
85C22×C4×D3—34no—
86C22×Dic6—31no—
87C3×#117C2×D318yes—
88C2×C3×C4⋊C4C2×D312yes—
89C2×C3×C22⋊C4C2×D312yes—
90C2×C3×C42C2×D312yes—
91C2×(C2×D3)⋊C4—34no—
92C2×Dic3⋊C4—34no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—32no—
97C2×C4×Dic3—38no—
98#893—316no—
99#887—316no—
100#67⋊C4—332no—
101#872—316no—
102C42×D3—316no—
103C23×C9—24no—
104C23×C9C22×C414yes—
105C23×C9C2412yes—
106C23×C9C2411yescharacteristic
107C22×D9—28no—
108C22×D9C22×C418yes—
109C22×D9C2414yes—
110C2×C4×C9—28no—
111C2×C4×C9C22×C414yes—
112C2×C4×C9C22×C414yes—
113C2×C4×C9C22×C4116yescomplemented
114C2×C4×C9C2418yes—
115C2×C4×C9C2412yes—
116C2×C4×C9C2412yes—
117#611C22×C4132yescomplemented
118C2×Dic9—24no—
119C2×Dic9—216no—
120C2×Dic9C22×C418yes—
121C2×Dic9#4118yescomplemented
122C2×Dic9C2414yes—
123C2×Dic9C2414yes—
124C2×Dic9C2414yes—
125D36C22×C4116yescomplemented
126C4×D9—232no—
127C4×D9C22×C4132yescomplemented
128Dic18C22×C4116yescomplemented
129C22×#41—91no—
130C4×#41—916no—
131C2×C4×Q8—92no—
132C2×C4×D4—92no—
133C2×C4×D4—94no—
134C2×#117—92no—
135C2×#117D911yescharacteristic, complemented
136C22×C42—91no—
137C22×C42—92no—
138C24×C3C22×D311yescharacteristic
139C23×D3—32no—
140C22×C3×C4C4×D318yes—
141C22×C3×C4C22×D314yes—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D314yes—
144C22×C3×C4C22×D311yescharacteristic
145C2×#67—316no—
146C2×#67—38no—
147C22×Dic3—32no—
148C22×Dic3—32no—
149C22×Dic3—38no—
150C22×Dic3—32no—
151C22×Dic3—68no—
152#235—364no—
153C2×D12—38no—
154C2×D12—34no—
155C2×C4×D3—316no—
156C2×C4×D3—38no—
157C2×C4×D3—316no—
158C2×C4×D3—616no—
159C2×Dic6—38no—
160C2×Dic6—34no—
161C3×C4⋊C4C22×D318yes—
162C3×C22⋊C4C22×D318yes—
163C3×C42C22×D318yes—
164(C2×D3)⋊C4—316no—
165Dic3⋊C4—316no—
166C4×Dic3—34no—
167C4×Dic3—316no—
168C4×Dic3—34no—
169C4×Dic3—38no—
170C22×C9—28no—
171C22×C9—24no—
172C22×C9C23×C414yes—
173C22×C9C23×C412yes—
174C22×C9C2×#4114yes—
175C22×C9C2511yescharacteristic
176C2×D9—216no—
177C2×D9—28no—
178C2×D9C23×C418yes—
179C4×C9—28no—
180C4×C9C23×C414yes—
181C4×C9C23×C414yes—
182Dic9—24no—
183Dic9C23×C418yes—
184Dic9C2×#4118yescomplemented
185C2×#41—916no—
186C2×#41—98no—
187C22×Q8—91no—
188C22×D4—92no—
189C22×D4—91no—
190C23×C4—92no—
191C23×C4—92no—
192C23×C4—94no—
193C23×C4C2×D911yescharacteristic
194C4×Q8—916no—
195C4×D4—916no—
196C4×D4—932no—
197#117—916no—
198#117C2×D918yescomplemented
199C2×C4⋊C4—94no—
200C2×C4⋊C4C2×D912yes—
201C2×C22⋊C4—94no—
202C2×C22⋊C4C2×D912yes—
203C2×C42—94no—
204C2×C42—92no—
205C2×C42—98no—
206C2×C42—91no—
207C2×C42—91no—
208C2×C42—916no—
209C2×C42C2×D912yes—
210C23×C3—24no—
211C23×C3C2×C4×D314yes—
212C23×C3C23×D312yes—
213C23×C3C23×D311yescharacteristic
214C22×D3—38no—
215C22×D3—34no—
216C22×D3—68no—
217C2×C3×C4—28no—
218C2×C3×C4C2×C4×D314yes—
219C2×C3×C4C2×C4×D314yes—
220C2×C3×C4C2×C4×D3116yes—
221C2×C3×C4C23×D318yes—
222C2×C3×C4C23×D312yes—
223C2×C3×C4C23×D312yes—
224#67—332no—
225C2×Dic3—38no—
226C2×Dic3—38no—
227C2×Dic3—34no—
228C2×Dic3—34no—
229C2×Dic3—34no—
230C2×Dic3—616no—
231C2×Dic3—64no—
232D12—316no—
233C4×D3—332no—
234C4×D3—632no—
235Dic6—316no—
236C2×C9—24no—
237C2×C9C4×#4114yescomplemented
238C2×C9C24×C411yescharacteristic
239C2×C9C22×#4112yes—
240D9—28no—
241C24—92no—
242C24C22×D911yescharacteristic
243#41—964no—
244C2×Q8—98no—
245C2×Q8—94no—
246C2×D4—916no—
247C2×D4—98no—
248C2×D4—98no—
249C2×D4—94no—
250C22×C4—92no—
251C22×C4—92no—
252C22×C4—916no—
253C22×C4—98no—
254C22×C4—92no—
255C22×C4—98no—
256C22×C4—916no—
257C22×C4—1816no—
258C22×C4—188no—
259C22×C4C4×D918yescomplemented
260C22×C4C22×D914yes—
261C22×C4C22×D911yescharacteristic
262C22×C4C22×D914yes—
263C22×C4C22×D911yescharacteristic
264C4⋊C4—916no—
265C4⋊C4C22×D918yes—
266C22⋊C4—916no—
267C22⋊C4C22×D918yes—
268C42—94no—
269C42—94no—
270C42—916no—
271C42—98no—
272C42C22×D918yes—
273C22×C3—24no—
274C22×C3—28no—
275C22×C3C22×C4×D314yes—
276C22×C3C22×C4×D312yes—
277C22×C3D3×#4114yes—
278C22×C3C24×D311yescharacteristic
279C2×D3—38no—
280C2×D3—68no—
281C2×D3—616no—
282C3×C4—28no—
283C3×C4C22×C4×D314yes—
284C3×C4C22×C4×D314yes—
285Dic3—38no—
286Dic3—38no—
287Dic3—64no—
288C9C2×C4×#4111yescharacteristic, complemented, Sylow
289C23—24no—
290C23—94no—
291C23—98no—
292C23—188no—
293C23C2×C4×D914yes—
294C23C23×D912yes—
295C23C23×D911yescharacteristic
296Q8—916no—
297D4—932no—
298D4—916no—
299C2×C4—28no—
300C2×C4—94no—
301C2×C4—94no—
302C2×C4—98no—
303C2×C4—98no—
304C2×C4—932no—
305C2×C4—94no—
306C2×C4—1832no—
307C2×C4—1816no—
308C2×C4—184no—
309C2×C4C2×C4×D914yes—
310C2×C4C2×C4×D914yes—
311C2×C4C2×C4×D9116yescomplemented
312C2×C4C23×D918yes—
313C2×C4C23×D912yes—
314C2×C4C23×D912yes—
315C2×C3—24no—
316C2×C3#552214yes—
317C2×C3C23×C4×D311yescharacteristic
318C2×C3C2×D3×#4112yes—
319D3—68no—
320C22—24no—
321C22—28no—
322C22—98no—
323C22—188no—
324C22—1816no—
325C22C22×C4×D914yes—
326C22C22×C4×D912yes—
327C22#41×D914yes—
328C22C24×D911yescharacteristic
329C4—28no—
330C4—98no—
331C4—98no—
332C4—184no—
333C4C22×C4×D914yes—
334C4C22×C4×D914yes—
335C3C2×#552211yescharacteristic
336C2—24no—
337C2—188no—
338C2#1058962414yesdirect product factor
339C2C23×C4×D911yescharacteristic
340C2C2×#41×D912yes—
subgroupG/H
centerC22×C4C22×D9
commutatorC2×C9C24×C4
FrattiniC22×C3C24×D3
FittingC2×C9×#117C2
socleC23×C3C23×D3
prime radicalC22×#3697C2
cosocleC22×C9C25
hypercenterC2×#117D9
hypocenterC9C2×C4×#41
LCSG ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×C9×#117C2semidirect
3. C22×C4×Dic9C2semidirect
4. #10589624C2direct (N × H)
5. C2×#63455C2semidirect
6. C2×#63449C2semidirect
7. C2×#611⋊C4C2semidirect
8. C2×#63434C2semidirect
9. C2×C42×D9C2semidirect
14. C2×#3697C4semidirect
20. C9×#117C22semidirect
30. C2×C4×Dic9C22semidirect
31. #63455C22semidirect
32. #63449C22semidirect
33. #611⋊C4C22semidirect
34. #63434C22semidirect
35. C42×D9C22semidirect
47. C22×C4×C9C2×C4semidirect
52. C2×#611C2×C4semidirect
59. #3697C2×C4semidirect
60. C2×D36C2×C4semidirect
63. C2×C4×D9C2×C4semidirect
66. C2×Dic18C2×C4semidirect
113. C2×C4×C9C22×C4semidirect
117. #611C22×C4semidirect
121. C2×Dic9#41semidirect
125. D36C22×C4semidirect
127. C4×D9C22×C4semidirect
128. Dic18C22×C4semidirect
135. C2×#117D9semidirect
184. Dic9C2×#41semidirect
198. #117C2×D9semidirect
237. C2×C9C4×#41semidirect
259. C22×C4C4×D9semidirect
288. C9C2×C4×#41semidirect
311. C2×C4C2×C4×D9semidirect
338. C2#10589624direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#36972
C2×C9×#1172
C22×C4×Dic92
#105896242
C2×#634552
C2×#634492
C2×#611⋊C42
C2×#634342
C2×C42×D92
C2×#55223