Finite Group Databasebeta

← C2×#10590706 #11858436

Subgroups — C2×#10590706 #11858436

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 337 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×#63841C212yesmaximal
3C2×#63644C211yesmaximal, characteristic, complemented
4C2×C3×#817C211yesmaximal, characteristic, complemented
5C2×#63575C212yesmaximal, complemented
6#10590706C218yesmaximal, direct product factor
7C2×#5106—31nomaximal
8C2×#4860—31nomaximal
9C22×C3×C4×D3C2211yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2212yes—
12C2×C3×C4⋊Dic3C2212yes—
13C22×C3×C3⋊C8C2211yescharacteristic
14C2×C3×D3×C8C418yescomplemented
15C2×C3×D3×C8C2214yes—
16C2×(C2×D3)⋊Dic3—22no—
17C2×Dic32—22no—
18#63841—24no—
19#63841C2218yes—
20#63644C2214yescomplemented
21C3×#817C2214yescomplemented
22#63575C2218yescomplemented
23C23×C3×C8—31no—
24C2×#926—32no—
25C22×D3×C8D311yescharacteristic
26C2×#892—32no—
27C2×C3×#106—31no—
28#5106—38no—
29C2×#818—32no—
30C2×#817—31no—
31C2×#817—31no—
32C2×#817—61no—
33C2×#817D311yescharacteristic, complemented
34C2×#807—32no—
35#4860—38no—
36C23×C3×D3D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—22no—
39C22×C3×Dic3—22no—
40C22×C3×Dic3D411yescharacteristic
41C2×C3×C4×D3C2×C414yes—
42C2×C3×C4×D3D412yes—
43C2×C3×C4×D3Q814yes—
44C2×C3×C4×D3C2312yes—
45C2×C32×C8C2×C414yes—
46C2×C32×C8C2312yes—
47C4⋊(C3⋊Dic3)—22no—
48C4⋊(C3⋊Dic3)C2314yes—
49C3×C4⋊Dic3—22no—
50C3×C4⋊Dic3C2314yes—
51C2×C3×C3⋊C8C2×C414yes—
52C2×C3×C3⋊C8C2312yes—
53C3×D3×C8C2×C4116yescomplemented
54(C2×D3)⋊Dic3—28no—
55Dic32—28no—
56C2×#427—91noSylow
57C23×C3×C4—31no—
58C22×C4×D3C2×D311yescharacteristic
59C22×C3×C8—21no—
60C22×C3×C8—31no—
61C22×C3×C8—38no—
62C22×C3×C8—34no—
63C22×C3×C8C2×D311yescharacteristic
64C22×C3×C8C2×D311yescharacteristic
65C2×C3×C4⋊C4—32no—
66C2×#217—62no—
67C2×(C2×D3)⋊C4—62no—
68#926—38no—
69#926—64no—
70C2×C4⋊Dic3—32no—
71C2×C4⋊Dic3—32no—
72C2×C4⋊Dic3—62no—
73C2×C4⋊Dic3C2×D312yes—
74C2×C4×Dic3—62no—
75C2×C4×Dic3—62no—
76C22×C3⋊C8C2×D311yescharacteristic
77C2×D3×C8Dic318yescomplemented
78C2×D3×C8C2×D314yes—
79#892—38no—
80#892—64no—
81C3×#106—34no—
82#818—38no—
83#817—34no—
84#817—34no—
85#817—64no—
86#817C2×D314yescomplemented
87#807—38no—
88C23×C32C2×D411yescharacteristic
89C22×C3×D3—24no—
90C22×C3×D3C4⋊C414yes—
91C22×C3×D3C2×D412yes—
92C2×C32×C4C22×C412yes—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×Q812yes—
95C2×C32×C4C2411yescharacteristic
96C2×C3⋊Dic3—24no—
97C2×C3⋊Dic3—44no—
98C2×C3×Dic3—24no—
99C2×C3×Dic3—44no—
100C2×C3×Dic3C4⋊C414yes—
101C2×C3×Dic3C2×D412yes—
102C3×C4×D3C4⋊C418yes—
103C3×C4×D3C22×C414yes—
104C3×C4×D3C2×Q814yes—
105C32×C8C22×C414yes—
106C3×C3⋊C8C22×C414yes—
107C23×C8—31no—
108C2×#117—92no—
109#427—98no—
110C2×#107—92no—
111C2×#106—31no—
112C2×#106—91no—
113C24×C3—31no—
114C23×D3D1211yescharacteristic
115C22×C3×C4—21no—
116C22×C3×C4—31no—
117C22×C3×C4—34no—
118C22×C3×C4—32no—
119C22×C3×C4—34no—
120C22×C3×C4—32no—
121C22×C3×C4—62no—
122C22×C3×C4C22×D311yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C22×Dic3—22no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C22×Dic3—122no—
128C22×Dic3D1211yescharacteristic
129C2×C4×D3Dic614yes—
130C2×C4×D3D1212yes—
131C2×C4×D3C2×Dic314yes—
132C2×C4×D3C22×D312yes—
133C2×C3×C8—24no—
134C2×C3×C8—22no—
135C2×C3×C8—34no—
136C2×C3×C8—32no—
137C2×C3×C8—316no—
138C2×C3×C8C4×D314yes—
139C2×C3×C8C2×Dic314yes—
140C2×C3×C8C22×D312yes—
141C2×C3×C8C22×D312yes—
142C3×C4⋊C4—34no—
143C3×C4⋊C4—62no—
144#217—68no—
145(C2×D3)⋊C4—68no—
146C4⋊Dic3—22no—
147C4⋊Dic3—34no—
148C4⋊Dic3—34no—
149C4⋊Dic3—64no—
150C4⋊Dic3—62no—
151C4⋊Dic3—62no—
152C4⋊Dic3—122no—
153C4⋊Dic3C22×D314yes—
154C4×Dic3—68no—
155C4×Dic3—68no—
156C2×C3⋊C8C2×Dic314yes—
157C2×C3⋊C8C22×D312yes—
158D3×C8C2×Dic3116yescomplemented
159C22×C32C2×C4⋊C412yes—
160C22×C32#13514yes—
161C22×C32C22×D411yescharacteristic
162C2×C3×D3—24no—
163C2×C3×D3—28no—
164C2×C3×D3C2×C4⋊C414yes—
165C32×C4C2×C4⋊C412yes—
166C32×C4C23×C411yescharacteristic
167C32×C4C22×Q811yescharacteristic
168C3⋊Dic3—44no—
169C3×Dic3—44no—
170C3×Dic3C2×C4⋊C414yes—
171C23×C4—31no—
172C22×C8—31no—
173C22×C8—38no—
174C22×C8—34no—
175C22×C8D3211yescharacteristic
176#117—98no—
177#117—184no—
178C2×C4⋊C4—32no—
179C2×C4⋊C4—92no—
180C2×C22⋊C4—182no—
181C2×C42—182no—
182#107—98no—
183#106—34no—
184#106—94no—
185C23×C3—21no—
186C23×C3—34no—
187C23×C3—32no—
188C23×C3—64no—
189C23×C3C2×D1211yescharacteristic
190C23×C3D3×D411yescharacteristic
191C22×D3—24no—
192C22×D3C4⋊Dic314yes—
193C22×D3C2×D1212yes—
194C2×C3×C4—21no—
195C2×C3×C4—22no—
196C2×C3×C4—21no—
197C2×C3×C4—22no—
198C2×C3×C4—34no—
199C2×C3×C4—32no—
200C2×C3×C4—38no—
201C2×C3×C4—34no—
202C2×C3×C4—34no—
203C2×C3×C4—64no—
204C2×C3×C4—124no—
205C2×C3×C4C2×Dic612yes—
206C2×C3×C4C2×C4×D312yes—
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×Q812yes—
210C2×C3×C4C22×Dic312yes—
211C2×C3×C4C23×D311yescharacteristic
212C2×C3×C4C23×D311yescharacteristic
213C2×Dic3—24no—
214C2×Dic3—44no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—124no—
218C2×Dic3—124no—
219C2×Dic3—124no—
220C2×Dic3—244no—
221C2×Dic3C4⋊Dic314yes—
222C2×Dic3C2×D1212yes—
223C4×D3C4⋊Dic318yes—
224C4×D3C2×Dic614yes—
225C4×D3C22×Dic314yes—
226C3×C8—24no—
227C3×C8—34no—
228C3×C8C2×C4×D314yes—
229C3×C8C22×Dic314yes—
230C3⋊C8C22×Dic314yes—
231C2×C32#42714yescomplemented
232C2×C32C22×C4⋊C411yescharacteristic
233C2×C32C2×#13512yes—
234C3×D3—24no—
235C24—31no—
236C22×C4—31no—
237C22×C4—32no—
238C22×C4—34no—
239C22×C4—32no—
240C22×C4—34no—
241C22×C4—62no—
242C22×C4—182no—
243C22×C4C2×D3211yescharacteristic
244C2×C8—32no—
245C2×C8—34no—
246C2×C8—316no—
247C2×C8D3×Dic314yes—
248C2×C8C2×D3212yes—
249C4⋊C4—34no—
250C4⋊C4—62no—
251C4⋊C4—94no—
252C4⋊C4—182no—
253C22⋊C4—188no—
254C42—188no—
255C22×C3—21no—
256C22×C3—24no—
257C22×C3—22no—
258C22×C3—34no—
259C22×C3—64no—
260C22×C3—68no—
261C22×C3D3×C4⋊C412yes—
262C22×C3#90414yes—
263C22×C3#91614yes—
264C22×C3C2×C4⋊Dic312yes—
265C22×C3C22×D1211yescharacteristic
266C22×C3C2×D3×D411yescharacteristic
267C2×D3—24no—
268C2×D3—28no—
269C2×D3C2×C4⋊Dic314yes—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—22no—
273C3×C4—34no—
274C3×C4—124no—
275C3×C4D3×C4⋊C412yes—
276C3×C4C2×C4⋊Dic312yes—
277C3×C4C22×Dic611yescharacteristic
278C3×C4C22×C4×D311yescharacteristic
279C3×C4C2×D3×Q811yescharacteristic
280C3×C4C23×Dic311yescharacteristic
281Dic3—44no—
282Dic3—124no—
283Dic3—124no—
284Dic3—244no—
285Dic3C2×C4⋊Dic314yes—
286C32C2×#42711yescharacteristic, complemented, Sylow
287C23—32no—
288C23—34no—
289C23—64no—
290C23D3×D1211yescharacteristic
291C2×C4—32no—
292C2×C4—34no—
293C2×C4—34no—
294C2×C4—34no—
295C2×C4—38no—
296C2×C4—64no—
297C2×C4—124no—
298C2×C4—184no—
299C2×C4—364no—
300C2×C4D3×Dic612yes—
301C2×C4D3×D1211yescharacteristic
302C2×C4C2×D3×Dic312yes—
303C2×C4C22×D3211yescharacteristic
304C8—34no—
305C8C2×D3×Dic314yes—
306C2×C3—21no—
307C2×C3—22no—
308C2×C3—24no—
309C2×C3—64no—
310C2×C3#486014yescomplemented
311C2×C3#510614yescomplemented
312C2×C3C2×D3×C4⋊C411yescharacteristic
313C2×C3C2×#90412yes—
314C2×C3C2×#91612yes—
315C2×C3C22×C4⋊Dic311yescharacteristic
316D3—24no—
317C22—34no—
318C22—64no—
319C22—68no—
320C22#6380614yes—
321C22D3×C4⋊Dic312yes—
322C22C2×D3×D1211yescharacteristic
323C4—34no—
324C4—124no—
325C4—364no—
326C4D3×C4⋊Dic312yes—
327C4C2×D3×Dic611yescharacteristic
328C4C22×D3×Dic311yescharacteristic
329C3—21no—
330C3C2×#486011yescharacteristic, complemented
331C3C2×#510611yescharacteristic, complemented
332C2—64no—
333C2#1059070614yesdirect product factor
334C2C2×#6380612yes—
335C2C2×D3×C4⋊Dic311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#427
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×#63644C2semidirect
4. C2×C3×#817C2semidirect
5. C2×#63575C2semidirect
6. #10590706C2direct (N × H)
14. C2×C3×D3×C8C4semidirect
20. #63644C22semidirect
21. C3×#817C22semidirect
22. #63575C22semidirect
33. C2×#817D3semidirect
53. C3×D3×C8C2×C4semidirect
77. C2×D3×C8Dic3semidirect
86. #817C2×D3semidirect
158. D3×C8C2×Dic3semidirect
231. C2×C32#427semidirect
286. C32C2×#427semidirect
310. C2×C3#4860semidirect
311. C2×C3#5106semidirect
330. C3C2×#4860semidirect
331. C3C2×#5106semidirect
333. C2#10590706direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×#638412
C2×#636442
C2×C3×#8172
C2×#635752
#105907062
C2×#51063
C2×#48603