Finite Group Databasebeta

← C2×#10590790 #11859951

Subgroups — C2×#10590790 #11859951

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63843C212yesmaximal
2C22×#3718C211yesmaximal, characteristic
3C2×C8×C3⋊Dic3C211yesmaximal, characteristic
4C2×C3×#816C212yesmaximal
5C2×#63576C211yesmaximal, characteristic
6#10590790C218yesmaximal, direct product factor
7C2×#4790—32nomaximal
8C22×C3×Dic6C2212yes—
9C22×C32×C8C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C2×Dic3⋊Dic3—22no—
14C2×Dic32—22no—
15#63843—24no—
16#63843C2218yes—
17C2×#3718C418yescomplemented
18C2×#3718C2214yes—
19C8×C3⋊Dic3C2214yes—
20C3×#816C2218yes—
21#63576C2214yes—
22C2×Q8×Dic3—32no—
23C22×#216—32no—
24C2×#887—32no—
25C2×C3×#103—32no—
26C2×#816D312yes—
27C2×C8×Dic3—32no—
28C2×C8×Dic3—61no—
29C2×#807—32no—
30#4790—316no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3D411yescharacteristic
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3×Dic3—22no—
35C22×C3×Dic3—22no—
36C2×C3×Dic6—22no—
37C2×C3×Dic6—24no—
38C2×C3×Dic6C2×C418yes—
39C2×C3×Dic6C2314yes—
40C2×C32×C8—22no—
41C2×C32×C8C2312yes—
42C4×C3⋊Dic3D412yes—
43C4×C3⋊Dic3C2312yes—
44C2×C3⋊(C3⋊C8)C2×C414yes—
45C2×C3⋊(C3⋊C8)C2312yes—
46C3×C4⋊Dic3—22no—
47C3×C4⋊Dic3C2314yes—
48Dic3⋊Dic3—28no—
49Dic32—28no—
50#3718C2×C4116yescomplemented
51C2×C4×Q16—91noSylow
52C22×C3×Q8—32no—
53C22×Dic6C2×D312yes—
54C22×C3×C8—21no—
55C22×C3×C8C2×D312yes—
56C2×C3×C4⋊C4—32no—
57Q8×Dic3—38no—
58Q8×Dic3—64no—
59C2×#216—316no—
60C2×#216—38no—
61C2×C4⋊Dic3—62no—
62C2×C4⋊Dic3C2×D312yes—
63C2×Dic3⋊C4—62no—
64C2×C4×Dic3—32no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—62no—
67C2×C4×Dic3—62no—
68C22×C3⋊C8—32no—
69C22×C3⋊C8—61no—
70#887—38no—
71#887—64no—
72C3×#103—38no—
73#816C2×D318yes—
74C8×Dic3—38no—
75C8×Dic3—64no—
76#807—38no—
77C23×C32C2×D411yescharacteristic
78C2×C32×C4C22×C412yes—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4#4112yes—
81C2×C32×C4C2411yescharacteristic
82C2×C3⋊Dic3—22no—
83C2×C3⋊Dic3Q1614yescomplemented
84C2×C3⋊Dic3C2×D412yes—
85C2×C3⋊Dic3C2×D412yes—
86C2×C3×Dic3—28no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—44no—
90C3×Dic6—28no—
91C3×Dic6—24no—
92C3×Dic6C22×C418yes—
93C32×C8—22no—
94C3⋊(C3⋊C8)C22×C414yes—
95C22×Q16—91no—
96C2×C4×Q8—92no—
97C4×Q16—98no—
98C2×#107—91no—
99C2×#103—32no—
100C2×C4×C8—91no—
101C2×C3×Q8—38no—
102C2×C3×Q8—34no—
103C2×C3×Q8—62no—
104C2×C3×Q8—64no—
105C22×C3×C4—21no—
106C22×C3×C4—62no—
107C22×C3×C4—62no—
108C22×C3×C4C22×D312yes—
109C22×Dic3—22no—
110C22×Dic3—22no—
111C22×Dic3—32no—
112C22×Dic3—32no—
113C22×Dic3—61no—
114C22×Dic3—61no—
115C2×Dic6—22no—
116C2×Dic6—24no—
117C2×Dic6C4×D318yes—
118C2×Dic6C22×D314yes—
119C2×C3×C8—24no—
120C2×C3×C8—24no—
121C2×C3×C8—22no—
122C2×C3×C8C22×D314yes—
123C3×C4⋊C4—34no—
124C3×C4⋊C4—62no—
125#216—332no—
126C4⋊Dic3—22no—
127C4⋊Dic3—68no—
128C4⋊Dic3C22×D314yes—
129Dic3⋊C4—68no—
130C4×Dic3—34no—
131C4×Dic3—34no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C4×Dic3—68no—
135C4×Dic3—68no—
136C2×C3⋊C8—38no—
137C2×C3⋊C8—34no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—64no—
140C22×C32C4×D412yes—
141C22×C32C2×Q1612yes—
142C22×C32#13512yes—
143C22×C32C22×D411yescharacteristic
144C32×C4C4×D412yes—
145C32×C4C23×C411yescharacteristic
146C32×C4C2×#4111yescharacteristic
147C3⋊Dic3—22no—
148C3⋊Dic3C2×Q1614yescomplemented
149C3×Dic3—28no—
150C3×Dic3—44no—
151C22×Q8—32no—
152C2×Q16—98no—
153C2×Q16—94no—
154C22×C8—91no—
155C22×C8D3211yescharacteristic
156C4×Q8—98no—
157C4×Q8—184no—
158C2×C4⋊C4—32no—
159C2×C4⋊C4—182no—
160C2×C42—91no—
161C2×C42—182no—
162#107—94no—
163#103—38no—
164C4×C8—94no—
165C23×C3—21no—
166C23×C3D3×D412yes—
167C3×Q8—38no—
168C3×Q8—68no—
169C3×Q8—64no—
170C2×C3×C4—21no—
171C2×C3×C4—22no—
172C2×C3×C4—21no—
173C2×C3×C4—22no—
174C2×C3×C4—68no—
175C2×C3×C4—64no—
176C2×C3×C4—64no—
177C2×C3×C4—124no—
178C2×C3×C4C2×C4×D314yes—
179C2×C3×C4D3×D412yes—
180C2×C3×C4#23714yes—
181C2×C3×C4C23×D312yes—
182C2×Dic3—28no—
183C2×Dic3—24no—
184C2×Dic3—24no—
185C2×Dic3—38no—
186C2×Dic3—34no—
187C2×Dic3—34no—
188C2×Dic3—44no—
189C2×Dic3—64no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194Dic6—28no—
195Dic6—24no—
196Dic6C2×C4×D318yes—
197C3×C8—24no—
198C3×C8—24no—
199C3⋊C8—38no—
200C3⋊C8—64no—
201C2×C32C4×Q1614yescomplemented
202C2×C32C2×C4×D411yescharacteristic
203C2×C32C22×Q1611yescharacteristic
204C2×C32C2×#13511yescharacteristic
205C2×Q8—34no—
206C2×Q8—38no—
207C2×Q8—62no—
208C2×Q8—64no—
209C22×C4—62no—
210C22×C4—62no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4C2×D3211yescharacteristic
214Q16—916no—
215C2×C8—22no—
216C2×C8—92no—
217C2×C8—94no—
218C2×C8C2×D3212yes—
219C4⋊C4—34no—
220C4⋊C4—62no—
221C4⋊C4—188no—
222C42—92no—
223C42—92no—
224C42—188no—
225C22×C3—21no—
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—22no—
229C22×C3#67⋊C414yes—
230C22×C3#91614yes—
231C22×C3D3×Q1614yes—
232C22×C3C2×D3×D412yes—
233C3×C4—21no—
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—68no—
237C3×C4—124no—
238C3×C4#67⋊C414yes—
239C3×C4C22×C4×D312yes—
240C3×C4C2×#23712yes—
241Dic3—28no—
242Dic3—38no—
243Dic3—44no—
244Dic3—64no—
245Dic3—64no—
246Dic3—64no—
247C32C2×C4×Q1611yescharacteristic, complemented, Sylow
248C23#380211yescharacteristic
249Q8—38no—
250Q8—64no—
251Q8—68no—
252C2×C4—64no—
253C2×C4—68no—
254C2×C4—64no—
255C2×C4—92no—
256C2×C4—94no—
257C2×C4—92no—
258C2×C4—124no—
259C2×C4—182no—
260C2×C4C4×D3212yes—
261C2×C4#380211yescharacteristic
262C2×C4#380512yes—
263C2×C4C22×D3211yescharacteristic
264C8—22no—
265C8—94no—
266C2×C3—24no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3#479018yescomplemented
271C2×C3C2×#67⋊C412yes—
272C2×C3C2×#91612yes—
273C2×C3C2×D3×Q1612yes—
274C22#6380212yes—
275C22#6380912yes—
276C22#6390212yes—
277C22C2×#380211yescharacteristic
278C4—68no—
279C4—94no—
280C4—124no—
281C4—182no—
282C4#6390212yes—
283C4C2×C4×D3211yescharacteristic
284C4C2×#380511yescharacteristic
285C3—21no—
286C3C2×#479012yescomplemented
287C2#1059079014yesdirect product factor
288C2C2×#6380211yescharacteristic
289C2C2×#6380911yescharacteristic
290C2C2×#6390211yescharacteristic
subgroupG/H
centerC23#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C2×D4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×C4×Q16
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
6. #10590790C2direct (N × H)
17. C2×#3718C4semidirect
50. #3718C2×C4semidirect
83. C2×C3⋊Dic3Q16semidirect
148. C3⋊Dic3C2×Q16semidirect
201. C2×C32C4×Q16semidirect
247. C32C2×C4×Q16semidirect
270. C2×C3#4790semidirect
286. C3C2×#4790semidirect
287. C2#10590790direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638432
C22×#37182
C2×C8×C3⋊Dic32
C2×C3×#8162
C2×#635762
#105907902
C2×#47903