Finite Group Databasebeta

← C2×#10590257 #11858804

Subgroups — C2×#10590257 #11858804

Order 1152.

989 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×C3×C4⋊(C3⋊C8)C212yesmaximal, complemented
3C2×#63557C212yesmaximal
4C2×#63555C211yesmaximal, characteristic, complemented
5C2×#63553C211yesmaximal, characteristic, complemented
6#10590257C218yesmaximal, direct product factor
7C2×#4840—32nomaximal
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C2×#3752C412yes—
11C2×#3750C412yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64081C414yes—
14#64081C2214yes—
15C22×C3×C3⋊C8C2212yes—
16C22×C3×C3⋊C8C2212yes—
17C3×C4⋊(C3⋊C8)C2218yescomplemented
18#63557C2218yes—
19#63555C2214yescomplemented
20#63553C2214yescomplemented
21C2×#872—32no—
22C2×#872—61no—
23C2×C3×C4⋊C8—32no—
24C2×(C2×D3)⋊C8—32no—
25C2×(C2×D3)⋊C8—32no—
26C2×#815—32no—
27C2×C8×Dic3—32no—
28C2×C4⋊(C3⋊C8)D312yescomplemented
29#4840—316no—
30C23×C3⋊D3C2×C411yescharacteristic
31C22×C32×C4C2×C412yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C412yes—
35C2×C4×C3⋊D3—24no—
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3C2312yes—
38C32×C42C2×C412yes—
39C32×C42C2312yes—
40#3752C2×C418yes—
41#3750C2×C418yes—
42C4×C3⋊Dic3C2×C412yes—
43C4×C3⋊Dic3C2312yes—
44C2×C3×C3⋊C8—24no—
45C2×C3×C3⋊C8—24no—
46C2×C3×C3⋊C8C2314yes—
47C2×C3×C3⋊C8C2314yes—
48C2×#433—91noSylow
49C22×C4×D3—32no—
50C22×C4×D3—61no—
51C22×C3×C8—32no—
52C22×C3×C8—32no—
53C2×C3×C42—21no—
54C2×C3×C42C2×D312yes—
55C2×(C2×D3)⋊C4—32no—
56C2×(C2×D3)⋊C4—32no—
57C2×(C2×D3)⋊C4—62no—
58C2×Dic3⋊C4—32no—
59C2×Dic3⋊C4—32no—
60C2×Dic3⋊C4—62no—
61C2×C4×Dic3—32no—
62C2×C4×Dic3—61no—
63C22×C3⋊C8C2×D312yes—
64C22×C3⋊C8C2×D312yes—
65#872—38no—
66#872—38no—
67#872—64no—
68#872—64no—
69C3×C4⋊C8—38no—
70(C2×D3)⋊C8—38no—
71(C2×D3)⋊C8—38no—
72#815—38no—
73C8×Dic3—38no—
74C4⋊(C3⋊C8)C2×D318yescomplemented
75C23×C32C22×C411yescharacteristic
76C22×C3⋊D3—22no—
77C22×C3⋊D3—24no—
78C22×C3⋊D3C22×C412yes—
79C2×C32×C4—24no—
80C2×C32×C4C22×C414yes—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4#4114yes—
83C2×C32×C4C2411yescharacteristic
84C2×C3⋊Dic3—22no—
85C2×C3⋊Dic3—24no—
86C2×C3⋊Dic3C22×C414yes—
87C2×C3⋊Dic3C22×C412yes—
88C4×C3⋊D3—24no—
89C4×C3⋊D3—24no—
90C3×C3⋊C8—24no—
91C3×C3⋊C8—24no—
92C2×#117—91no—
93#433—98no—
94C2×C4⋊C8—32no—
95C2×C22⋊C8—92no—
96C2×#97—91no—
97C2×C4×C8—91no—
98C23×D3—32no—
99C23×D3—61no—
100C22×C3×C4—22no—
101C22×C3×C4—21no—
102C22×C3×C4C4×D312yes—
103C22×C3×C4C4×D312yes—
104C22×C3×C4C22×D312yes—
105C22×Dic3—32no—
106C22×Dic3—32no—
107C22×Dic3—32no—
108C22×Dic3—61no—
109C22×Dic3—62no—
110C2×C4×D3—34no—
111C2×C4×D3—34no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—68no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C3×C8—34no—
118C2×C3×C8—34no—
119C2×C3×C8—64no—
120C2×C3×C8—64no—
121C3×C42—22no—
122C3×C42—22no—
123C3×C42C4×D314yes—
124C3×C42C22×D314yes—
125(C2×D3)⋊C4—38no—
126(C2×D3)⋊C4—38no—
127(C2×D3)⋊C4—68no—
128Dic3⋊C4—38no—
129Dic3⋊C4—38no—
130Dic3⋊C4—68no—
131C4×Dic3—34no—
132C4×Dic3—34no—
133C4×Dic3—62no—
134C4×Dic3—62no—
135C2×C3⋊C8—24no—
136C2×C3⋊C8—24no—
137C2×C3⋊C8C22×D314yes—
138C2×C3⋊C8C22×D314yes—
139C22×C32#11712yes—
140C22×C32#13114yes—
141C22×C32C23×C411yescharacteristic
142C2×C3⋊D3—22no—
143C2×C3⋊D3—24no—
144C2×C3⋊D3—44no—
145C32×C4—24no—
146C32×C4#11712yes—
147C32×C4C2×#4112yes—
148C3⋊Dic3—22no—
149C3⋊Dic3—24no—
150C23×C4—91no—
151C22×C8—32no—
152C22×C8—32no—
153#117—94no—
154#117—94no—
155C2×C4⋊C4—92no—
156C2×C22⋊C4—92no—
157C2×C42—91no—
158C2×C42D3211yescharacteristic
159C4⋊C8—38no—
160C22⋊C8—98no—
161#97—94no—
162C4×C8—94no—
163C23×C3—21no—
164C23×C3C2×C4×D312yes—
165C22×D3—34no—
166C22×D3—62no—
167C22×D3—64no—
168C22×D3—64no—
169C22×D3—64no—
170C22×D3—64no—
171C22×D3—124no—
172C2×C3×C4—24no—
173C2×C3×C4—24no—
174C2×C3×C4—21no—
175C2×C3×C4—24no—
176C2×C3×C4—21no—
177C2×C3×C4—24no—
178C2×C3×C4—44no—
179C2×C3×C4C2×C4×D314yes—
180C2×C3×C4C2×C4×D314yes—
181C2×C3×C4C2×C4×D312yes—
182C2×C3×C4#23714yes—
183C2×C3×C4#23914yes—
184C2×C3×C4C23×D312yes—
185C2×Dic3—34no—
186C2×Dic3—34no—
187C2×Dic3—34no—
188C2×Dic3—62no—
189C2×Dic3—64no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—124no—
195C4×D3—68no—
196C4×D3—68no—
197C4×D3—68no—
198C4×D3—64no—
199C4×D3—64no—
200C3×C8—64no—
201C3×C8—64no—
202C3⋊C8—24no—
203C3⋊C8—24no—
204C2×C32#43314yescomplemented
205C2×C32C2×#11711yescharacteristic
206C2×C32C2×#13112yes—
207C3⋊D3—42no—
208C24—91no—
209C22×C4—92no—
210C22×C4—91no—
211C22×C4—92no—
212C22×C4—92no—
213C22×C4—184no—
214C22×C4#62412yes—
215C22×C4C2×D3211yescharacteristic
216C2×C8—34no—
217C2×C8—34no—
218C2×C8—64no—
219C2×C8—64no—
220C4⋊C4—98no—
221C22⋊C4—98no—
222C42—92no—
223C42—92no—
224C42#62412yes—
225C42C2×D3212yes—
226C22×C3—21no—
227C22×C3—24no—
228C22×C3—22no—
229C22×C3#89214yes—
230C22×C3#90114yes—
231C22×C3#90714yes—
232C22×C3C22×C4×D312yes—
233C2×D3—64no—
234C2×D3—64no—
235C2×D3—64no—
236C2×D3—64no—
237C2×D3—124no—
238C2×D3—128no—
239C2×D3—128no—
240C3×C4—24no—
241C3×C4—24no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—44no—
245C3×C4#89214yes—
246C3×C4C2×#23712yes—
247C3×C4C2×#23912yes—
248Dic3—64no—
249Dic3—64no—
250Dic3—64no—
251Dic3—64no—
252Dic3—124no—
253C32C2×#43311yescharacteristic, complemented, Sylow
254C23—92no—
255C23—184no—
256C23—182no—
257C23C2×#62411yescharacteristic
258C2×C4—24no—
259C2×C4—94no—
260C2×C4—92no—
261C2×C4—184no—
262C2×C4—182no—
263C2×C4—184no—
264C2×C4—184no—
265C2×C4#379614yes—
266C2×C4C2×#62414yes—
267C2×C4C2×#62411yescharacteristic
268C2×C4C22×D3211yescharacteristic
269C8—64no—
270C8—64no—
271C2×C3—21no—
272C2×C3—24no—
273C2×C3—22no—
274C2×C3#484018yescomplemented
275C2×C3C2×#89212yes—
276C2×C3C2×#90112yes—
277C2×C3C2×#90712yes—
278D3—124no—
279D3—124no—
280C22—182no—
281C22—184no—
282C22—364no—
283C22#6381714yes—
284C22#6384912yes—
285C22C22×#62411yescharacteristic
286C4—24no—
287C4—182no—
288C4—184no—
289C4#6384912yes—
290C4C2×#379612yes—
291C3—21no—
292C3C2×#484012yescomplemented
293C2—362no—
294C2#1059025714yesdirect product factor
295C2C2×#6381712yes—
296C2C2×#6384911yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. C2×#63555C2semidirect
5. C2×#63553C2semidirect
6. #10590257C2direct (N × H)
17. C3×C4⋊(C3⋊C8)C22semidirect
19. #63555C22semidirect
20. #63553C22semidirect
28. C2×C4⋊(C3⋊C8)D3semidirect
74. C4⋊(C3⋊C8)C2×D3semidirect
204. C2×C32#433semidirect
253. C32C2×#433semidirect
274. C2×C3#4840semidirect
292. C3C2×#4840semidirect
294. C2#10590257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C3×C4⋊(C3⋊C8)2
C2×#635572
C2×#635552
C2×#635532
#105902572
C2×#48403