Finite Group Databasebeta

← C2×#10591062 #11858796

Subgroups — C2×#10591062 #11858796

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×#64135C211yesmaximal, characteristic
2C2×C3×#830C212yesmaximal
3C2×#63572C212yesmaximal, complemented
4C2×#63555C211yesmaximal, characteristic, complemented
5#10591062C218yesmaximal, direct product factor
6C2×#63553C211yesmaximal, characteristic, complemented
7C2×#4720—32nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3757C412yes—
10#64135C414yes—
11#64135C2214yes—
12C2×C4⋊(C3⋊Dic3)C412yes—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊C8C2212yes—
16C22×C3×C3⋊C8C2212yes—
17C3×#830C2218yes—
18#63572C2218yescomplemented
19#63555C2214yescomplemented
20#63553C2214yescomplemented
21C2×#926—32no—
22C2×#926—61no—
23C2×C3×C22⋊C8—32no—
24C2×#830D312yes—
25C2×#815—32no—
26C2×Dic3⋊C8—32no—
27C2×Dic3⋊C8—32no—
28C2×C8×Dic3—32no—
29#4720—316no—
30C24×C32C2×C411yescharacteristic
31C22×C32×C4—24no—
32C22×C32×C4C2×C411yescharacteristic
33C22×C32×C4C2×C412yes—
34C22×C32×C4C2312yes—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3C2×C412yes—
37C22×C3⋊Dic3C2×C412yes—
38#3757C2×C418yes—
39C4⋊(C3⋊Dic3)C2×C418yes—
40C4×C3⋊Dic3C2×C412yes—
41C4×C3⋊Dic3C2×C412yes—
42C4×C3⋊Dic3C2312yes—
43C4×C3⋊Dic3C2312yes—
44C2×C3×C3⋊C8—24no—
45C2×C3×C3⋊C8—24no—
46C2×C3×C3⋊C8C2314yes—
47C2×C3×C3⋊C8C2314yes—
48C2×#433—91noSylow
49C23×C3×C4—21no—
50C23×C3×C4C2×D312yes—
51C22×C3×C8—32no—
52C22×C3×C8—32no—
53C2×#217—32no—
54C2×#217—32no—
55C2×#217—62no—
56#926—38no—
57#926—38no—
58#926—64no—
59#926—64no—
60C2×C4⋊Dic3—32no—
61C2×C4⋊Dic3—32no—
62C2×C4⋊Dic3—62no—
63C2×C4×Dic3—32no—
64C2×C4×Dic3—32no—
65C2×C4×Dic3—61no—
66C2×C4×Dic3—61no—
67C22×C3⋊C8C2×D312yes—
68C22×C3⋊C8C2×D312yes—
69C3×C22⋊C8—38no—
70#830C2×D318yes—
71#815—38no—
72Dic3⋊C8—38no—
73Dic3⋊C8—38no—
74C8×Dic3—38no—
75C23×C32—22no—
76C23×C32—24no—
77C23×C32C22×C412yes—
78C23×C32C22×C411yescharacteristic
79C2×C32×C4—22no—
80C2×C32×C4—24no—
81C2×C32×C4—24no—
82C2×C32×C4C22×C412yes—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4#4114yes—
85C2×C32×C4C2411yescharacteristic
86C2×C3⋊Dic3—24no—
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3C22×C414yes—
89C2×C3⋊Dic3C22×C414yes—
90C3×C3⋊C8—24no—
91C3×C3⋊C8—24no—
92C2×#117—91no—
93#433—98no—
94C2×C4⋊C8—92no—
95C2×C22⋊C8—32no—
96C2×#97—91no—
97C2×C4×C8—91no—
98C24×C3—21no—
99C24×C3C4×D312yes—
100C22×C3×C4—28no—
101C22×C3×C4—24no—
102C22×C3×C4—24no—
103C22×C3×C4—21no—
104C22×C3×C4—22no—
105C22×C3×C4—22no—
106C22×C3×C4—21no—
107C22×C3×C4C4×D312yes—
108C22×C3×C4C4×D314yes—
109C22×C3×C4C22×D314yes—
110C22×C3×C4C22×D312yes—
111C22×Dic3—32no—
112C22×Dic3—32no—
113C22×Dic3—32no—
114C22×Dic3—32no—
115C22×Dic3—62no—
116C22×Dic3—62no—
117C2×C3×C8—34no—
118C2×C3×C8—34no—
119C2×C3×C8—64no—
120C2×C3×C8—64no—
121#217—38no—
122#217—38no—
123#217—68no—
124C4⋊Dic3—38no—
125C4⋊Dic3—38no—
126C4⋊Dic3—68no—
127C4×Dic3—34no—
128C4×Dic3—34no—
129C4×Dic3—34no—
130C4×Dic3—34no—
131C4×Dic3—62no—
132C4×Dic3—62no—
133C4×Dic3—62no—
134C4×Dic3—62no—
135C2×C3⋊C8—24no—
136C2×C3⋊C8—24no—
137C2×C3⋊C8C22×D314yes—
138C2×C3⋊C8C22×D314yes—
139C22×C32—22no—
140C22×C32—24no—
141C22×C32—44no—
142C22×C32#11712yes—
143C22×C32#13114yes—
144C22×C32C23×C411yescharacteristic
145C32×C4—22no—
146C32×C4#11712yes—
147C32×C4C2×#4112yes—
148C3⋊Dic3—24no—
149C3⋊Dic3—24no—
150C23×C4D3211yescharacteristic
151C22×C8—32no—
152C22×C8—32no—
153#117—94no—
154#117—94no—
155C2×C4⋊C4—92no—
156C2×C22⋊C4—92no—
157C2×C42—91no—
158C2×C42—91no—
159C4⋊C8—98no—
160C22⋊C8—38no—
161#97—94no—
162C4×C8—94no—
163C23×C3—24no—
164C23×C3—24no—
165C23×C3—24no—
166C23×C3—24no—
167C23×C3—21no—
168C23×C3—22no—
169C23×C3—44no—
170C23×C3C2×C4×D314yes—
171C23×C3C2×C4×D312yes—
172C2×C3×C4—24no—
173C2×C3×C4—28no—
174C2×C3×C4—28no—
175C2×C3×C4—24no—
176C2×C3×C4—28no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—21no—
180C2×C3×C4—24no—
181C2×C3×C4—21no—
182C2×C3×C4—22no—
183C2×C3×C4C2×C4×D314yes—
184C2×C3×C4C2×C4×D312yes—
185C2×C3×C4#23714yes—
186C2×C3×C4#23714yes—
187C2×C3×C4C23×D312yes—
188C2×Dic3—34no—
189C2×Dic3—34no—
190C2×Dic3—34no—
191C2×Dic3—34no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—64no—
195C2×Dic3—64no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—124no—
199C2×Dic3—124no—
200C3×C8—64no—
201C3×C8—64no—
202C3⋊C8—24no—
203C3⋊C8—24no—
204C2×C32—42no—
205C2×C32#43314yescomplemented
206C2×C32C2×#11711yescharacteristic
207C2×C32C2×#13112yes—
208C24#62411yescharacteristic
209C22×C4—24no—
210C22×C4—92no—
211C22×C4—92no—
212C22×C4#62411yescharacteristic
213C22×C4#62412yes—
214C22×C4C2×D3212yes—
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—92no—
225C42—92no—
226C22×C3—24no—
227C22×C3—24no—
228C22×C3—24no—
229C22×C3—24no—
230C22×C3—21no—
231C22×C3—24no—
232C22×C3—22no—
233C22×C3—44no—
234C22×C3—48no—
235C22×C3—48no—
236C22×C3#87714yes—
237C22×C3#90114yes—
238C22×C3#90714yes—
239C22×C3C22×C4×D312yes—
240C3×C4—24no—
241C3×C4—24no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4#87714yes—
245C3×C4C2×#23712yes—
246C3×C4C2×#23712yes—
247Dic3—64no—
248Dic3—64no—
249Dic3—64no—
250Dic3—64no—
251Dic3—124no—
252Dic3—124no—
253C32C2×#43311yescharacteristic, complemented, Sylow
254C23—24no—
255C23—22no—
256C23C2×#62412yes—
257C23C2×#62411yescharacteristic
258C2×C4—22no—
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—94no—
262C2×C4—94no—
263C2×C4—184no—
264C2×C4—184no—
265C2×C4#380514yes—
266C2×C4C2×#62412yes—
267C2×C4C2×#62411yescharacteristic
268C2×C4C22×D3211yescharacteristic
269C8—64no—
270C8—64no—
271C2×C3—24no—
272C2×C3—21no—
273C2×C3—22no—
274C2×C3—44no—
275C2×C3—44no—
276C2×C3#472018yescomplemented
277C2×C3C2×#87712yes—
278C2×C3C2×#90112yes—
279C2×C3C2×#90712yes—
280C22—22no—
281C22—24no—
282C22—44no—
283C22#6381714yes—
284C22#6395712yes—
285C22C22×#62411yescharacteristic
286C4—22no—
287C4—184no—
288C4—184no—
289C4#6395712yes—
290C4C2×#380512yes—
291C3—21no—
292C3C2×#472012yescomplemented
293C2—42no—
294C2#1059106214yesdirect product factor
295C2C2×#6381712yes—
296C2C2×#6395711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#63572C2semidirect
4. C2×#63555C2semidirect
5. #10591062C2direct (N × H)
6. C2×#63553C2semidirect
18. #63572C22semidirect
19. #63555C22semidirect
20. #63553C22semidirect
205. C2×C32#433semidirect
253. C32C2×#433semidirect
276. C2×C3#4720semidirect
292. C3C2×#4720semidirect
294. C2#10591062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×#8302
C2×#635722
C2×#635552
#105910622
C2×#635532
C2×#47203