Finite Group Databasebeta

← C2×#10592670 #11869374

Subgroups — C2×#10592670 #11869374

Order 1152.

1380 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic
2C2×#64133C211yesmaximal, characteristic
3C2×#63657C211yesmaximal, characteristic
4#10592670C218yesmaximal, direct product factor
5C2×#63637C212yesmaximal, complemented
6C2×#63635C212yesmaximal, complemented
7C2×#4971—34nomaximal
8C23×C32×C4—21no—
9C23×C32×C4C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C2×C32×C4⋊C4—21no—
12C2×C32×C4⋊C4—22no—
13C2×C32×C4⋊C4C2212yes—
14C2×C32×C4⋊C4C2214yes—
15C2×#3757—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17#64133—22no—
18#64133C2214yes—
19C2×#3750—21no—
20C22×C3⋊(C3⋊C8)C2212yes—
21#63657C2214yes—
22#63637C2218yescomplemented
23#63635C2218yescomplemented
24C22×C3×C4⋊C4D314yes—
25C2×#924—34no—
26C2×#830—34no—
27#4971—332no—
28C2×#810—38no—
29C2×#808—38no—
30C24×C32D411yescharacteristic
31C22×C32×C4—24no—
32C22×C32×C4—24no—
33C22×C32×C4—22no—
34C22×C32×C4—44no—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D412yes—
37C22×C32×C4C2312yes—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3—21no—
41C2×#634—24no—
42C2×#634—21no—
43C2×#634C2312yes—
44C32×C4⋊C4—24no—
45C32×C4⋊C4—22no—
46C32×C4⋊C4C2314yes—
47#3757—24no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)C2312yes—
50#3750—24no—
51C2×C3⋊(C3⋊C8)—24no—
52C2×C3⋊(C3⋊C8)C2314yes—
53C2×#483—91noSylow
54C23×C3×C4—24no—
55C23×C3×C4C2×D314yes—
56C22×Dic6—34no—
57C2×C3×C4⋊C4—24no—
58C2×C3×C4⋊C4—28no—
59C2×C3×C4⋊C4C2×D318yes—
60C2×C3×C4⋊C4C2×D3116yes—
61C2×#217—64no—
62C2×C4⋊Dic3—34no—
63#924—316no—
64#924—68no—
65C2×Dic3⋊C4—64no—
66C22×C3⋊C8—38no—
67#830—316no—
68#810—332no—
69#808—332no—
70C23×C32—22no—
71C23×C32—22no—
72C23×C32SD1614yes—
73C23×C32C2×D412yes—
74C23×C32C2×D411yescharacteristic
75C2×C32×C4—22no—
76C2×C32×C4—24no—
77C2×C32×C4—24no—
78C2×C32×C4—24no—
79C2×C32×C4—48no—
80C2×C32×C4—44no—
81C2×C32×C4C2×D412yes—
82C2×C32×C4C2×D411yescharacteristic
83C2×C32×C4#4114yes—
84C2×C32×C4C2411yescharacteristic
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—42no—
88C2×C3⋊Dic3—42no—
89#634—24no—
90#634—42no—
91C3⋊(C3⋊C8)—24no—
92C2×C22⋊Q8—91no—
93C22×C4⋊C4C3⋊D311yescharacteristic
94#483—98no—
95C2×#106—92no—
96C2×#103—92no—
97C2×C22⋊C8—91no—
98C24×C3#6714yes—
99C22×C3×C4—216no—
100C22×C3×C4—216no—
101C22×C3×C4—28no—
102C22×C3×C4—416no—
103C22×C3×C4#6714yes—
104C22×C3×C4#6718yes—
105C22×C3×C4C22×D318yes—
106C22×C3×C4C22×D314yes—
107C22×Dic3—64no—
108C22×Dic3—64no—
109C2×Dic6—38no—
110C2×Dic6—616no—
111C2×Dic6—64no—
112C3×C4⋊C4—216no—
113C3×C4⋊C4—28no—
114C3×C4⋊C4C22×D3116yes—
115#217—616no—
116C4⋊Dic3—38no—
117C4⋊Dic3—64no—
118Dic3⋊C4—616no—
119C2×C3⋊C8—316no—
120C2×C3⋊C8—616no—
121C22×C32—22no—
122C22×C32—22no—
123C22×C32—28no—
124C22×C32#12312yes—
125C22×C32C2×SD1614yes—
126C22×C32C2×SD1612yes—
127C22×C32#13712yes—
128C22×C32C22×D411yescharacteristic
129C32×C4—22no—
130C32×C4—44no—
131C32×C4#12312yes—
132C32×C4C2×#4112yes—
133C3⋊Dic3—42no—
134C3⋊Dic3—42no—
135C22×Q8—91no—
136C23×C4—21no—
137C23×C4C2×C3⋊D311yescharacteristic
138C22×C8—92no—
139C22⋊Q8—94no—
140C22⋊Q8—182no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—91no—
144C2×C4⋊C4—181no—
145C2×C4⋊C4C2×C3⋊D312yes—
146C2×C4⋊C4C2×C3⋊D314yes—
147C2×C22⋊C4—181no—
148#106—98no—
149#103—98no—
150C22⋊C8—94no—
151C23×C3—28no—
152C23×C3—28no—
153C23×C3#214116yes—
154C23×C3C2×#6718yes—
155C23×C3C2×#6714yes—
156C2×C3×C4—28no—
157C2×C3×C4—216no—
158C2×C3×C4—216no—
159C2×C3×C4—216no—
160C2×C3×C4—432no—
161C2×C3×C4—416no—
162C2×C3×C4#235116yes—
163C2×C3×C4C2×#6718yes—
164C2×C3×C4C2×#6714yes—
165C2×C3×C4C23×D314yes—
166C2×Dic3—68no—
167C2×Dic3—68no—
168C2×Dic3—128no—
169C2×Dic3—128no—
170Dic6—616no—
171Dic6—128no—
172C3⋊C8—616no—
173C2×C32—24no—
174C2×C32#48314yescomplemented
175C2×C32C2×#12311yescharacteristic
176C2×C32C22×SD1611yescharacteristic
177C2×C32C2×#13711yescharacteristic
178C24#63811yescharacteristic
179C2×Q8—92no—
180C2×Q8—181no—
181C2×Q8—184no—
182C22×C4—24no—
183C22×C4—24no—
184C22×C4—22no—
185C22×C4—44no—
186C22×C4—181no—
187C22×C4—181no—
188C22×C4#63812yes—
189C22×C4#63811yescharacteristic
190C22×C4C22×C3⋊D312yes—
191C22×C4C22×C3⋊D311yescharacteristic
192C2×C8—94no—
193C2×C8—184no—
194C4⋊C4—24no—
195C4⋊C4—22no—
196C4⋊C4—92no—
197C4⋊C4—181no—
198C4⋊C4—184no—
199C4⋊C4C22×C3⋊D314yes—
200C22⋊C4—184no—
201C22×C3—232no—
202C22×C3—28no—
203C22×C3—28no—
204C22×C3#92918yes—
205C22×C3C2×#214116yes—
206C22×C3C2×#21418yes—
207C22×C3#94218yes—
208C22×C3C22×#6714yes—
209C3×C4—28no—
210C3×C4—416no—
211C3×C4#92918yes—
212C3×C4C2×#23518yes—
213Dic3—128no—
214Dic3—128no—
215C32C2×#48311yescharacteristic, complemented, Sylow
216C23—22no—
217C23—22no—
218C23#375414yes—
219C23C2×#63812yes—
220C23C2×#63811yescharacteristic
221Q8—184no—
222Q8—362no—
223C2×C4—22no—
224C2×C4—24no—
225C2×C4—24no—
226C2×C4—24no—
227C2×C4—48no—
228C2×C4—44no—
229C2×C4—182no—
230C2×C4—182no—
231C2×C4—362no—
232C2×C4—362no—
233C2×C4#382814yes—
234C2×C4C2×#63812yes—
235C2×C4C2×#63811yescharacteristic
236C2×C4C23×C3⋊D311yescharacteristic
237C8—184no—
238C2×C3—216no—
239C2×C3#4971116yescomplemented
240C2×C3C2×#92914yes—
241C2×C3C22×#21414yes—
242C2×C3C2×#94214yes—
243C22—28no—
244C22—22no—
245C22—22no—
246C22#6413812yes—
247C22C2×#375414yes—
248C22C2×#375412yes—
249C22#6415112yes—
250C22C22×#63811yescharacteristic
251C4—22no—
252C4—44no—
253C4—362no—
254C4—362no—
255C4#6413812yes—
256C4C2×#382812yes—
257C3C2×#497114yescomplemented
258C2—24no—
259C2#1059267014yesdirect product factor
260C2C2×#6413811yescharacteristic
261C2C22×#375411yescharacteristic
262C2C2×#6415111yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C2×D4
prime radicalC24×C32D4
hypercenterC22×C4⋊C4C3⋊D3
hypocenterC32C2×#483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10592670C2direct (N × H)
5. C2×#63637C2semidirect
6. C2×#63635C2semidirect
22. #63637C22semidirect
23. #63635C22semidirect
174. C2×C32#483semidirect
215. C32C2×#483semidirect
239. C2×C3#4971semidirect
257. C3C2×#4971semidirect
259. C2#10592670direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×#641332
C2×#636572
#105926702
C2×#636372
C2×#636352
C2×#49713