Finite Group Databasebeta

← C2×#10593632 #11922983

Subgroups — C2×#10593632 #11922983

Order 1152.

654 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 654 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64259C212yesmaximal
2C2×C3×C8×A4C211yesmaximal, characteristic
3#10593632C214yesmaximal, direct product factor
4C2×#5398—33nomaximal
5C2×#5116—31nomaximal
6C2×C3×C4×A4C2211yescharacteristic
7C2×C3⋊SL(2,ℤ/4)—22no—
8#64259—22no—
9#64259C2214yes—
10C2×#3746—41nomaximal
11C3×C8×A4C2212yes—
12C2×A4⋊Q8—36no—
13C23×C3×C8D311yescharacteristic
14C2×#924—32no—
15C22×Dic12—31no—
16C2×C8×A4D313yes—
17#5398—312no—
18#5116—34no—
19#5116—34no—
20C2×#818—31no—
21C2×#816—32no—
22C22×C3×A4D411yescharacteristic
23C2×#634—42no—
24C3×C4×A4D411yescharacteristic
25C3×C4×A4C2311yescharacteristic
26C3⋊SL(2,ℤ/4)—24no—
27C2×C32×C8—41no—
28#3746—44no—
29C2×#467—91noSylow
30C23×C3×C4C2×D311yescharacteristic
31C22×Dic6—32no—
32C2×C4×A4C2×D313yes—
33C2×SL(2,ℤ/4)—66no—
34A4⋊Q8—312no—
35A4⋊Q8—66no—
36C22×C3×C8—31no—
37C22×C3×C8—31no—
38C22×C3×C8—32no—
39C22×C3×C8C2×D312yes—
40C2×#217—62no—
41C2×C4⋊Dic3—32no—
42#924—34no—
43#924—34no—
44#924—62no—
45#924—62no—
46C2×Dic3⋊C4—62no—
47C2×Dic12—34no—
48C2×Dic12—61no—
49C2×Dic12—62no—
50C2×Dic12—61no—
51C2×Dic12—123no—
52C8×A4C2×D316yes—
53#818—34no—
54#816—38no—
55C2×C3×A4Q1612yescomplemented
56C2×C3×A4C2×D411yescharacteristic
57C2×C32×C4—41no—
58C2×C3⋊Dic3—82no—
59#634—44no—
60#634—82no—
61C32×C8—42no—
62C22×Q16—91no—
63C23×C8C3⋊D311yescharacteristic
64C2×C22⋊Q8—92no—
65#467—94no—
66#467—94no—
67C2×#107—91no—
68C2×#103—92no—
69C24×C3D1211yescharacteristic
70C22×A4D1213yes—
71C22×C3×C4—31no—
72C22×C3×C4—31no—
73C22×C3×C4—31no—
74C22×C3×C4—31no—
75C22×C3×C4D1211yescharacteristic
76C22×C3×C4C22×D311yescharacteristic
77C22×Dic3—62no—
78C22×Dic3—62no—
79C2×Dic6—34no—
80C2×Dic6—62no—
81C2×Dic6—62no—
82C2×Dic6—62no—
83C2×Dic6—62no—
84C2×Dic6—62no—
85C2×Dic6—126no—
86C4×A4D1213yes—
87C4×A4C22×D313yes—
88SL(2,ℤ/4)—612no—
89C2×C3×C8—31no—
90C2×C3×C8—32no—
91C2×C3×C8—32no—
92C2×C3×C8—32no—
93C2×C3×C8—43no—
94C2×C3×C8—61no—
95C2×C3×C8S411yescharacteristic
96#217—64no—
97#217—64no—
98C4⋊Dic3—34no—
99C4⋊Dic3—62no—
100Dic3⋊C4—64no—
101Dic3⋊C4—64no—
102Dic12—64no—
103Dic12—64no—
104Dic12—1212no—
105C22×C32—41no—
106C3×A4C2×Q1611yescharacteristic, complemented
107C32×C4—41no—
108C32×C4—41no—
109C3⋊Dic3—84no—
110C22×Q8—92no—
111C23×C4C2×C3⋊D311yescharacteristic
112C2×Q16—94no—
113C2×Q16—181no—
114C2×Q16—182no—
115C2×Q16—181no—
116C22×C8—31no—
117C22×C8—31no—
118C22×C8—32no—
119C22×C8C2×C3⋊D312yes—
120C22⋊Q8—94no—
121C22⋊Q8—94no—
122C22⋊Q8—182no—
123C22⋊Q8—182no—
124C2×C4⋊C4—92no—
125C2×C4⋊C4—182no—
126C2×C22⋊C4—182no—
127#107—94no—
128#103—98no—
129C23×C3—31no—
130C23×C3—31no—
131C23×C3—32no—
132C23×C3Dic1212yescomplemented
133C23×C3C2×D1211yescharacteristic
134C2×A4Dic1216yescomplemented
135C2×A4C2×D1213yes—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—31no—
140C2×C3×C4—31no—
141C2×C3×C4—31no—
142C2×C3×C4—31no—
143C2×C3×C4—43no—
144C2×C3×C4—61no—
145C2×C3×C4C2×S411yescharacteristic
146C2×Dic3—64no—
147C2×Dic3—64no—
148C2×Dic3—122no—
149C2×Dic3—124no—
150C2×Dic3—122no—
151C2×Dic3—246no—
152Dic6—64no—
153Dic6—64no—
154Dic6—1212no—
155Dic6—122no—
156Dic6—122no—
157Dic6—246no—
158C3×C8—32no—
159C3×C8—46no—
160C3×C8C2×S412yes—
161C2×C32—42no—
162C2×C32—41no—
163C24C4⋊(C3⋊D3)11yescharacteristic
164C2×Q8—94no—
165C2×Q8—182no—
166C2×Q8—182no—
167C2×Q8—182no—
168C2×Q8—182no—
169C2×Q8—182no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—31no—
173C22×C4—31no—
174C22×C4—182no—
175C22×C4—182no—
176C22×C4C4⋊(C3⋊D3)11yescharacteristic
177C22×C4C22×C3⋊D311yescharacteristic
178Q16—184no—
179Q16—184no—
180C2×C8—31no—
181C2×C8—32no—
182C2×C8—32no—
183C2×C8—32no—
184C2×C8—61no—
185C2×C8C3⋊S411yescharacteristic
186C4⋊C4—94no—
187C4⋊C4—182no—
188C4⋊C4—184no—
189C4⋊C4—184no—
190C22⋊C4—184no—
191C22⋊C4—184no—
192C22×C3—32no—
193C22×C3—31no—
194C22×C3—32no—
195C22×C3—32no—
196C22×C3—31no—
197C22×C3—31no—
198C22×C3—43no—
199C22×C3—61no—
200C22×C3C2×Dic1211yescharacteristic, complemented
201C22×C3C4⋊S411yescharacteristic
202A4C2×Dic1213yescomplemented
203C3×C4—31no—
204C3×C4—31no—
205C3×C4—43no—
206C3×C4—43no—
207C3×C4C4⋊S411yescharacteristic
208C3×C4C22×S411yescharacteristic
209Dic3—124no—
210Dic3—124no—
211Dic3—2412no—
212C32—41noSylow
213C23—31no—
214C23—31no—
215C23—32no—
216C23#374612yescomplemented
217C23C2×C4⋊(C3⋊D3)11yescharacteristic
218Q8—184no—
219Q8—184no—
220Q8—362no—
221Q8—362no—
222C2×C4—31no—
223C2×C4—31no—
224C2×C4—31no—
225C2×C4—31no—
226C2×C4—31no—
227C2×C4—31no—
228C2×C4—31no—
229C2×C4—61no—
230C2×C4—184no—
231C2×C4—184no—
232C2×C4—362no—
233C2×C4—364no—
234C2×C4—362no—
235C2×C4C2×C3⋊S411yescharacteristic
236C8—32no—
237C8C2×C3⋊S412yes—
238C2×C3—31no—
239C2×C3—31no—
240C2×C3—32no—
241C2×C3—46no—
242C2×C3—43no—
243C2×C3#539812yescomplemented
244C2×C3C2×C4⋊S411yescharacteristic
245C22—32no—
246C22—31no—
247C22—32no—
248C22—32no—
249C22—31no—
250C22—31no—
251C22—61no—
252C22C2×#374611yescharacteristic, complemented
253C22C4⋊(C3⋊S4)11yescharacteristic
254C4—31no—
255C4—31no—
256C4—364no—
257C4—364no—
258C4C4⋊(C3⋊S4)11yescharacteristic
259C4C22×C3⋊S411yescharacteristic
260C3—43no—
261C3C2×#539811yescharacteristic, complemented
262C2—31no—
263C2—31no—
264C2—32no—
265C2#1059363212yesdirect product factor
266C2C2×C4⋊(C3⋊S4)11yescharacteristic
subgroupG/H
centerC22C4⋊(C3⋊S4)
commutator, cosocleC3×C4×A4C23
FrattiniC4C22×C3⋊S4
FittingC23×C3×C8D3
socleC24×C3D12
prime radicalC22×C3×A4D4
hypercenterC2×C8C3⋊S4
hypocenterC3×A4C2×Q16
LCSG ▷ C3×C4×A4 ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
3. #10593632C2direct (N × H)
55. C2×C3×A4Q16semidirect
106. C3×A4C2×Q16semidirect
132. C23×C3Dic12semidirect
134. C2×A4Dic12semidirect
200. C22×C3C2×Dic12semidirect
202. A4C2×Dic12semidirect
216. C23#3746semidirect
243. C2×C3#5398semidirect
252. C22C2×#3746semidirect
261. C3C2×#5398semidirect
265. C2#10593632direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642592
C2×C3×C8×A42
#105936322
C2×#53983
C2×#51163
C2×#37464