Finite Group Databasebeta

← C2×#10590904 #11873616

Subgroups — C2×#10590904 #11873616

Order 1152.

841 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 841 conjugacy classes of subgroups — too many to draw. Only its 212 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×#63873C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic
3C2×#63642C211yesmaximal, characteristic
4C2×C3×#816C212yesmaximal
5C2×#63565C212yesmaximal
6#10590904C218yesmaximal, direct product factor
7C2×#4797—32nomaximal
8C22×C3×Dic6C2212yes—
9C22×C32×C8C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C2×#3724—22no—
14C2×Dic3⋊Dic3—22no—
15#63873—22no—
16#63873C2214yes—
17#63872—22no—
18#63872C2214yes—
19#63642C2214yes—
20C3×#816C2218yes—
21#63565C2218yes—
22C2×#944—32no—
23C2×#890—32no—
24C2×C3×#103—32no—
25C2×#835—32no—
26C2×#816D312yes—
27C2×#815—32no—
28C2×#815—61no—
29C2×#810—32no—
30#4797—316no—
31C22×C32×C4C2311yescharacteristic
32C22×C3⋊Dic3D412yes—
33C22×C3×Dic3—22no—
34C22×C3×Dic3—22no—
35C2×C3×Dic6—24no—
36C2×C3×Dic6—24no—
37C2×C3×Dic6—22no—
38C2×C3×Dic6C2314yes—
39C2×C32×C8—22no—
40C2×C32×C8C2312yes—
41C4×C3⋊Dic3D412yes—
42C4×C3⋊Dic3C2312yes—
43C2×C3⋊(C3⋊C8)—22no—
44C2×C3⋊(C3⋊C8)C2312yes—
45C3×C4⋊Dic3—22no—
46C3×C4⋊Dic3C2314yes—
47#3724—28no—
48Dic3⋊Dic3—28no—
49C2×#491—91noSylow
50C22×C3×Q8—32no—
51C22×Dic6C2×D312yes—
52C22×C3×C8—21no—
53C22×C3×C8C2×D312yes—
54C2×C3×C4⋊C4—32no—
55#944—38no—
56#944—64no—
57C2×C4⋊Dic3—62no—
58C2×C4⋊Dic3C2×D312yes—
59C2×Dic3⋊C4—62no—
60C2×Dic3⋊C4—62no—
61C2×Dic3⋊C4—62no—
62C2×C4×Dic3—32no—
63C2×C4×Dic3—61no—
64C22×C3⋊C8—32no—
65C22×C3⋊C8—61no—
66#890—38no—
67#890—64no—
68C3×#103—38no—
69#835—38no—
70#816C2×D318yes—
71#815—38no—
72#815—64no—
73#810—38no—
74C23×C32C2×D411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C32×C4#4112yes—
77C2×C32×C4#4112yes—
78C2×C32×C4C2411yescharacteristic
79C2×C3⋊Dic3—24no—
80C2×C3⋊Dic3C2×D414yes—
81C2×C3×Dic3—24no—
82C2×C3×Dic3—24no—
83C2×C3×Dic3—44no—
84C2×C3×Dic3—44no—
85C3×Dic6—24no—
86C3×Dic6—24no—
87C3×Dic6—44no—
88C32×C8—22no—
89C3⋊(C3⋊C8)—22no—
90C2×C4⋊Q8—91no—
91C2×#125—91no—
92#491—98no—
93C2×#103—32no—
94C2×#103—92no—
95C2×#97—91no—
96C2×C3×Q8—34no—
97C2×C3×Q8—62no—
98C2×C3×Q8—64no—
99C2×C3×Q8—64no—
100C22×C3×C4—21no—
101C22×C3×C4—62no—
102C22×C3×C4—62no—
103C22×C3×C4C22×D312yes—
104C22×Dic3—22no—
105C22×Dic3—22no—
106C22×Dic3—32no—
107C22×Dic3—32no—
108C22×Dic3—62no—
109C2×Dic6—24no—
110C2×Dic6—24no—
111C2×Dic6—22no—
112C2×Dic6C22×D314yes—
113C2×C3×C8—24no—
114C2×C3×C8—24no—
115C2×C3×C8—22no—
116C2×C3×C8C22×D314yes—
117C3×C4⋊C4—34no—
118C3×C4⋊C4—62no—
119C4⋊Dic3—22no—
120C4⋊Dic3—68no—
121C4⋊Dic3C22×D314yes—
122Dic3⋊C4—68no—
123Dic3⋊C4—68no—
124Dic3⋊C4—68no—
125C4×Dic3—34no—
126C4×Dic3—34no—
127C4×Dic3—62no—
128C4×Dic3—62no—
129C2×C3⋊C8—34no—
130C2×C3⋊C8—62no—
131C2×C3⋊C8—64no—
132C2×C3⋊C8—64no—
133C22×C32#12412yes—
134C22×C32#13714yes—
135C22×C32C22×D411yescharacteristic
136C32×C4#12412yes—
137C32×C4C2×#4111yescharacteristic
138C32×C4C2×#4111yescharacteristic
139C3⋊Dic3—24no—
140C3×Dic3—44no—
141C3×Dic3—44no—
142C22×Q8—32no—
143C22×C8—91no—
144C22×C8D3211yescharacteristic
145C4⋊Q8—94no—
146C4⋊Q8—182no—
147#125—94no—
148#125—182no—
149C2×C4⋊C4—32no—
150C2×C4⋊C4—182no—
151C2×C4⋊C4—182no—
152C2×C42—91no—
153#103—38no—
154#103—98no—
155#97—94no—
156C23×C3—21no—
157C23×C3D3×D412yes—
158C3×Q8—64no—
159C3×Q8—64no—
160C3×Q8—124no—
161C2×C3×C4—21no—
162C2×C3×C4—22no—
163C2×C3×C4—21no—
164C2×C3×C4—22no—
165C2×C3×C4—64no—
166C2×C3×C4—64no—
167C2×C3×C4—124no—
168C2×C3×C4—124no—
169C2×C3×C4#23514yes—
170C2×C3×C4D3×D412yes—
171C2×C3×C4#23714yes—
172C2×C3×C4C23×D312yes—
173C2×Dic3—24no—
174C2×Dic3—24no—
175C2×Dic3—34no—
176C2×Dic3—34no—
177C2×Dic3—44no—
178C2×Dic3—44no—
179C2×Dic3—64no—
180C2×Dic3—64no—
181C2×Dic3—64no—
182C2×Dic3—124no—
183Dic6—24no—
184Dic6—24no—
185Dic6—44no—
186C3×C8—24no—
187C3×C8—24no—
188C3⋊C8—64no—
189C3⋊C8—64no—
190C2×C32#49114yescomplemented
191C2×C32C2×#12411yescharacteristic
192C2×C32C2×#13712yes—
193C2×Q8—34no—
194C2×Q8—62no—
195C2×Q8—64no—
196C2×Q8—64no—
197C22×C4—62no—
198C22×C4—62no—
199C22×C4—92no—
200C22×C4C2×D3211yescharacteristic
201C2×C8—22no—
202C2×C8—92no—
203C2×C8—182no—
204C2×C8C2×D3212yes—
205C4⋊C4—34no—
206C4⋊C4—62no—
207C4⋊C4—188no—
208C4⋊C4—188no—
209C42—92no—
210C42—92no—
211C22×C3—21no—
212C22×C3—24no—
213C22×C3—22no—
214C22×C3#88514yes—
215C22×C3#91514yes—
216C22×C3#91814yes—
217C22×C3C2×D3×D412yes—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—22no—
221C3×C4—124no—
222C3×C4—124no—
223C3×C4#88514yes—
224C3×C4C2×#23512yes—
225C3×C4C2×#23712yes—
226Dic3—44no—
227Dic3—44no—
228Dic3—64no—
229Dic3—64no—
230Dic3—124no—
231C32C2×#49111yescharacteristic, complemented, Sylow
232C23#380211yescharacteristic
233Q8—64no—
234Q8—64no—
235Q8—124no—
236C2×C4—64no—
237C2×C4—64no—
238C2×C4—94no—
239C2×C4—124no—
240C2×C4—124no—
241C2×C4—184no—
242C2×C4#379812yes—
243C2×C4#380211yescharacteristic
244C2×C4#380512yes—
245C2×C4C22×D3211yescharacteristic
246C8—22no—
247C8—182no—
248C2×C3—22no—
249C2×C3—24no—
250C2×C3—21no—
251C2×C3#479718yescomplemented
252C2×C3C2×#88512yes—
253C2×C3C2×#91512yes—
254C2×C3C2×#91812yes—
255C22#6381114yes—
256C22#6391512yes—
257C22C2×#380211yescharacteristic
258C4—124no—
259C4—124no—
260C4—184no—
261C4#6391512yes—
262C4C2×#379811yescharacteristic
263C4C2×#380511yescharacteristic
264C3—21no—
265C3C2×#479712yescomplemented
266C2#1059090414yesdirect product factor
267C2C2×#6381112yes—
268C2C2×#6391511yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32C2×#491
LCSG ▷ C2×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. #10590904C2direct (N × H)
190. C2×C32#491semidirect
231. C32C2×#491semidirect
251. C2×C3#4797semidirect
265. C3C2×#4797semidirect
266. C2#10590904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638732
C2×#638722
C2×#636422
C2×C3×#8162
C2×#635652
#105909042
C2×#47973