Finite Group Databasebeta

← #11790182

Subgroups — #11790182

Order 1152.

553 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63642C211yesmaximal, characteristic
2#10591357C212yesmaximal
3C2×#63576C211yesmaximal, characteristic
4C2×#63574C211yesmaximal, characteristic
5C3×#4551C212yesmaximal
6#68860—32nomaximal
7C22×C32×C8C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×C4⋊Dic3C2212yes—
12C2×Dic3⋊Dic3—22no—
13#63642—22no—
14#63579—22no—
15#63576C414yescomplemented
16#63574—22no—
17C2×#815—32no—
18C2×#815—61no—
19#4984—32no—
20#4972—32no—
21C2×#808—32no—
22C2×#807—32no—
23C3×#340—32no—
24#4551D312yes—
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3D412yes—
27C22×C3×Dic3—22no—
28C22×C3×Dic3—22no—
29C2×C32×C8—21no—
30C2×C32×C8—21no—
31C2×C32×C8Q812yes—
32C4×C3⋊Dic3—21no—
33C4×C3⋊Dic3—21no—
34C2×C3⋊(C3⋊C8)C2×C412yes—
35C2×C3⋊(C3⋊C8)D412yes—
36C2×C3⋊(C3⋊C8)Q812yes—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3—22no—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3C2×C414yes—
41Dic3⋊Dic3—44no—
42#1943—91noSylow
43C22×C3×C8—21no—
44C22×C3×C8C2×D312yes—
45C2×C3×C4⋊C4—32no—
46C2×C3×C4⋊C4—32no—
47C2×C4⋊Dic3—62no—
48C2×C4⋊Dic3C2×D312yes—
49C2×C4⋊Dic3C2×D312yes—
50C2×Dic3⋊C4—62no—
51C2×C4×Dic3—32no—
52C2×C4×Dic3—61no—
53C22×C3⋊C8—32no—
54C22×C3⋊C8—61no—
55C3⋊#95—62no—
56C3⋊#95—62no—
57#815—64no—
58#815—64no—
59#808—64no—
60#807—38no—
61C23×C32C2×D411yescharacteristic
62C2×C32×C4C22×C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4C2×Q811yescharacteristic
65C2×C32×C4C2×Q811yescharacteristic
66C2×C32×C4#4111yescharacteristic
67C2×C32×C4#4111yescharacteristic
68C2×C3⋊Dic3—22no—
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—22no—
71C2×C3×Dic3—24no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—42no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—42no—
77C32×C8—22no—
78C3⋊(C3⋊C8)C4⋊C414yescomplemented
79C2×#107—91no—
80C2×#106—91no—
81C2×#97—91no—
82#389—92no—
83#340—32no—
84C22×C3×C4—21no—
85C22×C3×C4—62no—
86C22×C3×C4—62no—
87C22×C3×C4C22×D312yes—
88C22×Dic3—22no—
89C22×Dic3—22no—
90C22×Dic3—32no—
91C22×Dic3—32no—
92C22×Dic3—62no—
93C2×C3×C8—22no—
94C2×C3×C8—22no—
95C2×C3×C8—22no—
96C2×C3×C8—22no—
97C2×C3×C8—22no—
98C2×C3×C8Dic614yes—
99C3×C4⋊C4—34no—
100C3×C4⋊C4—62no—
101C3×C4⋊C4—62no—
102C3×C4⋊C4—62no—
103C4⋊Dic3—22no—
104C4⋊Dic3—22no—
105C4⋊Dic3—22no—
106C4⋊Dic3—124no—
107C4⋊Dic3C4×D314yes—
108Dic3⋊C4—124no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C2×C3⋊C8—34no—
114C2×C3⋊C8—34no—
115C2×C3⋊C8—34no—
116C2×C3⋊C8—62no—
117C2×C3⋊C8—62no—
118C2×C3⋊C8—62no—
119C22×C32C4×D411yescharacteristic
120C22×C32#12111yescharacteristic
121C22×C32C4⋊Q811yescharacteristic
122C22×C32AGL(1,ℤ/8)12yes—
123C22×C32#13712yes—
124C32×C4C2×C4⋊C411yescharacteristic
125C32×C4C4×Q811yescharacteristic
126C32×C4C22⋊Q811yescharacteristic
127C32×C4#12511yescharacteristic
128C3⋊Dic3—42no—
129C3×Dic3—44no—
130C3×Dic3—82no—
131C22×C8—91no—
132C22×C8D3211yescharacteristic
133C2×C4⋊C4—32no—
134C2×C4⋊C4—32no—
135C2×C4⋊C4—182no—
136C2×C42—91no—
137#107—94no—
138#106—182no—
139#97—182no—
140#95—182no—
141C23×C3—21no—
142C23×C3D3×D412yes—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—64no—
150C2×C3×C4—122no—
151C2×C3×C4—122no—
152C2×C3×C4—122no—
153C2×C3×C4—122no—
154C2×C3×C4—122no—
155C2×C3×C4C2×Dic612yes—
156C2×C3×C4C2×C4×D312yes—
157C2×C3×C4#23512yes—
158C2×C3×C4D3×D412yes—
159C2×C3×C4#23712yes—
160C2×C3×C4D3×Q812yes—
161C2×Dic3—24no—
162C2×Dic3—42no—
163C2×Dic3—42no—
164C2×Dic3—42no—
165C2×Dic3—42no—
166C2×Dic3—42no—
167C2×Dic3—64no—
168C2×Dic3—62no—
169C2×Dic3—62no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—122no—
175C2×Dic3—122no—
176C3×C8—24no—
177C3×C8—24no—
178C3⋊C8—38no—
179C3⋊C8—64no—
180C2×C32#38911yescharacteristic
181C2×C32#44111yescharacteristic
182C2×C32#44211yescharacteristic
183C2×C32#46812yes—
184C2×C32#50112yes—
185C22×C4—62no—
186C22×C4—62no—
187C22×C4—92no—
188C22×C4C2×D3211yescharacteristic
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—92no—
192C2×C8—92no—
193C2×C8—92no—
194C2×C8#62712yes—
195C4⋊C4—34no—
196C4⋊C4—62no—
197C4⋊C4—62no—
198C4⋊C4—62no—
199C4⋊C4—364no—
200C42—181no—
201C42—181no—
202C22×C3—22no—
203C22×C3—22no—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3#67⋊C412yes—
208C22×C3#88412yes—
209C22×C3#88812yes—
210C22×C3#91112yes—
211C22×C3#91412yes—
212C22×C3#91512yes—
213C22×C3#91812yes—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—124no—
219C3×C4—242no—
220C3×C4C4×Dic612yes—
221C3×C4#87812yes—
222C3×C4#88912yes—
223C3×C4D3×C4⋊C412yes—
224Dic3—44no—
225Dic3—82no—
226Dic3—124no—
227Dic3—122no—
228Dic3—122no—
229C32#194311yescharacteristic, complemented, Sylow
230C23#380211yescharacteristic
231C2×C4—64no—
232C2×C4—122no—
233C2×C4—122no—
234C2×C4—122no—
235C2×C4—122no—
236C2×C4—122no—
237C2×C4—182no—
238C2×C4—182no—
239C2×C4—182no—
240C2×C4#379711yescharacteristic
241C2×C4#379811yescharacteristic
242C2×C4C4×D3211yescharacteristic
243C2×C4#380511yescharacteristic
244C2×C4C2×#62711yescharacteristic
245C2×C4#381111yescharacteristic
246C8—22no—
247C8—94no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—22no—
252C2×C3—22no—
253C2×C3#464712yes—
254C2×C3#478012yes—
255C2×C3#478512yes—
256C2×C3#478912yes—
257C2×C3#481212yes—
258C2×C3#485612yes—
259C2×C3#487612yes—
260C22#6379812yes—
261C22#6381112yes—
262C22#6390211yescharacteristic
263C22#6391211yescharacteristic
264C22#6391911yescharacteristic
265C4—124no—
266C4—242no—
267C4—362no—
268C4#6387011yescharacteristic
269C4#6388311yescharacteristic
270C4C4×#62711yescharacteristic
271C4#6398211yescharacteristic
272C3—21no—
273C3#6886012yescomplemented
274C2#1059074111yescharacteristic
275C2#1059079111yescharacteristic
276C2#1059084212yes—
277C2#1059090312yes—
278C2#1059132811yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1943
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
15. #63576C4semidirect
78. C3⋊(C3⋊C8)C4⋊C4semidirect
229. C32#1943semidirect
273. C3#68860semidirect

Maximal subgroups

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

subgroupindex
C2×#636422
#105913572
C2×#635762
C2×#635742
C3×#45512
#688603