Finite Group Databasebeta

← #11790215

Subgroups — #11790215

Order 1152.

553 conjugacy classes of subgroups.

The subgroup lattice has 289 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#68861—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#63576—22no—
16#63574C414yescomplemented
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⋊Dic3D411yescharacteristic
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3×Dic3—22no—
29C22×C3×Dic3—22no—
30C2×C32×C8—21no—
31C2×C32×C8—21no—
32C2×C32×C8Q812yes—
33C4×C3⋊Dic3—21no—
34C4×C3⋊Dic3—21no—
35C2×C3⋊(C3⋊C8)C2×C412yes—
36C2×C3⋊(C3⋊C8)D412yes—
37C2×C3⋊(C3⋊C8)Q812yes—
38C3×C4⋊Dic3—22no—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3C2×C414yes—
42Dic3⋊Dic3—44no—
43#1944—91noSylow
44C22×C3×C8—21no—
45C22×C3×C8C2×D312yes—
46C2×C3×C4⋊C4—32no—
47C2×C3×C4⋊C4—32no—
48C2×C4⋊Dic3—62no—
49C2×C4⋊Dic3C2×D312yes—
50C2×C4⋊Dic3C2×D312yes—
51C2×Dic3⋊C4—62no—
52C2×C4×Dic3—32no—
53C2×C4×Dic3—61no—
54C22×C3⋊C8—32no—
55C22×C3⋊C8—61no—
56C3⋊#95—62no—
57C3⋊#95—62no—
58#815—64no—
59#815—64no—
60#808—38no—
61#807—64no—
62C23×C32C2×D411yescharacteristic
63C2×C32×C4C22×C411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4C2×Q811yescharacteristic
66C2×C32×C4C2×Q811yescharacteristic
67C2×C32×C4#4111yescharacteristic
68C2×C32×C4#4111yescharacteristic
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—22no—
73C2×C3×Dic3—24no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76C2×C3×Dic3—42no—
77C2×C3×Dic3—42no—
78C2×C3×Dic3—42no—
79C32×C8—22no—
80C3⋊(C3⋊C8)C4⋊C414yescomplemented
81C2×#107—91no—
82C2×#106—91no—
83C2×#97—91no—
84#389—92no—
85#340—32no—
86C22×C3×C4—21no—
87C22×C3×C4—62no—
88C22×C3×C4—62no—
89C22×C3×C4C22×D312yes—
90C22×Dic3—22no—
91C22×Dic3—22no—
92C22×Dic3—32no—
93C22×Dic3—32no—
94C22×Dic3—61no—
95C22×Dic3—61no—
96C2×C3×C8—22no—
97C2×C3×C8—22no—
98C2×C3×C8—22no—
99C2×C3×C8—22no—
100C2×C3×C8—22no—
101C2×C3×C8Dic614yes—
102C3×C4⋊C4—34no—
103C3×C4⋊C4—62no—
104C3×C4⋊C4—62no—
105C3×C4⋊C4—62no—
106C4⋊Dic3—22no—
107C4⋊Dic3—22no—
108C4⋊Dic3—22no—
109C4⋊Dic3—124no—
110C4⋊Dic3C4×D314yes—
111Dic3⋊C4—124no—
112C4×Dic3—62no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116C2×C3⋊C8—34no—
117C2×C3⋊C8—34no—
118C2×C3⋊C8—34no—
119C2×C3⋊C8—62no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—62no—
122C22×C32C4×D411yescharacteristic
123C22×C32#12111yescharacteristic
124C22×C32C4⋊Q811yescharacteristic
125C22×C32AGL(1,ℤ/8)12yes—
126C22×C32#13712yes—
127C32×C4C2×C4⋊C411yescharacteristic
128C32×C4C4×Q811yescharacteristic
129C32×C4C22⋊Q811yescharacteristic
130C32×C4#12511yescharacteristic
131C3⋊Dic3—41no—
132C3⋊Dic3—41no—
133C3×Dic3—44no—
134C3×Dic3—82no—
135C22×C8—91no—
136C22×C8D3211yescharacteristic
137C2×C4⋊C4—32no—
138C2×C4⋊C4—32no—
139C2×C4⋊C4—182no—
140C2×C42—91no—
141#107—182no—
142#106—94no—
143#97—182no—
144#95—182no—
145C23×C3—21no—
146C23×C3D3×D412yes—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—64no—
154C2×C3×C4—122no—
155C2×C3×C4—122no—
156C2×C3×C4—122no—
157C2×C3×C4—122no—
158C2×C3×C4—122no—
159C2×C3×C4C2×Dic612yes—
160C2×C3×C4C2×C4×D312yes—
161C2×C3×C4#23512yes—
162C2×C3×C4D3×D412yes—
163C2×C3×C4#23712yes—
164C2×C3×C4D3×Q812yes—
165C2×Dic3—24no—
166C2×Dic3—42no—
167C2×Dic3—42no—
168C2×Dic3—42no—
169C2×Dic3—42no—
170C2×Dic3—42no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—62no—
179C2×Dic3—122no—
180C2×Dic3—122no—
181C3×C8—24no—
182C3×C8—24no—
183C3⋊C8—38no—
184C3⋊C8—64no—
185C2×C32#38911yescharacteristic
186C2×C32#44012yes—
187C2×C32#46911yescharacteristic
188C2×C32#47011yescharacteristic
189C2×C32#50112yes—
190C22×C4—62no—
191C22×C4—62no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4C2×D3211yescharacteristic
195C2×C8—21no—
196C2×C8—21no—
197C2×C8—92no—
198C2×C8—92no—
199C2×C8—92no—
200C2×C8#62712yes—
201C4⋊C4—34no—
202C4⋊C4—62no—
203C4⋊C4—62no—
204C4⋊C4—62no—
205C4⋊C4—364no—
206C42—181no—
207C42—181no—
208C22×C3—22no—
209C22×C3—22no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3#67⋊C412yes—
214C22×C3#88412yes—
215C22×C3#88812yes—
216C22×C3#91112yes—
217C22×C3#91412yes—
218C22×C3#91512yes—
219C22×C3#91812yes—
220C3×C4—21no—
221C3×C4—21no—
222C3×C4—21no—
223C3×C4—21no—
224C3×C4—124no—
225C3×C4—242no—
226C3×C4C4×Dic612yes—
227C3×C4#87812yes—
228C3×C4#88912yes—
229C3×C4D3×C4⋊C412yes—
230Dic3—44no—
231Dic3—82no—
232Dic3—122no—
233Dic3—122no—
234Dic3—122no—
235Dic3—122no—
236C32#194411yescharacteristic, complemented, Sylow
237C23#380211yescharacteristic
238C2×C4—64no—
239C2×C4—122no—
240C2×C4—122no—
241C2×C4—122no—
242C2×C4—122no—
243C2×C4—122no—
244C2×C4—182no—
245C2×C4—182no—
246C2×C4—181no—
247C2×C4—181no—
248C2×C4#379711yescharacteristic
249C2×C4#379811yescharacteristic
250C2×C4C4×D3211yescharacteristic
251C2×C4#380511yescharacteristic
252C2×C4C2×#62711yescharacteristic
253C2×C4#381111yescharacteristic
254C8—22no—
255C8—94no—
256C2×C3—22no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—22no—
261C2×C3#464712yes—
262C2×C3#475712yes—
263C2×C3#478212yes—
264C2×C3#481612yes—
265C2×C3#481712yes—
266C2×C3#485612yes—
267C2×C3#487612yes—
268C22#6379812yes—
269C22#6381112yes—
270C22#6390211yescharacteristic
271C22#6391211yescharacteristic
272C22#6391911yescharacteristic
273C4—124no—
274C4—242no—
275C4—361no—
276C4—361no—
277C4#6387011yescharacteristic
278C4#6388311yescharacteristic
279C4C4×#62711yescharacteristic
280C4#6398211yescharacteristic
281C3—21no—
282C3#6886112yescomplemented
283C2#1059074312yes—
284C2#1059084011yescharacteristic
285C2#1059085611yescharacteristic
286C2#1059090312yes—
287C2#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#1944
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
16. #63574C4semidirect
80. C3⋊(C3⋊C8)C4⋊C4semidirect
236. C32#1944semidirect
282. C3#68861semidirect

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
#688613