Finite Group Databasebeta

← #11790140

Subgroups — #11790140

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 307 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C3×#4928C212yesmaximal
3C2×#63576C211yesmaximal, characteristic
4C2×#63576C211yesmaximal, characteristic
5#10589163C212yesmaximal
6#69619—32nomaximal
7C2×C32×C42C2211yescharacteristic
8C22×C3⋊(C3⋊C8)C2211yescharacteristic
9C22×C3⋊(C3⋊C8)C2211yescharacteristic
10C2×C3×C4⋊Dic3C2212yes—
11C2×C3×C4⋊Dic3C2212yes—
12C2×C3×Dic3⋊C4—22no—
13C4×C3⋊(C3⋊C8)—22no—
14C3×C3⋊#95—22no—
15#63576—22no—
16#63576C414yescomplemented
17C3×#389—32no—
18C2×#807—32no—
19C2×#807—32no—
20#4928D312yes—
21C2×C4×C3⋊C8—32no—
22C2×C4×C3⋊C8—61no—
23#4529—32no—
24#4529—32no—
25C22×C32×C4D411yescharacteristic
26C22×C32×C4D411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C22×C3×Dic3—22no—
29C22×C3×Dic3—22no—
30C32×C42—21no—
31C32×C42—21no—
32C2×C3⋊(C3⋊C8)—21no—
33C2×C3⋊(C3⋊C8)—21no—
34C2×C3⋊(C3⋊C8)C2×C412yes—
35C2×C3⋊(C3⋊C8)D412yes—
36C2×C3⋊(C3⋊C8)Q812yes—
37C2×C3⋊(C3⋊C8)Q812yes—
38C3×C4⋊Dic3—22no—
39C3×C4⋊Dic3—22no—
40C3×C4⋊Dic3—22no—
41C3×C4⋊Dic3C2×C414yes—
42C3×Dic3⋊C4—44no—
43#1942—91noSylow
44C2×C3×C4⋊C4—32no—
45C2×C3×C4⋊C4—32no—
46C2×C3×C4⋊C4—62no—
47C2×C3×C42—21no—
48C2×C3×C42C2×D312yes—
49C2×C4⋊Dic3C2×D312yes—
50C2×C4⋊Dic3C2×D312yes—
51C2×Dic3⋊C4—22no—
52C22×C3⋊C8—32no—
53C22×C3⋊C8—32no—
54C22×C3⋊C8—61no—
55C22×C3⋊C8—61no—
56C3×#95—62no—
57C3⋊#95—22no—
58#807—38no—
59#807—64no—
60C4×C3⋊C8—64no—
61C4×C3⋊C8—64no—
62C23×C32C2×D411yescharacteristic
63C2×C32×C4—21no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4—21no—
67C2×C32×C4D812yes—
68C2×C32×C4Q1612yes—
69C2×C32×C4C22×C411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×Q811yescharacteristic
72C2×C32×C4C2×Q811yescharacteristic
73C2×C32×C4#4111yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C3×Dic3—24no—
76C2×C3×Dic3—42no—
77C2×C3×Dic3—42no—
78C2×C3×Dic3—42no—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C3⋊(C3⋊C8)—22no—
82C3⋊(C3⋊C8)C4⋊C414yescomplemented
83C2×#107—91no—
84C2×#107—91no—
85C2×C4×C8—91no—
86#389—32no—
87#340—92no—
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4—21no—
91C22×C3×C4—62no—
92C22×C3×C4—62no—
93C22×C3×C4#6712yes—
94C22×C3×C4#6712yes—
95C22×C3×C4C22×D312yes—
96C22×Dic3—22no—
97C22×Dic3—22no—
98C3×C4⋊C4—34no—
99C3×C4⋊C4—62no—
100C3×C4⋊C4—62no—
101C3×C4⋊C4—62no—
102C3×C4⋊C4—124no—
103C3×C42—22no—
104C3×C42—22no—
105C3×C42—22no—
106C3×C42—22no—
107C4⋊Dic3—22no—
108C4⋊Dic3—22no—
109C4⋊Dic3—22no—
110C4⋊Dic3C4×D314yes—
111Dic3⋊C4—44no—
112C2×C3⋊C8—34no—
113C2×C3⋊C8—34no—
114C2×C3⋊C8—34no—
115C2×C3⋊C8—34no—
116C2×C3⋊C8—62no—
117C2×C3⋊C8—62no—
118C2×C3⋊C8—62no—
119C2×C3⋊C8—62no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8—62no—
122C2×C3⋊C8—62no—
123C2×C3⋊C8—62no—
124C22×C32C4×D411yescharacteristic
125C22×C32#12111yescharacteristic
126C22×C32C4⋊Q811yescharacteristic
127C22×C32C2×D811yescharacteristic
128C22×C32C2×Q1611yescharacteristic
129C22×C32#13511yescharacteristic
130C22×C32#13511yescharacteristic
131C32×C4—22no—
132C32×C4—22no—
133C32×C4C2×C4⋊C411yescharacteristic
134C32×C4C4×Q811yescharacteristic
135C32×C4C22⋊Q811yescharacteristic
136C32×C4#12511yescharacteristic
137C3×Dic3—44no—
138C3×Dic3—82no—
139C22×C8—91no—
140C22×C8—91no—
141C2×C4⋊C4—32no—
142C2×C4⋊C4—32no—
143C2×C4⋊C4—62no—
144C2×C42D3211yescharacteristic
145#107—94no—
146#107—182no—
147C4×C8—182no—
148#95—62no—
149C23×C3—21no—
150C23×C3C2×#6712yes—
151C2×C3×C4—22no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—64no—
168C2×C3×C4—122no—
169C2×C3×C4—122no—
170C2×C3×C4—122no—
171C2×C3×C4—122no—
172C2×C3×C4—122no—
173C2×C3×C4#21314yes—
174C2×C3×C4#21614yes—
175C2×C3×C4C2×C4×D312yes—
176C2×C3×C4#23512yes—
177C2×C3×C4D3×D412yes—
178C2×C3×C4#23712yes—
179C2×C3×C4D3×Q812yes—
180C2×C3×C4D3×Q812yes—
181C2×Dic3—24no—
182C2×Dic3—42no—
183C2×Dic3—42no—
184C2×Dic3—42no—
185C2×Dic3—42no—
186C2×Dic3—42no—
187C3⋊C8—38no—
188C3⋊C8—64no—
189C3⋊C8—64no—
190C3⋊C8—64no—
191C2×C32#38911yescharacteristic
192C2×C32C4×D811yescharacteristic
193C2×C32C4×Q1611yescharacteristic
194C2×C32#46611yescharacteristic
195C2×C32#46711yescharacteristic
196C2×C32#49911yescharacteristic
197C2×C32#50011yescharacteristic
198C22×C4—62no—
199C22×C4—62no—
200C22×C4#62511yescharacteristic
201C22×C4#62511yescharacteristic
202C22×C4C2×D3211yescharacteristic
203C2×C8—92no—
204C2×C8—92no—
205C2×C8—92no—
206C2×C8—92no—
207C2×C8—181no—
208C2×C8—181no—
209C4⋊C4—34no—
210C4⋊C4—62no—
211C4⋊C4—62no—
212C4⋊C4—62no—
213C4⋊C4—124no—
214C42—21no—
215C42—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3C4×#6712yes—
224C22×C3C2×#21312yes—
225C22×C3#93912yes—
226C22×C3C2×#21612yes—
227C22×C3#94412yes—
228C22×C3#95012yes—
229C22×C3#95012yes—
230C3×C4—24no—
231C3×C4—24no—
232C3×C4—24no—
233C3×C4—24no—
234C3×C4—21no—
235C3×C4—21no—
236C3×C4—21no—
237C3×C4—21no—
238C3×C4—124no—
239C3×C4—242no—
240C3×C4#88712yes—
241C3×C4#88912yes—
242C3×C4D3×C4⋊C412yes—
243C3×C4#89612yes—
244Dic3—44no—
245Dic3—82no—
246C32#194211yescharacteristic, complemented, Sylow
247C23C2×#62511yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—64no—
253C2×C4—122no—
254C2×C4—122no—
255C2×C4—122no—
256C2×C4—122no—
257C2×C4—122no—
258C2×C4#371312yes—
259C2×C4#371812yes—
260C2×C4#379711yescharacteristic
261C2×C4#379711yescharacteristic
262C2×C4#379811yescharacteristic
263C2×C4C4×D3211yescharacteristic
264C2×C4#380511yescharacteristic
265C2×C4#381111yescharacteristic
266C8—94no—
267C8—182no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3#497612yes—
276C2×C3C4×#21312yes—
277C2×C3C4×#21612yes—
278C2×C3#503812yes—
279C2×C3#505112yes—
280C2×C3#506512yes—
281C2×C3#507812yes—
282C22C2×#371311yescharacteristic
283C22#6382211yescharacteristic
284C22#6382211yescharacteristic
285C22C2×#371811yescharacteristic
286C22#6387311yescharacteristic
287C22C4×#62511yescharacteristic
288C22#6398011yescharacteristic
289C4—22no—
290C4—22no—
291C4—124no—
292C4—242no—
293C4#6383811yescharacteristic
294C4#6386511yescharacteristic
295C4#6387011yescharacteristic
296C4#6388311yescharacteristic
297C3—21no—
298C3#6961912yescomplemented
299C2#1059031211yescharacteristic
300C2#1059031411yescharacteristic
301C2C4×#371311yescharacteristic
302C2C4×#371811yescharacteristic
303C2#1059116611yescharacteristic
304C2#1059118811yescharacteristic
305C2#1059133711yescharacteristic
subgroupG/H
centerC23C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1942
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
16. #63576C4semidirect
82. C3⋊(C3⋊C8)C4⋊C4semidirect
246. C32#1942semidirect
298. C3#69619semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C3⋊(C3⋊C8)2
C3×#49282
C2×#635762
#105891632
#696193