Finite Group Databasebeta

← #11786034

Subgroups — #11786034

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592674C211yesmaximal, characteristic
2#10591359C211yesmaximal, characteristic
3C2×#63553C211yesmaximal, characteristic
4C3×#4529C212yesmaximal
5#10589164C212yesmaximal
6#68847—32nomaximal
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
9C2×#3750—21no—
10C2×#3750—21no—
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C22×C3×C3⋊C8C2212yes—
14C2×#3724—21no—
15C2×#3724—21no—
16#63553C414yescomplemented
17C2×C8×Dic3—32no—
18#4975—32no—
19#4975—32no—
20#4975—61no—
21C3×#340—32no—
22#4551—32no—
23#4529—32no—
24#4529D312yes—
25C22×C32×C4—21no—
26C22×C32×C4C2311yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C22×C3×Dic3—22no—
31C32×C4⋊C4—22no—
32C4⋊(C3⋊Dic3)—22no—
33#3750—42no—
34#3750—42no—
35C4×C3⋊Dic3C2×C412yes—
36C4×C3⋊Dic3Q812yes—
37C3×C4⋊Dic3—22no—
38C3×C4⋊Dic3—22no—
39C2×C3×C3⋊C8—22no—
40C2×C3×C3⋊C8—22no—
41C2×C3×C3⋊C8C2×C414yes—
42#3724—42no—
43#3724—42no—
44#1834—91noSylow
45C22×C3×C8—32no—
46C2×C3×C4⋊C4—21no—
47C2×C3×C4⋊C4—32no—
48C2×C3×C4⋊C4C2×D312yes—
49C2×C4⋊Dic3—32no—
50C2×C4⋊Dic3—61no—
51C2×C4⋊Dic3C2×D312yes—
52C2×Dic3⋊C4—62no—
53C2×Dic3⋊C4—62no—
54C2×Dic3⋊C4—62no—
55C2×Dic3⋊C4—62no—
56C2×Dic3⋊C4—62no—
57C2×Dic3⋊C4—62no—
58C2×C4×Dic3—32no—
59C2×C4×Dic3—61no—
60C22×C3⋊C8C2×D312yes—
61C8×Dic3—38no—
62C23×C32C2×D411yescharacteristic
63C2×C32×C4—41no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4C22×C411yescharacteristic
67C2×C32×C4C2×Q811yescharacteristic
68C2×C32×C4#4112yes—
69C2×C32×C4#4112yes—
70C2×C3⋊Dic3—41no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3C4⋊C412yes—
74C2×C3⋊Dic3C4⋊C412yes—
75C2×C3⋊Dic3D812yes—
76C2×C3⋊Dic3SD1612yes—
77C2×C3⋊Dic3SD1612yes—
78C2×C3⋊Dic3Q1612yes—
79C2×C3×Dic3—42no—
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C3×C3⋊C8—24no—
83C2×C4×C8—91no—
84#384—91no—
85#384—91no—
86#340—32no—
87#340—92no—
88C22×C3×C4—22no—
89C22×C3×C4—22no—
90C22×C3×C4—21no—
91C22×C3×C4—62no—
92C22×C3×C4C22×D312yes—
93C22×Dic3—22no—
94C22×Dic3—32no—
95C22×Dic3—32no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C22×Dic3—62no—
99C22×Dic3—62no—
100C2×C3×C8—34no—
101C2×C3×C8—62no—
102C2×C3×C8—62no—
103C3×C4⋊C4—22no—
104C3×C4⋊C4—22no—
105C3×C4⋊C4—42no—
106C3×C4⋊C4—62no—
107C3×C4⋊C4—62no—
108C4⋊Dic3—22no—
109C4⋊Dic3—22no—
110C4⋊Dic3—62no—
111C4⋊Dic3—62no—
112C4⋊Dic3—122no—
113Dic3⋊C4—124no—
114Dic3⋊C4—124no—
115Dic3⋊C4—124no—
116Dic3⋊C4—124no—
117Dic3⋊C4—124no—
118Dic3⋊C4—124no—
119C4×Dic3—34no—
120C4×Dic3—34no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123C2×C3⋊C8—22no—
124C2×C3⋊C8—22no—
125C2×C3⋊C8C4×D314yes—
126C22×C32C2×C4⋊C411yescharacteristic
127C22×C32#12411yescharacteristic
128C22×C32#12411yescharacteristic
129C22×C32C2×D811yescharacteristic
130C22×C32C2×SD1611yescharacteristic
131C22×C32C2×SD1611yescharacteristic
132C22×C32C2×Q1611yescharacteristic
133C32×C4—81no—
134C32×C4#11712yes—
135C32×C4#12512yes—
136C3⋊Dic3—81no—
137C3⋊Dic3#10614yes—
138C3⋊Dic3#10714yes—
139C3×Dic3—82no—
140C22×C8—32no—
141C2×C4⋊C4—32no—
142C2×C4⋊C4—91no—
143C2×C4⋊C4—181no—
144C2×C4⋊C4—181no—
145C2×C4⋊C4—181no—
146C2×C4⋊C4—181no—
147C2×C4⋊C4D3211yescharacteristic
148C2×C42—91no—
149C4×C8—94no—
150C23×C3—21no—
151C23×C3D3×D412yes—
152C2×C3×C4—22no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—22no—
156C2×C3×C4—42no—
157C2×C3×C4—42no—
158C2×C3×C4—42no—
159C2×C3×C4—42no—
160C2×C3×C4—42no—
161C2×C3×C4—42no—
162C2×C3×C4—122no—
163C2×C3×C4—122no—
164C2×C3×C4—122no—
165C2×C3×C4C2×C4×D312yes—
166C2×C3×C4#23512yes—
167C2×C3×C4#23512yes—
168C2×C3×C4#23712yes—
169C2×C3×C4#23712yes—
170C2×C3×C4D3×Q812yes—
171C2×Dic3—34no—
172C2×Dic3—34no—
173C2×Dic3—34no—
174C2×Dic3—34no—
175C2×Dic3—34no—
176C2×Dic3—34no—
177C2×Dic3—42no—
178C2×Dic3—42no—
179C2×Dic3—42no—
180C2×Dic3—62no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—122no—
187C2×Dic3—122no—
188C2×Dic3—122no—
189C2×Dic3—122no—
190C2×Dic3—122no—
191C2×Dic3—122no—
192C3×C8—64no—
193C3⋊C8—24no—
194C2×C32#38211yescharacteristic
195C2×C32C2×#10611yescharacteristic
196C2×C32C2×#10711yescharacteristic
197C2×C32#48611yescharacteristic
198C2×C32#48611yescharacteristic
199C2×C32#48711yescharacteristic
200C2×C32#48711yescharacteristic
201C22×C4—21no—
202C22×C4—62no—
203C22×C4—91no—
204C22×C4—91no—
205C22×C4—181no—
206C22×C4C2×D3211yescharacteristic
207C2×C8—34no—
208C2×C8—62no—
209C2×C8—62no—
210C4⋊C4—22no—
211C4⋊C4—62no—
212C4⋊C4—62no—
213C4⋊C4—182no—
214C4⋊C4—362no—
215C4⋊C4—362no—
216C4⋊C4—362no—
217C4⋊C4—362no—
218C42—92no—
219C42—92no—
220C22×C3—21no—
221C22×C3—21no—
222C22×C3—21no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—21no—
227C22×C3#88512yes—
228C22×C3#88512yes—
229C22×C3D3×C4⋊C412yes—
230C22×C3D3×D812yes—
231C22×C3D3×SD1612yes—
232C22×C3D3×SD1612yes—
233C22×C3D3×Q1612yes—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—82no—
237C3×C4—82no—
238C3×C4—242no—
239C3×C4#87212yes—
240C3×C4#87712yes—
241C3×C4#88912yes—
242C3×C4#88912yes—
243Dic3—38no—
244Dic3—38no—
245Dic3—64no—
246Dic3—64no—
247Dic3—82no—
248Dic3—242no—
249Dic3—242no—
250C32#183411yescharacteristic, complemented, Sylow
251C23#381111yescharacteristic
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—92no—
256C2×C4—92no—
257C2×C4—92no—
258C2×C4—92no—
259C2×C4—92no—
260C2×C4—92no—
261C2×C4—122no—
262C2×C4—122no—
263C2×C4—122no—
264C2×C4—361no—
265C2×C4—361no—
266C2×C4—361no—
267C2×C4#379512yes—
268C2×C4#379711yescharacteristic
269C2×C4C4×D3211yescharacteristic
270C2×C4#380412yes—
271C8—64no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3#465012yes—
280C2×C3#476012yes—
281C2×C3#476012yes—
282C2×C3#479212yes—
283C2×C3#479212yes—
284C2×C3D3×#10612yes—
285C2×C3D3×#10712yes—
286C22#6388311yescharacteristic
287C22#6391311yescharacteristic
288C22#6392611yescharacteristic
289C22#6393011yescharacteristic
290C22#6394011yescharacteristic
291C22#6394411yescharacteristic
292C22#6395311yescharacteristic
293C4—81no—
294C4—94no—
295C4—94no—
296C4—242no—
297C4—721no—
298C4#6384712yes—
299C4#6387712yes—
300C3—21no—
301C3#6884712yescomplemented
302C2#1059055211yescharacteristic
303C2#1059056711yescharacteristic
304C2#1059057311yescharacteristic
305C2#1059057511yescharacteristic
306C2#1059124711yescharacteristic
307C2#1059140211yescharacteristic
308C2#1059153811yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1834
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
16. #63553C4semidirect
250. C32#1834semidirect
301. C3#68847semidirect

Maximal subgroups

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

subgroupindex
#105926742
#105913592
C2×#635532
C3×#45292
#105891642
#688473