Finite Group Databasebeta

← #11785523

Subgroups — #11785523

Order 1152.

579 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#948C211yesmaximal, characteristic
2#10592936C211yesmaximal, characteristic
3C3×#5237C211yesmaximal, characteristic
4C2×#63577C212yesmaximal, complemented
5#10589159C212yesmaximal, complemented
6#72014—31nomaximal
7#70134—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C2×#3748C2212yes—
10C3×#948—24no—
11C2×C3×#208C412yes—
12C2×C3×#208C2212yes—
13C2×C3×#208C2211yescharacteristic
14C22×C3×C3⋊C8C412yes—
15C22×C3×C3⋊C8C2211yescharacteristic
16#63663—21no—
17#63660—21no—
18C3×#836—21no—
19C3×#833—21no—
20#63577—24no—
21C2×C3×#131—31no—
22C2×#948D311yescharacteristic
23C3×#413—31no—
24#5237—31no—
25#5237—31no—
26#5237—61no—
27#5237D311yescharacteristic
28C2×#822—32no—
29C2×#819—32no—
30C3⋊#338—32no—
31C3⋊#338—32no—
32C32×#41—22no—
33C32×#41—22no—
34C2×C32×Q8D411yescharacteristic
35C2×C32×D4D411yescharacteristic
36C2×C32×D4Q812yes—
37C22×C32×C4C2×C412yes—
38C22×C32×C4C2311yescharacteristic
39#3748—22no—
40#3748—22no—
41C2×C3⋊(C3⋊C8)—22no—
42C3×#208—22no—
43C3×#208—24no—
44C3×#208—22no—
45C3×#208—22no—
46C2×C3×C3⋊C8—24no—
47C2×C3×C3⋊C8—22no—
48C2×C3×C3⋊C8C2×C412yes—
49C2×C3×C3⋊C8C2×C411yescharacteristic
50C2×C3×C3⋊C8C2×C411yescharacteristic
51C2×C3×C3⋊C8D414yes—
52#1813—91noSylow
53C2×C3×#41—21no—
54C2×C3×#41C2×D311yescharacteristic
55C2×C3×#41C2×D311yescharacteristic
56C3×#131—64no—
57C2×C3×M16—32no—
58C2×C3×M16—31no—
59C2×C3×M16—32no—
60C22×C3×C8—31no—
61C22×C3×C8—32no—
62#948—24no—
63C2×#208—32no—
64C2×#208—32no—
65C2×#208—62no—
66C2×#208Dic312yes—
67C2×#208C2×D312yes—
68C2×#208C2×D311yescharacteristic
69C22×C3⋊C8Dic312yes—
70C22×C3⋊C8C2×D311yescharacteristic
71C3×#101—61no—
72C3×#100—61no—
73#836—21no—
74#836—62no—
75#836—61no—
76#836—61no—
77#833—21no—
78#833—62no—
79#833—61no—
80#833—61no—
81#822—64no—
82#819—64no—
83C23×C32C4⋊C412yes—
84C23×C32C2×Q811yescharacteristic
85C32×Q8—22no—
86C32×D4—24no—
87C32×D4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4C4⋊C412yes—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D411yescharacteristic
93C2×C32×C4C2×D412yes—
94C2×C32×C4#4112yes—
95C3⋊(C3⋊C8)—42no—
96C3×C3⋊C8—22no—
97C3×C3⋊C8—42no—
98C3×C3⋊C8C22⋊C412yes—
99C3×C3⋊C8C22⋊C412yes—
100C2×#131—31no—
101C2×#108—92no—
102#413—31no—
103#413—91no—
104#338—92no—
105C3×#41—22no—
106C3×#41—22no—
107C3×#41—22no—
108C3×#41—22no—
109C3×#41—42no—
110C3×#41—42no—
111C2×C3×Q8—21no—
112C2×C3×Q8D1211yescharacteristic
113C2×C3×Q8#6711yescharacteristic
114C2×C3×D4—21no—
115C2×C3×D4—22no—
116C2×C3×D4Dic612yes—
117C2×C3×D4Dic612yes—
118C2×C3×D4D1211yescharacteristic
119C2×C3×D4#6711yescharacteristic
120C22×C3×C4—22no—
121C22×C3×C4—21no—
122C22×C3×C4C4×D312yes—
123C22×C3×C4C2×Dic312yes—
124C22×C3×C4C22×D311yescharacteristic
125C22×C3×C4C22×D311yescharacteristic
126C3×M16—64no—
127C3×M16—62no—
128C3×M16—62no—
129C3×M16—62no—
130C2×C3×C8—31no—
131C2×C3×C8—31no—
132C2×C3×C8—34no—
133C2×C3×C8—32no—
134C2×C3×C8—64no—
135C2×C3×C8—62no—
136#208—22no—
137#208—24no—
138#208—22no—
139#208—22no—
140#208—64no—
141#208—62no—
142#208—62no—
143#208—62no—
144#208—62no—
145#208—122no—
146C2×C3⋊C8—24no—
147C2×C3⋊C8—22no—
148C2×C3⋊C8—62no—
149C2×C3⋊C8—62no—
150C2×C3⋊C8—122no—
151C2×C3⋊C8C2×Dic312yes—
152C2×C3⋊C8C2×Dic311yescharacteristic
153C2×C3⋊C8C2×Dic311yescharacteristic
154C2×C3⋊C8#6714yes—
155C22×C32—22no—
156C22×C32—41no—
157C22×C32—42no—
158C22×C32C2×C4⋊C411yescharacteristic
159C22×C32C22⋊Q812yes—
160C32×C4—22no—
161C32×C4C2×C22⋊C411yescharacteristic
162C32×C4#11711yescharacteristic
163C32×C4#12112yes—
164C2×#41D3211yescharacteristic
165#131—64no—
166C2×M16—32no—
167C2×M16—31no—
168C2×M16—32no—
169C2×M16—92no—
170C22×C8—31no—
171C22×C8—32no—
172#108—184no—
173#101—61no—
174#101—181no—
175#100—61no—
176#100—181no—
177C23×C3—22no—
178C23×C3—21no—
179C23×C3Dic3⋊C412yes—
180C23×C3C4⋊Dic312yes—
181C23×C3C2×Dic611yescharacteristic
182C23×C3C2×Dic611yescharacteristic
183C3×Q8—22no—
184C3×Q8—22no—
185C3×Q8—42no—
186C3×D4—24no—
187C3×D4—24no—
188C3×D4—22no—
189C3×D4—22no—
190C3×D4—42no—
191C3×D4—44no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—21no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—22no—
201C2×C3×C4—42no—
202C2×C3×C4—42no—
203C2×C3×C4Dic3⋊C412yes—
204C2×C3×C4C4⋊Dic312yes—
205C2×C3×C4C2×C4×D311yescharacteristic
206C2×C3×C4C2×D1211yescharacteristic
207C2×C3×C4#23512yes—
208C2×C3×C4D3×D412yes—
209C2×C3×C4#23712yes—
210C2×C3×C4C22×Dic311yescharacteristic
211C2×C3×C4C2×#6711yescharacteristic
212C2×C3×C4C2×#6712yes—
213C3×C8—32no—
214C3×C8—32no—
215C3×C8—62no—
216C3×C8—122no—
217C3⋊C8—22no—
218C3⋊C8—42no—
219C3⋊C8—124no—
220C3⋊C8—122no—
221C3⋊C8—122no—
222C3⋊C8#21712yes—
223C3⋊C8#21712yes—
224C2×C32—21no—
225C2×C32—22no—
226C2×C32—42no—
227C2×C32#38011yescharacteristic
228#41—22no—
229#41—22no—
230C2×Q8#62611yescharacteristic
231C2×D4#62611yescharacteristic
232C2×D4#62712yes—
233C22×C4D3×Dic312yes—
234C22×C4C2×D3211yescharacteristic
235M16—64no—
236M16—62no—
237M16—62no—
238M16—62no—
239M16—182no—
240M16—182no—
241C2×C8—31no—
242C2×C8—31no—
243C2×C8—34no—
244C2×C8—32no—
245C2×C8—64no—
246C2×C8—62no—
247C2×C8—182no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—21no—
252C22×C3—42no—
253C22×C3—41no—
254C22×C3—41no—
255C22×C3—42no—
256C22×C3—42no—
257C22×C3—81no—
258C22×C3—82no—
259C22×C3#87812yes—
260C22×C3C2×Dic3⋊C411yescharacteristic
261C22×C3#92412yes—
262C22×C3C2×C4⋊Dic311yescharacteristic
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—22no—
268C3×C4—42no—
269C3×C4#87711yescharacteristic
270C3×C4D3×C22⋊C411yescharacteristic
271C3×C4#92611yescharacteristic
272C3×C4#93012yes—
273C3×C4#93912yes—
274C3×C4C2×#21711yescharacteristic
275C32#181311yescharacteristic, complemented, Sylow
276C23Dic3⋊Dic312yes—
277C23C2×#62711yescharacteristic
278Q8—22no—
279D4—24no—
280D4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4Dic3⋊Dic312yes—
284C2×C4C2×D3×Dic311yescharacteristic
285C2×C4#380412yes—
286C2×C4C2×#62611yescharacteristic
287C2×C4D3×#6712yes—
288C8—32no—
289C8—32no—
290C8—62no—
291C8—122no—
292C8—362no—
293C2×C3—21no—
294C2×C3—22no—
295C2×C3—21no—
296C2×C3—22no—
297C2×C3—21no—
298C2×C3—41no—
299C2×C3—42no—
300C2×C3—42no—
301C2×C3—42no—
302C2×C3—82no—
303C2×C3#494211yescharacteristic
304C2×C3#521211yescharacteristic
305C22—22no—
306C22—41no—
307C22—42no—
308C22#6396412yes—
309C22C2×Dic3⋊Dic311yescharacteristic
310C4—22no—
311C4#6395511yescharacteristic
312C4D3×#21711yescharacteristic
313C4#6397812yes—
314C3—21no—
315C3#7013411yescharacteristic, complemented
316C3#7201411yescharacteristic, complemented
317C2—21no—
318C2—22no—
319C2—42no—
320C2#1059171611yescharacteristic
subgroupG/H
centerC4#63955
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC2×C32×#41C22
socleC2×C32#380
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1813
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. C2×#63577C2semidirect
5. #10589159C2semidirect
275. C32#1813semidirect
315. C3#70134semidirect
316. C3#72014semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9482
#105929362
C3×#52372
C2×#635772
#105891592
#720143
#701343