Finite Group Databasebeta

← #11783381

Subgroups — #11783381

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 323 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64135C211yesmaximal, characteristic
2C2×C3×#926C212yesmaximal
3#10589187C214yesmaximal
4#71593—32nomaximal
5C23×C32×C4C2211yescharacteristic
6C2×#3757C2212yes—
7#64135—22no—
8#64135—22no—
9C2×C4⋊(C3⋊Dic3)C412yescomplemented
10C2×C4×C3⋊Dic3C412yescomplemented
11C2×C3×#217C2214yes—
12C3×#926—24no—
13C3×#926C418yescomplemented
14C2×C3×C4⋊Dic3—22no—
15C2×C3×C4×Dic3—22no—
16C2×C3×#117—32no—
17C2×#926—32no—
18C2×#926—61no—
19C2×#926D312yes—
20#4527—38no—
21C24×C32C2311yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C414yes—
25C22×C32×C4D412yes—
26C22×C32×C4D412yes—
27C22×C32×C4D412yes—
28C22×C32×C4Q812yes—
29C22×C3⋊Dic3C2×C414yes—
30C22×C3×Dic3—24no—
31#3757—24no—
32C4⋊(C3⋊Dic3)—24no—
33C4×C3⋊Dic3—22no—
34C4×C3⋊Dic3—22no—
35C3×#217—24no—
36C3×#217C2×C418yes—
37C3×C4⋊Dic3—28no—
38C3×C4×Dic3—28no—
39#1740—91noSylow
40C23×C3×C4—21no—
41C23×C3×C4C2×D312yes—
42C3×#117—38no—
43C3×#117—64no—
44C2×C3×C4⋊C4—62no—
45C2×C3×C22⋊C4—34no—
46C2×C3×C42—62no—
47C2×#217—34no—
48C2×#217—62no—
49C2×#217C2×D314yes—
50#926—24no—
51#926—64no—
52#926—64no—
53#926—62no—
54#926—62no—
55#926—62no—
56#926—62no—
57#926Dic318yescomplemented
58C2×C4⋊Dic3—22no—
59C2×C4⋊Dic3—34no—
60C2×C4⋊Dic3—62no—
61C2×C4×Dic3—22no—
62C2×C4×Dic3—34no—
63C2×C4×Dic3—62no—
64C23×C32—42no—
65C23×C32C22×C411yescharacteristic
66C23×C32C22×C412yes—
67C23×C32C2×D412yes—
68C23×C32C2×D411yescharacteristic
69C23×C32C2×Q811yescharacteristic
70C2×C32×C4C4212yes—
71C2×C32×C4C4212yes—
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C22⋊C411yescharacteristic
74C2×C32×C4C22⋊C412yes—
75C2×C32×C4C22⋊C414yes—
76C2×C32×C4C22⋊C414yes—
77C2×C32×C4C4⋊C412yes—
78C2×C32×C4C4⋊C412yes—
79C2×C32×C4C4⋊C414yes—
80C2×C32×C4C4⋊C414yes—
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3—44no—
83C2×C3×Dic3—28no—
84C2×C3×Dic3—48no—
85C2×#117—32no—
86C2×#117—91no—
87#342—94no—
88C24×C3—21no—
89C24×C3C22×D312yes—
90C22×C3×C4—24no—
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—22no—
94C22×C3×C4—22no—
95C22×C3×C4—22no—
96C22×C3×C4—22no—
97C22×C3×C4—64no—
98C22×C3×C4Dic614yes—
99C22×C3×C4C4×D314yes—
100C22×C3×C4C4×D312yes—
101C22×C3×C4C4×D312yes—
102C22×C3×C4D1212yes—
103C22×C3×C4D1212yes—
104C22×C3×C4C2×Dic314yes—
105C22×C3×C4#6714yes—
106C22×C3×C4#6712yes—
107C22×C3×C4#6712yes—
108C22×Dic3—24no—
109C22×Dic3—38no—
110C22×Dic3—64no—
111C3×C4⋊C4—68no—
112C3×C22⋊C4—38no—
113C3×C22⋊C4—64no—
114C3×C42—68no—
115#217—24no—
116#217—68no—
117#217—64no—
118#217—64no—
119#217C2×Dic318yes—
120C4⋊Dic3—28no—
121C4⋊Dic3—68no—
122C4⋊Dic3—64no—
123C4⋊Dic3—64no—
124C4×Dic3—28no—
125C4×Dic3—64no—
126C4×Dic3—64no—
127C4×Dic3—64no—
128C4×Dic3—64no—
129C22×C32—22no—
130C22×C32—24no—
131C22×C32—42no—
132C22×C32—41no—
133C22×C32—41no—
134C22×C32C2×C4211yescharacteristic
135C22×C32C2×C22⋊C411yescharacteristic
136C22×C32C2×C22⋊C412yes—
137C22×C32C2×C4⋊C411yescharacteristic
138C22×C32C2×C4⋊C412yes—
139C32×C4#9512yes—
140C32×C4#9512yes—
141C32×C4#9514yes—
142C3⋊Dic3—44no—
143C3×Dic3—48no—
144C23×C4D3211yescharacteristic
145#117—38no—
146#117—64no—
147#117—182no—
148#117—182no—
149C2×C4⋊C4—62no—
150C2×C4⋊C4—92no—
151C2×C22⋊C4—34no—
152C2×C22⋊C4—92no—
153C2×C42—62no—
154C2×C42—92no—
155C23×C3—22no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—22no—
159C23×C3—21no—
160C23×C3—44no—
161C23×C3—44no—
162C23×C3C2×Dic612yes—
163C23×C3C2×C4×D312yes—
164C23×C3C2×C4×D312yes—
165C23×C3C2×D1212yes—
166C23×C3C22×Dic312yes—
167C23×C3C2×#6712yes—
168C23×C3C2×#6712yes—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—24no—
172C2×C3×C4—24no—
173C2×C3×C4—21no—
174C2×C3×C4—22no—
175C2×C3×C4—21no—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—68no—
181C2×C3×C4—128no—
182C2×C3×C4C4×Dic314yes—
183C2×C3×C4C4×Dic314yes—
184C2×C3×C4Dic3⋊C414yes—
185C2×C3×C4Dic3⋊C414yes—
186C2×C3×C4Dic3⋊C414yes—
187C2×C3×C4Dic3⋊C414yes—
188C2×C3×C4C4⋊Dic314yes—
189C2×C3×C4C4⋊Dic314yes—
190C2×C3×C4(C2×D3)⋊C414yes—
191C2×C3×C4(C2×D3)⋊C414yes—
192C2×C3×C4(C2×D3)⋊C412yes—
193C2×C3×C4(C2×D3)⋊C412yes—
194C2×C3×C4(C2×D3)⋊C412yes—
195C2×C3×C4(C2×D3)⋊C412yes—
196C2×C3×C4#21714yes—
197C2×C3×C4#21714yes—
198C2×Dic3—28no—
199C2×Dic3—48no—
200C2×Dic3—68no—
201C2×Dic3—68no—
202C2×Dic3—128no—
203C2×Dic3—128no—
204C2×C32—21no—
205C2×C32—21no—
206C2×C32—22no—
207C2×C32—22no—
208C2×C32C2×#9511yescharacteristic
209C2×C32#41012yes—
210C24C2×D3211yescharacteristic
211C22×C4—64no—
212C22×C4—94no—
213C22×C4D3×Dic314yes—
214C22×C4#62411yescharacteristic
215C22×C4#62411yescharacteristic
216C22×C4#62512yes—
217C22×C4#62612yes—
218C22×C4#62612yes—
219C22×C4#62712yes—
220C4⋊C4—68no—
221C4⋊C4—184no—
222C22⋊C4—38no—
223C22⋊C4—64no—
224C22⋊C4—184no—
225C42—68no—
226C42—182no—
227C42—182no—
228C22×C3—24no—
229C22×C3—24no—
230C22×C3—24no—
231C22×C3—24no—
232C22×C3—21no—
233C22×C3—22no—
234C22×C3—21no—
235C22×C3—22no—
236C22×C3—21no—
237C22×C3—44no—
238C22×C3—42no—
239C22×C3—42no—
240C22×C3—42no—
241C22×C3—42no—
242C22×C3—44no—
243C22×C3—42no—
244C22×C3—42no—
245C22×C3C2×C4×Dic312yes—
246C22×C3C2×Dic3⋊C412yes—
247C22×C3C2×Dic3⋊C412yes—
248C22×C3C2×C4⋊Dic312yes—
249C22×C3C2×(C2×D3)⋊C412yes—
250C22×C3C2×(C2×D3)⋊C412yes—
251C22×C3C2×#21712yes—
252C3×C4—22no—
253C3×C4—24no—
254C3×C4—22no—
255C3×C4—128no—
256C3×C4C3⋊#9514yes—
257C3×C4C3⋊#9514yes—
258C3×C4C3⋊#9514yes—
259C3×C4C3⋊#9514yes—
260Dic3—48no—
261Dic3—128no—
262Dic3—128no—
263C32#174011yescharacteristic, complemented, Sylow
264C23—42no—
265C23C2×D3×Dic312yes—
266C23C2×#62411yescharacteristic
267C23C2×#62511yescharacteristic
268C23C2×#62612yes—
269C23C2×#62711yescharacteristic
270C2×C4—68no—
271C2×C4—128no—
272C2×C4—184no—
273C2×C4—364no—
274C2×C4Dic3212yes—
275C2×C4Dic3212yes—
276C2×C4(C2×D3)⋊Dic314yes—
277C2×C4(C2×D3)⋊Dic314yes—
278C2×C4#372211yescharacteristic
279C2×C4#372212yes—
280C2×C4#372211yescharacteristic
281C2×C4Dic3⋊Dic314yes—
282C2×C4Dic3⋊Dic314yes—
283C2×C4#372412yes—
284C2×C4#372412yes—
285C2×C3—22no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—22no—
289C2×C3—22no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3—22no—
294C2×C3—21no—
295C2×C3—42no—
296C2×C3—42no—
297C2×C3#500614yes—
298C2×C3C2×C3⋊#9512yes—
299C22—24no—
300C22—22no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22C2×Dic3211yescharacteristic
305C22C2×(C2×D3)⋊Dic312yes—
306C22C2×#372211yescharacteristic
307C22C2×Dic3⋊Dic312yes—
308C22C2×#372411yescharacteristic
309C4—128no—
310C4—364no—
311C4#6357914yes—
312C4#6357912yes—
313C4#6357912yes—
314C3—21no—
315C3#7159312yescomplemented
316C2—22no—
317C2—21no—
318C2—22no—
319C2—21no—
320C2#1059123212yes—
321C2C2×#6357911yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC22×C32C2×C42
FrattiniC24C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radical, cosocleC24×C32C23
hypercenterC23×C4D32
hypocenterC32#1740
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
9. C2×C4⋊(C3⋊Dic3)C4semidirect
10. C2×C4×C3⋊Dic3C4semidirect
13. C3×#926C4semidirect
57. #926Dic3semidirect
263. C32#1740semidirect
315. C3#71593semidirect

Maximal subgroups

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

subgroupindex
C2×#641352
C2×C3×#9262
#105891872
#715933