Finite Group Databasebeta

← #11788067

Subgroups — #11788067

Order 1152.

1296 conjugacy classes of subgroups.

The subgroup lattice has 321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3C2×#63659C212yesmaximal, complemented
4#10592911C211yesmaximal, characteristic, complemented
5#10589395C212yesmaximal, complemented
6#71681—34nomaximal
7C22×C32×D4—21no—
8C22×C32×D4C2211yescharacteristic
9C23×C32×C4C2211yescharacteristic
10C32×#121—22no—
11C32×#121C414yescomplemented
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4—21no—
14C2×#3757—21no—
15C2×C4⋊(C3⋊Dic3)C2212yes—
16C22×C3⋊(C3⋊C8)—22no—
17C22×C3⋊(C3⋊C8)—24no—
18C22×C3⋊(C3⋊C8)C2212yes—
19#63659—24no—
20#63658—21no—
21C2×C3×#121D314yes—
22C23×C3⋊C8—34no—
23C2×#832—38no—
24#5212—34no—
25#4529—38no—
26C24×C32—21no—
27C24×C32D411yescharacteristic
28C2×C32×D4—24no—
29C2×C32×D4—22no—
30C2×C32×D4—21no—
31C2×C32×D4—22no—
32C2×C32×D4—42no—
33C2×C32×D4—42no—
34C2×C32×D4C2×C412yes—
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4—21no—
38C22×C32×C4C2×C412yes—
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D412yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—22no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C412yes—
45C32×C22⋊C4—24no—
46#3757—42no—
47C4⋊(C3⋊Dic3)—22no—
48C4⋊(C3⋊Dic3)—22no—
49C2×C3⋊(C3⋊C8)—28no—
50C2×C3⋊(C3⋊C8)—22no—
51C2×C3⋊(C3⋊C8)—22no—
52C2×C3⋊(C3⋊C8)D414yescomplemented
53#1893—91noSylow
54C22×C3×D4—24no—
55C22×C3×D4C2×D314yes—
56C23×C3×C4C2×D314yes—
57C3×#121—28no—
58C3×#121Dic3116yescomplemented
59C2×C3×C4⋊C4C2×D314yes—
60C2×C3×C22⋊C4—24no—
61C2×#217—64no—
62C2×C4⋊Dic3—38no—
63C22×C3⋊C8—38no—
64C22×C3⋊C8—616no—
65C22×C3⋊C8—68no—
66#832—616no—
67C3⋊#95—64no—
68C23×C32—22no—
69C23×C32—22no—
70C23×C32—22no—
71C23×C32—42no—
72C23×C32—41no—
73C23×C32—41no—
74C23×C32—42no—
75C23×C32C22⋊C412yes—
76C23×C32D812yes—
77C23×C32SD1612yes—
78C23×C32C2×D411yescharacteristic
79C32×D4—24no—
80C32×D4—48no—
81C32×D4—41no—
82C32×D4—41no—
83C2×C32×C4—22no—
84C2×C32×C4—24no—
85C2×C32×C4—22no—
86C2×C32×C4—22no—
87C2×C32×C4—22no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4C22⋊C412yes—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D412yes—
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4112yes—
95C2×C3⋊Dic3—42no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3—42no—
98C3⋊(C3⋊C8)—24no—
99C23×C8—91no—
100C2×#121C3⋊D311yescharacteristic
101C2×#102—92no—
102#380—91no—
103#340—92no—
104C24×C3—24no—
105C24×C3#6714yes—
106C2×C3×D4—216no—
107C2×C3×D4—28no—
108C2×C3×D4—28no—
109C2×C3×D4—24no—
110C2×C3×D4—48no—
111C2×C3×D4—48no—
112C2×C3×D4C2×Dic318yes—
113C22×C3×C4—28no—
114C22×C3×C4—28no—
115C22×C3×C4—24no—
116C22×C3×C4C2×Dic318yes—
117C22×C3×C4#6714yes—
118C22×C3×C4#6718yes—
119C22×C3×C4C22×D314yes—
120C22×Dic3—68no—
121C3×C4⋊C4—24no—
122C3×C4⋊C4C2×Dic318yes—
123C3×C22⋊C4—216no—
124#217—128no—
125C4⋊Dic3—68no—
126C4⋊Dic3—68no—
127C2×C3⋊C8—316no—
128C2×C3⋊C8—632no—
129C2×C3⋊C8—68no—
130C2×C3⋊C8—68no—
131C22×C32—22no—
132C22×C32—22no—
133C22×C32—24no—
134C22×C32—24no—
135C22×C32—42no—
136C22×C32—42no—
137C22×C32—42no—
138C22×C32—82no—
139C22×C32—82no—
140C22×C32#10214yescomplemented
141C22×C32C2×C22⋊C411yescharacteristic
142C22×C32#12112yes—
143C22×C32C2×D811yescharacteristic
144C22×C32C2×SD1611yescharacteristic
145C22×C32#13512yes—
146C32×C4—22no—
147C32×C4—42no—
148C32×C4C4×D412yes—
149C32×C4#12011yescharacteristic
150C32×C4#12311yescharacteristic
151C3⋊Dic3—82no—
152C22×D4—21no—
153C22×D4C2×C3⋊D311yescharacteristic
154C23×C4C2×C3⋊D311yescharacteristic
155C22×C8—92no—
156C22×C8—184no—
157C22×C8—182no—
158#121—22no—
159#121C3⋊Dic314yescomplemented
160C2×C4⋊C4—92no—
161C2×C4⋊C4C2×C3⋊D311yescharacteristic
162C2×C22⋊C4—21no—
163C2×C22⋊C4—181no—
164#102—184no—
165#95—181no—
166C23×C3—28no—
167C23×C3—28no—
168C23×C3—28no—
169C23×C3—44no—
170C23×C3—44no—
171C23×C3—48no—
172C23×C3—48no—
173C23×C3#21318yes—
174C23×C3#21418yes—
175C23×C3#21718yes—
176C23×C3C2×#6714yes—
177C3×D4—216no—
178C3×D4—432no—
179C3×D4—44no—
180C3×D4—44no—
181C2×C3×C4—28no—
182C2×C3×C4—216no—
183C2×C3×C4—28no—
184C2×C3×C4—28no—
185C2×C3×C4—28no—
186C2×C3×C4—44no—
187C2×C3×C4—44no—
188C2×C3×C4#21718yes—
189C2×C3×C4D3×D418yes—
190C2×C3×C4#23718yes—
191C2×C3×C4C22×Dic314yes—
192C2×C3×C4C2×#6714yes—
193C2×Dic3—128no—
194C2×Dic3—128no—
195C2×Dic3—128no—
196C3⋊C8—616no—
197C2×C32—24no—
198C2×C32—82no—
199C2×C32#38611yescharacteristic
200C2×C32C2×#10211yescharacteristic
201C2×C32#41611yescharacteristic
202C2×C32#46512yes—
203C2×C32#46612yes—
204C24—21no—
205C24#63811yescharacteristic
206C2×D4—24no—
207C2×D4—22no—
208C2×D4—22no—
209C2×D4—21no—
210C2×D4—42no—
211C2×D4—42no—
212C2×D4C2×C3⋊Dic312yes—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—21no—
216C22×C4—182no—
217C22×C4C2×C3⋊Dic312yes—
218C22×C4#63811yescharacteristic
219C22×C4#63812yes—
220C22×C4C22×C3⋊D311yescharacteristic
221C2×C8—94no—
222C2×C8—188no—
223C2×C8—182no—
224C2×C8—182no—
225C4⋊C4—21no—
226C4⋊C4—182no—
227C4⋊C4—182no—
228C4⋊C4C2×C3⋊Dic312yes—
229C22⋊C4—24no—
230C22⋊C4—362no—
231C22×C3—28no—
232C22×C3—28no—
233C22×C3—216no—
234C22×C3—216no—
235C22×C3—48no—
236C22×C3—48no—
237C22×C3—48no—
238C22×C3—88no—
239C22×C3—88no—
240C22×C3#832116yescomplemented
241C22×C3C2×#21314yes—
242C22×C3C2×#21414yes—
243C22×C3#93918yes—
244C22×C3#95018yes—
245C22×C3C2×#21714yes—
246C3×C4—28no—
247C3×C4—48no—
248C3×C4D4×Dic318yes—
249C3×C4#93514yes—
250C3×C4#93714yes—
251Dic3—248no—
252C32#189311yescharacteristic, complemented, Sylow
253C23—22no—
254C23—22no—
255C23—22no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23#375312yes—
261C23#375412yes—
262C23#375712yes—
263C23C2×#63811yescharacteristic
264D4—24no—
265D4—48no—
266D4—41no—
267D4—41no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—362no—
276C2×C4—362no—
277C2×C4—362no—
278C2×C4#375712yes—
279C2×C4D4×C3⋊D312yes—
280C2×C4#383012yes—
281C2×C4C22×C3⋊Dic311yescharacteristic
282C2×C4C2×#63811yescharacteristic
283C8—184no—
284C2×C3—216no—
285C2×C3—88no—
286C2×C3#503818yes—
287C2×C3#504118yes—
288C2×C3C2×#83214yes—
289C2×C3#522014yes—
290C2×C3#523314yes—
291C22—22no—
292C22—22no—
293C22—24no—
294C22—24no—
295C22—42no—
296C22—42no—
297C22—42no—
298C22—82no—
299C22—82no—
300C22#6365914yescomplemented
301C22C2×#375311yescharacteristic
302C22C2×#375411yescharacteristic
303C22#6414812yes—
304C22#6415912yes—
305C22C2×#375711yescharacteristic
306C4—22no—
307C4—42no—
308C4—722no—
309C4D4×C3⋊Dic312yes—
310C4#6414411yescharacteristic
311C4#6414611yescharacteristic
312C3#7168114yescomplemented
313C2—24no—
314C2—82no—
315C2#1059273712yes—
316C2#1059274012yes—
317C2C2×#6365911yescharacteristic
318C2#1059291911yescharacteristic
319C2#1059293211yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
Fitting, prime radicalC2×C32×#121C2
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×#121C3⋊D3
hypocenterC32#1893
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. C23×C3⋊(C3⋊C8)C2semidirect
3. C2×#63659C2semidirect
4. #10592911C2semidirect
5. #10589395C2semidirect
11. C32×#121C4semidirect
52. C2×C3⋊(C3⋊C8)D4semidirect
58. C3×#121Dic3semidirect
140. C22×C32#102semidirect
159. #121C3⋊Dic3semidirect
240. C22×C3#832semidirect
252. C32#1893semidirect
300. C22#63659semidirect
312. C3#71681semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
C23×C3⋊(C3⋊C8)2
C2×#636592
#105929112
#105893952
#716813