Finite Group Databasebeta

← #11775569

Subgroups — #11775569

Order 1152.

1020 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic, complemented
3C2×#63657C211yesmaximal, characteristic, complemented
4#10589403C214yesmaximal, complemented
5#71675—34nomaximal
6C22×C32×D4—21no—
7C22×C32×D4C411yescharacteristic, complemented
8C23×C32×C4C2211yescharacteristic
9C32×#121—21no—
10C32×#121—21no—
11C32×#121C412yescomplemented
12C32×#121C2212yes—
13C2×C32×C4⋊C4C411yescharacteristic, complemented
14C2×C32×C22⋊C4—21no—
15C2×#3757—21no—
16C2×C4⋊(C3⋊Dic3)—21no—
17C22×C3⋊(C3⋊C8)—21no—
18#63658C2212yescomplemented
19#63657—21no—
20#63657C2212yescomplemented
21C2×C3×#121D314yes—
22#5212—34no—
23C2×#830—34no—
24#4537—316no—
25C24×C32—21no—
26C24×C32D411yescharacteristic
27C2×C32×D4—22no—
28C2×C32×D4—22no—
29C2×C32×D4—21no—
30C2×C32×D4—42no—
31C2×C32×D4—42no—
32C2×C32×D4—42no—
33C2×C32×D4C2×C412yes—
34C22×C32×C4—21no—
35C22×C32×C4—42no—
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3—22no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4C2×C412yes—
45C32×C22⋊C4—22no—
46C32×C22⋊C4—22no—
47#3757—42no—
48C4⋊(C3⋊Dic3)—42no—
49C2×C3⋊(C3⋊C8)—22no—
50C2×C3⋊(C3⋊C8)—42no—
51#1519—91noSylow
52C22×C3×D4—24no—
53C22×C3×D4Dic314yescomplemented
54C23×C3×C4C2×D314yes—
55C3×#121—24no—
56C3×#121—24no—
57C3×#121Dic318yescomplemented
58C3×#121C2×D318yes—
59C2×C3×C4⋊C4Dic314yescomplemented
60C2×C3×C22⋊C4—24no—
61C2×#217—64no—
62C2×C4⋊Dic3—64no—
63C22×C3⋊C8—64no—
64C3⋊#95—38no—
65#830—38no—
66#830—64no—
67C23×C32—22no—
68C23×C32—41no—
69C23×C32—41no—
70C23×C32—42no—
71C23×C32—42no—
72C23×C32—42no—
73C23×C32C22⋊C411yescharacteristic
74C23×C32C22⋊C411yescharacteristic
75C23×C32D812yes—
76C23×C32SD1612yes—
77C23×C32C2×D411yescharacteristic
78C32×D4—42no—
79C32×D4—44no—
80C32×D4—42no—
81C32×D4—42no—
82C32×D4—42no—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4—22no—
86C2×C32×C4—22no—
87C2×C32×C4—41no—
88C2×C32×C4—41no—
89C2×C32×C4—41no—
90C2×C32×C4—42no—
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C3⋊Dic3—42no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3—42no—
98C3⋊(C3⋊C8)—42no—
99C2×#121C3⋊D311yescharacteristic
100C2×C22⋊C8—91no—
101#380—91no—
102#327—94no—
103C24×C3—24no—
104C24×C3#6714yes—
105C2×C3×D4—28no—
106C2×C3×D4—28no—
107C2×C3×D4—24no—
108C2×C3×D4—48no—
109C2×C3×D4—48no—
110C2×C3×D4—48no—
111C2×C3×D4C2×Dic318yes—
112C22×C3×C4—24no—
113C22×C3×C4—48no—
114C22×C3×C4C2×Dic314yes—
115C22×C3×C4C2×Dic314yes—
116C22×C3×C4#6714yes—
117C22×C3×C4#6714yes—
118C22×C3×C4#6714yes—
119C22×C3×C4C22×D314yes—
120C22×Dic3—68no—
121C3×C4⋊C4—24no—
122C3×C4⋊C4C2×Dic318yes—
123C3×C22⋊C4—28no—
124C3×C22⋊C4—28no—
125#217—128no—
126C4⋊Dic3—128no—
127C2×C3⋊C8—68no—
128C2×C3⋊C8—128no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—42no—
136C22×C32—42no—
137C22×C32—42no—
138C22×C32—42no—
139C22×C32—42no—
140C22×C32—84no—
141C22×C32#10212yes—
142C22×C32#10212yes—
143C22×C32C2×C22⋊C411yescharacteristic
144C22×C32C2×D811yescharacteristic
145C22×C32C2×SD1611yescharacteristic
146C32×C4—21no—
147C32×C4—21no—
148C32×C4—21no—
149C32×C4—42no—
150C32×C4#9912yes—
151C3⋊Dic3—82no—
152C22×D4—21no—
153C22×D4C3⋊Dic311yescharacteristic, complemented
154C23×C4C2×C3⋊D311yescharacteristic
155C22×C8—181no—
156#121—21no—
157#121—21no—
158#121C3⋊Dic312yescomplemented
159#121C2×C3⋊D312yes—
160C2×C4⋊C4—181no—
161C2×C4⋊C4C3⋊Dic311yescharacteristic, complemented
162C2×C22⋊C4—21no—
163C2×C22⋊C4—181no—
164C22⋊C8—92no—
165C22⋊C8—181no—
166#95—92no—
167C23×C3—28no—
168C23×C3—44no—
169C23×C3—44no—
170C23×C3—48no—
171C23×C3—48no—
172C23×C3—48no—
173C23×C3#21318yes—
174C23×C3#21418yes—
175C23×C3#21714yes—
176C23×C3#21714yes—
177C23×C3C2×#6714yes—
178C3×D4—48no—
179C3×D4—416no—
180C3×D4—48no—
181C3×D4—48no—
182C3×D4—48no—
183C2×C3×C4—28no—
184C2×C3×C4—28no—
185C2×C3×C4—28no—
186C2×C3×C4—28no—
187C2×C3×C4—44no—
188C2×C3×C4—44no—
189C2×C3×C4—44no—
190C2×C3×C4—48no—
191C2×C3×C4#21714yes—
192C2×C3×C4#21714yes—
193C2×C3×C4C22×Dic314yes—
194C2×C3×C4C2×#6714yes—
195C2×Dic3—128no—
196C2×Dic3—128no—
197C2×Dic3—128no—
198C3⋊C8—128no—
199C2×C32—21no—
200C2×C32—22no—
201C2×C32—22no—
202C2×C32—21no—
203C2×C32—82no—
204C2×C32C2×#9911yescharacteristic
205C2×C32C2×#10211yescharacteristic
206C2×C32#42111yescharacteristic
207C24—21no—
208C24#63811yescharacteristic
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—21no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4C2×C3⋊Dic312yes—
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—182no—
219C22×C4C2×C3⋊Dic311yescharacteristic
220C22×C4C2×C3⋊Dic311yescharacteristic
221C22×C4#63811yescharacteristic
222C22×C4#63811yescharacteristic
223C22×C4#63811yescharacteristic
224C22×C4C22×C3⋊D311yescharacteristic
225C2×C8—182no—
226C2×C8—362no—
227C4⋊C4—21no—
228C4⋊C4—362no—
229C4⋊C4C2×C3⋊Dic312yes—
230C22⋊C4—22no—
231C22⋊C4—22no—
232C22⋊C4—362no—
233C22×C3—24no—
234C22×C3—24no—
235C22×C3—24no—
236C22×C3—24no—
237C22×C3—24no—
238C22×C3—24no—
239C22×C3—48no—
240C22×C3—48no—
241C22×C3—48no—
242C22×C3—48no—
243C22×C3—48no—
244C22×C3—816no—
245C22×C3#83218yes—
246C22×C3#83218yes—
247C22×C3C2×#21314yes—
248C22×C3C2×#21414yes—
249C22×C3C2×#21714yes—
250C3×C4—24no—
251C3×C4—24no—
252C3×C4—24no—
253C3×C4—48no—
254C3×C4#83418yes—
255Dic3—248no—
256C32#151911yescharacteristic, complemented, Sylow
257C23—22no—
258C23—41no—
259C23—41no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23#375312yes—
264C23#375412yes—
265C23#375711yescharacteristic
266C23#375711yescharacteristic
267C23C2×#63811yescharacteristic
268D4—42no—
269D4—42no—
270D4—42no—
271D4—44no—
272D4—42no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—362no—
282C2×C4—362no—
283C2×C4—362no—
284C2×C4#375711yescharacteristic
285C2×C4#375711yescharacteristic
286C2×C4C22×C3⋊Dic311yescharacteristic
287C2×C4C2×#63811yescharacteristic
288C8—362no—
289C2×C3—24no—
290C2×C3—28no—
291C2×C3—28no—
292C2×C3—24no—
293C2×C3—88no—
294C2×C3C2×#83214yes—
295C2×C3C2×#83414yes—
296C2×C3#523614yes—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—84no—
309C22#6365912yes—
310C22#6365912yes—
311C22C2×#375311yescharacteristic
312C22C2×#375411yescharacteristic
313C22C2×#375711yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—722no—
319C4#6366112yes—
320C3#7167514yescomplemented
321C2—21no—
322C2—22no—
323C2—21no—
324C2—22no—
325C2—82no—
326C2C2×#6365911yescharacteristic
327C2C2×#6366111yescharacteristic
328C2#1059293511yescharacteristic
subgroupG/H
centerC22C2×#3757
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
Fitting, prime radicalC2×C32×#121C2
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenterC2×#121C3⋊D3
hypocenterC32#1519
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
2. #10592911C2semidirect
3. C2×#63657C2semidirect
4. #10589403C2semidirect
7. C22×C32×D4C4semidirect
11. C32×#121C4semidirect
13. C2×C32×C4⋊C4C4semidirect
18. #63658C22semidirect
20. #63657C22semidirect
53. C22×C3×D4Dic3semidirect
57. C3×#121Dic3semidirect
59. C2×C3×C4⋊C4Dic3semidirect
153. C22×D4C3⋊Dic3semidirect
158. #121C3⋊Dic3semidirect
161. C2×C4⋊C4C3⋊Dic3semidirect
256. C32#1519semidirect
320. C3#71675semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1212
#105929112
C2×#636572
#105894032
#716753