Finite Group Databasebeta

← #11771234

Subgroups — #11771234

Order 1152.

495 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592906C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C3×#5207C211yesmaximal, characteristic
4#67685—31nomaximal
5#67626—31nomaximal
6C23×C32×C4C2211yescharacteristic
7C2×#3748C412yescomplemented
8C2×C3×#217C412yes—
9C2×C3×C4⋊Dic3—21no—
10C2×C3×#208—21no—
11#63657—21no—
12#63657—21no—
13C3×C3⋊#95—21no—
14C3×#830—21no—
15C3×#830C412yescomplemented
16C3×#407—31no—
17C3×#380—31no—
18#5212D311yescharacteristic
19#5207—31no—
20#5207—31no—
21#5207—61no—
22#5207D311yescharacteristic
23C24×C32C2×C411yescharacteristic
24C22×C32×C4—42no—
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4D411yescharacteristic
28C22×C32×C4D411yescharacteristic
29C22×C32×C4D411yescharacteristic
30C22×C32×C4Q811yescharacteristic
31C22×C3×Dic3—22no—
32#3748—42no—
33C2×C3⋊(C3⋊C8)—22no—
34C3×#217—42no—
35C3×C4⋊Dic3—42no—
36C3×#208—42no—
37C2×C3×C3⋊C8—22no—
38#1305—91noSylow
39C23×C3×C4—21no—
40C23×C3×C4C2×D311yescharacteristic
41C23×C3×C4C2×D311yescharacteristic
42C2×C3×M16—61no—
43C2×C3×C4⋊C4—61no—
44C2×C3×C22⋊C4—32no—
45C2×#217Dic312yes—
46C2×C4⋊Dic3—21no—
47C2×#208—21no—
48C2×#208—32no—
49C2×#208—32no—
50C2×#208—62no—
51C3×C22⋊C8—32no—
52C3×C22⋊C8—61no—
53C3×#95—61no—
54C3⋊#95—21no—
55#830—21no—
56#830—62no—
57#830—62no—
58#830—61no—
59#830—61no—
60#830—61no—
61#830—61no—
62#830Dic312yescomplemented
63C23×C32—21no—
64C23×C32—21no—
65C23×C32—41no—
66C23×C32—41no—
67C23×C32C4211yescharacteristic
68C23×C32C22⋊C411yescharacteristic
69C23×C32C4⋊C411yescharacteristic
70C2×C32×C4—22no—
71C2×C32×C4—22no—
72C2×C32×C4—22no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4—41no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22⋊C411yescharacteristic
78C2×C32×C4C4⋊C411yescharacteristic
79C2×C32×C4C4⋊C411yescharacteristic
80C2×C3×Dic3—42no—
81C2×C3×Dic3—42no—
82C2×C3×Dic3—42no—
83C3⋊(C3⋊C8)—42no—
84C3×C3⋊C8—42no—
85#407—31no—
86#407—91no—
87#380—31no—
88C24×C3—21no—
89C24×C3C4×D311yescharacteristic
90C24×C3C2×Dic311yescharacteristic
91C22×C3×C4—21no—
92C22×C3×C4—21no—
93C22×C3×C4—21no—
94C22×C3×C4—21no—
95C22×C3×C4—21no—
96C22×C3×C4—21no—
97C22×C3×C4—42no—
98C22×C3×C4—42no—
99C22×C3×C4—44no—
100C22×C3×C4—62no—
101C22×C3×C4Dic611yescharacteristic
102C22×C3×C4Dic611yescharacteristic
103C22×C3×C4C4×D311yescharacteristic
104C22×C3×C4C4×D311yescharacteristic
105C22×C3×C4C4×D311yescharacteristic
106C22×C3×C4D1211yescharacteristic
107C22×C3×C4D1211yescharacteristic
108C22×C3×C4C2×Dic311yescharacteristic
109C22×C3×C4#6711yescharacteristic
110C22×C3×C4#6711yescharacteristic
111C22×C3×C4#6711yescharacteristic
112C22×C3×C4#6711yescharacteristic
113C22×Dic3—22no—
114C3×M16—122no—
115C2×C3×C8—62no—
116C3×C4⋊C4—122no—
117C3×C22⋊C4—122no—
118#217—42no—
119C4⋊Dic3—42no—
120#208—42no—
121#208—124no—
122#208—122no—
123#208—122no—
124C2×C3⋊C8—22no—
125C2×C3⋊C8—64no—
126C2×C3⋊C8—62no—
127C2×C3⋊C8—62no—
128C22×C32—21no—
129C22×C32—21no—
130C22×C32—21no—
131C22×C32—21no—
132C22×C32—21no—
133C22×C32—21no—
134C22×C32—21no—
135C22×C32—21no—
136C22×C32—42no—
137C22×C32—42no—
138C22×C32#9511yescharacteristic
139C22×C32#10011yescharacteristic
140C22×C32#10111yescharacteristic
141C32×C4—21no—
142C32×C4—21no—
143C32×C4—21no—
144C32×C4#9912yes—
145C3×Dic3—82no—
146C23×C4D3211yescharacteristic
147C2×M16—61no—
148C2×M16—92no—
149C2×C4⋊C4—61no—
150C2×C22⋊C4—32no—
151C22⋊C8—32no—
152C22⋊C8—61no—
153C22⋊C8—181no—
154C22⋊C8—181no—
155#95—61no—
156C23×C3—21no—
157C23×C3—21no—
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—41no—
164C23×C3—41no—
165C23×C3—41no—
166C23×C3—41no—
167C23×C3—41no—
168C23×C3—41no—
169C23×C3—42no—
170C23×C3—42no—
171C23×C3C4×Dic311yescharacteristic
172C23×C3C4×Dic311yescharacteristic
173C23×C3Dic3⋊C411yescharacteristic
174C23×C3C4⋊Dic311yescharacteristic
175C23×C3(C2×D3)⋊C411yescharacteristic
176C23×C3#21711yescharacteristic
177C2×C3×C4—24no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—22no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4—42no—
189C2×C3×C4—42no—
190C2×C3×C4—41no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—122no—
200C2×C3×C4—122no—
201C2×C3×C4—122no—
202C2×C3×C4Dic3⋊C411yescharacteristic
203C2×C3×C4Dic3⋊C411yescharacteristic
204C2×C3×C4Dic3⋊C411yescharacteristic
205C2×C3×C4C4⋊Dic311yescharacteristic
206C2×C3×C4(C2×D3)⋊C411yescharacteristic
207C2×C3×C4(C2×D3)⋊C411yescharacteristic
208C2×C3×C4(C2×D3)⋊C411yescharacteristic
209C2×C3×C4#21711yescharacteristic
210C2×Dic3—42no—
211C2×Dic3—42no—
212C2×Dic3—42no—
213C3×C8—122no—
214C3⋊C8—42no—
215C3⋊C8—124no—
216C3⋊C8—122no—
217C3⋊C8—122no—
218C2×C32—21no—
219C2×C32—21no—
220C2×C32—41no—
221C2×C32—41no—
222C2×C32#34211yescharacteristic
223C2×C32#34311yescharacteristic
224C2×C32#34411yescharacteristic
225C24D3×Dic311yescharacteristic
226C22×C4—42no—
227C22×C4—62no—
228C22×C4D3×Dic311yescharacteristic
229C22×C4#62411yescharacteristic
230C22×C4#62511yescharacteristic
231C22×C4#62611yescharacteristic
232C22×C4#62611yescharacteristic
233C22×C4#62711yescharacteristic
234M16—122no—
235M16—362no—
236C2×C8—62no—
237C2×C8—182no—
238C4⋊C4—122no—
239C22⋊C4—122no—
240C22×C3—21no—
241C22×C3—21no—
242C22×C3—21no—
243C22×C3—21no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—21no—
260C22×C3—21no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—42no—
268C22×C3—42no—
269C22×C3—42no—
270C22×C3—42no—
271C22×C3—44no—
272C22×C3—44no—
273C22×C3#82311yescharacteristic
274C22×C3#82411yescharacteristic
275C22×C3C3⋊#9511yescharacteristic
276C22×C3C3⋊#9511yescharacteristic
277C22×C3#83311yescharacteristic
278C22×C3#83611yescharacteristic
279C3×C4—22no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—22no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—242no—
290C3×C4#80612yes—
291C3×C4#80612yes—
292Dic3—82no—
293C32#130511yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23Dic3211yescharacteristic
299C23(C2×D3)⋊Dic311yescharacteristic
300C23Dic3⋊Dic311yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—122no—
308C2×C4—122no—
309C2×C4—122no—
310C2×C4(C2×D3)⋊Dic311yescharacteristic
311C2×C4#372211yescharacteristic
312C2×C4Dic3⋊Dic311yescharacteristic
313C2×C4#372411yescharacteristic
314C8—122no—
315C8—362no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3—21no—
323C2×C3—41no—
324C2×C3—41no—
325C2×C3—42no—
326C2×C3—42no—
327C2×C3—41no—
328C2×C3—41no—
329C2×C3—41no—
330C2×C3—41no—
331C2×C3#452711yescharacteristic
332C2×C3#452711yescharacteristic
333C2×C3#453011yescharacteristic
334C2×C3#453311yescharacteristic
335C2×C3#455411yescharacteristic
336C2×C3#455611yescharacteristic
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—42no—
346C22—42no—
347C22#6355811yescharacteristic
348C22#6356011yescharacteristic
349C22#6357911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—242no—
354C4#6358112yes—
355C3—21no—
356C3#6762611yescharacteristic, complemented
357C3#6768511yescharacteristic, complemented
358C2—21no—
359C2—21no—
360C2—41no—
361C2—41no—
362C2#1058916711yescharacteristic
363C2#1058916911yescharacteristic
364C2#1058918711yescharacteristic
subgroupG/H
centerC22#63579
commutatorC23×C32C42
Frattini, hypercenterC23×C4D32
Fitting, cosocleC23×C32×C4C22
socleC22×C32#95
prime radicalC24×C32C2×C4
hypocenterC32#1305
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
7. C2×#3748C4semidirect
15. C3×#830C4semidirect
62. #830Dic3semidirect
293. C32#1305semidirect
356. C3#67626semidirect
357. C3#67685semidirect

Maximal subgroups

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

subgroupindex
#105929062
C3×#52122
C3×#52072
#676853
#676263