Finite Group Databasebeta

← #11776248

Subgroups — #11776248

Order 1152.

463 conjugacy classes of subgroups.

The subgroup lattice has 331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5470C211yesmaximal, characteristic
2#10592624C211yesmaximal, characteristic
3C3×#4925C211yesmaximal, characteristic
4#10589093C212yesmaximal, complemented
5#10589092C212yesmaximal, complemented
6#71829—31nomaximal
7#70777—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C3×#926C412yes—
10C3×#924—21no—
11C3×#924—21no—
12C3×#870C412yes—
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C3×C4×Dic6—21no—
16C3×C4×Dic6—21no—
17#63657—21no—
18C4⋊(C3⋊(C3⋊C8))C2212yes—
19C4×C3⋊(C3⋊C8)—21no—
20C3×#830—21no—
21C3×C4⋊(C3⋊C8)C2212yes—
22C3×C4×C3⋊C8—21no—
23C3×#533—31no—
24#5470D311yescharacteristic
25C3×#431—31no—
26#4925—31no—
27#4925—31no—
28#4925—61no—
29#4925D311yescharacteristic
30#4547—32no—
31#4547—32no—
32#4486—32no—
33#4482—32no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C2×C3×Dic6—21no—
38C2×C3×Dic6—21no—
39C32×C42C2×C411yescharacteristic
40C32×C42D411yescharacteristic
41C32×C42D411yescharacteristic
42C32×C42C2311yescharacteristic
43C2×C3⋊(C3⋊C8)—22no—
44C3×#217—22no—
45C3×C4⋊Dic3—21no—
46C3×C4⋊Dic3—21no—
47C3×C4⋊Dic3C2×C412yes—
48C3×C4⋊Dic3C2×C412yes—
49C3×Dic3⋊C4—22no—
50C3×Dic3⋊C4—22no—
51C3×C4×Dic3—22no—
52C2×C3×C3⋊C8—22no—
53#1544—91noSylow
54C3×C4⋊Q8—31no—
55C3×C4⋊Q8—31no—
56C3×#125—32no—
57C3×C22⋊Q8—61no—
58C3×C22⋊Q8—61no—
59C3×C4×Q8—61no—
60C3×C4×Q8—61no—
61C3×#117—32no—
62C2×C3×C42—21no—
63C2×C3×C42C2×D311yescharacteristic
64C2×C3×C42C2×D311yescharacteristic
65#926Dic312yes—
66#924—21no—
67#924—21no—
68#870Dic312yes—
69#869C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71C4×Dic6—21no—
72C4×Dic6—21no—
73C3×C4⋊C8—32no—
74C3×C22⋊C8—61no—
75C3×C4×C8—61no—
76#830—21no—
77#830—62no—
78#830—61no—
79#830—61no—
80C4⋊(C3⋊C8)—32no—
81C4⋊(C3⋊C8)—32no—
82C4⋊(C3⋊C8)—62no—
83C4⋊(C3⋊C8)C2×D312yes—
84C4×C3⋊C8—21no—
85C4×C3⋊C8—62no—
86C4×C3⋊C8—61no—
87C4×C3⋊C8—61no—
88C23×C32C22⋊C411yescharacteristic
89C2×C32×C4—22no—
90C2×C32×C4—22no—
91C2×C32×C4—22no—
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C3×Dic6—42no—
101C3×Dic6—42no—
102C3⋊(C3⋊C8)—42no—
103C3×C3⋊C8—42no—
104#533—31no—
105#431—31no—
106#431—91no—
107#332—92no—
108#332—92no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4C4×D311yescharacteristic
115C22×C3×C4D1211yescharacteristic
116C22×C3×C4C2×Dic311yescharacteristic
117C22×C3×C4#6711yescharacteristic
118C22×C3×C4#6711yescharacteristic
119C22×C3×C4#6711yescharacteristic
120C2×Dic6—21no—
121C2×Dic6—21no—
122C2×C3×C8—62no—
123C3×C4⋊C4—32no—
124C3×C4⋊C4—32no—
125C3×C4⋊C4—62no—
126C3×C4⋊C4—62no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C22⋊C4—62no—
130C3×C42—21no—
131C3×C42—21no—
132C3×C42—21no—
133C3×C42—21no—
134C3×C42—62no—
135C3×C42C4×D311yescharacteristic
136C3×C42D1211yescharacteristic
137C3×C42C2×Dic311yescharacteristic
138C3×C42#6711yescharacteristic
139C3×C42#6711yescharacteristic
140C3×C42#6711yescharacteristic
141C3×C42C22×D311yescharacteristic
142C3×C42C22×D311yescharacteristic
143#217—22no—
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3C2×Dic312yes—
147C4⋊Dic3C2×Dic312yes—
148Dic3⋊C4—22no—
149Dic3⋊C4—22no—
150C4×Dic3—22no—
151C2×C3⋊C8—22no—
152C2×C3⋊C8—64no—
153C2×C3⋊C8—62no—
154C2×C3⋊C8—62no—
155C22×C32—21no—
156C22×C32—21no—
157C22×C32—21no—
158C22×C32C2×C22⋊C411yescharacteristic
159C32×C4—21no—
160C32×C4—21no—
161C32×C4—21no—
162C32×C4#10112yes—
163C32×C4#13512yes—
164C32×C4#13512yes—
165C3×Dic3—42no—
166C3×Dic3—42no—
167C4⋊Q8—31no—
168C4⋊Q8—31no—
169#125—32no—
170C22⋊Q8—61no—
171C22⋊Q8—61no—
172C4×Q8—61no—
173C4×Q8—61no—
174#117—32no—
175C2×C42D3211yescharacteristic
176C4⋊C8—32no—
177C4⋊C8—92no—
178C22⋊C8—61no—
179C22⋊C8—181no—
180C4×C8—61no—
181C4×C8—181no—
182C23×C3—21no—
183C23×C3(C2×D3)⋊C411yescharacteristic
184C23×C3#21711yescharacteristic
185C3×Q8—122no—
186C3×Q8—122no—
187C2×C3×C4—24no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—62no—
203C2×C3×C4—62no—
204C2×C3×C4(C2×D3)⋊C411yescharacteristic
205C2×C3×C4(C2×D3)⋊C411yescharacteristic
206C2×C3×C4(C2×D3)⋊C411yescharacteristic
207C2×C3×C4#21711yescharacteristic
208C2×C3×C4#21711yescharacteristic
209C2×C3×C4#21711yescharacteristic
210C2×C3×C4C2×C4×D311yescharacteristic
211C2×C3×C4C2×D1211yescharacteristic
212C2×C3×C4C22×Dic311yescharacteristic
213C2×C3×C4C2×#6711yescharacteristic
214C2×C3×C4C2×#6711yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216C2×Dic3—22no—
217C2×Dic3—22no—
218Dic6—42no—
219Dic6—42no—
220C3×C8—122no—
221C3⋊C8—42no—
222C3⋊C8—124no—
223C3⋊C8—122no—
224C3⋊C8—122no—
225C2×C32—41no—
226C2×C32C2×#10111yescharacteristic
227C2×C32#41611yescharacteristic
228C2×C32#41611yescharacteristic
229C2×Q8—61no—
230C2×Q8—61no—
231C22×C4D3×Dic311yescharacteristic
232C22×C4#62511yescharacteristic
233C22×C4#62611yescharacteristic
234C2×C8—62no—
235C2×C8—182no—
236C4⋊C4—32no—
237C4⋊C4—32no—
238C4⋊C4—62no—
239C4⋊C4—62no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C22⋊C4—62no—
243C42—62no—
244C42D3×Dic311yescharacteristic
245C42#62511yescharacteristic
246C42#62611yescharacteristic
247C42C2×D3211yescharacteristic
248C22×C3—22no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—41no—
257C22×C3—41no—
258C22×C3C2×(C2×D3)⋊C411yescharacteristic
259C22×C3C2×#21711yescharacteristic
260C3×C4—22no—
261C3×C4—21no—
262C3×C4—21no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4—22no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—41no—
271C3×C4—41no—
272C3×C4—122no—
273C3×C4—122no—
274C3×C4#82412yes—
275C3×C4#83612yes—
276C3×C4#90412yes—
277C3×C4#95012yes—
278C3×C4#95012yes—
279C3×C4#95012yes—
280Dic3—42no—
281Dic3—42no—
282C32#154411yescharacteristic, complemented, Sylow
283C23(C2×D3)⋊Dic311yescharacteristic
284Q8—122no—
285Q8—122no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—62no—
290C2×C4—62no—
291C2×C4(C2×D3)⋊Dic311yescharacteristic
292C2×C4(C2×D3)⋊Dic311yescharacteristic
293C2×C4(C2×D3)⋊Dic311yescharacteristic
294C2×C4C2×D3×Dic311yescharacteristic
295C2×C4C2×#62511yescharacteristic
296C2×C4C2×#62611yescharacteristic
297C8—122no—
298C8—362no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—42no—
303C2×C3—41no—
304C2×C3—41no—
305C2×C3#500211yescharacteristic
306C2×C3#511311yescharacteristic
307C2×C3C2×#82411yescharacteristic
308C2×C3C2×#83611yescharacteristic
309C2×C3#523311yescharacteristic
310C2×C3#523311yescharacteristic
311C22—21no—
312C22—21no—
313C22—21no—
314C22C2×(C2×D3)⋊Dic311yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—122no—
319C4—122no—
320C4#6356012yes—
321C4#6382212yes—
322C4#6382912yes—
323C3—21no—
324C3#7077711yescharacteristic, complemented
325C3#7182911yescharacteristic, complemented
326C2—41no—
327C2C2×#6356011yescharacteristic
328C2#1059108311yescharacteristic
329C2#1059108411yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1544
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589093C2semidirect
5. #10589092C2semidirect
282. C32#1544semidirect
324. C3#70777semidirect
325. C3#71829semidirect

Maximal subgroups

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

subgroupindex
C3×#54702
#105926242
C3×#49252
#105890932
#105890922
#718293
#707773