Finite Group Databasebeta

← #11775911

Subgroups — #11775911

Order 1152.

479 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#10592625C211yesmaximal, characteristic
3C2×C3×#803C211yesmaximal, characteristic
4#10589088C214yesmaximal, complemented
5#71822—31nomaximal
6#69801—31nomaximal
7C2×C32×C42C2211yescharacteristic
8C3×#926C412yes—
9C3×#924—21no—
10C3×#924—21no—
11C22×C3×C3⋊C8—21no—
12C3×#870C2212yes—
13C3×#869C411yescharacteristic
14C3×#869C411yescharacteristic
15C3×C4×Dic6—21no—
16C3×C4×Dic6—21no—
17#63657—21no—
18C4⋊(C3⋊(C3⋊C8))—21no—
19#63630C2212yes—
20C3×#803—21no—
21C3×#803C2212yes—
22C3×#533—31no—
23#5470D311yescharacteristic
24C2×C3×#97—31no—
25#4926—31no—
26#4926—31no—
27#4926—61no—
28C2×#803D311yescharacteristic
29#4543—34no—
30#4465—34no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C2×C3×Dic6—21no—
35C2×C3×Dic6—21no—
36C32×C42C2×C411yescharacteristic
37C32×C42D411yescharacteristic
38C32×C42D411yescharacteristic
39C32×C42C2311yescharacteristic
40C2×C3⋊(C3⋊C8)—22no—
41C3×#217—22no—
42C3×C4⋊Dic3—21no—
43C3×C4⋊Dic3—21no—
44C3×C4⋊Dic3C2×C412yes—
45C3×C4⋊Dic3C2×C412yes—
46C3×Dic3⋊C4—22no—
47C3×Dic3⋊C4—22no—
48C3×C4×Dic3—22no—
49C2×C3×C3⋊C8—24no—
50C2×C3×C3⋊C8—22no—
51#1531—91noSylow
52C22×C3×C8—61no—
53C3×C4⋊Q8—31no—
54C3×C4⋊Q8—31no—
55C3×#125—32no—
56C3×C22⋊Q8—61no—
57C3×C22⋊Q8—61no—
58C3×C4×Q8—61no—
59C3×C4×Q8—61no—
60C3×#117—32no—
61C2×C3×C42—21no—
62C2×C3×C42C2×D311yescharacteristic
63C2×C3×C42C2×D311yescharacteristic
64#926Dic312yes—
65#924—21no—
66#924—21no—
67C22×C3⋊C8—21no—
68#870C2×D312yes—
69#869Dic311yescharacteristic
70#869Dic311yescharacteristic
71C4×Dic6—21no—
72C4×Dic6—21no—
73C3×#97—32no—
74C3×#97—61no—
75#830—62no—
76#830—61no—
77#830—61no—
78C4⋊(C3⋊C8)—62no—
79C4⋊(C3⋊C8)—61no—
80C4⋊(C3⋊C8)—61no—
81#803—21no—
82#803—32no—
83#803—32no—
84#803—62no—
85#803C2×D312yes—
86C23×C32C22⋊C411yescharacteristic
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—41no—
90C2×C32×C4C22⋊C411yescharacteristic
91C2×C32×C4C22⋊C411yescharacteristic
92C2×C32×C4C22⋊C411yescharacteristic
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C3×Dic3—22no—
97C2×C3×Dic3—22no—
98C3×Dic6—42no—
99C3×Dic6—42no—
100C3⋊(C3⋊C8)—42no—
101C3×C3⋊C8—24no—
102#533—31no—
103#432—91no—
104C2×#97—31no—
105#330—94no—
106C2×C3×Q8—61no—
107C2×C3×Q8—61no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4—21no—
111C22×C3×C4C4×D311yescharacteristic
112C22×C3×C4D1211yescharacteristic
113C22×C3×C4C2×Dic311yescharacteristic
114C22×C3×C4#6711yescharacteristic
115C22×C3×C4#6711yescharacteristic
116C22×C3×C4#6711yescharacteristic
117C2×Dic6—21no—
118C2×Dic6—21no—
119C2×C3×C8—64no—
120C2×C3×C8—62no—
121C3×C4⋊C4—32no—
122C3×C4⋊C4—32no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—62no—
126C3×C4⋊C4—62no—
127C3×C22⋊C4—62no—
128C3×C42—21no—
129C3×C42—21no—
130C3×C42—21no—
131C3×C42—21no—
132C3×C42—62no—
133C3×C42C4×D311yescharacteristic
134C3×C42D1211yescharacteristic
135C3×C42C2×Dic311yescharacteristic
136C3×C42#6711yescharacteristic
137C3×C42#6711yescharacteristic
138C3×C42#6711yescharacteristic
139C3×C42C22×D311yescharacteristic
140C3×C42C22×D311yescharacteristic
141#217—22no—
142C4⋊Dic3—21no—
143C4⋊Dic3—21no—
144C4⋊Dic3C2×Dic312yes—
145C4⋊Dic3C2×Dic312yes—
146Dic3⋊C4—22no—
147Dic3⋊C4—22no—
148C4×Dic3—22no—
149C2×C3⋊C8—24no—
150C2×C3⋊C8—22no—
151C2×C3⋊C8—64no—
152C2×C3⋊C8—62no—
153C2×C3⋊C8—62no—
154C22×C32—21no—
155C22×C32—21no—
156C22×C32#10112yes—
157C22×C32C2×C22⋊C411yescharacteristic
158C32×C4—21no—
159C32×C4—21no—
160C32×C4—21no—
161C32×C4—21no—
162C32×C4—21no—
163C32×C4#10412yes—
164C3×Dic3—42no—
165C3×Dic3—42no—
166C22×C8—61no—
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—181no—
177C22⋊C8—181no—
178#97—32no—
179#97—61no—
180#97—92no—
181C23×C3—21no—
182C23×C3(C2×D3)⋊C411yescharacteristic
183C23×C3#21711yescharacteristic
184C3×Q8—122no—
185C3×Q8—122no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—22no—
189C2×C3×C4—22no—
190C2×C3×C4—21no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—42no—
197C2×C3×C4—42no—
198C2×C3×C4—41no—
199C2×C3×C4—41no—
200C2×C3×C4—42no—
201C2×C3×C4—62no—
202C2×C3×C4—62no—
203C2×C3×C4(C2×D3)⋊C411yescharacteristic
204C2×C3×C4(C2×D3)⋊C411yescharacteristic
205C2×C3×C4(C2×D3)⋊C411yescharacteristic
206C2×C3×C4#21711yescharacteristic
207C2×C3×C4#21711yescharacteristic
208C2×C3×C4#21711yescharacteristic
209C2×C3×C4C2×C4×D311yescharacteristic
210C2×C3×C4C2×D1211yescharacteristic
211C2×C3×C4C22×Dic311yescharacteristic
212C2×C3×C4C2×#6711yescharacteristic
213C2×C3×C4C2×#6711yescharacteristic
214C2×C3×C4C2×#6711yescharacteristic
215C2×Dic3—22no—
216C2×Dic3—22no—
217Dic6—42no—
218Dic6—42no—
219C3×C8—64no—
220C3⋊C8—24no—
221C3⋊C8—124no—
222C3⋊C8—122no—
223C3⋊C8—122no—
224C2×C32—22no—
225C2×C32C2×#10111yescharacteristic
226C2×C32C2×#10411yescharacteristic
227C2×C32#42111yescharacteristic
228C2×Q8—61no—
229C2×Q8—61no—
230C22×C4D3×Dic311yescharacteristic
231C22×C4#62511yescharacteristic
232C22×C4#62611yescharacteristic
233C2×C8—64no—
234C2×C8—62no—
235C2×C8—182no—
236C4⋊C4—32no—
237C4⋊C4—32no—
238C4⋊C4—61no—
239C4⋊C4—61no—
240C4⋊C4—62no—
241C4⋊C4—62no—
242C22⋊C4—62no—
243C42—62no—
244C42D3×Dic311yescharacteristic
245C42#62511yescharacteristic
246C42#62611yescharacteristic
247C42C2×D3211yescharacteristic
248C22×C3—21no—
249C22×C3—21no—
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—22no—
253C22×C3—21no—
254C22×C3—41no—
255C22×C3—41no—
256C22×C3#82412yes—
257C22×C3#83612yes—
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—21no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—22no—
272C3×C4—41no—
273C3×C4—41no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—122no—
277C3×C4—122no—
278C3×C4#80512yes—
279C3×C4#83712yes—
280Dic3—42no—
281Dic3—42no—
282C32#153111yescharacteristic, complemented, Sylow
283C23(C2×D3)⋊Dic311yescharacteristic
284Q8—122no—
285Q8—122no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
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—64no—
298C8—362no—
299C2×C3—22no—
300C2×C3—22no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—42no—
305C2×C3C2×#80511yescharacteristic
306C2×C3C2×#82411yescharacteristic
307C2×C3#513911yescharacteristic
308C2×C3C2×#83611yescharacteristic
309C2×C3C2×#83711yescharacteristic
310C2×C3#523611yescharacteristic
311C22—21no—
312C22—21no—
313C22#6356012yes—
314C22C2×(C2×D3)⋊Dic311yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—122no—
321C4—122no—
322C4#6356912yes—
323C3—21no—
324C3#6980111yescharacteristic, complemented
325C3#7182211yescharacteristic, complemented
326C2—22no—
327C2C2×#6356011yescharacteristic
328C2C2×#6356911yescharacteristic
329C2#1059111011yescharacteristic
subgroupG/H
centerC22C2×(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#1531
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589088C2semidirect
282. C32#1531semidirect
324. C3#69801semidirect
325. C3#71822semidirect

Maximal subgroups

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

subgroupindex
C3×#54702
#105926252
C2×C3×#8032
#105890882
#718223
#698013