Finite Group Databasebeta

← #11786334

Subgroups — #11786334

Order 1152.

477 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×#63649C211yesmaximal, characteristic
2C2×C3×#822C211yesmaximal, characteristic
3C3×#5118C211yesmaximal, characteristic
4C2×#63578C211yesmaximal, characteristic
5C2×#63577C211yesmaximal, characteristic
6#10591115C211yesmaximal, characteristic
7C2×#63554C211yesmaximal, characteristic
8#70694—31nomaximal
9#70519—31nomaximal
10C2×C32×M16C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4×Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63649—22no—
18C3×#822—22no—
19C3×Dic3⋊C8—22no—
20#63578—22no—
21#63577—22no—
22Dic3⋊(C3⋊C8)—22no—
23#63554C414yes—
24C2×C3×#108—31no—
25C3×#423—31no—
26C2×#822—31no—
27C2×#822—31no—
28C2×#822—31no—
29C2×#822—31no—
30C2×#822—31no—
31C2×#822—61no—
32C2×#822D311yescharacteristic
33#5118—31no—
34#5118D311yescharacteristic
35C2×#819—31no—
36C2×#815—31no—
37#4924—31no—
38C2×#803—31no—
39C22×C32×C4C2311yescharacteristic
40C22×C3×Dic3Q812yes—
41C32×M16—21no—
42C32×M16—21no—
43C2×C32×C8—21no—
44#3748—21no—
45#3748—21no—
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)C2×C412yes—
48C2×C3⋊(C3⋊C8)D412yes—
49C2×C3⋊(C3⋊C8)Q812yes—
50C3×C4×Dic3C2×C412yes—
51C3×C4×Dic3D412yes—
52C3×#208—21no—
53C3×#208—21no—
54C3×#208—21no—
55C3×#208—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58C2×C3×C3⋊C8C2×C412yes—
59C2×C3×C3⋊C8D412yes—
60C2×C3×C3⋊C8Q812yes—
61#1849—91noSylow
62C2×C3×M16—21no—
63C2×C3×M16—31no—
64C2×C3×M16—31no—
65C2×C3×M16C2×D311yescharacteristic
66C2×C3×M16C2×D311yescharacteristic
67C22×C3×C8—31no—
68C2×C3×C42—31no—
69C2×C4×Dic3C2×D311yescharacteristic
70C2×#208—31no—
71C2×#208—31no—
72C2×#208—61no—
73C2×#208C2×D311yescharacteristic
74C2×#208C2×D311yescharacteristic
75C22×C3⋊C8—31no—
76C22×C3⋊C8—31no—
77C22×C3⋊C8—61no—
78C22×C3⋊C8C2×D311yescharacteristic
79C3×#108—62no—
80C3×C4⋊C8—62no—
81#822—22no—
82#822—62no—
83#822—62no—
84#822—62no—
85#822—62no—
86#822—64no—
87#822—62no—
88#819—62no—
89#815—34no—
90Dic3⋊C8—22no—
91Dic3⋊C8—62no—
92C4⋊(C3⋊C8)—62no—
93#803—34no—
94C23×C32C2×Q811yescharacteristic
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×Q811yescharacteristic
100C2×C32×C4C2×Q811yescharacteristic
101C2×C3×Dic3—42no—
102C2×C3×Dic3C4⋊C414yes—
103C32×C8—41no—
104C3⋊(C3⋊C8)—41no—
105C3⋊(C3⋊C8)C4⋊C414yes—
106C3×C3⋊C8—41no—
107C3×C3⋊C8—41no—
108C3×C3⋊C8C4⋊C414yes—
109C2×#108—31no—
110C2×#108—91no—
111C2×#108—91no—
112C2×#108—91no—
113#423—31no—
114#423—91no—
115C2×#97—91no—
116C22×C3×C4—21no—
117C22×C3×C4—32no—
118C22×C3×C4C22×D311yescharacteristic
119C22×C3×C4C22×D311yescharacteristic
120C22×Dic3Dic612yes—
121C3×M16—22no—
122C3×M16—21no—
123C3×M16—21no—
124C3×M16—21no—
125C3×M16—21no—
126C3×M16—41no—
127C3×M16—61no—
128C3×M16—61no—
129C3×M16—61no—
130C3×M16—61no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—32no—
134C2×C3×C8—32no—
135C2×C3×C8—32no—
136C2×C3×C8—41no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C3×C42—32no—
140C3×C42—32no—
141C4×Dic3C4×D312yes—
142C4×Dic3#6712yes—
143#208—21no—
144#208—21no—
145#208—21no—
146#208—21no—
147#208—62no—
148#208—61no—
149#208—61no—
150#208—61no—
151#208—61no—
152#208—121no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—21no—
155C2×C3⋊C8—32no—
156C2×C3⋊C8—32no—
157C2×C3⋊C8—32no—
158C2×C3⋊C8—32no—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—32no—
161C2×C3⋊C8—62no—
162C2×C3⋊C8—62no—
163C2×C3⋊C8—62no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8—121no—
167C2×C3⋊C8Dic612yes—
168C2×C3⋊C8C4×D312yes—
169C2×C3⋊C8#6712yes—
170C22×C32—22no—
171C22×C32C2×C4⋊C411yescharacteristic
172C22×C32C4⋊Q811yescharacteristic
173C22×C32C4⋊Q811yescharacteristic
174C32×C4C2×C4⋊C411yescharacteristic
175C32×C4C2×C4⋊C411yescharacteristic
176C32×C4#12711yescharacteristic
177C32×C4C4⋊Q811yescharacteristic
178C3×Dic3—24no—
179C2×M16—31no—
180C2×M16—31no—
181C2×M16—91no—
182C2×M16D3211yescharacteristic
183C22×C8—31no—
184C22×C8—91no—
185C2×C42—31no—
186#108—62no—
187#108—182no—
188#108—182no—
189#108—182no—
190C4⋊C8—62no—
191C4⋊C8—182no—
192#97—94no—
193C23×C3—21no—
194C23×C3C2×Dic611yescharacteristic
195C23×C3D3×Q811yescharacteristic
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—34no—
203C2×C3×C4—122no—
204C2×C3×C4C2×Dic611yescharacteristic
205C2×C3×C4C2×C4×D311yescharacteristic
206C2×C3×C4C2×C4×D311yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4D3×D411yescharacteristic
210C2×C3×C4D3×D411yescharacteristic
211C2×C3×C4D3×Q811yescharacteristic
212C2×C3×C4D3×Q811yescharacteristic
213C2×C3×C4D3×Q811yescharacteristic
214C2×C3×C4C2×#6711yescharacteristic
215C2×C3×C4C2×#6711yescharacteristic
216C2×Dic3—42no—
217C2×Dic3Dic3⋊C414yes—
218C3×C8—34no—
219C3×C8—42no—
220C3×C8—41no—
221C3×C8—41no—
222C3×C8—121no—
223C3×C8—121no—
224C3⋊C8—34no—
225C3⋊C8—34no—
226C3⋊C8—41no—
227C3⋊C8—41no—
228C3⋊C8—64no—
229C3⋊C8—122no—
230C3⋊C8—121no—
231C3⋊C8—121no—
232C3⋊C8Dic3⋊C414yes—
233C2×C32—21no—
234C2×C32—21no—
235C2×C32#38411yescharacteristic
236C2×C32#43012yes—
237C22×C4—32no—
238C22×C4C2×D3211yescharacteristic
239M16—21no—
240M16—21no—
241M16—61no—
242M16—61no—
243M16—61no—
244M16—61no—
245M16—181no—
246M16—181no—
247C2×C8—21no—
248C2×C8—32no—
249C2×C8—32no—
250C2×C8—32no—
251C2×C8—61no—
252C2×C8—61no—
253C2×C8—92no—
254C2×C8—92no—
255C2×C8—92no—
256C2×C8—181no—
257C42—32no—
258C42—32no—
259C22×C3—22no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—42no—
265C22×C3#88811yescharacteristic
266C22×C3#88811yescharacteristic
267C22×C3#88811yescharacteristic
268C22×C3D3×C4⋊C411yescharacteristic
269C22×C3C2×Dic3⋊C411yescharacteristic
270C22×C3#94411yescharacteristic
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—64no—
276C3×C4#88811yescharacteristic
277C3×C4D3×C4⋊C411yescharacteristic
278C3×C4D3×C4⋊C411yescharacteristic
279C3×C4D3×C4⋊C411yescharacteristic
280C3×C4C2×Dic3⋊C411yescharacteristic
281C3×C4#94011yescharacteristic
282C3×C4#94011yescharacteristic
283C3×C4#94411yescharacteristic
284Dic3—24no—
285C32#184911yescharacteristic, complemented, Sylow
286C23D3×Dic611yescharacteristic
287C2×C4—34no—
288C2×C4—122no—
289C2×C4D3×Dic611yescharacteristic
290C2×C4#379711yescharacteristic
291C2×C4C4×D3211yescharacteristic
292C2×C4D3×#6711yescharacteristic
293C2×C4D3×#6711yescharacteristic
294C2×C4#381111yescharacteristic
295C8—34no—
296C8—41no—
297C8—94no—
298C8—121no—
299C8—121no—
300C8—361no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3—21no—
304C2×C3—21no—
305C2×C3—21no—
306C2×C3—22no—
307C2×C3—41no—
308C2×C3—41no—
309C2×C3#489312yes—
310C2×C3#497511yescharacteristic
311C2×C3#497511yescharacteristic
312C2×C3#512412yes—
313C22—22no—
314C22#6383911yescharacteristic
315C22#6384011yescharacteristic
316C22D3×Dic3⋊C411yescharacteristic
317C4—64no—
318C4#6383911yescharacteristic
319C4D3×Dic3⋊C411yescharacteristic
320C4#6388311yescharacteristic
321C4#6397911yescharacteristic
322C3—21no—
323C3#7051911yescharacteristic, complemented
324C3#7069411yescharacteristic, complemented
325C2—21no—
326C2—21no—
327C2#1059097312yes—
328C2#1059124411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C2×Q8
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1849
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
285. C32#1849semidirect
323. C3#70519semidirect
324. C3#70694semidirect

Maximal subgroups

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

subgroupindex
C2×#636492
C2×C3×#8222
C3×#51182
C2×#635782
C2×#635772
#105911152
C2×#635542
#706943
#705193