Finite Group Databasebeta

← #11790539

Subgroups — #11790539

Order 1152.

421 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63649C211yesmaximal, characteristic
2C3×#5125C211yesmaximal, characteristic
3#10591143C211yesmaximal, characteristic
4C2×#63578C211yesmaximal, characteristic
5#10591057C211yesmaximal, characteristic
6C3×#4559C211yesmaximal, characteristic
7#10589169C211yesmaximal, characteristic
8#70725—31nomaximal
9#69015—31nomaximal
10C2×C32×M16C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63649C414yescomplemented
18C3×#819—22no—
19#63578—21no—
20#63578—21no—
21#63578—22no—
22#63554—21no—
23Dic3×C3⋊C8—21no—
24C3×#430—31no—
25#5125D311yescharacteristic
26#5124—31no—
27#5124—31no—
28C2×#822—31no—
29C2×#822—31no—
30C2×#822—31no—
31C2×#822—31no—
32C2×#822—61no—
33#5122—31no—
34#4997—31no—
35C3×#344—31no—
36#4559D311yescharacteristic
37#4556—31no—
38#4533—31no—
39C22×C32×C4C2311yescharacteristic
40C32×M16—21no—
41C32×M16C2×C412yes—
42C2×C32×C8—21no—
43#3748—21no—
44#3748C2×C412yes—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)C2×C412yes—
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)Q812yes—
50C3×#217Q812yes—
51C3×C4⋊Dic3—21no—
52C3×C4×Dic3—21no—
53C3×#208—21no—
54C3×#208—21no—
55C3×#208—21no—
56C3×#208—21no—
57C3×#208—21no—
58C3×#208D412yes—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#1953—91noSylow
63C2×C3×M16—21no—
64C2×C3×M16—31no—
65C2×C3×M16—31no—
66C2×C3×M16—31no—
67C2×C3×M16C2×D311yescharacteristic
68C2×C3×M16C2×D311yescharacteristic
69C3×#117—31no—
70#926C2×D311yescharacteristic
71C2×#208—31no—
72C2×#208—31no—
73C2×#208—61no—
74C2×#208C2×D311yescharacteristic
75C2×#208C2×D311yescharacteristic
76C2×#208C2×D311yescharacteristic
77C22×C3⋊C8—31no—
78C22×C3⋊C8—31no—
79C22×C3⋊C8—61no—
80C3×#108—62no—
81#822—34no—
82#822—34no—
83#822—64no—
84#822—61no—
85#822—61no—
86#822—61no—
87#822—61no—
88#822—62no—
89#822—62no—
90#819—22no—
91#815—61no—
92C8×Dic3—61no—
93#803—61no—
94C4×C3⋊C8—61no—
95C23×C32C2×Q811yescharacteristic
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×Q811yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—22no—
103C32×C8—22no—
104C3⋊(C3⋊C8)—22no—
105C3⋊(C3⋊C8)C4⋊C412yes—
106C3⋊(C3⋊C8)C4⋊C412yes—
107C3×C3⋊C8—22no—
108C3×C3⋊C8—41no—
109C3×C3⋊C8—41no—
110#430—31no—
111#430—91no—
112C2×#108—91no—
113C2×#108—91no—
114#405—91no—
115#344—31no—
116#344—91no—
117C22×C3×C4—21no—
118C22×C3×C4C22×D311yescharacteristic
119C22×C3×C4C22×D311yescharacteristic
120C3×M16—21no—
121C3×M16—21no—
122C3×M16—22no—
123C3×M16—32no—
124C3×M16—41no—
125C3×M16—61no—
126C3×M16—61no—
127C3×M16—61no—
128C3×M16—61no—
129C3×M16—61no—
130C3×M16C4×D312yes—
131C3×M16C4×D312yes—
132C2×C3×C8—21no—
133C2×C3×C8—21no—
134C2×C3×C8—41no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C2×C3×C8—61no—
138C3×C4⋊C4—61no—
139C3×C22⋊C4—32no—
140C3×C42—61no—
141#217Dic612yes—
142C4⋊Dic3—21no—
143C4×Dic3—21no—
144#208—21no—
145#208—21no—
146#208—21no—
147#208—21no—
148#208—21no—
149#208—32no—
150#208—32no—
151#208—62no—
152#208—61no—
153#208—61no—
154#208—121no—
155#208#6712yes—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—32no—
160C2×C3⋊C8—32no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—31no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—32no—
166C2×C3⋊C8—32no—
167C2×C3⋊C8—62no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—61no—
170C2×C3⋊C8—62no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8—61no—
173C2×C3⋊C8—121no—
174C22×C32—41no—
175C22×C32C4×Q811yescharacteristic
176C22×C32C22⋊Q811yescharacteristic
177C22×C32C4⋊Q811yescharacteristic
178C32×C4C2×C4⋊C411yescharacteristic
179C32×C4C4×D411yescharacteristic
180C32×C4#12111yescharacteristic
181C32×C4#12511yescharacteristic
182C3×Dic3—42no—
183C2×M16—31no—
184C2×M16—31no—
185C2×M16—31no—
186C2×M16—91no—
187C2×M16D3211yescharacteristic
188C22×C8—91no—
189#117—31no—
190#108—62no—
191#108—94no—
192#108—181no—
193#108—181no—
194#108—182no—
195#97—181no—
196C4×C8—181no—
197C23×C3—21no—
198C23×C3C2×Dic611yescharacteristic
199C23×C3D3×Q811yescharacteristic
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—62no—
207C2×C3×C4C2×C4×D311yescharacteristic
208C2×C3×C4C2×C4×D311yescharacteristic
209C2×C3×C4#23511yescharacteristic
210C2×C3×C4#23511yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4#23711yescharacteristic
215C2×C3×C4#23711yescharacteristic
216C2×C3×C4D3×Q811yescharacteristic
217C2×C3×C4D3×Q811yescharacteristic
218C2×C3×C4C2×#6711yescharacteristic
219C2×Dic3—22no—
220C3×C8—22no—
221C3×C8—22no—
222C3×C8—42no—
223C3×C8—62no—
224C3×C8—121no—
225C3×C8—121no—
226C3⋊C8—22no—
227C3⋊C8—32no—
228C3⋊C8—32no—
229C3⋊C8—32no—
230C3⋊C8—32no—
231C3⋊C8—41no—
232C3⋊C8—41no—
233C3⋊C8—62no—
234C3⋊C8—62no—
235C3⋊C8—62no—
236C3⋊C8—62no—
237C3⋊C8—122no—
238C2×C32—21no—
239C2×C32—21no—
240C2×C32—21no—
241C2×C32#38911yescharacteristic
242C22×C4C2×D3211yescharacteristic
243M16—21no—
244M16—32no—
245M16—61no—
246M16—61no—
247M16—61no—
248M16—61no—
249M16—61no—
250M16—92no—
251M16—181no—
252M16#62412yes—
253C2×C8—21no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8—61no—
257C2×C8—92no—
258C2×C8—91no—
259C2×C8—91no—
260C2×C8—92no—
261C2×C8—181no—
262C4⋊C4—61no—
263C22⋊C4—32no—
264C42—61no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—42no—
271C22×C3C4×Dic611yescharacteristic
272C22×C3#87811yescharacteristic
273C22×C3#88711yescharacteristic
274C22×C3#88811yescharacteristic
275C22×C3#89611yescharacteristic
276C22×C3#94411yescharacteristic
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—122no—
282C3×C4#67⋊C411yescharacteristic
283C3×C4#88411yescharacteristic
284C3×C4#88911yescharacteristic
285C3×C4#88911yescharacteristic
286C3×C4D3×C4⋊C411yescharacteristic
287C3×C4D3×C4⋊C411yescharacteristic
288C3×C4C4×#6711yescharacteristic
289C3×C4#93911yescharacteristic
290Dic3—42no—
291C32#195311yescharacteristic, complemented, Sylow
292C23D3×Dic611yescharacteristic
293C2×C4—62no—
294C2×C4#379511yescharacteristic
295C2×C4#379711yescharacteristic
296C2×C4#380211yescharacteristic
297C2×C4#380411yescharacteristic
298C2×C4C2×#62411yescharacteristic
299C2×C4D3×#6711yescharacteristic
300C8—22no—
301C8—62no—
302C8—92no—
303C8—92no—
304C8—121no—
305C8—121no—
306C8—182no—
307C2×C3—22no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—41no—
316C2×C3—41no—
317C2×C3#464711yescharacteristic
318C2×C3#497611yescharacteristic
319C22—41no—
320C22#6383911yescharacteristic
321C22#6384411yescharacteristic
322C22#6389911yescharacteristic
323C4—122no—
324C4#6384711yescharacteristic
325C4#6388511yescharacteristic
326C4#6390011yescharacteristic
327C4#6395211yescharacteristic
328C3—21no—
329C3#6901511yescharacteristic, complemented
330C3#7072511yescharacteristic, complemented
331C2—21no—
332C2—21no—
333C2—21no—
334C2#1059126411yescharacteristic
subgroupG/H
centerC4#63885
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#389
prime radicalC23×C32C2×Q8
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1953
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
17. #63649C4semidirect
291. C32#1953semidirect
329. C3#69015semidirect
330. C3#70725semidirect

Maximal subgroups

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

subgroupindex
C2×#636492
C3×#51252
#105911432
C2×#635782
#105910572
C3×#45592
#105891692
#707253
#690153