Finite Group Databasebeta

← #37544020

Subgroups — #37544020

Order 23168.

358 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041887C211yesmaximal, characteristic
2#26041755C211yesmaximal, characteristic
3#26041623C211yesmaximal, characteristic
4#26041618C211yesmaximal, characteristic
5#26041589C211yesmaximal, characteristic, complemented
6#26041584C211yesmaximal, characteristic, complemented
7#26041488C211yesmaximal, characteristic, complemented
8#26041487C211yesmaximal, characteristic, complemented
9#26041436C211yesmaximal, characteristic
10#26041433C211yesmaximal, characteristic
11#26041387C211yesmaximal, characteristic, complemented
12C4×#15668439C211yesmaximal, characteristic, complemented
13C4×#15668439C211yesmaximal, characteristic, complemented
14#26041341C211yesmaximal, characteristic
15#441×C181C211yesmaximal, characteristic, complemented
16C2×Q8×D181C2211yescharacteristic
17C2×Dic724C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668439C2211yescharacteristic
20#19153814C2211yescharacteristic
21#19153811—21no—
22#19153810—21no—
23#19153808—21no—
24#19153807C2211yescharacteristic
25#19153806—21no—
26#19153796C2211yescharacteristic
27#19153792C2211yescharacteristic
28Q8×Dic181C2211yescharacteristic
29C4×Dic362—21no—
30C4×Dic362C2211yescharacteristic
31C4×Dic362C2211yescharacteristic
32#19153781—21no—
33#19153781C2211yescharacteristic
34#19153774—21no—
35#19153774C2211yescharacteristic
36#19153773—21no—
37#19153773C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51C4×#13089678C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C4×Q8×C181C2211yescharacteristic
54C4×Q8×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×Dic362C2311yescharacteristic
62Q8×D181—22no—
63Q8×D181—22no—
64C2×C4×D181—21no—
65C2×C4×D181C2311yescharacteristic
66Dic724—22no—
67#15668439—22no—
68#15668439—22no—
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C4⋊Dic181—21no—
72C4⋊Dic181—21no—
73C4⋊Dic181—21no—
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428D411yescharacteristic
84#15668428D411yescharacteristic
85#15668426—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426D411yescharacteristic
89#15668426D411yescharacteristic
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96C2×Q8×C181C2311yescharacteristic
97C2×Q8×C181C2311yescharacteristic
98Q16×C181—22no—
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181—21no—
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C42×C181—21no—
106C42×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181C2×D411yescharacteristic
109Dic362—24no—
110Dic362—21no—
111Dic362—21no—
112Dic362—21no—
113Dic362#4112yes—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C2×Dic181C2×D411yescharacteristic
121C4×D181—24no—
122C4×D181—21no—
123C4×D181—21no—
124#13089678—21no—
125#13089678—21no—
126Q8×C181—21no—
127Q8×C181—21no—
128Q8×C181—21no—
129Q8×C181#4112yes—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181C2×D411yescharacteristic
135C2×C4×C181C2×D411yescharacteristic
136C2×C4×C181C2411yescharacteristic
137C8×C181—21no—
138C8×C181—21no—
139C22×C181C22×D411yescharacteristic
140C2×D181—21no—
141C2×D181—21no—
142C2×D181—21no—
143C4×C181—22no—
144C4×C181—21no—
145C4×C181—21no—
146C4×C181—41no—
147C4×C181—41no—
148C4×C181—41no—
149C4×C181C2×#4111yescharacteristic
150C4×C181C2×#4111yescharacteristic
151Dic181—22no—
152Dic181—21no—
153Dic181—21no—
154Dic181—21no—
155Dic181—41no—
156Dic181—41no—
157Dic181—41no—
158C2×C181#52511yescharacteristic
159C2×C181#57811yescharacteristic
160C2×C181#57811yescharacteristic
161D181—41no—
162C181#312711yescharacteristic, complemented, Sylow
163#3127—1811nomaximal, Sylow
164#541—1811no—
165#519—1811no—
166#485—1811no—
167#485—1811no—
168#479—1811no—
169#479—1811no—
170#462—1811no—
171#462—1811no—
172#451—1811no—
173#451—1811no—
174#441—1811no—
175#441D18111yescharacteristic, complemented
176C4×Q16—1811no—
177C4×Q16—1811no—
178#433—1811no—
179C22×Q8—1811no—
180C2×Q16—1811no—
181C2×Q16—1811no—
182C2×Q16—1811no—
183C2×Q16C2×D18111yescharacteristic
184C4⋊Q8—1811no—
185#126—3621no—
186#126—3621no—
187#125—3621no—
188#125—3621no—
189#125—1811no—
190C22⋊Q8—1811no—
191C22⋊Q8—1811no—
192C4×Q8—3621no—
193C4×Q8—3621no—
194C4×Q8—1811no—
195C4×Q8—1811no—
196C4×Q8—1811no—
197C4×Q8—1811no—
198C4×Q8C2×D18111yescharacteristic
199C4×Q8C2×D18111yescharacteristic
200#117—3621no—
201#117—3621no—
202#117—1811no—
203#117—1811no—
204#107—1811no—
205#107—1811no—
206#106—1811no—
207#106C2×D18111yescharacteristic
208C4⋊C8—1811no—
209C4⋊C8—1811no—
210#103—1811no—
211#103—1811no—
212#103—1811no—
213#103—1811no—
214#103—1811no—
215#103—1811no—
216#103C2×D18111yescharacteristic
217#103C2×D18111yescharacteristic
218C22⋊C8—1811no—
219C22⋊C8—1811no—
220#97C2×D18111yescharacteristic
221C4×C8—1811no—
222C2×Q8—3621no—
223C2×Q8—3622no—
224C2×Q8—3622no—
225C2×Q8—1811no—
226C2×Q8—1811no—
227C2×Q8C22×D18111yescharacteristic
228C2×Q8C22×D18111yescharacteristic
229C22×C4—3621no—
230C22×C4—1811no—
231Q16—22no—
232Q16—3622no—
233Q16—3622no—
234Q16—3622no—
235C2×C8—1811no—
236C2×C8—1811no—
237C2×C8C22×D18111yescharacteristic
238C2×C8C22×D18111yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—3621no—
242C4⋊C4—3621no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4—1811no—
255C4⋊C4C22×D18111yescharacteristic
256C4⋊C4C22×D18111yescharacteristic
257C22⋊C4—3621no—
258C22⋊C4—3621no—
259C22⋊C4—3621no—
260C22⋊C4—1811no—
261C22⋊C4—1811no—
262C42—21no—
263C42—21no—
264C42—3621no—
265C42—3621no—
266C42—3621no—
267C42—3621no—
268C42—3621no—
269C42—1811no—
270C42C22×D18111yescharacteristic
271C23—1811no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—3624no—
276Q8—3621no—
277Q8—3621no—
278Q8—3621no—
279Q8—1812no—
280Q8#1566844912yes—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—3624no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—3621no—
290C2×C4—3621no—
291C2×C4—3621no—
292C2×C4—1811no—
293C2×C4—1811no—
294C2×C4—1811no—
295C2×C4D4×D18111yescharacteristic
296C2×C4D4×D18111yescharacteristic
297C2×C4C23×D18111yescharacteristic
298C8—21no—
299C8—21no—
300C8—3621no—
301C8—3621no—
302C22—3621no—
303C22—3621no—
304C22—3621no—
305C22C2×D4×D18111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—3622no—
313C4—3621no—
314C4—3621no—
315C4—3621no—
316C4—7241no—
317C4—7241no—
318C4—7241no—
319C4#41×D18111yescharacteristic
320C4C2×#1566844911yescharacteristic
321C2—7241no—
322C2#2604178811yescharacteristic
323C2#2604209511yescharacteristic
324C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#441×C181C2
socleC22×C181C22×D4
prime radicalC22×D181C2×D4
hypercenter#441D181
hypocenterC181#3127
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
5. #26041589C2semidirect
6. #26041584C2semidirect
7. #26041488C2semidirect
8. #26041487C2semidirect
11. #26041387C2semidirect
12. C4×#15668439C2semidirect
13. C4×#15668439C2semidirect
15. #441×C181C2semidirect
162. C181#3127semidirect
175. #441D181semidirect

Maximal subgroups

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

subgroupindex
#260418872
#260417552
#260416232
#260416182
#260415892
#260415842
#260414882
#260414872
#260414362
#260414332
#260413872
C4×#156684392
#260413412
#441×C1812
#3127181