Finite Group Databasebeta

← #37545173

Subgroups — #37545173

Order 23168.

322 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041890C211yesmaximal, characteristic
2#26041887C211yesmaximal, characteristic
3#26041588C211yesmaximal, characteristic, complemented
4#26041587C211yesmaximal, characteristic, complemented
5#26041586C211yesmaximal, characteristic, complemented
6#26041584C211yesmaximal, characteristic, complemented
7#26041536C211yesmaximal, characteristic
8#26041534C211yesmaximal, characteristic
9#26041519C211yesmaximal, characteristic
10#26041517C211yesmaximal, characteristic
11#26041487C211yesmaximal, characteristic, complemented
12#26041487C211yesmaximal, characteristic, complemented
13#26041486C211yesmaximal, characteristic, complemented
14#26041304C211yesmaximal, characteristic
15#462×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19C2×C8×D181C2211yescharacteristic
20#19153814C2211yescharacteristic
21#19153811—21no—
22#19153811—21no—
23#19153811—21no—
24#19153810—21no—
25#19153808—21no—
26#19153808C2211yescharacteristic
27#19153807C2211yescharacteristic
28#19153806—21no—
29#19153806—21no—
30#19153806—21no—
31#19153796C2211yescharacteristic
32#19153792C2211yescharacteristic
33#19153792C2211yescharacteristic
34#19153792C2211yescharacteristic
35Q8×Dic181C2211yescharacteristic
36Q8×Dic181C2211yescharacteristic
37C4×Dic362C2211yescharacteristic
38#19153773C2211yescharacteristic
39#19153750C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153748C2211yescharacteristic
42#19153747C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153741C2211yescharacteristic
48#19153740C2211yescharacteristic
49#19153740C2211yescharacteristic
50#19153740C2211yescharacteristic
51#19153740C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C4⋊Q8×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#103×C181C2211yescharacteristic
59C2×Dic362C2311yescharacteristic
60C2×C4×D181C2311yescharacteristic
61#15668439—41no—
62#15668439—41no—
63#15668432—41no—
64C2×#13089678C2311yescharacteristic
65C2×#13089678C2311yescharacteristic
66C8×D181—41no—
67C4⋊Dic181—21no—
68C4⋊Dic181—21no—
69C4⋊Dic181—21no—
70C4⋊Dic181—21no—
71C4⋊Dic181C2311yescharacteristic
72C4⋊Dic181C2311yescharacteristic
73C4⋊Dic181C2311yescharacteristic
74#15668428—21no—
75#15668428—21no—
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#15668426—21no—
89#15668426D411yescharacteristic
90#15668426D411yescharacteristic
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181—21no—
94C4×Dic181C2311yescharacteristic
95C2×Q8×C181C2311yescharacteristic
96C2×Q8×C181C2311yescharacteristic
97C2×Q8×C181C2311yescharacteristic
98Q16×C181—41no—
99Q16×C181—41no—
100C2×C8×C181C2311yescharacteristic
101C2×C8×C181C2311yescharacteristic
102C4⋊C4×C181—21no—
103C4⋊C4×C181—21no—
104C4⋊C4×C181—21no—
105C4⋊C4×C181C2311yescharacteristic
106C42×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181C2×D411yescharacteristic
109Dic362—21no—
110Dic362—21no—
111C2×Dic181—21no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181C2×D411yescharacteristic
116C2×Dic181C2×D411yescharacteristic
117C2×Dic181C2×D411yescharacteristic
118C4×D181—21no—
119C4×D181—21no—
120#13089678—21no—
121#13089678—21no—
122Q8×C181—21no—
123Q8×C181—21no—
124Q8×C181—21no—
125Q8×C181—21no—
126Q8×C181—21no—
127Q8×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181C2×D411yescharacteristic
133C2×C4×C181C2×D411yescharacteristic
134C2×C4×C181C2411yescharacteristic
135C8×C181—21no—
136C8×C181—21no—
137C22×C181C22×D411yescharacteristic
138C2×D181—21no—
139C2×D181—21no—
140C2×D181—21no—
141C4×C181—21no—
142C4×C181—21no—
143C4×C181—41no—
144C4×C181—41no—
145C4×C181—41no—
146C4×C181—41no—
147C4×C181H(5,𝔽2)11yescharacteristic
148C4×C1812−1+411yescharacteristic
149Dic181—21no—
150Dic181—21no—
151Dic181—21no—
152Dic181—41no—
153Dic181—41no—
154Dic181—41no—
155Dic181—41no—
156C2×C181#53711yescharacteristic
157C2×C181#57811yescharacteristic
158C2×C181#57811yescharacteristic
159D181—41no—
160C181#326111yescharacteristic, complemented, Sylow
161#3261—1811nomaximal, Sylow
162#541—1811no—
163#541—1811no—
164#479—1811no—
165#479—1811no—
166#479—1811no—
167#479—1811no—
168#470—1811no—
169#470—1811no—
170#467—1811no—
171#467—1811no—
172#462—1811no—
173#462—1811no—
174#462—1811no—
175#462D18111yescharacteristic, complemented
176#424—1811no—
177C2×Q16—1811no—
178C2×Q16—1811no—
179C2×Q16C2×D18111yescharacteristic
180C2×Q16C2×D18111yescharacteristic
181C2×M16—1811no—
182C22×C8—1811no—
183C4⋊Q8—1811no—
184C4⋊Q8C2×D18111yescharacteristic
185#126—3621no—
186#126—3621no—
187#126—3621no—
188#126—3621no—
189#125—3621no—
190#125—3621no—
191#125—3621no—
192#125—3621no—
193#125—1811no—
194#125—1811no—
195C22⋊Q8—1811no—
196C22⋊Q8—1811no—
197C22⋊Q8—1811no—
198C22⋊Q8—1811no—
199C4×Q8—1811no—
200C4×Q8—1811no—
201C4×Q8—1811no—
202C4×Q8C2×D18111yescharacteristic
203#117—1811no—
204#107—1811no—
205#107—1811no—
206#106—1811no—
207#106—1811no—
208C4⋊C8—1811no—
209C4⋊C8—1811no—
210C4⋊C8—1811no—
211C4⋊C8C2×D18111yescharacteristic
212#103—1811no—
213#103—1811no—
214#103—1811no—
215#103—1811no—
216#103—1811no—
217#103—1811no—
218#103C2×D18111yescharacteristic
219#103C2×D18111yescharacteristic
220C2×Q8—1811no—
221C2×Q8C22×D18111yescharacteristic
222C2×Q8C22×D18111yescharacteristic
223C2×Q8C22×D18111yescharacteristic
224C22×C4—1811no—
225Q16—41no—
226Q16—41no—
227Q16—7241no—
228Q16—7241no—
229M16—7241no—
230C2×C8—1811no—
231C2×C8—1811no—
232C2×C8—7241no—
233C2×C8C22×D18111yescharacteristic
234C2×C8C22×D18111yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—3621no—
239C4⋊C4—3621no—
240C4⋊C4—3621no—
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⋊C4—1811no—
256C4⋊C4C22×D18111yescharacteristic
257C22⋊C4—3621no—
258C22⋊C4—3621no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—1811no—
262C22⋊C4—1811no—
263C42—21no—
264C42—3621no—
265C42—3621no—
266C42—3621no—
267C42—1811no—
268C42C22×D18111yescharacteristic
269C23—1811no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—3621no—
277Q8—3621no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—3621no—
283C2×C4—3621no—
284C2×C4—3621no—
285C2×C4—3621no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—1811no—
289C2×C4—1811no—
290C2×C4—1811no—
291C2×C4D4×D18111yescharacteristic
292C2×C4D4×D18111yescharacteristic
293C2×C4C23×D18111yescharacteristic
294C8—21no—
295C8—21no—
296C8—3621no—
297C8—3621no—
298C22—3621no—
299C22—3621no—
300C22—3621no—
301C22C2×D4×D18111yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—3621no—
309C4—3621no—
310C4—3621no—
311C4—7241no—
312C4—7241no—
313C4—7241no—
314C4—7241no—
315C4#1915386111yescharacteristic
316C4#1915386311yescharacteristic
317C2—7241no—
318C2#2604185811yescharacteristic
319C2#2604209211yescharacteristic
320C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#462×C181C2
socleC22×C181C22×D4
prime radicalC22×D181C2×D4
hypercenter#462D181
hypocenterC181#3261
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #26041588C2semidirect
4. #26041587C2semidirect
5. #26041586C2semidirect
6. #26041584C2semidirect
11. #26041487C2semidirect
12. #26041487C2semidirect
13. #26041486C2semidirect
15. #462×C181C2semidirect
160. C181#3261semidirect
175. #462D181semidirect

Maximal subgroups

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

subgroupindex
#260418902
#260418872
#260415882
#260415872
#260415862
#260415842
#260415362
#260415342
#260415192
#260415172
#260414872
#260414862
#260413042
#462×C1812
#3261181