Finite Group Databasebeta

← #37544968

Subgroups — #37544968

Order 23168.

332 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041907C211yesmaximal, characteristic, complemented
2#26041689C211yesmaximal, characteristic, complemented
3#26041678C211yesmaximal, characteristic, complemented
4#26041643C211yesmaximal, characteristic, complemented
5#26041625C211yesmaximal, characteristic, complemented
6#26041600C211yesmaximal, characteristic, complemented
7#26041600C211yesmaximal, characteristic, complemented
8#26041595C211yesmaximal, characteristic, complemented
9#26041590C211yesmaximal, characteristic, complemented
10#26041579C211yesmaximal, characteristic, complemented
11#26041579C211yesmaximal, characteristic, complemented
12#26041569C211yesmaximal, characteristic, complemented
13#26041559C211yesmaximal, characteristic, complemented
14#26041340C211yesmaximal, characteristic, complemented
15#540×C181C211yesmaximal, characteristic
16#19153816C2211yescharacteristic
17#19153816C2211yescharacteristic
18#19153815—21no—
19#19153808C2211yescharacteristic
20#19153808C2211yescharacteristic
21#19153807—21no—
22#19153793—21no—
23#19153793—21no—
24#19153775C2211yescharacteristic
25C2×C4⋊Dic181C2211yescharacteristic
26#19153749C2211yescharacteristic
27#19153749C2211yescharacteristic
28#19153749C2211yescharacteristic
29#19153749C2211yescharacteristic
30#19153747C2211yescharacteristic
31#19153747C2211yescharacteristic
32#19153747C2211yescharacteristic
33#19153747C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35C4⋊#13089678C2211yescharacteristic
36#19153737C2211yescharacteristic
37#19153737C2211yescharacteristic
38#19153737C2211yescharacteristic
39#19153737C2211yescharacteristic
40#19153737C2211yescharacteristic
41#19153737C2211yescharacteristic
42#19153737C2211yescharacteristic
43#19153737C2211yescharacteristic
44C22⋊#13089678C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46#19153727C2211yescharacteristic
47C4×#13089678C2211yescharacteristic
48#127×C181C2211yescharacteristic
49#125×C181C2211yescharacteristic
50#123×C181—21no—
51#123×C181—21no—
52#121×C181—21no—
53#121×C181—21no—
54#121×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56C4×D4×C181C2211yescharacteristic
57C4×D4×C181C2211yescharacteristic
58#117×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C22×Dic181—21no—
62C2×#13089678C2311yescharacteristic
63C2×#13089678C2311yescharacteristic
64C2×#13089678C2311yescharacteristic
65C2×#13089678C2311yescharacteristic
66C4⋊Dic181—21no—
67C4⋊Dic181—21no—
68C4⋊Dic181—21no—
69C4⋊Dic181C2311yescharacteristic
70C4⋊Dic181C2311yescharacteristic
71C4⋊Dic181C2311yescharacteristic
72C4⋊Dic181C2311yescharacteristic
73#15668428—21no—
74#15668428—21no—
75#15668428—21no—
76#15668428—21no—
77C22⋊Dic181—21no—
78C4×Dic181—21no—
79C2×D4×C181—21no—
80C2×D4×C181—21no—
81C2×D4×C181—21no—
82C2×D4×C181—21no—
83C2×D4×C181C2311yescharacteristic
84C2×D4×C181C2311yescharacteristic
85C22×C4×C181—21no—
86C22×C4×C181—21no—
87C22×C4×C181C2311yescharacteristic
88C4⋊C4×C181—21no—
89C4⋊C4×C181—21no—
90C4⋊C4×C181D411yescharacteristic
91C4⋊C4×C181D411yescharacteristic
92C4⋊C4×C181C2311yescharacteristic
93C4⋊C4×C181C2311yescharacteristic
94C22⋊C4×C181—21no—
95C22⋊C4×C181—21no—
96C22⋊C4×C181—21no—
97C22⋊C4×C181—21no—
98C22⋊C4×C181D411yescharacteristic
99C22⋊C4×C181D411yescharacteristic
100C42×C181C2311yescharacteristic
101C42×C181C2311yescharacteristic
102Dic362—81no—
103Dic362—81no—
104C2×Dic181—21no—
105C2×Dic181—21no—
106C2×Dic181—21no—
107C2×Dic181—21no—
108C2×Dic181—81no—
109#13089678—21no—
110#13089678—21no—
111#13089678—21no—
112#13089678—21no—
113C23×C181—21no—
114C23×C181—21no—
115C23×C181C2×D411yescharacteristic
116D4×C181—21no—
117D4×C181—21no—
118D4×C181—21no—
119D4×C181—21no—
120D4×C181—81no—
121D4×C181—81no—
122D4×C181—81no—
123D4×C181—81no—
124C2×C4×C181—21no—
125C2×C4×C181—21no—
126C2×C4×C181—21no—
127C2×C4×C181—21no—
128C2×C4×C181—81no—
129C2×C4×C181—81no—
130C2×C4×C181C2×D411yescharacteristic
131C2×C4×C181C2×D411yescharacteristic
132C2×C4×C181C2×D411yescharacteristic
133C2×C4×C181C2×D411yescharacteristic
134C2×C4×C181C2×D411yescharacteristic
135C2×C4×C181C2411yescharacteristic
136C22×C181—21no—
137C22×C181—21no—
138C22×C181—21no—
139C22×C181—41no—
140C22×C181—41no—
141C22×C181—41no—
142C22×C181—41no—
143C22×C181—41no—
144C22×C181—41no—
145C22×C181C22×D411yescharacteristic
146C4×C181—21no—
147C4×C181—21no—
148C4×C181—21no—
149C4×C181—21no—
150C4×C181—21no—
151C4×C181—41no—
152C4×C181—41no—
153C4×C1812−1+411yescharacteristic
154C4×C1812−1+411yescharacteristic
155Dic181—41no—
156Dic181—41no—
157Dic181—41no—
158Dic181—41no—
159C2×C181—41no—
160C2×C181—81no—
161C2×C181—81no—
162C2×C181#53611yescharacteristic
163C2×C181#57611yescharacteristic
164C2×C181#57711yescharacteristic
165C181#324111yescharacteristic, complemented, Sylow
166#3241—1811nomaximal, Sylow
167#544—1811no—
168#540D18111yescharacteristic
169#501—1811no—
170#499—1811no—
171#490—1811no—
172#486—1811no—
173#482—1811no—
174#482—1811no—
175#481—1811no—
176#480—1811no—
177#478—1811no—
178#478—1811no—
179#476—1811no—
180#474—1811no—
181#433—1811no—
182C4⋊Q8—3621no—
183C4⋊Q8—1811no—
184C4⋊Q8—1811no—
185#127C2×D18111yescharacteristic
186#125—3621no—
187#125—1811no—
188#125—1811no—
189#125C2×D18111yescharacteristic
190#123—21no—
191#123—21no—
192C22⋊Q8—3621no—
193C22⋊Q8—3621no—
194#121—21no—
195#121—21no—
196#121C2×D18111yescharacteristic
197#121C2×D18111yescharacteristic
198C4×D4C2×D18111yescharacteristic
199C4×D4C2×D18111yescharacteristic
200#117—1811no—
201#117C2×D18111yescharacteristic
202C2×C4⋊C4—1811no—
203#107—1811no—
204#107—1811no—
205#107—1811no—
206#107—1811no—
207#106—1811no—
208#106—1811no—
209#106—1811no—
210#106—1811no—
211C4⋊C8—1811no—
212C4⋊C8—1811no—
213#102—1811no—
214#102—1811no—
215#102—1811no—
216#102—1811no—
217#102—1811no—
218#102—1811no—
219#102—1811no—
220#102—1811no—
221C22⋊C8—1811no—
222C22⋊C8—1811no—
223#97—1811no—
224C4×C8—1811no—
225C2×Q8—3621no—
226C2×Q8—3621no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C22×D18111yescharacteristic
232C2×D4C22×D18111yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—3621no—
236C22×C4C22×D18111yescharacteristic
237C2×C8—1811no—
238C2×C8—1811no—
239C2×C8—1811no—
240C2×C8—1811no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—3621no—
244C4⋊C4—3621no—
245C4⋊C4—3621no—
246C4⋊C4—3621no—
247C4⋊C4—3621no—
248C4⋊C4—3621no—
249C4⋊C4—3621no—
250C4⋊C4—1811no—
251C4⋊C4—1811no—
252C4⋊C4—1811no—
253C4⋊C4—1811no—
254C4⋊C4C22⋊D18111yescharacteristic
255C4⋊C4C22⋊D18111yescharacteristic
256C4⋊C4C22×D18111yescharacteristic
257C4⋊C4C22×D18111yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—3621no—
263C22⋊C4C22⋊D18111yescharacteristic
264C22⋊C4C22⋊D18111yescharacteristic
265C42—3621no—
266C42C22×D18111yescharacteristic
267C42C22×D18111yescharacteristic
268C23—21no—
269C23—21no—
270C23C2×C22⋊D18111yescharacteristic
271Q8—14481no—
272Q8—14481no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—3621no—
290C2×C4—3621no—
291C2×C4—14481no—
292C2×C4C2×C22⋊D18111yescharacteristic
293C2×C4C2×C22⋊D18111yescharacteristic
294C2×C4C2×C22⋊D18111yescharacteristic
295C2×C4C2×C22⋊D18111yescharacteristic
296C2×C4C2×C22⋊D18111yescharacteristic
297C2×C4C23×D18111yescharacteristic
298C8—3621no—
299C8—3621no—
300C8—3621no—
301C8—3621no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×C22⋊D18111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—7241no—
320C4—7241no—
321C4—7241no—
322C4—7241no—
323C4#1915386311yescharacteristic
324C4#1915386311yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2#2604185011yescharacteristic
329C2#2604208211yescharacteristic
330C2#2604209011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting, prime radical#540×C181C2
socleC22×C181C22×D4
hypercenter#540D181
hypocenterC181#3241
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #26041907C2semidirect
2. #26041689C2semidirect
3. #26041678C2semidirect
4. #26041643C2semidirect
5. #26041625C2semidirect
6. #26041600C2semidirect
7. #26041600C2semidirect
8. #26041595C2semidirect
9. #26041590C2semidirect
10. #26041579C2semidirect
11. #26041579C2semidirect
12. #26041569C2semidirect
13. #26041559C2semidirect
14. #26041340C2semidirect
165. C181#3241semidirect

Maximal subgroups

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

subgroupindex
#260419072
#260416892
#260416782
#260416432
#260416252
#260416002
#260415952
#260415902
#260415792
#260415692
#260415592
#260413402
#540×C1812
#3241181