Finite Group Databasebeta

← #37544969

Subgroups — #37544969

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#26041909C211yesmaximal, characteristic, complemented
2#26041883C211yesmaximal, characteristic
3#26041688C211yesmaximal, characteristic, complemented
4#26041678C211yesmaximal, characteristic, complemented
5#26041625C211yesmaximal, characteristic, complemented
6#26041602C211yesmaximal, characteristic, complemented
7#26041601C211yesmaximal, characteristic, complemented
8#26041596C211yesmaximal, characteristic, complemented
9#26041591C211yesmaximal, characteristic, complemented
10#26041581C211yesmaximal, characteristic, complemented
11#26041577C211yesmaximal, characteristic, complemented
12#26041567C211yesmaximal, characteristic, complemented
13#26041557C211yesmaximal, characteristic, complemented
14#26041341C211yesmaximal, characteristic, complemented
15#490×C181C211yesmaximal, characteristic, complemented
16#19153816C2211yescharacteristic
17#19153815—21no—
18#19153815C2211yescharacteristic
19#19153808C2211yescharacteristic
20#19153807C2211yescharacteristic
21#19153806—21no—
22#19153797—21no—
23#19153797—21no—
24#19153796—21no—
25#19153794—21no—
26#19153788—21no—
27#19153788—21no—
28#19153787C2211yescharacteristic
29#19153787C2211yescharacteristic
30D4×Dic181C2211yescharacteristic
31D4×Dic181C2211yescharacteristic
32#19153774C2211yescharacteristic
33#19153773C2211yescharacteristic
34C4⋊C4×D181C2211yescharacteristic
35#19153750C2211yescharacteristic
36#19153750C2211yescharacteristic
37#19153749C2211yescharacteristic
38#19153749C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153748C2211yescharacteristic
41#19153747C2211yescharacteristic
42#19153747C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51C4×#13089678C2211yescharacteristic
52#127×C181C2211yescharacteristic
53#125×C181C2211yescharacteristic
54#102×C181C2211yescharacteristic
55#102×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×C22⋊D181—21no—
62C2×C22⋊D181—21no—
63C22×Dic181—21no—
64C22×Dic181—21no—
65C2×C4×D181—21no—
66C2×C4×D181C2311yescharacteristic
67C2×#13089678C2311yescharacteristic
68C2×#13089678C2311yescharacteristic
69C4⋊Dic181—21no—
70C4⋊Dic181—21no—
71C4⋊Dic181C2311yescharacteristic
72C4⋊Dic181C2311yescharacteristic
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75#15668428—21no—
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428D411yescharacteristic
81#15668428D411yescharacteristic
82C22⋊Dic181—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86#15668426—21no—
87#15668426D411yescharacteristic
88#15668426D411yescharacteristic
89C4×Dic181—21no—
90C4×Dic181C2311yescharacteristic
91C2×D4×C181—21no—
92C2×D4×C181—21no—
93C2×D4×C181C2311yescharacteristic
94C2×D4×C181C2311yescharacteristic
95C2×C8×C181C2311yescharacteristic
96C2×C8×C181C2311yescharacteristic
97C4⋊C4×C181—21no—
98C4⋊C4×C181—21no—
99C4⋊C4×C181C2311yescharacteristic
100C4⋊C4×C181C2311yescharacteristic
101C42×C181C2311yescharacteristic
102C22×D181C2×D411yescharacteristic
103Dic362—81no—
104Dic362—81no—
105C22⋊D181—81no—
106C22⋊D181—81no—
107C2×Dic181—21no—
108C2×Dic181—21no—
109C2×Dic181—21no—
110C2×Dic181—21no—
111C2×Dic181—81no—
112C2×Dic181—81no—
113C2×Dic181C2×D411yescharacteristic
114C2×Dic181C2×D411yescharacteristic
115C2×Dic181C2×D411yescharacteristic
116C4×D181—21no—
117C4×D181—21no—
118C4×D181—81no—
119#13089678—21no—
120#13089678—21no—
121C23×C181—21no—
122C23×C181—21no—
123D4×C181—21no—
124D4×C181—21no—
125D4×C181—21no—
126D4×C181—21no—
127D4×C181—81no—
128D4×C181—81no—
129C2×C4×C181—21no—
130C2×C4×C181—21no—
131C2×C4×C181C2×D411yescharacteristic
132C2×C4×C181C2×D411yescharacteristic
133C2×C4×C181C2411yescharacteristic
134C8×C181—21no—
135C8×C181—21no—
136C22×C181—41no—
137C22×C181—41no—
138C22×C181—41no—
139C22×C181—41no—
140C22×C181—41no—
141C22×C181—41no—
142C22×C181C22×D411yescharacteristic
143C2×D181—21no—
144C2×D181—21no—
145C2×D181—21no—
146C4×C181—21no—
147C4×C181—21no—
148C4×C181—41no—
149C4×C181—41no—
150C4×C1812−1+411yescharacteristic
151C4×C1812−1+411yescharacteristic
152Dic181—21no—
153Dic181—21no—
154Dic181—21no—
155Dic181—41no—
156Dic181—41no—
157Dic181—41no—
158Dic181—41no—
159C2×C181—81no—
160C2×C181—81no—
161C2×C181#53611yescharacteristic
162C2×C181#57611yescharacteristic
163C2×C181#57711yescharacteristic
164D181—41no—
165C181#324111yescharacteristic, complemented, Sylow
166#3241—1811nomaximal, Sylow
167#544—1811no—
168#540—1811no—
169#501—1811no—
170#499—1811no—
171#490D18111yescharacteristic, complemented
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—3621no—
191#123—3621no—
192C22⋊Q8—3621no—
193C22⋊Q8—3621no—
194#121—3621no—
195#121—3621no—
196#121—1811no—
197#121—1811no—
198C4×D4—1811no—
199C4×D4—1811no—
200#117—1811no—
201#117—1811no—
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#102C2×D18111yescharacteristic
218#102C2×D18111yescharacteristic
219#102C2×D18111yescharacteristic
220#102C2×D18111yescharacteristic
221C22⋊C8—1811no—
222C22⋊C8—1811no—
223#97C2×D18111yescharacteristic
224C4×C8—1811no—
225C2×Q8—3621no—
226C2×Q8—3621no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—3621no—
230C2×D4—3621no—
231C2×D4C22×D18111yescharacteristic
232C2×D4C22×D18111yescharacteristic
233C22×C4—3621no—
234C22×C4—3621no—
235C22×C4—3621no—
236C22×C4—1811no—
237C2×C8—1811no—
238C2×C8—1811no—
239C2×C8C22×D18111yescharacteristic
240C2×C8C22×D18111yescharacteristic
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⋊C4—1811no—
255C4⋊C4—1811no—
256C4⋊C4C22×D18111yescharacteristic
257C4⋊C4C22×D18111yescharacteristic
258C22⋊C4—3621no—
259C22⋊C4—3621no—
260C22⋊C4—3621no—
261C22⋊C4—3621no—
262C22⋊C4—3621no—
263C22⋊C4—1811no—
264C22⋊C4—1811no—
265C42—3621no—
266C42—1811no—
267C42C22×D18111yescharacteristic
268C23—21no—
269C23—21no—
270C23—1811no—
271Q8—14481no—
272Q8—14481no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—14481no—
280D4—14481no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—3621no—
284C2×C4—3621no—
285C2×C4—3621no—
286C2×C4—3621no—
287C2×C4—3621no—
288C2×C4—3621no—
289C2×C4—14481no—
290C2×C4—14481no—
291C2×C4—14481no—
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—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—3621no—
309C22—3621no—
310C22—3621no—
311C22C2×D4×D18111yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—3621no—
317C4—3621no—
318C4—3621no—
319C4—7241no—
320C4—7241no—
321C4—7241no—
322C4—7241no—
323C4#1915386311yescharacteristic
324C4#1915386311yescharacteristic
325C2—81no—
326C2—81no—
327C2—7241no—
328C2#2604184911yescharacteristic
329C2#2604208311yescharacteristic
330C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#490×C181C2
socleC22×C181C22×D4
prime radical#26041883C2
hypercenter#490D181
hypocenterC181#3241
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #26041909C2semidirect
3. #26041688C2semidirect
4. #26041678C2semidirect
5. #26041625C2semidirect
6. #26041602C2semidirect
7. #26041601C2semidirect
8. #26041596C2semidirect
9. #26041591C2semidirect
10. #26041581C2semidirect
11. #26041577C2semidirect
12. #26041567C2semidirect
13. #26041557C2semidirect
14. #26041341C2semidirect
15. #490×C181C2semidirect
165. C181#3241semidirect
171. #490D181semidirect

Maximal subgroups

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

subgroupindex
#260419092
#260418832
#260416882
#260416782
#260416252
#260416022
#260416012
#260415962
#260415912
#260415812
#260415772
#260415672
#260415572
#260413412
#490×C1812
#3241181