Finite Group Databasebeta

← #37546340

Subgroups — #37546340

Order 23168.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041993C211yesmaximal, characteristic
2#26041984C211yesmaximal, characteristic, complemented
3#26041683C211yesmaximal, characteristic, complemented
4#26041622C211yesmaximal, characteristic, complemented
5#26041621C211yesmaximal, characteristic, complemented
6#26041591C211yesmaximal, characteristic, complemented
7#26041573C211yesmaximal, characteristic, complemented
8#26041567C211yesmaximal, characteristic, complemented
9#26041524C211yesmaximal, characteristic, complemented
10#26041523C211yesmaximal, characteristic, complemented
11#26041370C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic, complemented
13#26041320C211yesmaximal, characteristic, complemented
14#26041319C211yesmaximal, characteristic, complemented
15#480×C181C211yesmaximal, characteristic, complemented
16C2×#15668437C2211yescharacteristic
17C2×#15668433C2211yescharacteristic
18C2×#15668432C2211yescharacteristic
19#19153815C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153806—21no—
22#19153803—21no—
23#19153802—21no—
24#19153796C2211yescharacteristic
25#19153795—21no—
26#19153795C2211yescharacteristic
27#19153794—21no—
28#19153788—21no—
29#19153787C2211yescharacteristic
30#19153781C2211yescharacteristic
31D4×Dic181C2211yescharacteristic
32C4×C22⋊D181—21no—
33C4×C22⋊D181C2211yescharacteristic
34#19153775C2211yescharacteristic
35#19153774C2211yescharacteristic
36#19153772—21no—
37C4⋊C4×D181C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153748C2211yescharacteristic
43#19153747C2211yescharacteristic
44#19153747C2211yescharacteristic
45#19153745C2211yescharacteristic
46#19153741C2211yescharacteristic
47#19153741C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#121×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C22⋊D181D411yescharacteristic
64C22×Dic181—21no—
65C2×C4×D181—21no—
66C2×C4×D181C2311yescharacteristic
67#15668437—22no—
68#15668433—22no—
69#15668432—22no—
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C4⋊Dic181—21no—
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76#15668428—21no—
77#15668428—21no—
78#15668428—21no—
79#15668428—21no—
80#15668428—21no—
81#15668428D411yescharacteristic
82C22⋊Dic181—21no—
83C22⋊Dic181—21no—
84C22⋊Dic181—21no—
85C22⋊Dic181—21no—
86C22⋊Dic181D411yescharacteristic
87#15668426—21no—
88#15668426—21no—
89#15668426D411yescharacteristic
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181C2311yescharacteristic
94C2×D4×C181—21no—
95C2×D4×C181C2311yescharacteristic
96C22×C4×C181—21no—
97C22×C4×C181C2311yescharacteristic
98C2×C8×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C4⋊C4×C181—21no—
101C4⋊C4×C181C2311yescharacteristic
102C4⋊C4×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C22⋊C4×C181—21no—
105C22×D181C2×D411yescharacteristic
106Dic362—21no—
107Dic362—21no—
108Dic362—81no—
109Dic362—81no—
110C22⋊D181—22no—
111C22⋊D181—81no—
112C2×Dic181—21no—
113C2×Dic181—21no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—42no—
117C2×Dic181C2×D411yescharacteristic
118C2×Dic181C2×D411yescharacteristic
119C2×Dic181C2×D411yescharacteristic
120C4×D181—21no—
121C4×D181—21no—
122C4×D181—81no—
123#13089678—21no—
124#13089678#4112yes—
125C23×C181—21no—
126C23×C181C2×D411yescharacteristic
127D4×C181—21no—
128D4×C181—21no—
129D4×C181—81no—
130C2×C4×C181—21no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—81no—
136C2×C4×C181C2×D411yescharacteristic
137C2×C4×C181C2411yescharacteristic
138C8×C181—21no—
139C8×C181—21no—
140C22×C181—21no—
141C22×C181—21no—
142C22×C181—21no—
143C22×C181—41no—
144C22×C181—41no—
145C22×C181—41no—
146C22×C181C22×D411yescharacteristic
147C2×D181—21no—
148C2×D181—21no—
149C2×D181—21no—
150C4×C181—21no—
151C4×C181—41no—
152C4×C181—41no—
153C4×C181—41no—
154C4×C181C2×#4111yescharacteristic
155C4×C1812−1+411yescharacteristic
156Dic181—21no—
157Dic181—21no—
158Dic181—41no—
159Dic181—41no—
160Dic181—41no—
161Dic181—41no—
162Dic181#13712yes—
163C2×C181—41no—
164C2×C181—81no—
165C2×C181#54711yescharacteristic
166C2×C181C2×#13711yescharacteristic
167C2×C181#57611yescharacteristic
168D181—41no—
169C181#335711yescharacteristic, complemented, Sylow
170#3357—1811nomaximal, Sylow
171#555—1811no—
172#554—1811no—
173#500—1811no—
174#485—1811no—
175#485—1811no—
176#480—1811no—
177#480D18111yescharacteristic, complemented
178#477—1811no—
179#476—1811no—
180#468—1811no—
181#468—1811no—
182C4×SD16—1811no—
183#436—1811no—
184#428—1811no—
185#428—1811no—
186C2×SD16—1811no—
187C2×M16—1811no—
188C2×M16—1811no—
189C4⋊Q8—1811no—
190C4⋊Q8—1811no—
191#125—3621no—
192#124—3621no—
193#124—3621no—
194C22⋊Q8—3621no—
195C22⋊Q8—3621no—
196C22⋊Q8—1811no—
197C22⋊Q8—1811no—
198#121—3621no—
199#121—1811no—
200#121C2×D18111yescharacteristic
201C4×Q8—1811no—
202C4×D4—3621no—
203C4×D4—1811no—
204C4×D4—1811no—
205#117—3621no—
206#117—1811no—
207#117—1811no—
208C2×C4⋊C4—1811no—
209C2×C4⋊C4C2×D18111yescharacteristic
210#107—1811no—
211#107—1811no—
212#107—1811no—
213#107—1811no—
214#107C2×D18111yescharacteristic
215#107C2×D18111yescharacteristic
216#106—1811no—
217#106—1811no—
218#106—1811no—
219C4⋊C8—1811no—
220#103—1811no—
221#103—1811no—
222#103—1811no—
223#102—1811no—
224#102C2×D18111yescharacteristic
225#102C2×D18111yescharacteristic
226C22⋊C8—1811no—
227C22⋊C8C2×D18111yescharacteristic
228C4×C8—1811no—
229C2×Q8—3621no—
230C2×Q8—3621no—
231C2×Q8—1811no—
232C2×D4—21no—
233C2×D4—3621no—
234C2×D4—1811no—
235C2×D4C22×D18111yescharacteristic
236C22×C4—21no—
237C22×C4—3621no—
238C22×C4—3621no—
239C22×C4—1811no—
240C22×C4C22×D18111yescharacteristic
241SD16—3622no—
242M16—3622no—
243M16—3622no—
244C2×C8—1811no—
245C2×C8—1811no—
246C2×C8C22×D18111yescharacteristic
247C2×C8C22×D18111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—3621no—
250C4⋊C4—3621no—
251C4⋊C4—3621no—
252C4⋊C4—3621no—
253C4⋊C4—3621no—
254C4⋊C4—3621no—
255C4⋊C4—1811no—
256C4⋊C4—1811no—
257C4⋊C4—1811no—
258C4⋊C4—1811no—
259C4⋊C4C22×D18111yescharacteristic
260C4⋊C4C22×D18111yescharacteristic
261C4⋊C4C22×D18111yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—3621no—
264C22⋊C4—3621no—
265C22⋊C4—3621no—
266C22⋊C4—3621no—
267C22⋊C4—3621no—
268C22⋊C4—3621no—
269C22⋊C4—1811no—
270C22⋊C4—1811no—
271C42—3621no—
272C42—3621no—
273C42—3621no—
274C42—1811no—
275C23—21no—
276C23—1811no—
277C23D4×D18111yescharacteristic
278Q8—3621no—
279Q8—3621no—
280Q8—14481no—
281Q8—14481no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—3622no—
286D4—14481no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—3621no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—3621no—
297C2×C4—3621no—
298C2×C4—3621no—
299C2×C4—14481no—
300C2×C4—1811no—
301C2×C4—1811no—
302C2×C4—1811no—
303C2×C4—7242no—
304C2×C4D4×D18111yescharacteristic
305C2×C4C23×D18111yescharacteristic
306C8—21no—
307C8—21no—
308C8—3621no—
309C8—1812no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—3621no—
317C22—3621no—
318C22—3621no—
319C22C2×D4×D18111yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—3621no—
325C4—3621no—
326C4—1812no—
327C4—7241no—
328C4—7241no—
329C4—7241no—
330C4—7241no—
331C4#41×D18111yescharacteristic
332C4#1915386311yescharacteristic
333C2—41no—
334C2—81no—
335C2—7241no—
336C2#2604192711yescharacteristic
337C2#137×D18111yescharacteristic
338C2#2604208011yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#480×C181C2
socleC22×C181C22×D4
prime radical#26041993C2
hypercenter#480D181
hypocenterC181#3357
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #26041984C2semidirect
3. #26041683C2semidirect
4. #26041622C2semidirect
5. #26041621C2semidirect
6. #26041591C2semidirect
7. #26041573C2semidirect
8. #26041567C2semidirect
9. #26041524C2semidirect
10. #26041523C2semidirect
11. #26041370C2semidirect
12. #26041354C2semidirect
13. #26041320C2semidirect
14. #26041319C2semidirect
15. #480×C181C2semidirect
169. C181#3357semidirect
177. #480D181semidirect

Maximal subgroups

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

subgroupindex
#260419932
#260419842
#260416832
#260416222
#260416212
#260415912
#260415732
#260415672
#260415242
#260415232
#260413702
#260413542
#260413202
#260413192
#480×C1812
#3357181