Finite Group Databasebeta

← #37545786

Subgroups — #37545786

Order 23168.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042003C211yesmaximal, characteristic, complemented
2#26041937C211yesmaximal, characteristic
3#26041618C211yesmaximal, characteristic, complemented
4#26041602C211yesmaximal, characteristic, complemented
5#26041571C211yesmaximal, characteristic, complemented
6#26041524C211yesmaximal, characteristic, complemented
7#26041519C211yesmaximal, characteristic, complemented
8#26041498C211yesmaximal, characteristic, complemented
9#26041442C211yesmaximal, characteristic, complemented
10#26041436C211yesmaximal, characteristic, complemented
11#26041387C211yesmaximal, characteristic, complemented
12#26041352C211yesmaximal, characteristic, complemented
13#26041286C211yesmaximal, characteristic, complemented
14#26041272C211yesmaximal, characteristic, complemented
15#489×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×Q8×D181C2211yescharacteristic
18C2×Dic724C2211yescharacteristic
19C2×#15668439C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22C2×C8×D181C2211yescharacteristic
23#19153811—21no—
24#19153811—21no—
25#19153805—21no—
26#19153802—21no—
27#19153796C2211yescharacteristic
28#19153796C2211yescharacteristic
29#19153793—21no—
30#19153792C2211yescharacteristic
31#19153789—21no—
32#19153787C2211yescharacteristic
33Q8×Dic181—21no—
34C4×Dic362C2211yescharacteristic
35C4×Dic362C2211yescharacteristic
36C4×D724C2211yescharacteristic
37#19153776—21no—
38#19153774C2211yescharacteristic
39#19153774C2211yescharacteristic
40#19153749C2211yescharacteristic
41#19153749C2211yescharacteristic
42#19153748C2211yescharacteristic
43C4⋊#13089678C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53#124×C181C2211yescharacteristic
54#103×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—41no—
61C2×Dic362—21no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64Q8×D181—22no—
65Q8×D181—41no—
66C2×D724D411yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71C2×C4×D181C2311yescharacteristic
72C2×C4×D181C2311yescharacteristic
73Dic724—22no—
74#15668439—41no—
75#15668437—41no—
76#15668432—41no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C8×D181—41no—
80C4⋊Dic181—21no—
81C4⋊Dic181—21no—
82C4⋊Dic181D411yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426D411yescharacteristic
95#15668426D411yescharacteristic
96C4×Dic181—21no—
97C4×Dic181—21no—
98C4×Dic181—21no—
99C4×Dic181—21no—
100C2×Q8×C181—21no—
101C2×Q8×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C22⋊C4×C181—21no—
109C22⋊C4×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181C2×D411yescharacteristic
112C22×D181C2×D411yescharacteristic
113Dic362—21no—
114Dic362—21no—
115Dic362—21no—
116Dic362—42no—
117Dic362#4112yes—
118D724—41no—
119C22⋊D181—42no—
120C22⋊D181—42no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—42no—
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C4×D181—21no—
129C4×D181—21no—
130C4×D181—21no—
131C4×D181—21no—
132C4×D181—42no—
133#13089678—21no—
134#13089678—21no—
135C23×C181—21no—
136Q8×C181—21no—
137Q8×C181—21no—
138Q8×C181—42no—
139D4×C181—21no—
140D4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181C2×D411yescharacteristic
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181—41no—
152C22×C181C22×D411yescharacteristic
153C2×D181—21no—
154C2×D181—21no—
155C2×D181—21no—
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181—41no—
164C4×C181C2×#4111yescharacteristic
165C4×C181H(5,𝔽2)11yescharacteristic
166Dic181—21no—
167Dic181—21no—
168Dic181—22no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172C2×C181—81no—
173C2×C181#54611yescharacteristic
174C2×C181#57511yescharacteristic
175C2×C181#57811yescharacteristic
176D181—41no—
177D181—41no—
178C181#331311yescharacteristic, complemented, Sylow
179#3313—1811nomaximal, Sylow
180#556—1811no—
181#548—1811no—
182#489D18111yescharacteristic, complemented
183#485—1811no—
184#482—1811no—
185#477—1811no—
186#468—1811no—
187#467—1811no—
188#464—1811no—
189#452—1811no—
190#451—1811no—
191#441—1811no—
192#435—1811no—
193#419—1811no—
194#416—1811no—
195C2×#41—1811no—
196C22×Q8—1811no—
197C2×Q16—1811no—
198C2×Q16—1811no—
199C2×SD16—1811no—
200C2×M16—1811no—
201C22×C8—1811no—
202C4⋊Q8C2×D18111yescharacteristic
203#126—3621no—
204#126—3621no—
205#124—3621no—
206#124—3621no—
207#124C2×D18111yescharacteristic
208C22⋊Q8—3621no—
209C22⋊Q8—1811no—
210C22⋊Q8—1811no—
211C22⋊Q8—1811no—
212#121—3621no—
213#121—1811no—
214C4×Q8—3621no—
215C4×Q8—1811no—
216C4×Q8—1811no—
217C4×D4—3621no—
218C4×D4—1811no—
219#117—1811no—
220#117—1811no—
221#107—1811no—
222#107—1811no—
223#106—1811no—
224C4⋊C8—1811no—
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103C2×D18111yescharacteristic
231#103C2×D18111yescharacteristic
232#102—1811no—
233#102C2×D18111yescharacteristic
234#102C2×D18111yescharacteristic
235C22⋊C8—1811no—
236C22⋊C8—1811no—
237#97C2×D18111yescharacteristic
238#41—3622no—
239#41—7241no—
240C2×Q8—21no—
241C2×Q8—3621no—
242C2×Q8—3622no—
243C2×Q8—1811no—
244C2×Q8—1811no—
245C2×Q8—7241no—
246C2×Q8C22×D18111yescharacteristic
247C2×D4—3621no—
248C2×D4—3621no—
249C2×D4—1811no—
250C2×D4C22×D18111yescharacteristic
251C22×C4—3621no—
252C22×C4—3621no—
253C22×C4—1811no—
254C22×C4—1811no—
255Q16—3622no—
256Q16—7241no—
257SD16—7241no—
258M16—7241no—
259C2×C8—1811no—
260C2×C8—1811no—
261C2×C8—7241no—
262C2×C8C22×D18111yescharacteristic
263C2×C8C22×D18111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—1811no—
271C4⋊C4—1811no—
272C4⋊C4—1811no—
273C4⋊C4C22×D18111yescharacteristic
274C4⋊C4C22×D18111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—3621no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—1811no—
284C22⋊C4—1811no—
285C42—3621no—
286C42—3621no—
287C42—3621no—
288C42—3621no—
289C42C22×D18111yescharacteristic
290C23—21no—
291C23—1811no—
292C23—1811no—
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—3621no—
297Q8—3621no—
298Q8—3621no—
299Q8—1812no—
300Q8—7242no—
301D4—21no—
302D4—21no—
303D4—7241no—
304D4—7242no—
305D4—7242no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3621no—
310C2×C4—3621no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—1811no—
318C2×C4—1811no—
319C2×C4—7242no—
320C2×C4—7242no—
321C2×C4D4×D18111yescharacteristic
322C2×C4D4×D18111yescharacteristic
323C2×C4C23×D18111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3621no—
327C8—3621no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—3621no—
332C22—3621no—
333C22—3621no—
334C22—3621no—
335C22—3621no—
336C22—3621no—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3621no—
344C4—3621no—
345C4—3622no—
346C4—7241no—
347C4—7241no—
348C4—7241no—
349C4#41×D18111yescharacteristic
350C4#1915386211yescharacteristic
351C2—81no—
352C2—7241no—
353C2—7241no—
354C2#2604192211yescharacteristic
355C2#2604207511yescharacteristic
356C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#489×C181C2
socleC22×C181C22×D4
prime radical#26041937C2
hypercenter#489D181
hypocenterC181#3313
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #26042003C2semidirect
3. #26041618C2semidirect
4. #26041602C2semidirect
5. #26041571C2semidirect
6. #26041524C2semidirect
7. #26041519C2semidirect
8. #26041498C2semidirect
9. #26041442C2semidirect
10. #26041436C2semidirect
11. #26041387C2semidirect
12. #26041352C2semidirect
13. #26041286C2semidirect
14. #26041272C2semidirect
15. #489×C181C2semidirect
178. C181#3313semidirect
182. #489D181semidirect

Maximal subgroups

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

subgroupindex
#260420032
#260419372
#260416182
#260416022
#260415712
#260415242
#260415192
#260414982
#260414422
#260414362
#260413872
#260413522
#260412862
#260412722
#489×C1812
#3313181