Finite Group Databasebeta

← #37542593

Subgroups — #37542593

Order 23168.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153837C211yesmaximal, characteristic
2#26041761C211yesmaximal, characteristic, complemented
3#26041758C211yesmaximal, characteristic, complemented
4#26041381C211yesmaximal, characteristic, complemented
5#26041380C211yesmaximal, characteristic, complemented
6#26041378C211yesmaximal, characteristic, complemented
7C4×#15668439C211yesmaximal, characteristic, complemented
8#26041371C211yesmaximal, characteristic, complemented
9C4×#15668434C211yesmaximal, characteristic, complemented
10#26041359C211yesmaximal, characteristic, complemented
11#107×D181C211yesmaximal, characteristic, complemented
12#26041279C211yesmaximal, characteristic, complemented
13#26041277C211yesmaximal, characteristic, complemented
14#26041236C211yesmaximal, characteristic, complemented
15#440×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18#19153837C418yescomplemented
19C2×#15668439C2211yescharacteristic
20C2×#15668438C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668432C2211yescharacteristic
23C2×C8×D181C2211yescharacteristic
24Q8×Dic181C2211yescharacteristic
25C4×Dic362C2211yescharacteristic
26#19153781C2211yescharacteristic
27C4×D724—21no—
28C4×D724C2211yescharacteristic
29D4×Dic181C2211yescharacteristic
30#19153778—21no—
31#19153778C2211yescharacteristic
32C4×C22⋊D181—21no—
33#19153776—21no—
34#19153773—21no—
35#19153773C2211yescharacteristic
36#19153772—21no—
37C2×#15668428—21no—
38C4⋊C4×D181—21no—
39C4⋊C4×D181C2211yescharacteristic
40C4⋊C4×D181C2211yescharacteristic
41#19153750C2211yescharacteristic
42#19153749C2211yescharacteristic
43#19153749C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153726C2211yescharacteristic
51C4×#13089678C2211yescharacteristic
52C8×Dic181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C4×Q8×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic
56#107×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#97×C181C2211yescharacteristic
60#15668450—22no—
61#15668450C2×C414yescomplemented
62#15668448—22no—
63#15668448C2×C414yescomplemented
64C2×Dic362C2311yescharacteristic
65C2×D724—21no—
66C2×D724C2311yescharacteristic
67C2×C22⋊D181—21no—
68C22×Dic181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76#15668439C2×C414yescomplemented
77#15668438C2×C414yescomplemented
78#15668434C2×C414yescomplemented
79#15668432—22no—
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C8×D181C2×C414yescomplemented
83C4⋊Dic181—21no—
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90#15668428D411yescharacteristic
91#15668428D411yescharacteristic
92C22⋊Dic181—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C4×Dic181—21no—
99C4×Dic181—21no—
100C4×Dic181C2311yescharacteristic
101C2×Q8×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104SD16×C181C2×C414yescomplemented
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C42×C181—21no—
112C42×C181C2311yescharacteristic
113C22×D181—21no—
114C22×D181C2×D411yescharacteristic
115Dic362—21no—
116Dic362C22×C412yes—
117D724—24no—
118D724—21no—
119D724C22×C412yes—
120C22⋊D181—24no—
121C2×Dic181—21no—
122C2×Dic181—24no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—81no—
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C4×D181—24no—
130C4×D181—81no—
131C4×D181—81no—
132C4×D181—81no—
133C4×D181—81no—
134C4×D181C22×C412yes—
135C4×D181#4112yes—
136#13089678—21no—
137#13089678C22×C412yes—
138C23×C181—21no—
139Q8×C181—21no—
140Q8×C181C22×C412yes—
141D4×C181—21no—
142D4×C181C22×C412yes—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—81no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2×D411yescharacteristic
149C2×C4×C181C2411yescharacteristic
150C8×C181—21no—
151C8×C181C22×C412yes—
152C22×C181—22no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—22no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181C4×D412yes—
162C4×C181—22no—
163C4×C181—21no—
164C4×C181—21no—
165C4×C181—41no—
166C4×C181—41no—
167C4×C181C23×C411yescharacteristic
168C4×C181C2×#4111yescharacteristic
169Dic181—22no—
170Dic181—21no—
171Dic181—21no—
172Dic181—41no—
173Dic181—41no—
174Dic181C4×D412yes—
175C2×C181—42no—
176C2×C181C2×C4×D411yescharacteristic
177C2×C181#57611yescharacteristic
178C2×C181#57811yescharacteristic
179D181—22no—
180D181—42no—
181C181#295111yescharacteristic, complemented, Sylow
182#2951—1811nomaximal, Sylow
183C2×#135—1811no—
184#520—1811no—
185#520—1811no—
186#440—1811no—
187#440—1811no—
188#440—1811no—
189#440D18111yescharacteristic, complemented
190C4×Q16—1811no—
191C4×Q16—1811no—
192C4×D8—1811no—
193C4×D8—1811no—
194C2×#107—1811no—
195#417—1811no—
196#417—1811no—
197#405—1811no—
198C2×#41—1811no—
199C2×#41—1811no—
200#135—1818no—
201C2×Q16—1811no—
202C2×SD16—1811no—
203C2×SD16C2×D18111yescharacteristic
204C2×D8—1811no—
205C2×M16—1811no—
206C22×C8—1811no—
207C4×Q8—1811no—
208C4×Q8—1811no—
209C4×Q8—1811no—
210C4×Q8C2×D18111yescharacteristic
211C4×D4—3621no—
212C4×D4—3621no—
213C4×D4—3621no—
214C4×D4—3621no—
215C4×D4—1811no—
216C4×D4—1811no—
217C4×D4—1811no—
218C4×D4C2×D18111yescharacteristic
219#117—3621no—
220#117—3621no—
221#117—1811no—
222C2×C4⋊C4—3621no—
223C2×C4⋊C4—3621no—
224C2×C4⋊C4—1811no—
225C2×C4⋊C4—1811no—
226#107—1811no—
227#107—1811no—
228#107—1811no—
229#107C2×D18111yescharacteristic
230#103—1811no—
231#103—1811no—
232#103—1811no—
233#103C2×D18111yescharacteristic
234#102—1811no—
235#102—1811no—
236#102—1811no—
237#102C2×D18111yescharacteristic
238#97—1811no—
239#97C2×D18111yescharacteristic
240C4×C8—1811no—
241C4×C8—1811no—
242#41—3622no—
243#41—3622no—
244#41—1814no—
245#41—1814no—
246C2×Q8—1811no—
247C2×Q8C22×D18111yescharacteristic
248C2×D4—3621no—
249C2×D4—3621no—
250C2×D4—1811no—
251C2×D4C22×D18111yescharacteristic
252C22×C4—21no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—3621no—
258C22×C4—3621no—
259C22×C4—3621no—
260C22×C4—1811no—
261Q16—1814no—
262SD16—1814no—
263SD16C4×D18114yescomplemented
264D8—1814no—
265M16—3622no—
266C2×C8—1811no—
267C2×C8—1811no—
268C2×C8—1814no—
269C2×C8C22×D18111yescharacteristic
270C2×C8C22×D18111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—1811no—
278C4⋊C4—1811no—
279C4⋊C4—1811no—
280C4⋊C4—1811no—
281C4⋊C4C22×D18111yescharacteristic
282C4⋊C4C22×D18111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—1811no—
288C22⋊C4—1811no—
289C42—21no—
290C42—3621no—
291C42—3621no—
292C42—3621no—
293C42—1811no—
294C42C22×D18111yescharacteristic
295C23—21no—
296C23—3621no—
297C23—1811no—
298Q8—21no—
299Q8—3621no—
300Q8—1812no—
301Q8C2×C4×D18112yes—
302D4—21no—
303D4—3624no—
304D4—3624no—
305D4—3621no—
306D4—1812no—
307D4C2×C4×D18112yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—3624no—
313C2×C4—3621no—
314C2×C4—3624no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—14481no—
318C2×C4—14481no—
319C2×C4—14481no—
320C2×C4—14481no—
321C2×C4—14481no—
322C2×C4—1811no—
323C2×C4—1811no—
324C2×C4—1811no—
325C2×C4—1812no—
326C2×C4—1812no—
327C2×C4D4×D18111yescharacteristic
328C2×C4D4×D18111yescharacteristic
329C2×C4C23×D18111yescharacteristic
330C8—21no—
331C8—3621no—
332C8—1812no—
333C8C2×C4×D18112yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—3621no—
338C22—3621no—
339C22—3622no—
340C22—1812no—
341C22—7241no—
342C22—7241no—
343C22C2×D4×D18111yescharacteristic
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—3622no—
350C4—3621no—
351C4—3621no—
352C4—1812no—
353C4—7241no—
354C4—7241no—
355C4C22×C4×D18111yescharacteristic
356C4#41×D18111yescharacteristic
357C2—42no—
358C2—3622no—
359C2—7242no—
360C2C4×D4×D18111yescharacteristic
361C2#2604208311yescharacteristic
362C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutatorC4×C181C23×C4
FrattiniC2×C4C23×D181
Fitting#440×C181C2
socleC22×C181C22×D4
prime radicalC2×#19153837C2
cosocleC2×C4×C181C24
hypercenter#440D181
hypocenterC181#2951
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #26041761C2semidirect
3. #26041758C2semidirect
4. #26041381C2semidirect
5. #26041380C2semidirect
6. #26041378C2semidirect
7. C4×#15668439C2semidirect
8. #26041371C2semidirect
9. C4×#15668434C2semidirect
10. #26041359C2semidirect
11. #107×D181C2semidirect
12. #26041279C2semidirect
13. #26041277C2semidirect
14. #26041236C2semidirect
15. #440×C181C2semidirect
18. #19153837C4semidirect
61. #15668450C2×C4semidirect
63. #15668448C2×C4semidirect
76. #15668439C2×C4semidirect
77. #15668438C2×C4semidirect
78. #15668434C2×C4semidirect
82. C8×D181C2×C4semidirect
104. SD16×C181C2×C4semidirect
181. C181#2951semidirect
189. #440D181semidirect
263. SD16C4×D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538372
#260417612
#260417582
#260413812
#260413802
#260413782
C4×#156684392
#260413712
C4×#156684342
#260413592
#107×D1812
#260412792
#260412772
#260412362
#440×C1812
#2951181