Finite Group Databasebeta

← #37542552

Subgroups — #37542552

Order 23168.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153843C211yesmaximal, characteristic
2#26041761C211yesmaximal, characteristic, complemented
3#26041751C211yesmaximal, characteristic, complemented
4#26041392C211yesmaximal, characteristic, complemented
5#26041388C211yesmaximal, characteristic, complemented
6#26041382C211yesmaximal, characteristic, complemented
7SD16×Dic181C211yesmaximal, characteristic, complemented
8C4×#15668436C211yesmaximal, characteristic, complemented
9#26041361C211yesmaximal, characteristic, complemented
10C4×#15668434C211yesmaximal, characteristic, complemented
11#26041320C211yesmaximal, characteristic, complemented
12#26041274C211yesmaximal, characteristic, complemented
13#102×D181C211yesmaximal, characteristic, complemented
14#26041236C211yesmaximal, characteristic, complemented
15#440×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18#19153843C418yescomplemented
19C2×#15668436C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668432C2211yescharacteristic
23C2×C8×D181C2211yescharacteristic
24Q8×Dic181C2211yescharacteristic, complemented
25C4×D724—21no—
26C4×D724C2211yescharacteristic
27C4×D724C2211yescharacteristic, complemented
28D4×Dic181C2211yescharacteristic
29#19153778—21no—
30#19153778C2211yescharacteristic
31#19153778C2211yescharacteristic, complemented
32C4×C22⋊D181—21no—
33#19153776—21no—
34#19153774C2211yescharacteristic
35#19153773—21no—
36#19153773C2211yescharacteristic
37C4⋊C4×D181—21no—
38C4⋊C4×D181C2211yescharacteristic
39C2×#15668426—21no—
40C22⋊C4×D181—21no—
41#19153749C2211yescharacteristic, complemented
42#19153748C2211yescharacteristic, complemented
43#19153747C2211yescharacteristic, complemented
44#19153740C2211yescharacteristic, complemented
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic, complemented
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic, complemented
50#19153726C2211yescharacteristic, complemented
51C4×#13089678C2211yescharacteristic, complemented
52C8×Dic181C2211yescharacteristic, complemented
53C2×SD16×C181C2211yescharacteristic
54C4×Q8×C181C2211yescharacteristic, complemented
55C4×D4×C181C2211yescharacteristic
56#107×C181C2211yescharacteristic, complemented
57#103×C181C2211yescharacteristic, complemented
58#102×C181C2211yescharacteristic
59#97×C181C2211yescharacteristic, complemented
60C23×D181—21no—
61#15668450—22no—
62#15668450C2×C414yescomplemented
63C2×D724—21no—
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67D4×D181—22no—
68D4×D181C2×C414yescomplemented
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×D181—21no—
76C2×C4×D181C2311yescharacteristic
77#15668436C2×C414yescomplemented
78D1448C2×C414yescomplemented
79#15668434C2×C414yescomplemented
80#15668432C2×C414yescomplemented
81C2×#13089678C2311yescharacteristic
82C2×#13089678C2311yescharacteristic
83C8×D181—22no—
84C4⋊Dic181—21no—
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428D411yescharacteristic
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426D411yescharacteristic
97#15668426D411yescharacteristic
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×D181—21no—
115C22×D181—24no—
116C22×D181—81no—
117C22×D181—81no—
118C22×D181C2×D411yescharacteristic
119D724—24no—
120D724—21no—
121D724—21no—
122D724C22×C412yes—
123D724C22×C412yes—
124C22⋊D181—24no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—81no—
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C4×D181—24no—
132C4×D181—81no—
133C4×D181—81no—
134C4×D181—81no—
135C4×D181—81no—
136C4×D181—81no—
137C4×D181C22×C412yes—
138C4×D181#4112yes—
139#13089678—21no—
140#13089678C22×C412yes—
141C23×C181—21no—
142Q8×C181—21no—
143Q8×C181C22×C412yes—
144D4×C181—21no—
145D4×C181C22×C412yes—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—81no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181C22×C412yes—
155C22×C181—22no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181C22×D411yescharacteristic
159C2×D181—21no—
160C2×D181—21no—
161C2×D181—22no—
162C2×D181—22no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—84no—
168C2×D181C4×D412yes—
169C4×C181—22no—
170C4×C181—21no—
171C4×C181—21no—
172C4×C181—41no—
173C4×C181—41no—
174C4×C181C23×C411yescharacteristic
175C4×C181C2×#4111yescharacteristic
176Dic181—21no—
177Dic181—21no—
178Dic181—41no—
179Dic181—41no—
180Dic181C4×D412yes—
181C2×C181—42no—
182C2×C181C2×C4×D411yescharacteristic
183C2×C181#57611yescharacteristic
184C2×C181#57711yescharacteristic
185D181—22no—
186D181—42no—
187D181—42no—
188C181#294611yescharacteristic, complemented, Sylow
189#2946—1811nomaximal, Sylow
190C2×AGL(1,ℤ/8)—1811no—
191#520—1811no—
192#518—1811no—
193#442—1811no—
194#442—1811no—
195#440—1811no—
196#440D18111yescharacteristic, complemented
197C4×SD16—1811no—
198C4×SD16—1811no—
199C4×D8—1811no—
200C4×D8—1811no—
201#428—1811no—
202#416—1811no—
203C2×#102—1811no—
204#405—1811no—
205C2×#41—1811no—
206C22×D4—1811no—
207AGL(1,ℤ/8)—1818no—
208C2×SD16—1811no—
209C2×SD16C2×D18111yescharacteristic
210C2×D8—1811no—
211C2×D8—1811no—
212C2×M16—1811no—
213C22×C8—1811no—
214C4×Q8—1811no—
215C4×Q8C2×D18111yescharacteristic, complemented
216C4×D4—3621no—
217C4×D4—3621no—
218C4×D4—3621no—
219C4×D4—3621no—
220C4×D4—1811no—
221C4×D4—1811no—
222C4×D4—1811no—
223C4×D4—1811no—
224C4×D4—1811no—
225C4×D4C2×D18111yescharacteristic
226#117—3621no—
227#117—1811no—
228#117—1811no—
229C2×C4⋊C4—3621no—
230C2×C4⋊C4—1811no—
231C2×C22⋊C4—3621no—
232C2×C22⋊C4—3621no—
233#107—1811no—
234#107C2×D18111yescharacteristic, complemented
235#106—1811no—
236#106—1811no—
237#103—1811no—
238#103C2×D18111yescharacteristic, complemented
239#102—1811no—
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102C2×D18111yescharacteristic
245#97—1811no—
246#97C2×D18111yescharacteristic, complemented
247C4×C8—1811no—
248C4×C8—1811no—
249C24—3621no—
250#41—3622no—
251#41—1814no—
252C2×Q8C22×D18111yescharacteristic
253C2×D4—3621no—
254C2×D4—3622no—
255C2×D4—3621no—
256C2×D4—1814no—
257C2×D4—1811no—
258C2×D4—1811no—
259C2×D4C22×D18111yescharacteristic
260C22×C4—21no—
261C22×C4—3621no—
262C22×C4—3621no—
263C22×C4—3621no—
264C22×C4—3621no—
265C22×C4—3621no—
266C22×C4—3621no—
267C22×C4—3621no—
268C22×C4—1811no—
269SD16—1814no—
270SD16C4×D18114yescomplemented
271D8—1814no—
272D8—1814no—
273M16—1814no—
274C2×C8—3622no—
275C2×C8—1811no—
276C2×C8—1811no—
277C2×C8C22×D18111yescharacteristic
278C2×C8C22×D18111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—3621no—
281C4⋊C4—3621no—
282C4⋊C4—1811no—
283C4⋊C4—1811no—
284C4⋊C4—1811no—
285C4⋊C4—1811no—
286C4⋊C4C22×D18111yescharacteristic
287C4⋊C4C22×D18111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—1811no—
296C22⋊C4—1811no—
297C42—21no—
298C42—3621no—
299C42—3621no—
300C42—1811no—
301C42C22×D18111yescharacteristic
302C23—21no—
303C23—3624no—
304C23—3621no—
305C23—3621no—
306C23—14481no—
307C23—14481no—
308C23—1811no—
309Q8—21no—
310Q8C2×C4×D18112yes—
311D4—21no—
312D4—3624no—
313D4—3624no—
314D4—3621no—
315D4—3621no—
316D4—1812no—
317D4—1812no—
318D4C2×C4×D18112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—81no—
323C2×C4—3624no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—14481no—
327C2×C4—14481no—
328C2×C4—14481no—
329C2×C4—14481no—
330C2×C4—14481no—
331C2×C4—14481no—
332C2×C4—1811no—
333C2×C4—1811no—
334C2×C4—1811no—
335C2×C4—1812no—
336C2×C4—1812no—
337C2×C4D4×D18111yescharacteristic
338C2×C4D4×D18111yescharacteristic
339C2×C4C23×D18111yescharacteristic
340C8—21no—
341C8—3621no—
342C8—1812no—
343C8C2×C4×D18112yes—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—3621no—
348C22—3621no—
349C22—3622no—
350C22—3622no—
351C22—14484no—
352C22—1812no—
353C22—7241no—
354C22—7241no—
355C22—7241no—
356C22—7241no—
357C22C2×D4×D18111yescharacteristic
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—3621no—
364C4—3621no—
365C4—1812no—
366C4—7241no—
367C4—7241no—
368C4C22×C4×D18111yescharacteristic
369C4#41×D18111yescharacteristic
370C2—42no—
371C2—3622no—
372C2—7242no—
373C2—7242no—
374C2C4×D4×D18111yescharacteristic
375C2#2604208311yescharacteristic
376C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutatorC4×C181C23×C4
FrattiniC2×C4C23×D181
Fitting#440×C181C2
socleC22×C181C22×D4
prime radicalC2×#19153843C2
cosocleC2×C4×C181C24
hypercenter#440D181
hypocenterC181#2946
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. #26041751C2semidirect
4. #26041392C2semidirect
5. #26041388C2semidirect
6. #26041382C2semidirect
7. SD16×Dic181C2semidirect
8. C4×#15668436C2semidirect
9. #26041361C2semidirect
10. C4×#15668434C2semidirect
11. #26041320C2semidirect
12. #26041274C2semidirect
13. #102×D181C2semidirect
14. #26041236C2semidirect
15. #440×C181C2semidirect
18. #19153843C4semidirect
24. Q8×Dic181C22semidirect
27. C4×D724C22semidirect
31. #19153778C22semidirect
41. #19153749C22semidirect
42. #19153748C22semidirect
43. #19153747C22semidirect
44. #19153740C22semidirect
46. #19153738C22semidirect
49. #19153736C22semidirect
50. #19153726C22semidirect
51. C4×#13089678C22semidirect
52. C8×Dic181C22semidirect
54. C4×Q8×C181C22semidirect
56. #107×C181C22semidirect
57. #103×C181C22semidirect
59. #97×C181C22semidirect
62. #15668450C2×C4semidirect
68. D4×D181C2×C4semidirect
77. #15668436C2×C4semidirect
78. D1448C2×C4semidirect
79. #15668434C2×C4semidirect
80. #15668432C2×C4semidirect
104. SD16×C181C2×C4semidirect
188. C181#2946semidirect
196. #440D181semidirect
215. C4×Q8C2×D181semidirect
234. #107C2×D181semidirect
238. #103C2×D181semidirect
246. #97C2×D181semidirect
270. SD16C4×D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538432
#260417612
#260417512
#260413922
#260413882
#260413822
SD16×Dic1812
C4×#156684362
#260413612
C4×#156684342
#260413202
#260412742
#102×D1812
#260412362
#440×C1812
#2946181