Finite Group Databasebeta

← #37542550

Subgroups — #37542550

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×#19153840C211yesmaximal, characteristic
2#26041758C211yesmaximal, characteristic, complemented
3#26041751C211yesmaximal, characteristic, complemented
4#26041388C211yesmaximal, characteristic, complemented
5#26041381C211yesmaximal, characteristic, complemented
6#26041376C211yesmaximal, characteristic, complemented
7#26041366C211yesmaximal, characteristic, complemented
8C4×#15668437C211yesmaximal, characteristic, complemented
9D8×Dic181C211yesmaximal, characteristic, complemented
10C4×#15668434C211yesmaximal, characteristic, complemented
11#26041318C211yesmaximal, characteristic, complemented
12#26041272C211yesmaximal, characteristic, complemented
13#102×D181C211yesmaximal, characteristic, complemented
14#26041236C211yesmaximal, characteristic, complemented
15#442×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18#19153840C418yescomplemented
19C2×#15668438C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668432C2211yescharacteristic
23C2×C8×D181C2211yescharacteristic
24C4×Dic362C2211yescharacteristic, complemented
25#19153781C2211yescharacteristic, complemented
26C4×D724C2211yescharacteristic
27D4×Dic181C2211yescharacteristic
28D4×Dic181C2211yescharacteristic, complemented
29#19153778C2211yescharacteristic
30C4×C22⋊D181—21no—
31C4×C22⋊D181—21no—
32#19153776—21no—
33#19153776—21no—
34#19153774C2211yescharacteristic
35#19153773C2211yescharacteristic
36#19153772—21no—
37C2×#15668428—21no—
38C4⋊C4×D181C2211yescharacteristic
39C2×#15668426—21no—
40C22⋊C4×D181—21no—
41#19153750C2211yescharacteristic, complemented
42#19153749C2211yescharacteristic, complemented
43#19153747C2211yescharacteristic, complemented
44#19153741C2211yescharacteristic, complemented
45#19153739C2211yescharacteristic, complemented
46#19153738C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153737C2211yescharacteristic, complemented
49#19153736C2211yescharacteristic
50#19153726C2211yescharacteristic, complemented
51C4×#13089678C2211yescharacteristic, complemented
52C8×Dic181C2211yescharacteristic, complemented
53C2×D8×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic, complemented
56#106×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic, complemented
59#97×C181C2211yescharacteristic, complemented
60C23×D181—21no—
61#15668448—22no—
62#15668448C2×C414yescomplemented
63C2×Dic362C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67D4×D181—22no—
68D4×D181C2×C414yescomplemented
69C22×Dic181—21no—
70C22×Dic181—21no—
71C22×Dic181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76#15668438C2×C414yescomplemented
77#15668437C2×C414yescomplemented
78#15668434C2×C414yescomplemented
79#15668432C2×C414yescomplemented
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C8×D181—22no—
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428D411yescharacteristic
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C4×Dic181—21no—
99C4×Dic181—21no—
100C4×Dic181C2311yescharacteristic
101C2×D4×C181C2311yescharacteristic
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104C22×C4×C181—21no—
105D8×C181C2×C414yescomplemented
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22⋊C4×C181—21no—
112C42×C181C2311yescharacteristic
113C22×D181—21no—
114C22×D181—24no—
115C22×D181—81no—
116C22×D181—81no—
117C22×D181C2×D411yescharacteristic
118Dic362—21no—
119Dic362C22×C412yes—
120D724—21no—
121D724C22×C412yes—
122C22⋊D181—24no—
123C22⋊D181—24no—
124C2×Dic181—21no—
125C2×Dic181—24no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—81no—
129C2×Dic181—81no—
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—81no—
134C4×D181—81no—
135C4×D181—81no—
136C4×D181C22×C412yes—
137C4×D181#4112yes—
138#13089678—21no—
139#13089678C22×C412yes—
140C23×C181—21no—
141C23×C181—21no—
142D4×C181—21no—
143D4×C181—21no—
144D4×C181C22×C412yes—
145D4×C181C22×C412yes—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—81no—
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—22no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181C22×D411yescharacteristic
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—22no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—84no—
168C2×D181C4×D412yes—
169C4×C181—21no—
170C4×C181—21no—
171C4×C181—41no—
172C4×C181—41no—
173C4×C181C23×C411yescharacteristic
174C4×C181C2×#4111yescharacteristic
175Dic181—22no—
176Dic181—21no—
177Dic181—21no—
178Dic181—41no—
179Dic181—41no—
180Dic181C4×D412yes—
181C2×C181—42no—
182C2×C181—42no—
183C2×C181C2×C4×D411yescharacteristic
184C2×C181#57611yescharacteristic
185C2×C181#57711yescharacteristic
186D181—22no—
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#442D18111yescharacteristic, complemented
195#440—1811no—
196#440—1811no—
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×SD16—1811no—
210C2×D8—1811no—
211C2×D8C2×D18111yescharacteristic
212C2×M16—1811no—
213C22×C8—1811no—
214C4×Q8—1811no—
215C4×Q8—1811no—
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×D4C2×D18111yescharacteristic
225C4×D4C2×D18111yescharacteristic, complemented
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#107—1811no—
235#106—1811no—
236#106C2×D18111yescharacteristic, complemented
237#103—1811no—
238#103—1811no—
239#102—1811no—
240#102—1811no—
241#102—1811no—
242#102—1811no—
243#102C2×D18111yescharacteristic
244#102C2×D18111yescharacteristic, complemented
245#97—1811no—
246#97C2×D18111yescharacteristic, complemented
247C4×C8—1811no—
248C4×C8—1811no—
249C24—3621no—
250#41—3622no—
251#41—1814no—
252C2×Q8—1811no—
253C2×D4—3621no—
254C2×D4—3622no—
255C2×D4—3621no—
256C2×D4—1814no—
257C2×D4—1811no—
258C2×D4C22×D18111yescharacteristic
259C2×D4C22×D18111yescharacteristic
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—3621no—
263C22×C4—3621no—
264C22×C4—3621no—
265C22×C4—3621no—
266C22×C4—3621no—
267C22×C4—3621no—
268C22×C4—1811no—
269SD16—1814no—
270SD16—1814no—
271D8—1814no—
272D8C4×D18114yescomplemented
273M16—1814no—
274C2×C8—3622no—
275C2×C8—1811no—
276C2×C8—1811no—
277C2×C8C22×D18111yescharacteristic
278C2×C8C22×D18111yescharacteristic
279C4⋊C4—3621no—
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—21no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—1811no—
296C22⋊C4—1811no—
297C42—3621no—
298C42—3621no—
299C42—3621no—
300C42—1811no—
301C42C22×D18111yescharacteristic
302C23—21no—
303C23—21no—
304C23—3624no—
305C23—3621no—
306C23—14481no—
307C23—14481no—
308C23—1811no—
309Q8—3621no—
310Q8—1812no—
311D4—21no—
312D4—21no—
313D4—3624no—
314D4—3624no—
315D4—3621no—
316D4—1812no—
317D4C2×C4×D18112yes—
318D4C2×C4×D18112yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—3621no—
324C2×C4—3624no—
325C2×C4—3621no—
326C2×C4—3621no—
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—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—3621no—
351C22—3621no—
352C22—3622no—
353C22—14484no—
354C22—1812no—
355C22—7241no—
356C22—7241no—
357C22C2×D4×D18111yescharacteristic
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—3622no—
363C4—3621no—
364C4—3621no—
365C4—1812no—
366C4—7241no—
367C4—7241no—
368C4C22×C4×D18111yescharacteristic
369C4#41×D18111yescharacteristic
370C2—42no—
371C2—42no—
372C2—3622no—
373C2—7242no—
374C2C4×D4×D18111yescharacteristic
375C2#2604208311yescharacteristic
376C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutatorC4×C181C23×C4
FrattiniC2×C4C23×D181
Fitting#442×C181C2
socleC22×C181C22×D4
prime radicalC2×#19153840C2
cosocleC2×C4×C181C24
hypercenter#442D181
hypocenterC181#2946
LCSG ▷ C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #26041758C2semidirect
3. #26041751C2semidirect
4. #26041388C2semidirect
5. #26041381C2semidirect
6. #26041376C2semidirect
7. #26041366C2semidirect
8. C4×#15668437C2semidirect
9. D8×Dic181C2semidirect
10. C4×#15668434C2semidirect
11. #26041318C2semidirect
12. #26041272C2semidirect
13. #102×D181C2semidirect
14. #26041236C2semidirect
15. #442×C181C2semidirect
18. #19153840C4semidirect
24. C4×Dic362C22semidirect
25. #19153781C22semidirect
28. D4×Dic181C22semidirect
41. #19153750C22semidirect
42. #19153749C22semidirect
43. #19153747C22semidirect
44. #19153741C22semidirect
45. #19153739C22semidirect
48. #19153737C22semidirect
50. #19153726C22semidirect
51. C4×#13089678C22semidirect
52. C8×Dic181C22semidirect
55. C4×D4×C181C22semidirect
56. #106×C181C22semidirect
58. #102×C181C22semidirect
59. #97×C181C22semidirect
62. #15668448C2×C4semidirect
68. D4×D181C2×C4semidirect
76. #15668438C2×C4semidirect
77. #15668437C2×C4semidirect
78. #15668434C2×C4semidirect
79. #15668432C2×C4semidirect
105. D8×C181C2×C4semidirect
188. C181#2946semidirect
194. #442D181semidirect
225. C4×D4C2×D181semidirect
236. #106C2×D181semidirect
244. #102C2×D181semidirect
246. #97C2×D181semidirect
272. D8C4×D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538402
#260417582
#260417512
#260413882
#260413812
#260413762
#260413662
C4×#156684372
D8×Dic1812
C4×#156684342
#260413182
#260412722
#102×D1812
#260412362
#442×C1812
#2946181