Finite Group Databasebeta

← #37543263

Subgroups — #37543263

Order 23168.

504 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153843C211yesmaximal, characteristic, complemented
2C2×#19153839C211yesmaximal, characteristic, complemented
3#26041847C211yesmaximal, characteristic, complemented
4#26041761C211yesmaximal, characteristic, complemented
5#26041503C211yesmaximal, characteristic, complemented
6#26041497C211yesmaximal, characteristic, complemented
7#26041491C211yesmaximal, characteristic, complemented
8#26041479C211yesmaximal, characteristic, complemented
9#26041477C211yesmaximal, characteristic, complemented
10#26041475C211yesmaximal, characteristic, complemented
11#26041473C211yesmaximal, characteristic, complemented
12#26041304C211yesmaximal, characteristic, complemented
13#26041279C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#464×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668450C2211yescharacteristic
18C2×D4×D181C2211yescharacteristic
19#19153843—24no—
20#19153839—24no—
21C2×#15668436C2211yescharacteristic
22C2×#15668436C2211yescharacteristic, complemented
23C2×#15668436C2211yescharacteristic, complemented
24C2×D1448C2211yescharacteristic
25C2×D1448C2211yescharacteristic, complemented
26C2×#15668434C2211yescharacteristic
27C2×#15668432C2211yescharacteristic
28C2×C8×D181C2211yescharacteristic
29#19153813C2211yescharacteristic
30#19153812C2211yescharacteristic
31#19153805C2211yescharacteristic
32#19153789—21no—
33#19153789—21no—
34#19153786—21no—
35#19153786—21no—
36Q8×Dic181C2211yescharacteristic, complemented
37C4×D724—21no—
38C4×D724C2211yescharacteristic, complemented
39#19153778—21no—
40#19153778C2211yescharacteristic, complemented
41#19153773—21no—
42#19153773C2211yescharacteristic
43C4⋊C4×D181—21no—
44C4⋊C4×D181C2211yescharacteristic
45C4⋊#13089678C2211yescharacteristic, complemented
46#19153745C2211yescharacteristic, complemented
47#19153745C2211yescharacteristic, complemented
48#19153740C2211yescharacteristic, complemented
49#19153738C2211yescharacteristic
50#19153738C2211yescharacteristic, complemented
51#19153737C2211yescharacteristic
52#19153736C2211yescharacteristic
53#19153736C2211yescharacteristic, complemented
54C2×Q16×C181C2211yescharacteristic, complemented
55C2×SD16×C181C2211yescharacteristic
56#124×C181C2211yescharacteristic
57C4×Q8×C181C2211yescharacteristic, complemented
58C4⋊C8×C181C2211yescharacteristic, complemented
59#103×C181C2211yescharacteristic, complemented
60#102×C181C2211yescharacteristic
61C23×D181—21no—
62#15668450—22no—
63#15668450—22no—
64#15668450—22no—
65#15668450D414yescomplemented
66C2×D724—21no—
67C2×D724—21no—
68C2×D724—21no—
69C2×D724—21no—
70C2×D724C2311yescharacteristic
71C2×D724C2311yescharacteristic
72C2×D724C2311yescharacteristic
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181—21no—
76D4×D181—22no—
77D4×D181—22no—
78C2×C4×D181—21no—
79C2×C4×D181—21no—
80C2×C4×D181—21no—
81C2×C4×D181—21no—
82C2×C4×D181—21no—
83C2×C4×D181C2311yescharacteristic
84#15668436—22no—
85#15668436—22no—
86#15668436—22no—
87D1448—22no—
88D1448—22no—
89#15668434—22no—
90#15668432—22no—
91C2×#13089678C2311yescharacteristic
92C2×#13089678C2311yescharacteristic
93C8×D181—22no—
94C4⋊Dic181—21no—
95C4⋊Dic181C2311yescharacteristic
96#15668428—21no—
97#15668428D411yescharacteristic
98#15668428D411yescharacteristic
99#15668426—21no—
100#15668426—21no—
101#15668426—21no—
102#15668426—21no—
103#15668426D411yescharacteristic
104#15668426D411yescharacteristic
105C4×Dic181—21no—
106C4×Dic181C2311yescharacteristic
107C2×Q8×C181C2311yescharacteristic
108C2×Q8×C181C2311yescharacteristic
109C2×D4×C181C2311yescharacteristic
110Q16×C181—22no—
111SD16×C181—22no—
112C2×C8×C181C2311yescharacteristic
113C2×C8×C181C2311yescharacteristic
114C4⋊C4×C181—21no—
115C4⋊C4×C181C2311yescharacteristic
116C22⋊C4×C181—21no—
117C22⋊C4×C181—21no—
118C42×C181—21no—
119C42×C181C2311yescharacteristic
120C22×D181—21no—
121C22×D181—21no—
122C22×D181—21no—
123C22×D181—42no—
124C22×D181—81no—
125C22×D181—81no—
126C22×D181C2×D411yescharacteristic
127D724—24no—
128D724—21no—
129D724—21no—
130D724—21no—
131D724—21no—
132D724—21no—
133D724—42no—
134D724—81no—
135D724—81no—
136D724C2×D412yes—
137C22⋊D181—42no—
138C22⋊D181—81no—
139C22⋊D181—81no—
140C2×Dic181—21no—
141C2×Dic181C2×D411yescharacteristic
142C2×Dic181C2×D411yescharacteristic
143C2×Dic181C2×D411yescharacteristic
144C4×D181—24no—
145C4×D181—42no—
146C4×D181—81no—
147C4×D181—81no—
148C4×D181—81no—
149C4×D181C2×D412yes—
150C4×D181#4112yes—
151#13089678—21no—
152#13089678—21no—
153C23×C181—21no—
154Q8×C181—21no—
155Q8×C181—21no—
156Q8×C181—21no—
157Q8×C181C2×D412yes—
158D4×C181—21no—
159D4×C181—21no—
160C2×C4×C181—21no—
161C2×C4×C181—21no—
162C2×C4×C181—21no—
163C2×C4×C181C2×D411yescharacteristic
164C2×C4×C181C2×D411yescharacteristic
165C2×C4×C181C2411yescharacteristic
166C8×C181—21no—
167C8×C181—21no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181C22×D411yescharacteristic
172C2×D181—21no—
173C2×D181—21no—
174C2×D181—22no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181—41no—
183C2×D181—84no—
184C2×D181#12112yes—
185C4×C181—22no—
186C4×C181—21no—
187C4×C181—21no—
188C4×C181—41no—
189C4×C181—41no—
190C4×C181C22×D411yescharacteristic
191C4×C181C2×#4111yescharacteristic
192Dic181—21no—
193Dic181—21no—
194Dic181—41no—
195Dic181#12112yes—
196C2×C181—81no—
197C2×C181C2×#12111yescharacteristic
198C2×C181#57611yescharacteristic
199C2×C181#57711yescharacteristic
200D181—22no—
201D181—42no—
202D181—81no—
203D181—81no—
204C181#304511yescharacteristic, complemented, Sylow
205#3045—1811nomaximal, Sylow
206C2×AGL(1,ℤ/8)—1811no—
207C2×#135—1811no—
208#535—1811no—
209#520—1811no—
210#464—1811no—
211#464D18111yescharacteristic, complemented
212#463—1811no—
213#463—1811no—
214#460—1811no—
215#460—1811no—
216#459—1811no—
217#459—1811no—
218#424—1811no—
219#417—1811no—
220C2×#102—1811no—
221C2×#41—1811no—
222C2×#41—1811no—
223C22×D4—1811no—
224AGL(1,ℤ/8)—3624no—
225#135—3624no—
226C2×Q16C2×D18111yescharacteristic, complemented
227C2×SD16—1811no—
228C2×SD16—1811no—
229C2×SD16—1811no—
230C2×SD16C2×D18111yescharacteristic
231C2×D8—1811no—
232C2×D8—1811no—
233C2×D8—1811no—
234C2×M16—1811no—
235C22×C8—1811no—
236#127—1811no—
237#127—1811no—
238#124—1811no—
239#124C2×D18111yescharacteristic
240#121—3621no—
241#121—3621no—
242#120—3621no—
243#120—3621no—
244C4×Q8—1811no—
245C4×Q8C2×D18111yescharacteristic, complemented
246C4×D4—3621no—
247C4×D4—3621no—
248C4×D4—1811no—
249C4×D4—1811no—
250#117—3621no—
251#117—1811no—
252C2×C4⋊C4—3621no—
253C2×C4⋊C4—1811no—
254C4⋊C8—1811no—
255C4⋊C8—1811no—
256C4⋊C8—1811no—
257C4⋊C8C2×D18111yescharacteristic, complemented
258#103—1811no—
259#103C2×D18111yescharacteristic, complemented
260#102—1811no—
261#102—1811no—
262#102—1811no—
263#102—1811no—
264#102—1811no—
265#102C2×D18111yescharacteristic
266C24—3621no—
267#41—3622no—
268#41—3622no—
269#41—3622no—
270#41—1814no—
271C2×Q8C22×D18111yescharacteristic
272C2×Q8C22×D18111yescharacteristic
273C2×D4—3621no—
274C2×D4—3621no—
275C2×D4—3622no—
276C2×D4—3622no—
277C2×D4—3621no—
278C2×D4—3621no—
279C2×D4—3621no—
280C2×D4—3621no—
281C2×D4—3621no—
282C2×D4—1811no—
283C2×D4—1811no—
284C2×D4—1811no—
285C2×D4C22×D18111yescharacteristic
286C22×C4—3621no—
287C22×C4—3621no—
288C22×C4—3621no—
289C22×C4—3621no—
290C22×C4—3621no—
291C22×C4—1811no—
292Q16—22no—
293SD16—22no—
294SD16—3622no—
295SD16—3622no—
296SD16—3622no—
297D8—3622no—
298D8—3622no—
299D8—3622no—
300M16—3622no—
301C2×C8—3622no—
302C2×C8—1811no—
303C2×C8—1811no—
304C2×C8C22×D18111yescharacteristic
305C2×C8C22×D18111yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—3621no—
308C4⋊C4—3621no—
309C4⋊C4—1811no—
310C4⋊C4—1811no—
311C4⋊C4—1811no—
312C4⋊C4C22×D18111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—3621no—
316C22⋊C4—3621no—
317C22⋊C4—3621no—
318C22⋊C4—3621no—
319C22⋊C4—1811no—
320C22⋊C4—1811no—
321C42—21no—
322C42—3621no—
323C42—1811no—
324C42C22×D18111yescharacteristic
325C23—21no—
326C23—3621no—
327C23—3621no—
328C23—3621no—
329C23—14481no—
330C23—14481no—
331C23—1811no—
332C23—7242no—
333Q8—21no—
334Q8—21no—
335Q8—21no—
336Q8D4×D18112yes—
337D4—21no—
338D4—21no—
339D4—3624no—
340D4—3621no—
341D4—3621no—
342D4—3621no—
343D4—3621no—
344D4—3621no—
345D4—14481no—
346D4—14481no—
347D4—14481no—
348D4—14481no—
349D4—1812no—
350D4—7242no—
351D4—7242no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3624no—
356C2×C4—3621no—
357C2×C4—14481no—
358C2×C4—14481no—
359C2×C4—14481no—
360C2×C4—1811no—
361C2×C4—1811no—
362C2×C4—1811no—
363C2×C4—1812no—
364C2×C4—1812no—
365C2×C4—7242no—
366C2×C4D4×D18111yescharacteristic
367C2×C4D4×D18111yescharacteristic
368C2×C4C23×D18111yescharacteristic
369C8—21no—
370C8—21no—
371C8—3621no—
372C8—3621no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—3621no—
377C22—3621no—
378C22—3622no—
379C22—14484no—
380C22—1812no—
381C22—7241no—
382C22—7241no—
383C22—7241no—
384C22—7241no—
385C22—7241no—
386C22—7241no—
387C22—7241no—
388C22—7241no—
389C22C2×D4×D18111yescharacteristic
390C4—22no—
391C4—21no—
392C4—21no—
393C4—41no—
394C4—41no—
395C4—3621no—
396C4—3621no—
397C4—1812no—
398C4—7241no—
399C4C2×D4×D18111yescharacteristic
400C4#41×D18111yescharacteristic
401C2—81no—
402C2—3622no—
403C2—14481no—
404C2—14481no—
405C2—7242no—
406C2#121×D18111yescharacteristic
407C2#2604208111yescharacteristic
408C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#464×C181C2
socleC22×C181C22×D4
hypercenter#464D181
hypocenterC181#3045
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#19153843C2semidirect
2. C2×#19153839C2semidirect
3. #26041847C2semidirect
4. #26041761C2semidirect
5. #26041503C2semidirect
6. #26041497C2semidirect
7. #26041491C2semidirect
8. #26041479C2semidirect
9. #26041477C2semidirect
10. #26041475C2semidirect
11. #26041473C2semidirect
12. #26041304C2semidirect
13. #26041279C2semidirect
14. #102×D181C2semidirect
15. #464×C181C2semidirect
22. C2×#15668436C22semidirect
23. C2×#15668436C22semidirect
25. C2×D1448C22semidirect
36. Q8×Dic181C22semidirect
38. C4×D724C22semidirect
40. #19153778C22semidirect
45. C4⋊#13089678C22semidirect
46. #19153745C22semidirect
47. #19153745C22semidirect
48. #19153740C22semidirect
50. #19153738C22semidirect
53. #19153736C22semidirect
54. C2×Q16×C181C22semidirect
57. C4×Q8×C181C22semidirect
58. C4⋊C8×C181C22semidirect
59. #103×C181C22semidirect
65. #15668450D4semidirect
204. C181#3045semidirect
211. #464D181semidirect
226. C2×Q16C2×D181semidirect
245. C4×Q8C2×D181semidirect
257. C4⋊C8C2×D181semidirect
259. #103C2×D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538432
C2×#191538392
#260418472
#260417612
#260415032
#260414972
#260414912
#260414792
#260414772
#260414752
#260414732
#260413042
#260412792
#102×D1812
#464×C1812
#3045181