Finite Group Databasebeta

← #37543261

Subgroups — #37543261

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×#19153840C211yesmaximal, characteristic, complemented
2C2×#19153837C211yesmaximal, characteristic, complemented
3#26041847C211yesmaximal, characteristic, complemented
4#26041758C211yesmaximal, characteristic, complemented
5#26041504C211yesmaximal, characteristic, complemented
6#26041498C211yesmaximal, characteristic, complemented
7#26041496C211yesmaximal, characteristic, complemented
8#26041480C211yesmaximal, characteristic, complemented
9#26041478C211yesmaximal, characteristic, complemented
10#26041474C211yesmaximal, characteristic, complemented
11#26041472C211yesmaximal, characteristic, complemented
12#26041304C211yesmaximal, characteristic, complemented
13#26041279C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#463×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18C2×D4×D181C2211yescharacteristic
19#19153840—24no—
20#19153837—24no—
21C2×#15668439C2211yescharacteristic, complemented
22C2×#15668438C2211yescharacteristic
23C2×#15668438C2211yescharacteristic, complemented
24C2×#15668437C2211yescharacteristic
25C2×#15668434C2211yescharacteristic
26C2×#15668434C2211yescharacteristic, complemented
27C2×#15668432C2211yescharacteristic
28C2×C8×D181C2211yescharacteristic
29#19153813C2211yescharacteristic
30#19153812C2211yescharacteristic
31#19153805C2211yescharacteristic
32#19153789—21no—
33#19153789—21no—
34#19153786—21no—
35#19153786—21no—
36C4×Dic362C2211yescharacteristic, complemented
37#19153781C2211yescharacteristic, complemented
38D4×Dic181C2211yescharacteristic, complemented
39C4×C22⋊D181—21no—
40#19153776—21no—
41#19153773C2211yescharacteristic
42#19153772—21no—
43C2×#15668428—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×SD16×C181C2211yescharacteristic, complemented
55C2×D8×C181C2211yescharacteristic
56#124×C181C2211yescharacteristic
57C4×D4×C181C2211yescharacteristic, complemented
58C4⋊C8×C181C2211yescharacteristic, complemented
59#103×C181C2211yescharacteristic, complemented
60#102×C181C2211yescharacteristic
61C23×D181—21no—
62#15668450—22no—
63#15668450—22no—
64#15668448—22no—
65#15668448D414yescomplemented
66C2×Dic362C2311yescharacteristic
67C2×D724—21no—
68C2×D724—21no—
69C2×D724—21no—
70C2×D724C2311yescharacteristic
71C2×D724C2311yescharacteristic
72C2×C22⋊D181—21no—
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181—21no—
76D4×D181—22no—
77D4×D181—22no—
78C22×Dic181—21no—
79C22×Dic181—21no—
80C2×C4×D181—21no—
81C2×C4×D181—21no—
82C2×C4×D181C2311yescharacteristic
83#15668439—22no—
84#15668438—22no—
85#15668438—22no—
86#15668437—22no—
87#15668434—22no—
88#15668434—22no—
89#15668432—22no—
90C2×#13089678C2311yescharacteristic
91C2×#13089678C2311yescharacteristic
92C8×D181—22no—
93C4⋊Dic181C2311yescharacteristic
94#15668428—21no—
95#15668428—21no—
96#15668428—21no—
97#15668428D411yescharacteristic
98#15668428D411yescharacteristic
99C22⋊Dic181—21no—
100#15668426—21no—
101#15668426—21no—
102#15668426D411yescharacteristic
103#15668426D411yescharacteristic
104C4×Dic181—21no—
105C4×Dic181—21no—
106C4×Dic181C2311yescharacteristic
107C2×Q8×C181C2311yescharacteristic
108C2×D4×C181C2311yescharacteristic
109C2×D4×C181C2311yescharacteristic
110C22×C4×C181—21no—
111SD16×C181—22no—
112D8×C181—22no—
113C2×C8×C181C2311yescharacteristic
114C2×C8×C181C2311yescharacteristic
115C4⋊C4×C181C2311yescharacteristic
116C22⋊C4×C181—21no—
117C22⋊C4×C181—21no—
118C22⋊C4×C181—21no—
119C42×C181C2311yescharacteristic
120C22×D181—21no—
121C22×D181—21no—
122C22×D181—42no—
123C22×D181—81no—
124C22×D181—81no—
125C22×D181C2×D411yescharacteristic
126Dic362—21no—
127Dic362C2×D412yes—
128D724—21no—
129D724—21no—
130D724—21no—
131D724—21no—
132D724—42no—
133D724—81no—
134D724—81no—
135C22⋊D181—24no—
136C22⋊D181—42no—
137C22⋊D181—81no—
138C22⋊D181—81no—
139C2×Dic181—21no—
140C2×Dic181—24no—
141C2×Dic181—21no—
142C2×Dic181—81no—
143C2×Dic181C2×D411yescharacteristic
144C2×Dic181C2×D411yescharacteristic
145C2×Dic181C2×D411yescharacteristic
146C4×D181—42no—
147C4×D181—81no—
148C4×D181C2×D412yes—
149C4×D181#4112yes—
150#13089678—21no—
151#13089678—21no—
152C23×C181—21no—
153C23×C181—21no—
154Q8×C181—21no—
155Q8×C181—21no—
156D4×C181—21no—
157D4×C181—21no—
158D4×C181—21no—
159D4×C181C2×D412yes—
160C2×C4×C181—21no—
161C2×C4×C181—21no—
162C2×C4×C181—81no—
163C2×C4×C181C2×D411yescharacteristic
164C2×C4×C181C2×D411yescharacteristic
165C2×C4×C181C2411yescharacteristic
166C8×C181—21no—
167C8×C181—21no—
168C22×C181—22no—
169C22×C181—41no—
170C22×C181—41no—
171C22×C181—41no—
172C22×C181—41no—
173C22×C181—41no—
174C22×C181C22×D411yescharacteristic
175C2×D181—21no—
176C2×D181—21no—
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—21no—
186C4×C181—21no—
187C4×C181—41no—
188C4×C181—41no—
189C4×C181C22×D411yescharacteristic
190C4×C181C2×#4111yescharacteristic
191Dic181—22no—
192Dic181—21no—
193Dic181—21no—
194Dic181—41no—
195Dic181#12112yes—
196C2×C181—42no—
197C2×C181—81no—
198C2×C181C2×#12111yescharacteristic
199C2×C181#57611yescharacteristic
200C2×C181#57711yescharacteristic
201D181—22no—
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#464—1811no—
212#463—1811no—
213#463D18111yescharacteristic, complemented
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×Q16—1811no—
227C2×SD16—1811no—
228C2×SD16—1811no—
229C2×SD16—1811no—
230C2×SD16C2×D18111yescharacteristic, complemented
231C2×D8—1811no—
232C2×D8—1811no—
233C2×D8C2×D18111yescharacteristic
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×Q8—1811no—
246C4×D4—3621no—
247C4×D4—3621no—
248C4×D4—1811no—
249C4×D4C2×D18111yescharacteristic, complemented
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×Q8—1811no—
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×D4C22×D18111yescharacteristic
285C2×D4C22×D18111yescharacteristic
286C22×C4—21no—
287C22×C4—3621no—
288C22×C4—3621no—
289C22×C4—3621no—
290C22×C4—3621no—
291C22×C4—1811no—
292Q16—3622no—
293SD16—22no—
294SD16—3622no—
295SD16—3622no—
296SD16—3622no—
297D8—22no—
298D8—3622no—
299D8—3622no—
300M16—3622no—
301C2×C8—3622no—
302C2×C8—1811no—
303C2×C8—1811no—
304C2×C8C22×D18111yescharacteristic
305C2×C8C22×D18111yescharacteristic
306C4⋊C4—3621no—
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—21no—
316C22⋊C4—3621no—
317C22⋊C4—3621no—
318C22⋊C4—3621no—
319C22⋊C4—1811no—
320C22⋊C4—1811no—
321C42—3621no—
322C42—3621no—
323C42—1811no—
324C42C22×D18111yescharacteristic
325C23—21no—
326C23—21no—
327C23—3621no—
328C23—3621no—
329C23—14481no—
330C23—14481no—
331C23—1811no—
332C23—7242no—
333Q8—21no—
334Q8—21no—
335Q8—3621no—
336Q8—1812no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—3624no—
341D4—3621no—
342D4—3621no—
343D4—3621no—
344D4—3621no—
345D4—14481no—
346D4—14481no—
347D4—14481no—
348D4—14481no—
349D4—7242no—
350D4—7242no—
351D4D4×D18112yes—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—81no—
355C2×C4—3621no—
356C2×C4—3624no—
357C2×C4—3621no—
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—22no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—3621no—
380C22—3621no—
381C22—14484no—
382C22—1812no—
383C22—7241no—
384C22—7241no—
385C22—7241no—
386C22—7241no—
387C22—7241no—
388C22—7241no—
389C22C2×D4×D18111yescharacteristic
390C4—21no—
391C4—21no—
392C4—41no—
393C4—41no—
394C4—3622no—
395C4—3621no—
396C4—3621no—
397C4—1812no—
398C4—7241no—
399C4C2×D4×D18111yescharacteristic
400C4#41×D18111yescharacteristic
401C2—42no—
402C2—81no—
403C2—3622no—
404C2—14481no—
405C2—14481no—
406C2#121×D18111yescharacteristic
407C2#2604208311yescharacteristic
408C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#463×C181C2
socleC22×C181C22×D4
hypercenter#463D181
hypocenterC181#3045
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#19153840C2semidirect
2. C2×#19153837C2semidirect
3. #26041847C2semidirect
4. #26041758C2semidirect
5. #26041504C2semidirect
6. #26041498C2semidirect
7. #26041496C2semidirect
8. #26041480C2semidirect
9. #26041478C2semidirect
10. #26041474C2semidirect
11. #26041472C2semidirect
12. #26041304C2semidirect
13. #26041279C2semidirect
14. #102×D181C2semidirect
15. #463×C181C2semidirect
21. C2×#15668439C22semidirect
23. C2×#15668438C22semidirect
26. C2×#15668434C22semidirect
36. C4×Dic362C22semidirect
37. #19153781C22semidirect
38. D4×Dic181C22semidirect
45. C4⋊#13089678C22semidirect
46. #19153745C22semidirect
47. #19153745C22semidirect
48. #19153740C22semidirect
50. #19153738C22semidirect
53. #19153736C22semidirect
54. C2×SD16×C181C22semidirect
57. C4×D4×C181C22semidirect
58. C4⋊C8×C181C22semidirect
59. #103×C181C22semidirect
65. #15668448D4semidirect
204. C181#3045semidirect
213. #463D181semidirect
230. C2×SD16C2×D181semidirect
249. C4×D4C2×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×#191538402
C2×#191538372
#260418472
#260417582
#260415042
#260414982
#260414962
#260414802
#260414782
#260414742
#260414722
#260413042
#260412792
#102×D1812
#463×C1812
#3045181