Finite Group Databasebeta

← #37544560

Subgroups — #37544560

Order 23168.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041789C211yesmaximal, characteristic, complemented
2#26041786C211yesmaximal, characteristic, complemented
3#26041621C211yesmaximal, characteristic, complemented
4#26041618C211yesmaximal, characteristic, complemented
5#26041601C211yesmaximal, characteristic, complemented
6#26041600C211yesmaximal, characteristic, complemented
7#26041536C211yesmaximal, characteristic, complemented
8#26041529C211yesmaximal, characteristic, complemented
9#26041524C211yesmaximal, characteristic, complemented
10#26041522C211yesmaximal, characteristic, complemented
11#26041441C211yesmaximal, characteristic, complemented
12#26041438C211yesmaximal, characteristic, complemented
13#26041421C211yesmaximal, characteristic, complemented
14#26041241C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C22×C4×D181C2211yescharacteristic
18C2×#15668439C2211yescharacteristic, complemented
19C2×#15668437C2211yescharacteristic, complemented
20C2×#15668432C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22#19153798—21no—
23#19153797—21no—
24#19153796C2211yescharacteristic
25#19153795C2211yescharacteristic
26#19153792C2211yescharacteristic
27#19153792C2211yescharacteristic
28#19153787C2211yescharacteristic
29#19153787C2211yescharacteristic
30#19153787C2211yescharacteristic
31#19153784—21no—
32#19153784—21no—
33D4×Dic181—21no—
34C4×C22⋊D181—21no—
35C4×C22⋊D181—21no—
36#19153776—21no—
37#19153775C2211yescharacteristic
38#19153774C2211yescharacteristic
39#19153750C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153748C2211yescharacteristic, complemented
42#19153747C2211yescharacteristic, complemented
43#19153741C2211yescharacteristic, complemented
44#19153741C2211yescharacteristic, complemented
45#19153740C2211yescharacteristic, complemented
46#19153737C2211yescharacteristic, complemented
47#19153737C2211yescharacteristic, complemented
48#19153737C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153728C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic, complemented
54C2×D8×C181C2211yescharacteristic, complemented
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic
59C23×D181D411yescharacteristic
60#15668448—41no—
61#15668448—41no—
62C2×Dic362C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C22×Dic181—21no—
68C22×Dic181D411yescharacteristic
69C2×C4×D181—41no—
70C2×C4×D181—41no—
71C2×C4×D181D411yescharacteristic
72C2×C4×D181D411yescharacteristic
73C2×C4×D181C2311yescharacteristic
74C2×C4×D181C2311yescharacteristic
75#15668439—41no—
76#15668437—41no—
77#15668432—41no—
78#15668432—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C4⋊Dic181—21no—
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97C4×Dic181—21no—
98C4×Dic181—21no—
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×D4×C181—21no—
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C2×D4×C181C2311yescharacteristic
106C22×C4×C181—21no—
107C22×C4×C181C2311yescharacteristic
108SD16×C181—41no—
109D8×C181—41no—
110C2×C8×C181C2311yescharacteristic
111C2×C8×C181C2311yescharacteristic
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—41no—
115C22×D181—41no—
116C22×D181—41no—
117C22×D181C2×D411yescharacteristic
118C22×D181C2×D411yescharacteristic
119Dic362—21no—
120Dic362—21no—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—42no—
124C22⋊D181—42no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—41no—
130C2×Dic181—42no—
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—21no—
134C4×D181—21no—
135C4×D181—21no—
136C4×D181—21no—
137C4×D181—41no—
138C4×D181—41no—
139#13089678—21no—
140#13089678—21no—
141C23×C181—21no—
142C23×C181—21no—
143C23×C181C2×D411yescharacteristic
144Q8×C181—21no—
145Q8×C181—21no—
146D4×C181—21no—
147D4×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—42no—
151D4×C181—42no—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—42no—
157C2×C4×C181C2×D411yescharacteristic
158C2×C4×C181C2411yescharacteristic
159C8×C181—21no—
160C8×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—21no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—41no—
170C22×C181C22×D411yescharacteristic
171C2×D181—21no—
172C2×D181—21no—
173C2×D181—21no—
174C2×D181—21no—
175C2×D181—21no—
176C2×D181—21no—
177C2×D181—44no—
178C4×C181—21no—
179C4×C181—41no—
180C4×C181—41no—
181C4×C181H(5,𝔽2)11yescharacteristic
182C4×C181H(5,𝔽2)11yescharacteristic
183Dic181—21no—
184Dic181—21no—
185Dic181—41no—
186Dic181—41no—
187Dic181—41no—
188Dic181—41no—
189C2×C181—41no—
190C2×C181—81no—
191C2×C181—81no—
192C2×C181#53411yescharacteristic
193C2×C181#57511yescharacteristic
194C2×C181#57511yescharacteristic
195D181—41no—
196D181—41no—
197C181#319711yescharacteristic, complemented, Sylow
198#3197—1811nomaximal, Sylow
199#525—1811no—
200#525—1811no—
201#485—1811no—
202#485—1811no—
203#482—1811no—
204#482—1811no—
205#470—1811no—
206#469—1811no—
207#468—1811no—
208#468—1811no—
209#452—1811no—
210#452—1811no—
211#449—1811no—
212#449D18111yescharacteristic, complemented
213#407—1811no—
214C2×#41—1811no—
215C2×#41C2×D18111yescharacteristic
216C23×C4—1811no—
217C2×Q16—1811no—
218C2×SD16—1811no—
219C2×SD16C2×D18111yescharacteristic, complemented
220C2×D8C2×D18111yescharacteristic, complemented
221C2×M16—1811no—
222C2×M16—1811no—
223#123—3621no—
224#123—3621no—
225C22⋊Q8—1811no—
226C22⋊Q8—1811no—
227C22⋊Q8—1811no—
228C22⋊Q8—1811no—
229#121—1811no—
230#121—1811no—
231#121—1811no—
232#121C2×D18111yescharacteristic
233#120—3621no—
234#120—3621no—
235C4×D4—3621no—
236C4×D4—3621no—
237C4×D4—3621no—
238C4×D4—3621no—
239#117—1811no—
240#117—1811no—
241#107—1811no—
242#107—1811no—
243#106—1811no—
244#106—1811no—
245#103—1811no—
246#103—1811no—
247#103—1811no—
248#103C2×D18111yescharacteristic, complemented
249#102—1811no—
250#102—1811no—
251#102—1811no—
252#102C2×D18111yescharacteristic, complemented
253C22⋊C8—1811no—
254C22⋊C8—1811no—
255C22⋊C8—1811no—
256C22⋊C8C2×D18111yescharacteristic
257C24—1811no—
258#41—41no—
259#41—41no—
260#41—7241no—
261#41—7241no—
262C2×Q8—1811no—
263C2×Q8C22×D18111yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4C22×D18111yescharacteristic
271C2×D4C22×D18111yescharacteristic
272C22×C4—21no—
273C22×C4—3621no—
274C22×C4—1811no—
275C22×C4—1811no—
276C22×C4—1811no—
277C22×C4—1811no—
278C22×C4—1811no—
279C22×C4—7241no—
280C22×C4—7241no—
281C22×C4C22×D18111yescharacteristic
282Q16—7241no—
283SD16—41no—
284SD16—7241no—
285D8—41no—
286M16—7241no—
287M16—7241no—
288C2×C8—1811no—
289C2×C8—1811no—
290C2×C8C22×D18111yescharacteristic
291C2×C8C22×D18111yescharacteristic
292C4⋊C4—3621no—
293C4⋊C4—3621no—
294C4⋊C4—3621no—
295C4⋊C4—3621no—
296C4⋊C4—1811no—
297C4⋊C4—1811no—
298C4⋊C4—1811no—
299C4⋊C4C22×D18111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C42—3621no—
311C42—3621no—
312C23—21no—
313C23—21no—
314C23—1811no—
315C23—1811no—
316C23—7241no—
317C23—7241no—
318C23—7241no—
319C23D4×D18111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—3621no—
323Q8—3621no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—7242no—
331D4—7242no—
332D4—7242no—
333D4—7242no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—3621no—
340C2×C4—3621no—
341C2×C4—3621no—
342C2×C4—3621no—
343C2×C4—3621no—
344C2×C4—3621no—
345C2×C4—3621no—
346C2×C4—3621no—
347C2×C4—1811no—
348C2×C4—1811no—
349C2×C4—7241no—
350C2×C4—7241no—
351C2×C4—7241no—
352C2×C4—7242no—
353C2×C4D4×D18111yescharacteristic
354C2×C4C23×D18111yescharacteristic
355C8—21no—
356C8—21no—
357C8—3621no—
358C8—3621no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—3621no—
369C22—3621no—
370C22—3621no—
371C22—3621no—
372C22—3621no—
373C22—3621no—
374C22—7244no—
375C22C2×D4×D18111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—3621no—
380C4—3621no—
381C4—7241no—
382C4—7241no—
383C4—7241no—
384C4—7241no—
385C4#1915386111yescharacteristic
386C4#1915386111yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—7241no—
391C2—7241no—
392C2#2604183911yescharacteristic
393C2#2604207511yescharacteristic
394C2#2604207611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3197
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #26041789C2semidirect
2. #26041786C2semidirect
3. #26041621C2semidirect
4. #26041618C2semidirect
5. #26041601C2semidirect
6. #26041600C2semidirect
7. #26041536C2semidirect
8. #26041529C2semidirect
9. #26041524C2semidirect
10. #26041522C2semidirect
11. #26041441C2semidirect
12. #26041438C2semidirect
13. #26041421C2semidirect
14. #26041241C2semidirect
15. #449×C181C2semidirect
18. C2×#15668439C22semidirect
19. C2×#15668437C22semidirect
39. #19153750C22semidirect
40. #19153749C22semidirect
41. #19153748C22semidirect
42. #19153747C22semidirect
43. #19153741C22semidirect
44. #19153741C22semidirect
45. #19153740C22semidirect
46. #19153737C22semidirect
47. #19153737C22semidirect
48. #19153737C22semidirect
53. C2×SD16×C181C22semidirect
54. C2×D8×C181C22semidirect
56. #103×C181C22semidirect
57. #102×C181C22semidirect
197. C181#3197semidirect
212. #449D181semidirect
219. C2×SD16C2×D181semidirect
220. C2×D8C2×D181semidirect
248. #103C2×D181semidirect
252. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260417892
#260417862
#260416212
#260416182
#260416012
#260416002
#260415362
#260415292
#260415242
#260415222
#260414412
#260414382
#260414212
#260412412
#449×C1812
#3197181