Finite Group Databasebeta

← #37545917

Subgroups — #37545917

Order 23168.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041981C211yesmaximal, characteristic, complemented
2#26041926C211yesmaximal, characteristic, complemented
3#26041632C211yesmaximal, characteristic, complemented
4#26041623C211yesmaximal, characteristic, complemented
5#26041590C211yesmaximal, characteristic, complemented
6#26041578C211yesmaximal, characteristic, complemented
7#26041524C211yesmaximal, characteristic, complemented
8#26041492C211yesmaximal, characteristic, complemented
9#26041422C211yesmaximal, characteristic, complemented
10#26041411C211yesmaximal, characteristic, complemented
11#26041359C211yesmaximal, characteristic, complemented
12#26041355C211yesmaximal, characteristic, complemented
13#26041282C211yesmaximal, characteristic, complemented
14#26041281C211yesmaximal, characteristic, complemented
15#469×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×D4×D181C2211yescharacteristic
18C2×#15668437C2211yescharacteristic, complemented
19C2×#15668434C2211yescharacteristic
20C2×#15668432C2211yescharacteristic
21#19153809—21no—
22#19153807C2211yescharacteristic, complemented
23#19153803C2211yescharacteristic
24#19153800—21no—
25#19153798—21no—
26#19153796C2211yescharacteristic
27#19153788—21no—
28#19153787—21no—
29#19153787C2211yescharacteristic
30#19153784—21no—
31D4×Dic181—21no—
32D4×Dic181C2211yescharacteristic, complemented
33#19153778C2211yescharacteristic
34C4×C22⋊D181C2211yescharacteristic
35#19153774C2211yescharacteristic
36C2×C4⋊Dic181C2211yescharacteristic, complemented
37C22⋊C4×D181—21no—
38#19153749C2211yescharacteristic, complemented
39#19153749C2211yescharacteristic, complemented
40#19153745C2211yescharacteristic, complemented
41#19153741C2211yescharacteristic, complemented
42#19153741C2211yescharacteristic, complemented
43#19153739C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic, complemented
52C2×D8×C181C2211yescharacteristic
53C2×M16×C181C2211yescharacteristic, complemented
54#121×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic, complemented
56#106×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—22no—
61#15668449—41no—
62C2×Dic362C2311yescharacteristic
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181D411yescharacteristic
68D4×D181—22no—
69D4×D181—41no—
70C22×Dic181—21no—
71C22×Dic181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181C2311yescharacteristic
75#15668437—41no—
76#15668434—22no—
77#15668432—41no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C4⋊Dic181—21no—
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428D411yescharacteristic
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181D411yescharacteristic
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C2×D4×C181—21no—
99C2×D4×C181—21no—
100C2×D4×C181C2311yescharacteristic
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181C2311yescharacteristic
103D8×C181—41no—
104M16×C181—41no—
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C22⋊C4×C181—21no—
110C22⋊C4×C181—21no—
111C22×D181—21no—
112C22×D181—42no—
113C22×D181—42no—
114C22×D181—81no—
115C22×D181C2×D411yescharacteristic
116Dic362—21no—
117Dic362—21no—
118D724—21no—
119D724#4112yes—
120C22⋊D181—41no—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—81no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—81no—
128C2×Dic181—81no—
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—42no—
135C4×D181—81no—
136#13089678—21no—
137#13089678—21no—
138C23×C181—21no—
139C23×C181—21no—
140C23×C181C2×D411yescharacteristic
141D4×C181—21no—
142D4×C181—21no—
143D4×C181—21no—
144D4×C181—21no—
145D4×C181—42no—
146D4×C181—81no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2411yescharacteristic
153C8×C181—21no—
154C8×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181C22×D411yescharacteristic
165C2×D181—21no—
166C2×D181—22no—
167C2×D181—21no—
168C2×D181—21no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—84no—
172C4×C181—21no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181C2×#4111yescharacteristic
176C4×C181H(5,𝔽2)11yescharacteristic
177Dic181—21no—
178Dic181—21no—
179Dic181—21no—
180Dic181—41no—
181Dic181—41no—
182Dic181—41no—
183C2×C181—41no—
184C2×C181—81no—
185C2×C181—81no—
186C2×C181#54611yescharacteristic
187C2×C181#57511yescharacteristic
188C2×C181#57611yescharacteristic
189D181—41no—
190D181—42no—
191C181#332211yescharacteristic, complemented, Sylow
192#3322—1811nomaximal, Sylow
193#553—1811no—
194#546—1811no—
195#488—1811no—
196#485—1811no—
197#480—1811no—
198#478—1811no—
199#469D18111yescharacteristic, complemented
200#468—1811no—
201#463—1811no—
202#449—1811no—
203#447—1811no—
204C4×D8—1811no—
205#436—1811no—
206#418—1811no—
207#417—1811no—
208C2×#41—1811no—
209C22×D4—1811no—
210C2×SD16—1811no—
211C2×D8—1811no—
212C2×D8C2×D18111yescharacteristic
213C2×M16—1811no—
214C2×M16C2×D18111yescharacteristic, complemented
215#126—3621no—
216#125—1811no—
217#124—1811no—
218#123—3621no—
219#123—3621no—
220C22⋊Q8—1811no—
221#121—3621no—
222#121—3621no—
223#121—1811no—
224#121C2×D18111yescharacteristic
225#121C2×D18111yescharacteristic, complemented
226#120—3621no—
227C4×D4—3621no—
228C4×D4—1811no—
229C4×D4—1811no—
230C4×D4—1811no—
231#117—1811no—
232C2×C4⋊C4—1811no—
233C2×C22⋊C4—3621no—
234#107—1811no—
235#107—1811no—
236#106C2×D18111yescharacteristic, complemented
237C4⋊C8—1811no—
238#103—1811no—
239#103—1811no—
240#103—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102C2×D18111yescharacteristic
247#102C2×D18111yescharacteristic, complemented
248C22⋊C8—1811no—
249C22⋊C8—1811no—
250C4×C8—1811no—
251C24—3621no—
252#41—3622no—
253#41—7241no—
254C2×Q8—1811no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—3622no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—1811no—
262C2×D4—1811no—
263C2×D4—7241no—
264C2×D4C22×D18111yescharacteristic
265C2×D4C22×D18111yescharacteristic
266C22×C4—3621no—
267C22×C4—3621no—
268C22×C4—3621no—
269C22×C4—3621no—
270C22×C4—1811no—
271C22×C4C22×D18111yescharacteristic
272SD16—7241no—
273D8—41no—
274D8—3622no—
275M16—41no—
276M16—7241no—
277C2×C8—1811no—
278C2×C8—1811no—
279C2×C8C22×D18111yescharacteristic
280C2×C8C22×D18111yescharacteristic
281C4⋊C4—3621no—
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—1811no—
286C4⋊C4—1811no—
287C4⋊C4—1811no—
288C4⋊C4C22×D18111yescharacteristic
289C4⋊C4C22×D18111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—1811no—
300C22⋊C4—1811no—
301C42—3621no—
302C42—1811no—
303C23—21no—
304C23—21no—
305C23—3621no—
306C23—14481no—
307C23—1811no—
308C23—7242no—
309C23—7242no—
310C23D4×D18111yescharacteristic
311Q8—3621no—
312Q8—3621no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—42no—
318D4—81no—
319D4—3621no—
320D4—14481no—
321D4—1812no—
322D4—7241no—
323D4—7242no—
324D4—7242no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—14481no—
335C2×C4—14481no—
336C2×C4—14481no—
337C2×C4—1811no—
338C2×C4—1811no—
339C2×C4—1811no—
340C2×C4—7242no—
341C2×C4D4×D18111yescharacteristic
342C2×C4C23×D18111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3621no—
346C8—3621no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—3621no—
357C22—3622no—
358C22—3621no—
359C22—3621no—
360C22—14484no—
361C22—7241no—
362C22—7241no—
363C22C2×D4×D18111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—3621no—
368C4—3621no—
369C4—3621no—
370C4—7241no—
371C4—7241no—
372C4—7241no—
373C4#41×D18111yescharacteristic
374C4#1915386111yescharacteristic
375C2—41no—
376C2—81no—
377C2—81no—
378C2—7241no—
379C2—7242no—
380C2#2604191811yescharacteristic
381C2#2604207511yescharacteristic
382C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#469×C181C2
socleC22×C181C22×D4
hypercenter#469D181
hypocenterC181#3322
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #26041981C2semidirect
2. #26041926C2semidirect
3. #26041632C2semidirect
4. #26041623C2semidirect
5. #26041590C2semidirect
6. #26041578C2semidirect
7. #26041524C2semidirect
8. #26041492C2semidirect
9. #26041422C2semidirect
10. #26041411C2semidirect
11. #26041359C2semidirect
12. #26041355C2semidirect
13. #26041282C2semidirect
14. #26041281C2semidirect
15. #469×C181C2semidirect
18. C2×#15668437C22semidirect
22. #19153807C22semidirect
32. D4×Dic181C22semidirect
36. C2×C4⋊Dic181C22semidirect
38. #19153749C22semidirect
39. #19153749C22semidirect
40. #19153745C22semidirect
41. #19153741C22semidirect
42. #19153741C22semidirect
43. #19153739C22semidirect
49. C22⋊#13089678C22semidirect
51. C8×Dic181C22semidirect
53. C2×M16×C181C22semidirect
55. #121×C181C22semidirect
56. #106×C181C22semidirect
58. #102×C181C22semidirect
191. C181#3322semidirect
199. #469D181semidirect
214. C2×M16C2×D181semidirect
225. #121C2×D181semidirect
236. #106C2×D181semidirect
247. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419812
#260419262
#260416322
#260416232
#260415902
#260415782
#260415242
#260414922
#260414222
#260414112
#260413592
#260413552
#260412822
#260412812
#469×C1812
#3322181