Finite Group Databasebeta

← #37544780

Subgroups — #37544780

Order 23168.

388 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041882C211yesmaximal, characteristic, complemented
2#26041850C211yesmaximal, characteristic, complemented
3#26041667C211yesmaximal, characteristic, complemented
4#26041650C211yesmaximal, characteristic, complemented
5#26041646C211yesmaximal, characteristic, complemented
6#26041632C211yesmaximal, characteristic, complemented
7#26041493C211yesmaximal, characteristic, complemented
8#26041492C211yesmaximal, characteristic, complemented
9#26041483C211yesmaximal, characteristic, complemented
10#26041482C211yesmaximal, characteristic, complemented
11#26041424C211yesmaximal, characteristic, complemented
12#26041420C211yesmaximal, characteristic, complemented
13#26041417C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#449×C181C211yesmaximal, characteristic, complemented
16C22×Dic362C2211yescharacteristic
17C2×#15668438C2211yescharacteristic
18C2×#15668438C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C2×#15668436C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23#19153814C2211yescharacteristic
24#19153814C2211yescharacteristic
25#19153812C2211yescharacteristic
26#19153807C2211yescharacteristic
27#19153803C2211yescharacteristic
28#19153803C2211yescharacteristic
29#19153800—21no—
30#19153798—21no—
31#19153797—21no—
32#19153797—21no—
33#19153795—21no—
34#19153795—21no—
35#19153790C2211yescharacteristic
36#19153788—21no—
37#19153787—21no—
38D4×Dic181C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153775C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55#121×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—41no—
61C2×Dic362—41no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C22×Dic181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71#15668438—41no—
72#15668438—41no—
73#15668437—41no—
74#15668437—41no—
75#15668436—41no—
76#15668434—41no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C4⋊Dic181—21no—
80C4⋊Dic181D411yescharacteristic
81C4⋊Dic181D411yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181D411yescharacteristic
94C22⋊Dic181D411yescharacteristic
95#15668426—21no—
96#15668426—21no—
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
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—21no—
115Dic362—21no—
116Dic362—21no—
117Dic362—21no—
118Dic362—21no—
119Dic362—42no—
120D724—21no—
121D724—21no—
122C22⋊D181—81no—
123C22⋊D181—81no—
124C22⋊D181—81no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—42no—
129C2×Dic181—81no—
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C2×Dic181C2×D411yescharacteristic
134C4×D181—81no—
135#13089678—21no—
136#13089678—21no—
137C23×C181—21no—
138C23×C181—21no—
139C23×C181C2×D411yescharacteristic
140Q8×C181—21no—
141Q8×C181—21no—
142D4×C181—21no—
143D4×C181—21no—
144D4×C181—21no—
145D4×C181—21no—
146D4×C181—42no—
147D4×C181—81no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—42no—
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2411yescharacteristic
155C8×C181—21no—
156C8×C181—21no—
157C22×C181—21no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181C22×D411yescharacteristic
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C4×C181—21no—
171C4×C181—41no—
172C4×C181—41no—
173C4×C181H(5,𝔽2)11yescharacteristic
174C4×C181H(5,𝔽2)11yescharacteristic
175Dic181—21no—
176Dic181—21no—
177Dic181—21no—
178Dic181—21no—
179Dic181—41no—
180Dic181—41no—
181Dic181—41no—
182C2×C181—41no—
183C2×C181—81no—
184C2×C181—81no—
185C2×C181#53511yescharacteristic
186C2×C181#57711yescharacteristic
187C2×C181#57711yescharacteristic
188D181—81no—
189C181#322111yescharacteristic, complemented, Sylow
190#3221—1811nomaximal, Sylow
191#540—1811no—
192#536—1811no—
193#496—1811no—
194#492—1811no—
195#491—1811no—
196#488—1811no—
197#463—1811no—
198#463—1811no—
199#461—1811no—
200#461—1811no—
201#449—1811no—
202#449D18111yescharacteristic, complemented
203#448—1811no—
204#448—1811no—
205#433—1811no—
206C2×#41C2×D18111yescharacteristic
207C22×Q8—1811no—
208C2×SD16—1811no—
209C2×SD16—1811no—
210C2×SD16—1811no—
211C2×SD16—1811no—
212C2×SD16—1811no—
213C2×SD16C2×D18111yescharacteristic
214C2×D8—1811no—
215C2×D8C2×D18111yescharacteristic
216C4⋊Q8—1811no—
217C4⋊Q8—1811no—
218#127—1811no—
219#125—1811no—
220#124—1811no—
221#124—1811no—
222#123—3621no—
223#123—3621no—
224#123—3621no—
225#123—3621no—
226C22⋊Q8—3621no—
227C22⋊Q8—3621no—
228#121—3621no—
229#121—3621no—
230#121—1811no—
231#121C2×D18111yescharacteristic
232C4×D4—1811no—
233C4×D4—1811no—
234#117—1811no—
235C4⋊C8—1811no—
236C4⋊C8—1811no—
237#103—1811no—
238#103—1811no—
239#103—1811no—
240#103—1811no—
241#103—1811no—
242#103C2×D18111yescharacteristic
243#102—1811no—
244#102C2×D18111yescharacteristic
245C22⋊C8—1811no—
246C22⋊C8C2×D18111yescharacteristic
247#97—1811no—
248C4×C8—1811no—
249#41—41no—
250#41—41no—
251C2×Q8—3621no—
252C2×Q8—1811no—
253C2×Q8—1811no—
254C2×Q8—7241no—
255C2×Q8—7241no—
256C2×Q8C22×D18111yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—1811no—
263C2×D4C22×D18111yescharacteristic
264C2×D4C22×D18111yescharacteristic
265C22×C4—21no—
266C22×C4—3621no—
267C22×C4—3621no—
268C22×C4—3621no—
269C22×C4C22×D18111yescharacteristic
270SD16—41no—
271SD16—7241no—
272SD16—7241no—
273SD16—7241no—
274SD16—7241no—
275SD16—7241no—
276D8—41no—
277D8—7241no—
278C2×C8—1811no—
279C2×C8—1811no—
280C2×C8C22×D18111yescharacteristic
281C2×C8C22×D18111yescharacteristic
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—3621no—
286C4⋊C4—3621no—
287C4⋊C4—3621no—
288C4⋊C4—1811no—
289C4⋊C4—1811no—
290C4⋊C4—1811no—
291C4⋊C4C22×D18111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—1811no—
301C22⋊C4—1811no—
302C42—1811no—
303C42—1811no—
304C23—21no—
305C23—21no—
306C23—3621no—
307C23D4×D18111yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—3621no—
311Q8—3621no—
312Q8—3621no—
313Q8—3621no—
314Q8—7242no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—81no—
321D4—3621no—
322D4—3621no—
323D4—14481no—
324D4—14481no—
325D4—14481no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—14481no—
335C2×C4—14481no—
336C2×C4—1811no—
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—7241no—
357C22—7241no—
358C22—7241no—
359C22C2×D4×D18111yescharacteristic
360C4—21no—
361C4—41no—
362C4—41no—
363C4—3621no—
364C4—3621no—
365C4—3621no—
366C4—3621no—
367C4—7241no—
368C4—7241no—
369C4—7241no—
370C4#1915386111yescharacteristic
371C4#1915386111yescharacteristic
372C2—41no—
373C2—81no—
374C2—81no—
375C2—14481no—
376C2#2604184411yescharacteristic
377C2#2604208611yescharacteristic
378C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#449×C181C2
socleC22×C181C22×D4
hypercenter#449D181
hypocenterC181#3221
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. #26041882C2semidirect
2. #26041850C2semidirect
3. #26041667C2semidirect
4. #26041650C2semidirect
5. #26041646C2semidirect
6. #26041632C2semidirect
7. #26041493C2semidirect
8. #26041492C2semidirect
9. #26041483C2semidirect
10. #26041482C2semidirect
11. #26041424C2semidirect
12. #26041420C2semidirect
13. #26041417C2semidirect
14. #26041337C2semidirect
15. #449×C181C2semidirect
189. C181#3221semidirect
202. #449D181semidirect

Maximal subgroups

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

subgroupindex
#260418822
#260418502
#260416672
#260416502
#260416462
#260416322
#260414932
#260414922
#260414832
#260414822
#260414242
#260414202
#260414172
#260413372
#449×C1812
#3221181