Finite Group Databasebeta

← #37544729

Subgroups — #37544729

Order 23168.

390 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041831C211yesmaximal, characteristic, complemented
2#26041825C211yesmaximal, characteristic
3#26041672C211yesmaximal, characteristic, complemented
4#26041670C211yesmaximal, characteristic, complemented
5#26041640C211yesmaximal, characteristic, complemented
6#26041637C211yesmaximal, characteristic, complemented
7#26041488C211yesmaximal, characteristic, complemented
8#26041487C211yesmaximal, characteristic, complemented
9#26041478C211yesmaximal, characteristic, complemented
10#26041477C211yesmaximal, characteristic, complemented
11#26041443C211yesmaximal, characteristic, complemented
12#26041441C211yesmaximal, characteristic, complemented
13#26041439C211yesmaximal, characteristic, complemented
14#26041333C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×Dic724C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668439C2211yescharacteristic
20C2×#15668438C2211yescharacteristic
21C2×#15668437C2211yescharacteristic
22C2×#15668436C2211yescharacteristic
23#19153815C2211yescharacteristic
24#19153814C2211yescharacteristic
25#19153814C2211yescharacteristic
26#19153812C2211yescharacteristic
27#19153806—21no—
28#19153805C2211yescharacteristic
29#19153803C2211yescharacteristic
30#19153795C2211yescharacteristic
31#19153793—21no—
32#19153788—21no—
33#19153788—21no—
34Q8×Dic181C2211yescharacteristic
35#19153781—21no—
36#19153781C2211yescharacteristic
37C4×C22⋊D181—21no—
38C4×C22⋊D181—21no—
39#19153772—21no—
40C2×C4×Dic181C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C2×SD16×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668449—41no—
60#15668449—41no—
61C2×Dic362—21no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C22×Dic181D411yescharacteristic
69C22×Dic181D411yescharacteristic
70C2×C4×D181—21no—
71Dic724—41no—
72#15668439—41no—
73#15668439—41no—
74#15668438—41no—
75#15668437—41no—
76#15668436—41no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C4⋊Dic181—21no—
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91#15668426—21no—
92#15668426—21no—
93C4×Dic181—21no—
94C4×Dic181—21no—
95C4×Dic181D411yescharacteristic
96C4×Dic181D411yescharacteristic
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×Q8×C181C2311yescharacteristic
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181—21no—
106C22×C4×C181C2311yescharacteristic
107Q16×C181—41no—
108SD16×C181—41no—
109C2×C8×C181C2311yescharacteristic
110C2×C8×C181C2311yescharacteristic
111C4⋊C4×C181—21no—
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—42no—
123C22⋊D181—42no—
124C22⋊D181—42no—
125C2×Dic181—22no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—21no—
129C2×Dic181—41no—
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C2×Dic181C2×D411yescharacteristic
134C4×D181—42no—
135#13089678—21no—
136#13089678—21no—
137C23×C181—21no—
138C23×C181C2×D411yescharacteristic
139Q8×C181—21no—
140Q8×C181—21no—
141Q8×C181—21no—
142Q8×C181—21no—
143D4×C181—21no—
144D4×C181—21no—
145D4×C181—42no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—42no—
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2411yescharacteristic
154C8×C181—21no—
155C8×C181—21no—
156C22×C181—21no—
157C22×C181—21no—
158C22×C181—21no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181C22×D411yescharacteristic
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—41no—
166C4×C181—21no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181—41no—
170C4×C181H(5,𝔽2)11yescharacteristic
171C4×C181H(5,𝔽2)11yescharacteristic
172Dic181—21no—
173Dic181—21no—
174Dic181—21no—
175Dic181—41no—
176Dic181—41no—
177Dic181—41no—
178Dic181#13712yes—
179C2×C181—41no—
180C2×C181—81no—
181C2×C181#53511yescharacteristic
182C2×C181C2×#13711yescharacteristic
183C2×C181#57511yescharacteristic
184D181—81no—
185C181#321611yescharacteristic, complemented, Sylow
186#3216—1811nomaximal, Sylow
187#533—1811no—
188#532—1811no—
189#497—1811no—
190#497—1811no—
191#489—1811no—
192#489—1811no—
193#462—1811no—
194#462—1811no—
195#460—1811no—
196#460—1811no—
197#452—1811no—
198#452—1811no—
199#452—1811no—
200#452D18111yescharacteristic, complemented
201#432—1811no—
202C2×#41—1811no—
203C2×#41C2×D18111yescharacteristic
204C2×Q16—1811no—
205C2×Q16—1811no—
206C2×Q16—1811no—
207C2×Q16C2×D18111yescharacteristic
208C2×SD16—1811no—
209C2×SD16—1811no—
210C2×SD16—1811no—
211C2×SD16C2×D18111yescharacteristic
212C4⋊Q8—1811no—
213C4⋊Q8—1811no—
214C4⋊Q8—1811no—
215#127—1811no—
216#125—3621no—
217#124—1811no—
218#124—1811no—
219C22⋊Q8—3621no—
220C22⋊Q8—1811no—
221C22⋊Q8C2×D18111yescharacteristic
222#121—3621no—
223#121—3621no—
224C4×Q8—3621no—
225C4×Q8—1811no—
226C4×Q8—1811no—
227C4×D4—3621no—
228C4×D4—3621no—
229#117—3621no—
230C2×C42—1811no—
231C4⋊C8—1811no—
232C4⋊C8—1811no—
233#103—1811no—
234#103—1811no—
235#103—1811no—
236#103C2×D18111yescharacteristic
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102C2×D18111yescharacteristic
241C22⋊C8—1811no—
242C22⋊C8C2×D18111yescharacteristic
243#97—1811no—
244#97—1811no—
245#41—41no—
246#41—41no—
247#41—7241no—
248#41—7241no—
249C2×Q8—3621no—
250C2×Q8—1811no—
251C2×Q8—1811no—
252C2×Q8C22×D18111yescharacteristic
253C2×Q8C22×D18111yescharacteristic
254C2×D4—21no—
255C2×D4—3621no—
256C2×D4—3621no—
257C2×D4—3621no—
258C2×D4—1811no—
259C2×D4C22×D18111yescharacteristic
260C22×C4—21no—
261C22×C4—3621no—
262C22×C4—1811no—
263C22×C4—1811no—
264C22×C4C22×D18111yescharacteristic
265Q16—41no—
266Q16—7241no—
267Q16—7241no—
268Q16—7241no—
269SD16—41no—
270SD16—7241no—
271SD16—7241no—
272SD16—7241no—
273C2×C8—1811no—
274C2×C8—1811no—
275C2×C8C22×D18111yescharacteristic
276C2×C8C22×D18111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—3621no—
281C4⋊C4—3621no—
282C4⋊C4—3621no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—3621no—
286C4⋊C4—1811no—
287C4⋊C4C22×D18111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C42—3621no—
295C42—3621no—
296C42—1811no—
297C42—1811no—
298C42—1811no—
299C42—1811no—
300C23—21no—
301C23—3621no—
302C23D4×D18111yescharacteristic
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—3621no—
308Q8—3621no—
309Q8—3621no—
310Q8—3621no—
311Q8—7242no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—3621no—
316D4—3621no—
317D4—7242no—
318D4—7242no—
319D4—7242no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—3622no—
327C2×C4—3621no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—1811no—
331C2×C4—1811no—
332C2×C4—1811no—
333C2×C4—1811no—
334C2×C4—7242no—
335C2×C4—7241no—
336C2×C4D4×D18111yescharacteristic
337C2×C4C23×D18111yescharacteristic
338C8—21no—
339C8—21no—
340C8—3621no—
341C8—3621no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—7241no—
349C22—7241no—
350C22—7241no—
351C22C2×D4×D18111yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3621no—
357C4—3621no—
358C4—3621no—
359C4—1812no—
360C4—7241no—
361C4—7241no—
362C4—7241no—
363C4#1915386111yescharacteristic
364C4#1915386111yescharacteristic
365C2—41no—
366C2—81no—
367C2—14481no—
368C2#2604184411yescharacteristic
369C2#137×D18111yescharacteristic
370C2#2604207611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
prime radical#26041825C2
hypercenter#452D181
hypocenterC181#3216
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #26041831C2semidirect
3. #26041672C2semidirect
4. #26041670C2semidirect
5. #26041640C2semidirect
6. #26041637C2semidirect
7. #26041488C2semidirect
8. #26041487C2semidirect
9. #26041478C2semidirect
10. #26041477C2semidirect
11. #26041443C2semidirect
12. #26041441C2semidirect
13. #26041439C2semidirect
14. #26041333C2semidirect
15. #452×C181C2semidirect
185. C181#3216semidirect
200. #452D181semidirect

Maximal subgroups

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

subgroupindex
#260418312
#260418252
#260416722
#260416702
#260416402
#260416372
#260414882
#260414872
#260414782
#260414772
#260414432
#260414412
#260414392
#260413332
#452×C1812
#3216181