Finite Group Databasebeta

← #37546736

Subgroups — #37546736

Order 23168.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042001C211yesmaximal, characteristic, complemented
2#26041949C211yesmaximal, characteristic, complemented
3#26041666C211yesmaximal, characteristic, complemented
4#26041665C211yesmaximal, characteristic, complemented
5#26041650C211yesmaximal, characteristic, complemented
6#26041496C211yesmaximal, characteristic, complemented
7#26041495C211yesmaximal, characteristic, complemented
8#26041482C211yesmaximal, characteristic, complemented
9#26041478C211yesmaximal, characteristic, complemented
10#26041473C211yesmaximal, characteristic, complemented
11#26041408C211yesmaximal, characteristic, complemented
12#26041377C211yesmaximal, characteristic, complemented
13#26041376C211yesmaximal, characteristic, complemented
14#26041359C211yesmaximal, characteristic, complemented
15#460×C181C211yesmaximal, characteristic, complemented
16C2×#15668448—21no—
17C2×#15668438C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×D1448C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24#19153814C2211yescharacteristic
25#19153812C2211yescharacteristic
26#19153812C2211yescharacteristic
27#19153811—21no—
28#19153810—21no—
29#19153805C2211yescharacteristic
30#19153804C2211yescharacteristic
31#19153794—21no—
32#19153788—21no—
33#19153788—21no—
34#19153787—21no—
35C4×Dic362C2211yescharacteristic
36#19153781C2211yescharacteristic
37C4×D724C2211yescharacteristic
38D4×Dic181C2211yescharacteristic
39D4×Dic181C2211yescharacteristic
40#19153778C2211yescharacteristic
41#19153773—21no—
42#19153749C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153741C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153727C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54#127×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668448—44no—
60C2×Dic362D411yescharacteristic
61C2×Dic362C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×D724C2311yescharacteristic
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C22×Dic181—21no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72#15668438—41no—
73#15668437—22no—
74#15668437—41no—
75#15668436—22no—
76D1448—41no—
77#15668434—22no—
78#15668434—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C4⋊Dic181D411yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428D411yescharacteristic
87#15668428D411yescharacteristic
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181—21no—
102C2×D4×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104SD16×C181—41no—
105SD16×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C42×C181—21no—
111C42×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—21no—
114Dic362—22no—
115Dic362—21no—
116Dic362—21no—
117D724—21no—
118D724—21no—
119D724—21no—
120D724—21no—
121C22⋊D181—42no—
122C22⋊D181—42no—
123C22⋊D181—81no—
124C22⋊D181—81no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—42no—
128C2×Dic181—42no—
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—42no—
134C4×D181—42no—
135#13089678—21no—
136#13089678#4112yescomplemented
137C23×C181—21no—
138C23×C181—21no—
139Q8×C181—21no—
140Q8×C181—21no—
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×C181C2×D411yescharacteristic
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2411yescharacteristic
152C8×C181—21no—
153C8×C181—21no—
154C22×C181—41no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181C22×D411yescharacteristic
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C4×C181—21no—
168C4×C181—21no—
169C4×C181—41no—
170C4×C181—41no—
171C4×C181C2×#4111yescharacteristic
172C4×C181H(5,𝔽2)11yescharacteristic
173Dic181—21no—
174Dic181—21no—
175Dic181—21no—
176Dic181—41no—
177Dic181—41no—
178Dic181AGL(1,ℤ/8)12yes—
179C2×C181—81no—
180C2×C181—81no—
181C2×C181#55011yescharacteristic
182C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C181#57711yescharacteristic
184D181—81no—
185D181—81no—
186C181#339711yescharacteristic, complemented, Sylow
187#3397—1811nomaximal, Sylow
188#556—1811no—
189#550—1811no—
190#496—1811no—
191#496—1811no—
192#492—1811no—
193#463—1811no—
194#463—1811no—
195#461—1811no—
196#460—1811no—
197#460D18111yescharacteristic, complemented
198#459—1811no—
199#446—1811no—
200#440—1811no—
201#440—1811no—
202C4×D8—1811no—
203C2×#41—3621no—
204C2×SD16—1811no—
205C2×SD16—1811no—
206C2×SD16—1811no—
207C2×SD16—1811no—
208C2×SD16C2×D18111yescharacteristic
209C2×SD16C2×D18111yescharacteristic
210C2×D8—1811no—
211C2×D8—1811no—
212C2×D8—1811no—
213C4⋊Q8—1811no—
214#127—1811no—
215#127—1811no—
216#127C2×D18111yescharacteristic
217#126—3621no—
218#126—3621no—
219#124—1811no—
220#124—1811no—
221C22⋊Q8—3621no—
222#121—3621no—
223#121—3621no—
224#121—3621no—
225C4×Q8—1811no—
226C4×Q8—1811no—
227C4×Q8C2×D18111yescharacteristic
228C4×D4—1811no—
229C4×D4—1811no—
230C4×D4—1811no—
231C4×D4—1811no—
232#117—3621no—
233#107—1811no—
234C4⋊C8—1811no—
235C4⋊C8—1811no—
236C4⋊C8C2×D18111yescharacteristic
237#103—1811no—
238#103—1811no—
239#102—1811no—
240#102—1811no—
241#102C2×D18111yescharacteristic
242#102C2×D18111yescharacteristic
243#97—1811no—
244#97—1811no—
245C4×C8—1811no—
246#41—7244no—
247C2×Q8—1811no—
248C2×Q8—1811no—
249C2×Q8C22×D18111yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—3621no—
256C2×D4—1811no—
257C2×D4—1811no—
258C2×D4C22×D18111yescharacteristic
259C2×D4C22×D18111yescharacteristic
260C22×C4—3621no—
261C22×C4—3621no—
262C22×C4—3621no—
263C22×C4—3621no—
264SD16—41no—
265SD16—41no—
266SD16—3622no—
267SD16—3622no—
268SD16—7241no—
269SD16—7241no—
270D8—3622no—
271D8—7241no—
272D8—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—1811no—
282C4⋊C4—1811no—
283C4⋊C4—1811no—
284C4⋊C4—1811no—
285C4⋊C4C22×D18111yescharacteristic
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C42—21no—
295C42—3621no—
296C42—1811no—
297C42—1811no—
298C42C22×D18111yescharacteristic
299C23—21no—
300C23—21no—
301C23—3621no—
302C23—3621no—
303Q8—21no—
304Q8—21no—
305Q8—3622no—
306Q8—3621no—
307Q8—3621no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—81no—
314D4—3621no—
315D4—3621no—
316D4—3621no—
317D4—3621no—
318D4—14481no—
319D4—14481no—
320D4—7242no—
321D4—7242no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—1811no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—1811no—
330C2×C4—7242no—
331C2×C4—7242no—
332C2×C4—7242no—
333C2×C4—7242no—
334C2×C4D4×D18111yescharacteristic
335C2×C4D4×D18111yescharacteristic
336C2×C4C23×D18111yescharacteristic
337C8—21no—
338C8—21no—
339C8—3621no—
340C8—1812no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—7241no—
348C22—7241no—
349C22—7241no—
350C22—7241no—
351C22—7241no—
352C22—7241no—
353C22C2×D4×D18111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—3621no—
359C4—3621no—
360C4—3621no—
361C4—1812no—
362C4—7241no—
363C4—7241no—
364C4#41×D18111yescharacteristic
365C4#1915386111yescharacteristic
366C2—81no—
367C2—81no—
368C2—14481no—
369C2—14481no—
370C2#2604194711yescharacteristic
371C2AGL(1,ℤ/8)×D18111yescharacteristic
372C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#460×C181C2
socleC22×C181C22×D4
hypercenter#460D181
hypocenterC181#3397
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #26042001C2semidirect
2. #26041949C2semidirect
3. #26041666C2semidirect
4. #26041665C2semidirect
5. #26041650C2semidirect
6. #26041496C2semidirect
7. #26041495C2semidirect
8. #26041482C2semidirect
9. #26041478C2semidirect
10. #26041473C2semidirect
11. #26041408C2semidirect
12. #26041377C2semidirect
13. #26041376C2semidirect
14. #26041359C2semidirect
15. #460×C181C2semidirect
136. #13089678#41semidirect
186. C181#3397semidirect
197. #460D181semidirect

Maximal subgroups

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

subgroupindex
#260420012
#260419492
#260416662
#260416652
#260416502
#260414962
#260414952
#260414822
#260414782
#260414732
#260414082
#260413772
#260413762
#260413592
#460×C1812
#3397181