Finite Group Databasebeta

← #37546447

Subgroups — #37546447

Order 23168.

382 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042006C211yesmaximal, characteristic, complemented
2#26041949C211yesmaximal, characteristic
3#26041642C211yesmaximal, characteristic, complemented
4#26041624C211yesmaximal, characteristic, complemented
5#26041577C211yesmaximal, characteristic, complemented
6#26041576C211yesmaximal, characteristic, complemented
7#26041557C211yesmaximal, characteristic, complemented
8#26041478C211yesmaximal, characteristic, complemented
9#26041478C211yesmaximal, characteristic, complemented
10#26041476C211yesmaximal, characteristic, complemented
11#26041407C211yesmaximal, characteristic, complemented
12#26041381C211yesmaximal, characteristic, complemented
13#26041376C211yesmaximal, characteristic, complemented
14#26041370C211yesmaximal, characteristic, complemented
15#490×C181C211yesmaximal, characteristic, complemented
16C2×#15668448—21no—
17C2×#15668438C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668437C2211yescharacteristic
20#19153815—21no—
21#19153815C2211yescharacteristic
22#19153812C2211yescharacteristic
23#19153812C2211yescharacteristic
24#19153807C2211yescharacteristic
25#19153806—21no—
26#19153806—21no—
27#19153788—21no—
28#19153788—21no—
29#19153787—21no—
30C4×Dic362C2211yescharacteristic
31C4×Dic362C2211yescharacteristic
32#19153781—21no—
33#19153781C2211yescharacteristic
34#19153781C2211yescharacteristic
35C4×D724C2211yescharacteristic
36D4×Dic181C2211yescharacteristic
37D4×Dic181C2211yescharacteristic
38#19153750C2211yescharacteristic
39#19153749C2211yescharacteristic
40#19153747C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#127×C181C2211yescharacteristic
53#125×C181C2211yescharacteristic
54#102×C181C2211yescharacteristic
55#102×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58#97×C181C2211yescharacteristic
59#15668448—44no—
60C2×Dic362—21no—
61C2×Dic362D411yescharacteristic
62C2×Dic362C2311yescharacteristic
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—
71#15668438—22no—
72#15668437—22no—
73#15668437—22no—
74C2×#13089678C2311yescharacteristic
75C2×#13089678C2311yescharacteristic
76C4⋊Dic181—21no—
77C4⋊Dic181D411yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428D411yescharacteristic
86#15668428D411yescharacteristic
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89#15668426—21no—
90C4×Dic181—21no—
91C4×Dic181—21no—
92C4×Dic181—21no—
93C4×Dic181C2311yescharacteristic
94C4×Dic181C2311yescharacteristic
95C2×D4×C181—21no—
96C2×D4×C181—21no—
97C2×D4×C181C2311yescharacteristic
98C2×D4×C181C2311yescharacteristic
99C2×C8×C181C2311yescharacteristic
100C2×C8×C181C2311yescharacteristic
101C4⋊C4×C181—21no—
102C4⋊C4×C181—21no—
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C42×C181C2311yescharacteristic
106C22×D181—21no—
107Dic362—21no—
108Dic362—22no—
109Dic362—42no—
110Dic362#4112yescomplemented
111D724—21no—
112D724—21no—
113C22⋊D181—42no—
114C22⋊D181—42no—
115C22⋊D181—81no—
116C22⋊D181—81no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—42no—
121C2×Dic181—42no—
122C2×Dic181C2×D411yescharacteristic
123C2×Dic181C2×D411yescharacteristic
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C4×D181—42no—
127#13089678—21no—
128#13089678—21no—
129C23×C181—21no—
130C23×C181—21no—
131D4×C181—21no—
132D4×C181—21no—
133D4×C181—21no—
134D4×C181—21no—
135D4×C181—42no—
136D4×C181—81no—
137C2×C4×C181—21no—
138C2×C4×C181—21no—
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2411yescharacteristic
142C8×C181—21no—
143C8×C181—21no—
144C22×C181—41no—
145C22×C181—41no—
146C22×C181—41no—
147C22×C181—41no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181C22×D411yescharacteristic
151C2×D181—41no—
152C2×D181—41no—
153C2×D181—41no—
154C4×C181—21no—
155C4×C181—21no—
156C4×C181—41no—
157C4×C181—41no—
158C4×C181C2×#4111yescharacteristic
159C4×C1812−1+411yescharacteristic
160Dic181—22no—
161Dic181—21no—
162Dic181—21no—
163Dic181—21no—
164Dic181—41no—
165Dic181—41no—
166Dic181AGL(1,ℤ/8)12yes—
167C2×C181—81no—
168C2×C181—81no—
169C2×C181#54811yescharacteristic
170C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C181#57711yescharacteristic
172D181—81no—
173C181#336811yescharacteristic, complemented, Sylow
174#3368—1811nomaximal, Sylow
175#557—1811no—
176#550—1811no—
177#490—1811no—
178#490D18111yescharacteristic, complemented
179#486—1811no—
180#478—1811no—
181#478—1811no—
182#474—1811no—
183#460—1811no—
184#460—1811no—
185#460—1811no—
186#446—1811no—
187#440—1811no—
188#440—1811no—
189C4×SD16—1811no—
190C2×#41—3621no—
191C2×SD16—1811no—
192C2×SD16—1811no—
193C2×SD16—1811no—
194C4⋊Q8—3621no—
195C4⋊Q8—1811no—
196#127—1811no—
197#127—1811no—
198#127C2×D18111yescharacteristic
199#125—3621no—
200#125—3621no—
201#125—1811no—
202#125C2×D18111yescharacteristic
203#121—3621no—
204#121—3621no—
205#121—3621no—
206C4×Q8—3621no—
207C4×Q8—1811no—
208C4×Q8—1811no—
209C4×Q8—1811no—
210C4×Q8—1811no—
211C4×D4—1811no—
212C4×D4—1811no—
213C4×D4—1811no—
214#107—1811no—
215#107—1811no—
216#106—1811no—
217C4⋊C8—1811no—
218C4⋊C8—1811no—
219C4⋊C8—1811no—
220#103—1811no—
221#102—1811no—
222#102—1811no—
223#102—1811no—
224#102—1811no—
225#102—1811no—
226#102C2×D18111yescharacteristic
227#102C2×D18111yescharacteristic
228#102C2×D18111yescharacteristic
229#102C2×D18111yescharacteristic
230#97—1811no—
231#97C2×D18111yescharacteristic
232C4×C8—1811no—
233#41—7244no—
234C2×Q8—3621no—
235C2×Q8—1811no—
236C2×Q8—1811no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—3621no—
240C2×D4—3621no—
241C2×D4—3621no—
242C2×D4—3621no—
243C2×D4—1811no—
244C2×D4C22×D18111yescharacteristic
245C2×D4C22×D18111yescharacteristic
246C22×C4—3621no—
247C22×C4—3621no—
248C22×C4—3621no—
249SD16—3622no—
250SD16—3622no—
251SD16—3622no—
252C2×C8—1811no—
253C2×C8—1811no—
254C2×C8C22×D18111yescharacteristic
255C2×C8C22×D18111yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—3621no—
259C4⋊C4—3621no—
260C4⋊C4—3621no—
261C4⋊C4—3621no—
262C4⋊C4—3621no—
263C4⋊C4—3621no—
264C4⋊C4—1811no—
265C4⋊C4—1811no—
266C4⋊C4—1811no—
267C4⋊C4—1811no—
268C4⋊C4—1811no—
269C4⋊C4C22×D18111yescharacteristic
270C4⋊C4C22×D18111yescharacteristic
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C42—3621no—
275C42—3621no—
276C42—3621no—
277C42—1811no—
278C42—1811no—
279C42C22×D18111yescharacteristic
280C23—21no—
281C23—21no—
282C23—3621no—
283Q8—3622no—
284Q8—3621no—
285Q8—1812no—
286Q8—7242no—
287D4—21no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—81no—
293D4—3621no—
294D4—3621no—
295D4—14481no—
296D4—14481no—
297D4—7242no—
298D4—7242no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—3621no—
302C2×C4—3621no—
303C2×C4—3621no—
304C2×C4—1811no—
305C2×C4—1811no—
306C2×C4—1811no—
307C2×C4—1811no—
308C2×C4—7242no—
309C2×C4—7242no—
310C2×C4—7242no—
311C2×C4D4×D18111yescharacteristic
312C2×C4D4×D18111yescharacteristic
313C2×C4C23×D18111yescharacteristic
314C8—21no—
315C8—21no—
316C8—3621no—
317C8—3621no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—7241no—
325C22—7241no—
326C22—7241no—
327C22C2×D4×D18111yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—3622no—
333C4—3621no—
334C4—3621no—
335C4—3621no—
336C4—1812no—
337C4—7241no—
338C4—7241no—
339C4#41×D18111yescharacteristic
340C4#1915386311yescharacteristic
341C2—81no—
342C2—81no—
343C2—14481no—
344C2#2604193711yescharacteristic
345C2AGL(1,ℤ/8)×D18111yescharacteristic
346C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#490×C181C2
socleC22×C181C22×D4
prime radical#26041949C2
hypercenter#490D181
hypocenterC181#3368
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #26042006C2semidirect
3. #26041642C2semidirect
4. #26041624C2semidirect
5. #26041577C2semidirect
6. #26041576C2semidirect
7. #26041557C2semidirect
8. #26041478C2semidirect
9. #26041478C2semidirect
10. #26041476C2semidirect
11. #26041407C2semidirect
12. #26041381C2semidirect
13. #26041376C2semidirect
14. #26041370C2semidirect
15. #490×C181C2semidirect
110. Dic362#41semidirect
173. C181#3368semidirect
178. #490D181semidirect

Maximal subgroups

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

subgroupindex
#260420062
#260419492
#260416422
#260416242
#260415772
#260415762
#260415572
#260414782
#260414762
#260414072
#260413812
#260413762
#260413702
#490×C1812
#3368181