Finite Group Databasebeta

← #37545830

Subgroups — #37545830

Order 23168.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041984C211yesmaximal, characteristic, complemented
2#26041935C211yesmaximal, characteristic
3#26041637C211yesmaximal, characteristic, complemented
4#26041611C211yesmaximal, characteristic, complemented
5#26041563C211yesmaximal, characteristic, complemented
6#26041538C211yesmaximal, characteristic, complemented
7#26041506C211yesmaximal, characteristic, complemented
8#26041500C211yesmaximal, characteristic, complemented
9#26041442C211yesmaximal, characteristic, complemented
10#26041437C211yesmaximal, characteristic, complemented
11#26041385C211yesmaximal, characteristic, complemented
12#26041347C211yesmaximal, characteristic, complemented
13#26041277C211yesmaximal, characteristic, complemented
14C2×#19153739C211yesmaximal, characteristic, complemented
15#481×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C22×Dic362C2211yescharacteristic
18C2×Dic724C2211yescharacteristic
19C2×Dic724C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C2×#15668432C2211yescharacteristic
22C22×#13089678C2211yescharacteristic
23#19153815C2211yescharacteristic
24#19153806—21no—
25#19153803C2211yescharacteristic
26#19153802—21no—
27#19153796C2211yescharacteristic
28#19153796C2211yescharacteristic
29#19153795—21no—
30#19153795C2211yescharacteristic
31#19153794—21no—
32#19153793—21no—
33#19153788—21no—
34#19153781C2211yescharacteristic
35#19153781C2211yescharacteristic
36D4×Dic181—21no—
37C4×C22⋊D181—21no—
38C4×C22⋊D181C2211yescharacteristic
39C4⋊C4×D181C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153726C2211yescharacteristic
52#121×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#106×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—41no—
61C2×Dic362—21no—
62C2×Dic362—22no—
63C2×Dic362—21no—
64C2×Dic362—41no—
65C2×Dic362C2311yescharacteristic
66C2×Dic362C2311yescharacteristic
67C2×Dic362C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181D411yescharacteristic
70C22×Dic181—21no—
71C22×Dic181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74Dic724—22no—
75Dic724—41no—
76#15668437—41no—
77#15668432—41no—
78C2×#13089678—41no—
79C2×#13089678C2311yescharacteristic
80C2×#13089678C2311yescharacteristic
81C4⋊Dic181—21no—
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181D411yescharacteristic
94#15668426—21no—
95#15668426—21no—
96#15668426D411yescharacteristic
97C4×Dic181—21no—
98C4×Dic181—21no—
99C4×Dic181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C4⋊C4×C181—21no—
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—21no—
115Dic362—21no—
116Dic362—21no—
117Dic362—42no—
118Dic362—81no—
119Dic362#4112yes—
120C22⋊D181—22no—
121C22⋊D181—42no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—42no—
127C2×Dic181—42no—
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C4×D181—21no—
132C4×D181—21no—
133C4×D181—81no—
134#13089678—21no—
135#13089678—21no—
136C23×C181—21no—
137C23×C181C2×D411yescharacteristic
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—42no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—81no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2411yescharacteristic
149C8×C181—21no—
150C8×C181—21no—
151C22×C181—21no—
152C22×C181—21no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181—41no—
156C22×C181#13712yes—
157C22×C181C22×D411yescharacteristic
158C2×D181—21no—
159C2×D181—21no—
160C2×D181—21no—
161C4×C181—21no—
162C4×C181—41no—
163C4×C181—41no—
164C4×C181—41no—
165C4×C181C2×#4111yescharacteristic
166C4×C181H(5,𝔽2)11yescharacteristic
167Dic181—21no—
168Dic181—22no—
169Dic181—21no—
170Dic181—21no—
171Dic181—41no—
172Dic181—41no—
173Dic181—41no—
174C2×C181—22no—
175C2×C181—81no—
176C2×C181#54611yescharacteristic
177C2×C181C2×#13711yescharacteristic
178C2×C181#57711yescharacteristic
179D181—41no—
180C181#331611yescharacteristic, complemented, Sylow
181#3316—1811nomaximal, Sylow
182#554—1811no—
183#548—1811no—
184#489—1811no—
185#483—1811no—
186#481D18111yescharacteristic, complemented
187#475—1811no—
188#470—1811no—
189#465—1811no—
190#464—1811no—
191#452—1811no—
192#451—1811no—
193#441—1811no—
194#435—1811no—
195#417—1811no—
196C2×#103—1811no—
197C2×#41—1811no—
198C22×Q8—1811no—
199C2×Q16—1811no—
200C2×Q16—1811no—
201C2×SD16—1811no—
202C2×M16—1811no—
203C22×C8—1811no—
204C4⋊Q8—1811no—
205#125—3621no—
206#124—3621no—
207#124—1811no—
208C22⋊Q8—3621no—
209C22⋊Q8—3621no—
210C22⋊Q8—3621no—
211C22⋊Q8—1811no—
212C22⋊Q8—1811no—
213C22⋊Q8—1811no—
214#121—3621no—
215#121C2×D18111yescharacteristic
216C4×Q8—1811no—
217C4×Q8—1811no—
218C4×D4—3621no—
219C4×D4—3621no—
220C4×D4—1811no—
221C2×C4⋊C4—1811no—
222C2×C4⋊C4C2×D18111yescharacteristic
223#106—1811no—
224#106C2×D18111yescharacteristic
225#106C2×D18111yescharacteristic
226C4⋊C8—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103—1811no—
231#103—1811no—
232#103—1811no—
233#103—1811no—
234#102—1811no—
235#102C2×D18111yescharacteristic
236#102C2×D18111yescharacteristic
237C22⋊C8—1811no—
238C22⋊C8C2×D18111yescharacteristic
239#97—1811no—
240#41—3622no—
241#41—7241no—
242C2×Q8—3621no—
243C2×Q8—3622no—
244C2×Q8—3621no—
245C2×Q8—1811no—
246C2×Q8—1811no—
247C2×Q8—1811no—
248C2×Q8—7241no—
249C2×D4—21no—
250C2×D4—3621no—
251C2×D4—1811no—
252C2×D4C22×D18111yescharacteristic
253C22×C4—21no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—1811no—
258C22×C4C22×D18111yescharacteristic
259Q16—3622no—
260Q16—7241no—
261SD16—7241no—
262M16—7241no—
263C2×C8—1811no—
264C2×C8—1811no—
265C2×C8—7241no—
266C2×C8C22×D18111yescharacteristic
267C2×C8C22×D18111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—3621no—
273C4⋊C4—3621no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—1811no—
277C4⋊C4—1811no—
278C4⋊C4C22×D18111yescharacteristic
279C4⋊C4C22×D18111yescharacteristic
280C4⋊C4C22×D18111yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—1811no—
288C22⋊C4—1811no—
289C42—3621no—
290C42—3621no—
291C42—1811no—
292C23—21no—
293C23—1811no—
294C23D4×D18111yescharacteristic
295Q8—3621no—
296Q8—3621no—
297Q8—3621no—
298Q8—3621no—
299Q8—3621no—
300Q8—14481no—
301Q8—1812no—
302Q8—7242no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—3622no—
307D4—7242no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—81no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—3621no—
318C2×C4—3621no—
319C2×C4—3621no—
320C2×C4—14481no—
321C2×C4—1811no—
322C2×C4—1811no—
323C2×C4—1811no—
324C2×C4—7242no—
325C2×C4—7242no—
326C2×C4D4×D18111yescharacteristic
327C2×C4C23×D18111yescharacteristic
328C8—21no—
329C8—21no—
330C8—3621no—
331C8—3621no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3621no—
338C22—3621no—
339C22—3621no—
340C22#1915384512yes—
341C22C2×D4×D18111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3621no—
347C4—3622no—
348C4—3621no—
349C4—3621no—
350C4—7241no—
351C4—7241no—
352C4—7241no—
353C4#41×D18111yescharacteristic
354C4#1915386211yescharacteristic
355C2—22no—
356C2—81no—
357C2—7241no—
358C2#2604192111yescharacteristic
359C2C2×#1915384511yescharacteristic
360C2#2604208911yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#481×C181C2
socleC22×C181C22×D4
prime radical#26041935C2
hypercenter#481D181
hypocenterC181#3316
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #26041984C2semidirect
3. #26041637C2semidirect
4. #26041611C2semidirect
5. #26041563C2semidirect
6. #26041538C2semidirect
7. #26041506C2semidirect
8. #26041500C2semidirect
9. #26041442C2semidirect
10. #26041437C2semidirect
11. #26041385C2semidirect
12. #26041347C2semidirect
13. #26041277C2semidirect
14. C2×#19153739C2semidirect
15. #481×C181C2semidirect
180. C181#3316semidirect
186. #481D181semidirect

Maximal subgroups

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

subgroupindex
#260419842
#260419352
#260416372
#260416112
#260415632
#260415382
#260415062
#260415002
#260414422
#260414372
#260413852
#260413472
#260412772
C2×#191537392
#481×C1812
#3316181