Finite Group Databasebeta

← #37546030

Subgroups — #37546030

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#26041987C211yesmaximal, characteristic, complemented
2#26041928C211yesmaximal, characteristic
3#26041628C211yesmaximal, characteristic, complemented
4#26041610C211yesmaximal, characteristic, complemented
5#26041608C211yesmaximal, characteristic, complemented
6#26041567C211yesmaximal, characteristic, complemented
7#26041535C211yesmaximal, characteristic, complemented
8#26041534C211yesmaximal, characteristic, complemented
9#26041487C211yesmaximal, characteristic, complemented
10#26041438C211yesmaximal, characteristic, complemented
11SD16×Dic181C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic, complemented
13#26041280C211yesmaximal, characteristic, complemented
14#26041277C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668433C2211yescharacteristic
19C2×#15668432C2211yescharacteristic
20#19153815C2211yescharacteristic
21#19153814C2211yescharacteristic
22#19153806—21no—
23#19153799—21no—
24#19153797—21no—
25#19153796—21no—
26#19153795C2211yescharacteristic
27#19153793—21no—
28#19153792C2211yescharacteristic
29#19153792C2211yescharacteristic
30#19153788—21no—
31Q8×Dic181C2211yescharacteristic
32D4×Dic181C2211yescharacteristic
33C4×C22⋊D181C2211yescharacteristic
34#19153776—21no—
35C2×C4⋊Dic181C2211yescharacteristic
36C2×#15668428—21no—
37C4⋊C4×D181C2211yescharacteristic
38#19153748C2211yescharacteristic
39#19153748C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153740C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153740C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C2×SD16×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—41no—
61C2×Dic362—21no—
62C2×Dic362C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181D411yescharacteristic
65C22×Dic181—21no—
66C22×Dic181—21no—
67C22×Dic181—21no—
68C2×C4×D181—21no—
69C2×C4×D181C2311yescharacteristic
70#15668439—41no—
71#15668433—41no—
72#15668432—41no—
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C4⋊Dic181—21no—
76C4⋊Dic181—21no—
77C4⋊Dic181C2311yescharacteristic
78C4⋊Dic181C2311yescharacteristic
79C4⋊Dic181C2311yescharacteristic
80#15668428—21no—
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428D411yescharacteristic
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181D411yescharacteristic
91#15668426—21no—
92#15668426—21no—
93#15668426D411yescharacteristic
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96#41×C181—22no—
97#41×C181—41no—
98C2×Q8×C181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181C2311yescharacteristic
104Q16×C181—41no—
105SD16×C181—22no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—81no—
115C22⋊D181—22no—
116C22⋊D181—42no—
117C2×Dic181—21no—
118C2×Dic181—21no—
119C2×Dic181—21no—
120C2×Dic181—21no—
121C2×Dic181—42no—
122C2×Dic181—42no—
123C2×Dic181—81no—
124C2×Dic181C2×D411yescharacteristic
125C2×Dic181C2×D411yescharacteristic
126C2×Dic181C2×D411yescharacteristic
127C4×D181—21no—
128C4×D181—21no—
129C4×D181—81no—
130#13089678—21no—
131#13089678—21no—
132C23×C181—21no—
133C23×C181C2×D411yescharacteristic
134Q8×C181—21no—
135Q8×C181—21no—
136Q8×C181—21no—
137Q8×C181—21no—
138D4×C181—21no—
139D4×C181—42no—
140D4×C181#4112yes—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—42no—
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2411yescharacteristic
149C8×C181—21no—
150C8×C181—21no—
151C22×C181—21no—
152C22×C181—22no—
153C22×C181—21no—
154C22×C181—21no—
155C22×C181—41no—
156C22×C181—41no—
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—21no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172Dic181—41no—
173Dic181#13712yes—
174C2×C181—41no—
175C2×C181—42no—
176C2×C181#54611yescharacteristic
177C2×C181C2×#13711yescharacteristic
178C2×C181#57711yescharacteristic
179D181—41no—
180C181#333111yescharacteristic, complemented, Sylow
181#3331—1811nomaximal, Sylow
182#554—1811no—
183#547—1811no—
184#487—1811no—
185#483—1811no—
186#483—1811no—
187#476—1811no—
188#470—1811no—
189#470—1811no—
190#462—1811no—
191#452—1811no—
192#452D18111yescharacteristic, complemented
193C4×SD16—1811no—
194#436—1811no—
195#417—1811no—
196#417—1811no—
197C2×#41—1811no—
198C2×#41C2×D18111yescharacteristic
199C2×Q16—1811no—
200C2×Q16C2×D18111yescharacteristic
201C2×SD16C2×D18111yescharacteristic
202C2×M16—1811no—
203C2×M16—1811no—
204C4⋊Q8—1811no—
205C4⋊Q8—1811no—
206#125—3621no—
207#123—3621no—
208#123—3621no—
209C22⋊Q8—3621no—
210C22⋊Q8—3621no—
211C22⋊Q8—1811no—
212C22⋊Q8—1811no—
213C22⋊Q8—1811no—
214C22⋊Q8C2×D18111yescharacteristic
215#121—3621no—
216C4×Q8—1811no—
217C4×D4—3621no—
218C4×D4—1811no—
219C4×D4—1811no—
220C2×C4⋊C4—3621no—
221C2×C4⋊C4—1811no—
222C2×C4⋊C4—1811no—
223#106—1811no—
224#106—1811no—
225#106—1811no—
226C4⋊C8—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103—1811no—
231#103—1811no—
232#103—1811no—
233#103C2×D18111yescharacteristic
234#102—1811no—
235#102—1811no—
236#102C2×D18111yescharacteristic
237C22⋊C8—1811no—
238C22⋊C8C2×D18111yescharacteristic
239C4×C8—1811no—
240#41—22no—
241#41—41no—
242#41—3622no—
243#41—7241no—
244C2×Q8—3621no—
245C2×Q8—1811no—
246C2×Q8C22×D18111yescharacteristic
247C2×Q8C22×D18111yescharacteristic
248C2×D4—21no—
249C2×D4—3621no—
250C2×D4—1811no—
251C2×D4C22×D18111yescharacteristic
252C22×C4—21no—
253C22×C4—3621no—
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—1811no—
258C22×C4C22×D18111yescharacteristic
259Q16—41no—
260Q16—7241no—
261SD16—22no—
262M16—7241no—
263M16—7241no—
264C2×C8—1811no—
265C2×C8—1811no—
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—3621no—
277C4⋊C4—3621no—
278C4⋊C4—1811no—
279C4⋊C4—1811no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4C22×D18111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—1811no—
289C22⋊C4—1811no—
290C42—3621no—
291C42—1811no—
292C23—21no—
293C23—1811no—
294C23D4×D18111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—3621no—
300Q8—3621no—
301Q8—14481no—
302D4—21no—
303D4—42no—
304D4—3622no—
305D4—7242no—
306D4#1566844812yes—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—3621no—
318C2×C4—3621no—
319C2×C4—14481no—
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—22no—
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—3621no—
339C22—3621no—
340C22—3621no—
341C22C2×D4×D18111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3621no—
347C4—3621no—
348C4—1812no—
349C4—7241no—
350C4—7241no—
351C4—7241no—
352C4—7241no—
353C4C2×#1566844811yescharacteristic
354C4#1915386111yescharacteristic
355C2—41no—
356C2—42no—
357C2—7241no—
358C2#2604191611yescharacteristic
359C2#137×D18111yescharacteristic
360C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
prime radical#26041928C2
hypercenter#452D181
hypocenterC181#3331
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. #26041987C2semidirect
3. #26041628C2semidirect
4. #26041610C2semidirect
5. #26041608C2semidirect
6. #26041567C2semidirect
7. #26041535C2semidirect
8. #26041534C2semidirect
9. #26041487C2semidirect
10. #26041438C2semidirect
11. SD16×Dic181C2semidirect
12. #26041354C2semidirect
13. #26041280C2semidirect
14. #26041277C2semidirect
15. #452×C181C2semidirect
180. C181#3331semidirect
192. #452D181semidirect

Maximal subgroups

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

subgroupindex
#260419872
#260419282
#260416282
#260416102
#260416082
#260415672
#260415352
#260415342
#260414872
#260414382
SD16×Dic1812
#260413542
#260412802
#260412772
#452×C1812
#3331181