Finite Group Databasebeta

← #385×D181 #37536129

Subgroups — #385×D181 #37536129

Order 23168.

1232 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D181C211yesmaximal, characteristic
2C2×C4⋊C4×D181C212yesmaximal, complemented
3C2×C22⋊C4×D181C211yesmaximal, characteristic
4C2×C22⋊C4×D181C211yesmaximal, characteristic
5#26041154C211yesmaximal, characteristic, complemented
6#26041153C212yesmaximal, complemented
7#26041152C211yesmaximal, characteristic, complemented
8#26041151C211yesmaximal, characteristic, complemented
9#26041150C212yesmaximal, complemented
10#95×D181C212yesmaximal, complemented
11#385×C181C211yesmaximal, characteristic, complemented
12C24×D181C2211yescharacteristic
13C23×Dic181C2211yescharacteristic
14C22×C4×D181—24no—
15C22×C4×D181—28no—
16C22×C4×D181C2211yescharacteristic
17C22×C4×D181C2212yes—
18C22×C4×D181C2211yescharacteristic
19C22×C4×D181C2212yes—
20C22×C4×D181C2212yes—
21C2×C4⋊Dic181C2212yescomplemented
22C2×#15668428C2212yescomplemented
23C2×#15668428C2212yescomplemented
24C4⋊C4×D181—28no—
25C2×C22⋊Dic181C2211yescharacteristic
26C2×C22⋊Dic181C2211yescharacteristic
27C2×#15668426C2211yescharacteristic
28C2×#15668426C2211yescharacteristic
29C2×#15668426C2212yes—
30C22⋊C4×D181—24no—
31C22⋊C4×D181C418yescomplemented
32#19153723C2212yescomplemented
33#19153723C2212yescomplemented
34#19153723C2212yescomplemented
35C23×C4×C181C2211yescharacteristic
36C2×C4⋊C4×C181C2212yescomplemented
37C2×C22⋊C4×C181C2211yescharacteristic
38C2×C22⋊C4×C181C2211yescharacteristic
39#95×C181C2212yescomplemented
40C23×D181—24no—
41C23×D181—24no—
42C23×D181C2×C414yes—
43C23×D181D414yes—
44C23×D181Q814yes—
45C23×D181C2311yescharacteristic
46C23×D181C2311yescharacteristic
47C22×Dic181—24no—
48C22×Dic181—22no—
49C22×Dic181C2311yescharacteristic
50C22×Dic181C2311yescharacteristic
51C22×Dic181C2312yes—
52C22×Dic181C2312yes—
53C2×C4×D181—232no—
54C2×C4×D181—24no—
55C2×C4×D181—24no—
56C2×C4×D181—24no—
57C2×C4×D181—24no—
58C2×C4×D181—24no—
59C2×C4×D181—24no—
60C2×C4×D181—22no—
61C2×C4×D181—22no—
62C2×C4×D181—24no—
63C2×C4×D181—24no—
64C2×C4×D181—24no—
65C2×C4×D181C2×C418yescomplemented
66C2×C4×D181D418yes—
67C4⋊Dic181—24no—
68#15668428—24no—
69#15668428—24no—
70C22⋊Dic181—22no—
71C22⋊Dic181C2×C414yescomplemented
72#15668426—22no—
73#15668426—22no—
74#15668426C2×C418yescomplemented
75C24×C181C2311yescharacteristic
76C22×C4×C181—22no—
77C22×C4×C181—24no—
78C22×C4×C181C2311yescharacteristic
79C22×C4×C181C2311yescharacteristic
80C22×C4×C181C2312yes—
81C22×C4×C181C2312yes—
82C4⋊C4×C181—24no—
83C22⋊C4×C181—22no—
84C22⋊C4×C181C2×C414yescomplemented
85C22×D181—22no—
86C22×D181—22no—
87C22×D181—216no—
88C22×D181—28no—
89C22×D181—216no—
90C22×D181—28no—
91C22×D181C4⋊C4116yescomplemented
92C22×D181C22×C412yes—
93C22×D181C22×C412yes—
94C22×D181C2×D412yes—
95C22×D181C2×D412yes—
96C22×D181C2×D414yes—
97C22×D181C2×Q812yes—
98C22×D181C2×Q812yes—
99C22×D181#4114yes—
100C2×Dic181—28no—
101C2×Dic181—22no—
102C2×Dic181—22no—
103C2×Dic181—22no—
104C2×Dic181—22no—
105C2×Dic181—21no—
106C2×Dic181—21no—
107C2×Dic181—22no—
108C2×Dic181—22no—
109C2×Dic181C22×C414yescomplemented
110C2×Dic181C2×D414yes—
111C4×D181—216no—
112C4×D181—216no—
113C4×D181—216no—
114C4×D181—44no—
115C4×D181—44no—
116C23×C181—22no—
117C23×C181—22no—
118C23×C181C22×C412yes—
119C23×C181C2×D412yes—
120C23×C181C2×Q812yes—
121C23×C181C2411yescharacteristic
122C2×C4×C181—28no—
123C2×C4×C181—22no—
124C2×C4×C181—22no—
125C2×C4×C181—22no—
126C2×C4×C181—22no—
127C2×C4×C181—21no—
128C2×C4×C181—21no—
129C2×C4×C181—22no—
130C2×C4×C181—22no—
131C2×C4×C181C22×C414yescomplemented
132C2×C4×C181C2×D414yes—
133C22×C181—24no—
134C22×C181—22no—
135C22×C181—24no—
136C22×C181—22no—
137C22×C181C2×C4⋊C414yescomplemented
138C22×C181C23×C411yescharacteristic
139C22×C181C22×D411yescharacteristic
140C22×C181C22×D412yes—
141C22×C181C22×Q811yescharacteristic
142C22×C181C2×#4112yes—
143C2×D181—24no—
144C2×D181—22no—
145C2×D181—24no—
146C2×D181—22no—
147C2×D181—232no—
148C2×D181C2×C4⋊C414yes—
149C2×D181C2×C4⋊C414yescomplemented
150C2×D181C4×D418yes—
151C2×D181#12014yes—
152C2×D181C22⋊Q818yes—
153C2×D181#12314yes—
154C4×C181—24no—
155C4×C181—24no—
156C4×C181—41no—
157C4×C181—41no—
158Dic181—24no—
159Dic181—24no—
160Dic181—41no—
161Dic181—41no—
162C2×C181—24no—
163C2×C181C22×C4⋊C411yescharacteristic
164C2×C181C2×C4×D412yes—
165C2×C181C2×#12011yescharacteristic
166C2×C181C2×C22⋊Q812yes—
167C2×C181C2×#12311yescharacteristic
168D181—24no—
169D181#38518yesdirect product factor
170C181C2×#38511yescharacteristic, complemented, Sylow
171C2×#385—1811nomaximal, Sylow
172C24×C4—1811no—
173C22×C4⋊C4—1812no—
174C22×C22⋊C4—1811no—
175C22×C22⋊C4—1811no—
176#385—1811no—
177#385—1812no—
178#385—1811no—
179#385—1811no—
180#385—1812no—
181#385D18111yescharacteristic, direct product factor
182C2×#95—1812no—
183C25—1811no—
184C23×C4—3624no—
185C23×C4—3628no—
186C23×C4—1811no—
187C23×C4—1811no—
188C23×C4—1811no—
189C23×C4—1812no—
190C23×C4—1812no—
191C23×C4—1812no—
192C23×C4C2×D18111yescharacteristic
193C2×C4⋊C4—3628no—
194C2×C4⋊C4—1812no—
195C2×C4⋊C4—1812no—
196C2×C4⋊C4—1812no—
197C2×C4⋊C4C2×D18112yescomplemented
198C2×C22⋊C4—3624no—
199C2×C22⋊C4—1811no—
200C2×C22⋊C4—1811no—
201C2×C22⋊C4—1811no—
202C2×C22⋊C4—1811no—
203C2×C22⋊C4—1812no—
204C2×C22⋊C4—1818no—
205C2×C22⋊C4C2×D18111yescharacteristic
206C2×C22⋊C4C2×D18111yescharacteristic
207#95—1812no—
208#95—1812no—
209#95—1812no—
210#95C2×D18112yescomplemented
211C24—3624no—
212C24—3624no—
213C24—1814no—
214C24—1814no—
215C24—1814no—
216C24—1811no—
217C24—1811no—
218C24C22×D18111yescharacteristic
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—36232no—
222C22×C4—3624no—
223C22×C4—3624no—
224C22×C4—3624no—
225C22×C4—3624no—
226C22×C4—3624no—
227C22×C4—3624no—
228C22×C4—3622no—
229C22×C4—3622no—
230C22×C4—3624no—
231C22×C4—3624no—
232C22×C4—3622no—
233C22×C4—3624no—
234C22×C4—3624no—
235C22×C4—1811no—
236C22×C4—1811no—
237C22×C4—1812no—
238C22×C4—1812no—
239C22×C4—1818no—
240C22×C4—1818no—
241C22×C4C22×D18111yescharacteristic
242C22×C4C22×D18111yescharacteristic
243C22×C4C22×D18112yes—
244C22×C4C22×D18112yes—
245C4⋊C4—24no—
246C4⋊C4—3624no—
247C4⋊C4—3624no—
248C4⋊C4—3624no—
249C22⋊C4—22no—
250C22⋊C4—3622no—
251C22⋊C4—3622no—
252C22⋊C4—3622no—
253C22⋊C4—1814no—
254C22⋊C4—1818no—
255C22⋊C4C4×D18114yescomplemented
256C23—22no—
257C23—22no—
258C23—3628no—
259C23—36216no—
260C23—36216no—
261C23—3628no—
262C23—3622no—
263C23—3622no—
264C23—18116no—
265C23—1812no—
266C23—1812no—
267C23—1812no—
268C23—1812no—
269C23—1812no—
270C23—1814no—
271C23—1812no—
272C23—1814no—
273C23C2×C4×D18112yes—
274C23D4×D18112yes—
275C23Q8×D18112yes—
276C23C23×D18111yescharacteristic
277C2×C4—28no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—36216no—
287C2×C4—36216no—
288C2×C4—36216no—
289C2×C4—3628no—
290C2×C4—3622no—
291C2×C4—3622no—
292C2×C4—3622no—
293C2×C4—3622no—
294C2×C4—3621no—
295C2×C4—3621no—
296C2×C4—3622no—
297C2×C4—3622no—
298C2×C4—1814no—
299C2×C4—1814no—
300C2×C4—7244no—
301C2×C4—7244no—
302C2×C4C2×C4×D18114yescomplemented
303C2×C4D4×D18114yes—
304C22—24no—
305C22—22no—
306C22—24no—
307C22—22no—
308C22—36232no—
309C22—3624no—
310C22—3622no—
311C22—3624no—
312C22—3622no—
313C22—1814no—
314C22—1814no—
315C22—1818no—
316C22—1814no—
317C22—1818no—
318C22—1814no—
319C22C4⋊C4×D18114yescomplemented
320C22C22×C4×D18111yescharacteristic
321C22C2×D4×D18111yescharacteristic
322C22C2×D4×D18112yes—
323C22C2×Q8×D18111yescharacteristic
324C22#41×D18112yes—
325C4—24no—
326C4—24no—
327C4—41no—
328C4—41no—
329C4—3624no—
330C4—3624no—
331C4—7241no—
332C4—7241no—
333C2—24no—
334C2—3624no—
335C2—1818no—
336C2C2×C4⋊C4×D18111yescharacteristic
337C2C4×D4×D18112yes—
338C2#120×D18111yescharacteristic
339C2C22⋊Q8×D18112yes—
340C2#123×D18111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutatorC22×C181C23×C4
Fitting#385×C181C2
socle, cosocleC23×C181C24
prime radicalC24×D181C22
hypercenter#385D181
hypocenterC181C2×#385
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D181C2semidirect
5. #26041154C2semidirect
6. #26041153C2semidirect
7. #26041152C2semidirect
8. #26041151C2semidirect
9. #26041150C2semidirect
10. #95×D181C2semidirect
11. #385×C181C2semidirect
21. C2×C4⋊Dic181C22semidirect
22. C2×#15668428C22semidirect
23. C2×#15668428C22semidirect
31. C22⋊C4×D181C4semidirect
32. #19153723C22semidirect
33. #19153723C22semidirect
34. #19153723C22semidirect
36. C2×C4⋊C4×C181C22semidirect
39. #95×C181C22semidirect
65. C2×C4×D181C2×C4semidirect
71. C22⋊Dic181C2×C4semidirect
74. #15668426C2×C4semidirect
84. C22⋊C4×C181C2×C4semidirect
91. C22×D181C4⋊C4semidirect
109. C2×Dic181C22×C4semidirect
131. C2×C4×C181C22×C4semidirect
137. C22×C181C2×C4⋊C4semidirect
149. C2×D181C2×C4⋊C4semidirect
169. D181#385direct (N × H)
170. C181C2×#385semidirect
181. #385D181direct (N × H)
197. C2×C4⋊C4C2×D181semidirect
210. #95C2×D181semidirect
255. C22⋊C4C4×D181semidirect
302. C2×C4C2×C4×D181semidirect
319. C22C4⋊C4×D181semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1812
C2×C4⋊C4×D1812
C2×C22⋊C4×D1812
#260411542
#260411532
#260411522
#260411512
#260411502
#95×D1812
#385×C1812
C2×#385181