Finite Group Databasebeta

← #37543963

Subgroups — #37543963

Order 23168.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041880C211yesmaximal, characteristic, complemented
2#26041751C211yesmaximal, characteristic, complemented
3#26041605C211yesmaximal, characteristic, complemented
4#26041602C211yesmaximal, characteristic, complemented
5#26041581C211yesmaximal, characteristic, complemented
6#26041578C211yesmaximal, characteristic, complemented
7#26041473C211yesmaximal, characteristic, complemented
8#26041472C211yesmaximal, characteristic, complemented
9#26041414C211yesmaximal, characteristic, complemented
10#26041411C211yesmaximal, characteristic, complemented
11#26041392C211yesmaximal, characteristic, complemented
12C4×#15668434C211yesmaximal, characteristic, complemented
13C4×#15668434C211yesmaximal, characteristic, complemented
14#26041341C211yesmaximal, characteristic, complemented
15#442×C181C211yesmaximal, characteristic, complemented
16C2×D4×D181C2211yescharacteristic
17C2×D1448C2211yescharacteristic
18C2×#15668434C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20#19153812C2211yescharacteristic, complemented
21#19153807C2211yescharacteristic, complemented
22#19153799—21no—
23#19153798—21no—
24#19153791C2211yescharacteristic
25#19153790—21no—
26#19153789—21no—
27#19153787C2211yescharacteristic
28C4×D724C2211yescharacteristic
29C4×D724C2211yescharacteristic, complemented
30D4×Dic181C2211yescharacteristic
31#19153778C2211yescharacteristic
32C4×C22⋊D181—21no—
33#19153776—21no—
34#19153774C2211yescharacteristic
35#19153773C2211yescharacteristic
36C2×#15668426—21no—
37C22⋊C4×D181—21no—
38#19153749C2211yescharacteristic, complemented
39#19153749C2211yescharacteristic, complemented
40#19153748C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic, complemented
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51C4×#13089678C2211yescharacteristic, complemented
52C2×D8×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic, complemented
55#106×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic, complemented
58#97×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C2×D724—21no—
61C2×D724C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67D4×D181—22no—
68D4×D181—22no—
69C22×Dic181—21no—
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74D1448—22no—
75#15668434—22no—
76#15668434—22no—
77C2×#13089678C2311yescharacteristic
78C2×#13089678C2311yescharacteristic
79C4⋊Dic181—21no—
80C4⋊Dic181C2311yescharacteristic
81C4⋊Dic181C2311yescharacteristic
82#15668428—21no—
83#15668428D411yescharacteristic
84#15668428D411yescharacteristic
85C22⋊Dic181—21no—
86C22⋊Dic181—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426D411yescharacteristic
93#15668426D411yescharacteristic
94C4×Dic181—21no—
95C4×Dic181C2311yescharacteristic
96C2×D4×C181C2311yescharacteristic
97C2×D4×C181C2311yescharacteristic
98C22×C4×C181—21no—
99C22×C4×C181—21no—
100D8×C181—22no—
101C2×C8×C181C2311yescharacteristic
102C2×C8×C181C2311yescharacteristic
103C4⋊C4×C181C2311yescharacteristic
104C4⋊C4×C181C2311yescharacteristic
105C22⋊C4×C181—21no—
106C22⋊C4×C181—21no—
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109C22×D181—24no—
110C22×D181—21no—
111C22×D181—81no—
112C22×D181—81no—
113C22×D181C2×D411yescharacteristic
114D724—21no—
115D724—21no—
116D724—21no—
117D724—81no—
118D724#4112yes—
119C22⋊D181—24no—
120C22⋊D181—81no—
121C22⋊D181—81no—
122C22⋊D181—81no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—81no—
126C2×Dic181C2×D411yescharacteristic
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C4×D181—21no—
130C4×D181—21no—
131C4×D181—81no—
132C4×D181—81no—
133C4×D181—81no—
134#13089678—21no—
135#13089678—21no—
136C23×C181—21no—
137C23×C181—21no—
138D4×C181—21no—
139D4×C181—21no—
140D4×C181—21no—
141D4×C181#4112yes—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—81no—
145C2×C4×C181—81no—
146C2×C4×C181C2×D411yescharacteristic
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2411yescharacteristic
149C8×C181—21no—
150C8×C181—21no—
151C22×C181—22no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181—41no—
155C22×C181—41no—
156C22×C181—41no—
157C22×C181C22×D411yescharacteristic
158C2×D181—21no—
159C2×D181—22no—
160C2×D181—21no—
161C2×D181—21no—
162C2×D181—41no—
163C2×D181—41no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—84no—
168C4×C181—21no—
169C4×C181—21no—
170C4×C181—41no—
171C4×C181—41no—
172C4×C181C2×#4111yescharacteristic
173C4×C181C2×#4111yescharacteristic
174Dic181—21no—
175Dic181—21no—
176Dic181—21no—
177Dic181—41no—
178Dic181—41no—
179C2×C181—42no—
180C2×C181—81no—
181C2×C181#52511yescharacteristic
182C2×C181#57611yescharacteristic
183C2×C181#57611yescharacteristic
184D181—41no—
185D181—42no—
186D181—81no—
187C181#312211yescharacteristic, complemented, Sylow
188#3122—1811nomaximal, Sylow
189#540—1811no—
190#518—1811no—
191#482—1811no—
192#482—1811no—
193#478—1811no—
194#478—1811no—
195#459—1811no—
196#459—1811no—
197#447—1811no—
198#447—1811no—
199#442—1811no—
200#442D18111yescharacteristic, complemented
201C4×D8—1811no—
202C4×D8—1811no—
203#433—1811no—
204C22×D4—1811no—
205C2×D8—1811no—
206C2×D8—1811no—
207C2×D8—1811no—
208C2×D8C2×D18111yescharacteristic
209#127—1811no—
210#125—1811no—
211#123—3621no—
212#123—3621no—
213#121—3621no—
214#121—3621no—
215#121—1811no—
216#121—1811no—
217C4×D4—3621no—
218C4×D4—3621no—
219C4×D4—1811no—
220C4×D4—1811no—
221C4×D4—1811no—
222C4×D4—1811no—
223C4×D4C2×D18111yescharacteristic
224C4×D4C2×D18111yescharacteristic, complemented
225#117—1811no—
226#117—1811no—
227C2×C22⋊C4—3621no—
228C2×C22⋊C4—3621no—
229#107—1811no—
230#107—1811no—
231#106—1811no—
232#106C2×D18111yescharacteristic, complemented
233C4⋊C8—1811no—
234C4⋊C8—1811no—
235#102—1811no—
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102—1811no—
240#102—1811no—
241#102C2×D18111yescharacteristic
242#102C2×D18111yescharacteristic, complemented
243C22⋊C8—1811no—
244C22⋊C8—1811no—
245#97C2×D18111yescharacteristic, complemented
246C4×C8—1811no—
247C24—3621no—
248C2×D4—3621no—
249C2×D4—3622no—
250C2×D4—3622no—
251C2×D4—3621no—
252C2×D4—3621no—
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4—1811no—
257C2×D4C22×D18111yescharacteristic
258C2×D4C22×D18111yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—3621no—
262C22×C4—3621no—
263C22×C4—3621no—
264C22×C4—3621no—
265C22×C4—1811no—
266D8—22no—
267D8—3622no—
268D8—3622no—
269D8—3622no—
270C2×C8—1811no—
271C2×C8—1811no—
272C2×C8C22×D18111yescharacteristic
273C2×C8C22×D18111yescharacteristic
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—1811no—
277C4⋊C4—1811no—
278C4⋊C4—1811no—
279C4⋊C4—1811no—
280C4⋊C4C22×D18111yescharacteristic
281C4⋊C4C22×D18111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—1811no—
292C22⋊C4—1811no—
293C42—3621no—
294C42—1811no—
295C42C22×D18111yescharacteristic
296C23—21no—
297C23—21no—
298C23—3624no—
299C23—3621no—
300C23—3621no—
301C23—14481no—
302C23—14481no—
303C23—1811no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—3624no—
308D4—3621no—
309D4—3621no—
310D4—3621no—
311D4—14481no—
312D4—14481no—
313D4—14481no—
314D4—14481no—
315D4—1812no—
316D4#1566844912yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—14481no—
326C2×C4—14481no—
327C2×C4—14481no—
328C2×C4—14481no—
329C2×C4—1811no—
330C2×C4—1811no—
331C2×C4—1811no—
332C2×C4D4×D18111yescharacteristic
333C2×C4D4×D18111yescharacteristic
334C2×C4C23×D18111yescharacteristic
335C8—21no—
336C8—21no—
337C8—3621no—
338C8—3621no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—3621no—
346C22—3622no—
347C22—3621no—
348C22—3621no—
349C22—14484no—
350C22—7241no—
351C22—7241no—
352C22—7241no—
353C22—7241no—
354C22—7241no—
355C22C2×D4×D18111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—3621no—
361C4—3621no—
362C4—3621no—
363C4—7241no—
364C4—7241no—
365C4#41×D18111yescharacteristic
366C4C2×#1566844911yescharacteristic
367C2—42no—
368C2—81no—
369C2—14481no—
370C2—7241no—
371C2—7242no—
372C2#2604178811yescharacteristic
373C2#2604208311yescharacteristic
374C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#442×C181C2
socleC22×C181C22×D4
hypercenter#442D181
hypocenterC181#3122
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #26041880C2semidirect
2. #26041751C2semidirect
3. #26041605C2semidirect
4. #26041602C2semidirect
5. #26041581C2semidirect
6. #26041578C2semidirect
7. #26041473C2semidirect
8. #26041472C2semidirect
9. #26041414C2semidirect
10. #26041411C2semidirect
11. #26041392C2semidirect
12. C4×#15668434C2semidirect
13. C4×#15668434C2semidirect
14. #26041341C2semidirect
15. #442×C181C2semidirect
20. #19153812C22semidirect
21. #19153807C22semidirect
29. C4×D724C22semidirect
38. #19153749C22semidirect
39. #19153749C22semidirect
40. #19153748C22semidirect
41. #19153745C22semidirect
42. #19153745C22semidirect
44. #19153738C22semidirect
46. #19153737C22semidirect
48. #19153736C22semidirect
51. C4×#13089678C22semidirect
54. C4×D4×C181C22semidirect
55. #106×C181C22semidirect
57. #102×C181C22semidirect
58. #97×C181C22semidirect
187. C181#3122semidirect
200. #442D181semidirect
224. C4×D4C2×D181semidirect
232. #106C2×D181semidirect
242. #102C2×D181semidirect
245. #97C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260418802
#260417512
#260416052
#260416022
#260415812
#260415782
#260414732
#260414722
#260414142
#260414112
#260413922
C4×#156684342
#260413412
#442×C1812
#3122181