Finite Group Databasebeta

← #37546808

Subgroups — #37546808

Order 23168.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042014C211yesmaximal, characteristic, complemented
2#26042011C211yesmaximal, characteristic, complemented
3#26041669C211yesmaximal, characteristic, complemented
4#26041665C211yesmaximal, characteristic, complemented
5#26041664C211yesmaximal, characteristic, complemented
6#26041503C211yesmaximal, characteristic, complemented
7#26041497C211yesmaximal, characteristic, complemented
8#26041496C211yesmaximal, characteristic, complemented
9#26041475C211yesmaximal, characteristic, complemented
10#26041473C211yesmaximal, characteristic, complemented
11#26041408C211yesmaximal, characteristic, complemented
12#26041382C211yesmaximal, characteristic, complemented
13#26041377C211yesmaximal, characteristic, complemented
14#26041359C211yesmaximal, characteristic, complemented
15#464×C181C211yesmaximal, characteristic, complemented
16C2×#15668436C2211yescharacteristic
17C2×#15668436C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23#19153813C2211yescharacteristic
24#19153812C2211yescharacteristic
25#19153805C2211yescharacteristic
26#19153805C2211yescharacteristic
27#19153805C2211yescharacteristic
28#19153804—21no—
29#19153802—21no—
30#19153801—21no—
31#19153801—21no—
32#19153800—21no—
33#19153798—21no—
34Q8×Dic181C2211yescharacteristic
35C4×Dic362C2211yescharacteristic
36C4×D724—21no—
37C4×D724C2211yescharacteristic
38D4×Dic181C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153778C2211yescharacteristic
41#19153776—21no—
42#19153749C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153738C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153727C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54#124×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59C2×Dic362D411yescharacteristic
60C2×D724—21no—
61C2×D724—21no—
62C2×D724C2311yescharacteristic
63C2×D724C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C22×Dic181—21no—
68C2×C4×D181—21no—
69C2×C4×D181—21no—
70C2×C4×D181—21no—
71#15668436—22no—
72#15668436—22no—
73#15668436—41no—
74D1448—41no—
75D1448—41no—
76#15668434—22no—
77#15668434—41no—
78C2×#13089678C2311yescharacteristic
79C2×#13089678C2311yescharacteristic
80C4⋊Dic181—21no—
81C4⋊Dic181D411yescharacteristic
82C4⋊Dic181C2311yescharacteristic
83#15668428D411yescharacteristic
84#15668428D411yescharacteristic
85C22⋊Dic181—21no—
86#15668426—21no—
87#15668426—21no—
88#15668426—21no—
89#15668426—21no—
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95C4×Dic181—21no—
96C4×Dic181C2311yescharacteristic
97C4×Dic181C2311yescharacteristic
98C2×Q8×C181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181C2311yescharacteristic
101Q16×C181—41no—
102SD16×C181—41no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181—21no—
106C4⋊C4×C181C2311yescharacteristic
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C42×C181—21no—
110C42×C181C2311yescharacteristic
111C22×D181—21no—
112C22×D181—21no—
113C22×D181—21no—
114Dic362—41no—
115D724—21no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—21no—
120D724—21no—
121D724—42no—
122D724—81no—
123C22⋊D181—42no—
124C22⋊D181—81no—
125C2×Dic181—21no—
126C2×Dic181—81no—
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C4×D181—81no—
132C4×D181—81no—
133C4×D181—81no—
134#13089678—21no—
135#13089678#4112yes—
136C23×C181—21no—
137Q8×C181—21no—
138Q8×C181—21no—
139Q8×C181—21no—
140Q8×C181—21no—
141D4×C181—21no—
142D4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181C2×D411yescharacteristic
147C2×C4×C181C2×D411yescharacteristic
148C2×C4×C181C2411yescharacteristic
149C8×C181—21no—
150C8×C181—21no—
151C22×C181—41no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181C22×D411yescharacteristic
155C2×D181—41no—
156C2×D181—41no—
157C2×D181—41no—
158C2×D181—41no—
159C2×D181—41no—
160C2×D181—41no—
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C4×C181—21no—
165C4×C181—21no—
166C4×C181—41no—
167C4×C181—41no—
168C4×C181—41no—
169C4×C181C2×#4111yescharacteristic
170C4×C181H(5,𝔽2)11yescharacteristic
171Dic181—21no—
172Dic181—21no—
173Dic181—21no—
174Dic181—21no—
175Dic181—41no—
176C2×C181—81no—
177C2×C181#55011yescharacteristic
178C2×C181#57511yescharacteristic
179C2×C181#57611yescharacteristic
180D181—81no—
181D181—81no—
182D181—81no—
183C181#340311yescharacteristic, complemented, Sylow
184#3403—1811nomaximal, Sylow
185#559—1811no—
186#559—1811no—
187#496—1811no—
188#496—1811no—
189#495—1811no—
190#464—1811no—
191#464D18111yescharacteristic, complemented
192#463—1811no—
193#463—1811no—
194#459—1811no—
195#459—1811no—
196#446—1811no—
197#440—1811no—
198#440—1811no—
199C4×D8—1811no—
200C2×Q16C2×D18111yescharacteristic
201C2×SD16—1811no—
202C2×SD16—1811no—
203C2×SD16—1811no—
204C2×SD16C2×D18111yescharacteristic
205C2×D8—1811no—
206C2×D8—1811no—
207C2×D8—1811no—
208C2×D8—1811no—
209#127—1811no—
210#127—1811no—
211#124—3621no—
212#124—3621no—
213#124—1811no—
214#124—1811no—
215#124—1811no—
216#124C2×D18111yescharacteristic
217#123—3621no—
218#123—3621no—
219#123—3621no—
220#123—3621no—
221C4×Q8—1811no—
222C4×Q8—1811no—
223C4×Q8C2×D18111yescharacteristic
224C4×D4—3621no—
225C4×D4—3621no—
226C4×D4—1811no—
227C4×D4—1811no—
228C4×D4—1811no—
229C4×D4—1811no—
230#107—1811no—
231C4⋊C8—1811no—
232C4⋊C8—1811no—
233C4⋊C8C2×D18111yescharacteristic
234#103—1811no—
235#103C2×D18111yescharacteristic
236#102—1811no—
237#102—1811no—
238#102—1811no—
239#102C2×D18111yescharacteristic
240#97—1811no—
241#97—1811no—
242C4×C8—1811no—
243C2×Q8—1811no—
244C2×Q8C22×D18111yescharacteristic
245C2×Q8C22×D18111yescharacteristic
246C2×D4—3621no—
247C2×D4—3621no—
248C2×D4—3621no—
249C2×D4—3621no—
250C2×D4—1811no—
251C2×D4—1811no—
252C2×D4—1811no—
253C2×D4C22×D18111yescharacteristic
254C22×C4—3621no—
255C22×C4—3621no—
256C22×C4—3621no—
257C22×C4—3621no—
258Q16—41no—
259SD16—41no—
260SD16—3622no—
261SD16—3622no—
262SD16—7241no—
263D8—3622no—
264D8—7241no—
265D8—7241no—
266D8—7241no—
267C2×C8—1811no—
268C2×C8—1811no—
269C2×C8C22×D18111yescharacteristic
270C2×C8C22×D18111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—3621no—
273C4⋊C4—1811no—
274C4⋊C4—1811no—
275C4⋊C4—1811no—
276C4⋊C4—1811no—
277C4⋊C4C22×D18111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—3621no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C42—21no—
291C42—3621no—
292C42—1811no—
293C42—1811no—
294C42C22×D18111yescharacteristic
295C23—21no—
296C23—3621no—
297C23—3621no—
298C23—3621no—
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—7241no—
304D4—21no—
305D4—21no—
306D4—3621no—
307D4—3621no—
308D4—3621no—
309D4—3621no—
310D4—3621no—
311D4—3621no—
312D4—14481no—
313D4—14481no—
314D4—7242no—
315D4—7242no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—3621no—
320C2×C4—14481no—
321C2×C4—14481no—
322C2×C4—14481no—
323C2×C4—14481no—
324C2×C4—1811no—
325C2×C4—1811no—
326C2×C4—1811no—
327C2×C4—1811no—
328C2×C4D4×D18111yescharacteristic
329C2×C4D4×D18111yescharacteristic
330C2×C4C23×D18111yescharacteristic
331C8—21no—
332C8—21no—
333C8—3621no—
334C8—1812no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—7241no—
339C22—7241no—
340C22—7241no—
341C22—7241no—
342C22—7241no—
343C22—7241no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22C2×D4×D18111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—3621no—
354C4—3621no—
355C4—3621no—
356C4—3621no—
357C4—7241no—
358C4#41×D18111yescharacteristic
359C4#1915386111yescharacteristic
360C2—81no—
361C2—14481no—
362C2—14481no—
363C2—14481no—
364C2#2604194711yescharacteristic
365C2#2604207811yescharacteristic
366C2#2604208111yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#464×C181C2
socleC22×C181C22×D4
hypercenter#464D181
hypocenterC181#3403
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #26042014C2semidirect
2. #26042011C2semidirect
3. #26041669C2semidirect
4. #26041665C2semidirect
5. #26041664C2semidirect
6. #26041503C2semidirect
7. #26041497C2semidirect
8. #26041496C2semidirect
9. #26041475C2semidirect
10. #26041473C2semidirect
11. #26041408C2semidirect
12. #26041382C2semidirect
13. #26041377C2semidirect
14. #26041359C2semidirect
15. #464×C181C2semidirect
183. C181#3403semidirect
191. #464D181semidirect

Maximal subgroups

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

subgroupindex
#260420142
#260420112
#260416692
#260416652
#260416642
#260415032
#260414972
#260414962
#260414752
#260414732
#260414082
#260413822
#260413772
#260413592
#464×C1812
#3403181