Finite Group Databasebeta

← #37543998

Subgroups — #37543998

Order 23168.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041900C211yesmaximal, characteristic, complemented
2#26041609C211yesmaximal, characteristic, complemented
3#26041597C211yesmaximal, characteristic, complemented
4#26041569C211yesmaximal, characteristic, complemented
5#26041564C211yesmaximal, characteristic, complemented
6#26041501C211yesmaximal, characteristic, complemented
7#26041494C211yesmaximal, characteristic, complemented
8#26041441C211yesmaximal, characteristic, complemented
9#26041424C211yesmaximal, characteristic
10#26041389C211yesmaximal, characteristic, complemented
11#26041384C211yesmaximal, characteristic, complemented
12C4×#15668436C211yesmaximal, characteristic, complemented
13C4×#15668437C211yesmaximal, characteristic, complemented
14#26041340C211yesmaximal, characteristic, complemented
15#520×C181C211yesmaximal, characteristic, complemented
16C2×#15668439C2211yescharacteristic
17C2×#15668437C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×#15668434C2211yescharacteristic
20#19153816C2211yescharacteristic
21#19153811—21no—
22#19153804C2211yescharacteristic
23#19153802—21no—
24#19153798—21no—
25#19153795C2211yescharacteristic
26#19153794—21no—
27#19153790C2211yescharacteristic
28C4×Dic362C2211yescharacteristic
29C4×D724C2211yescharacteristic
30#19153747C2211yescharacteristic
31#19153747C2211yescharacteristic
32#19153747C2211yescharacteristic
33#19153747C2211yescharacteristic
34C4⋊#13089678C2211yescharacteristic
35C4⋊#13089678C2211yescharacteristic
36#19153740C2211yescharacteristic
37#19153740C2211yescharacteristic
38#19153739C2211yescharacteristic
39#19153739C2211yescharacteristic
40#19153737C2211yescharacteristic
41#19153737C2211yescharacteristic
42#19153736C2211yescharacteristic
43#19153736C2211yescharacteristic
44C22⋊#13089678C2211yescharacteristic
45C22⋊#13089678C2211yescharacteristic
46#19153727C2211yescharacteristic
47C4×#13089678C2211yescharacteristic
48C2×#41×C181C2211yescharacteristic
49C4×Q8×C181C2211yescharacteristic
50C4×Q8×C181C2211yescharacteristic
51C4×D4×C181—21no—
52C4×D4×C181—21no—
53C4×D4×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic
55#117×C181—21no—
56#117×C181C2211yescharacteristic
57C2×C4⋊C4×C181—21no—
58C2×C4⋊C4×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362C2311yescharacteristic
61C2×D724C2311yescharacteristic
62C2×C22⋊D181—21no—
63C2×C4×D181—21no—
64#15668439—22no—
65#15668437—22no—
66#15668436—22no—
67#15668434—22no—
68C2×#13089678C2311yescharacteristic
69C2×#13089678C2311yescharacteristic
70C2×#13089678C2311yescharacteristic
71C2×#13089678C2311yescharacteristic
72C4⋊Dic181—21no—
73C4⋊Dic181C2311yescharacteristic
74C4⋊Dic181C2311yescharacteristic
75#15668428—21no—
76#15668428—21no—
77C22⋊Dic181—21no—
78#15668426—21no—
79#15668426—21no—
80#15668426—21no—
81#15668426—21no—
82C4×Dic181—21no—
83#41×C181—22no—
84#41×C181—22no—
85C2×Q8×C181C2311yescharacteristic
86C2×D4×C181—21no—
87C2×D4×C181C2311yescharacteristic
88C22×C4×C181—21no—
89C22×C4×C181—21no—
90C22×C4×C181—21no—
91C22×C4×C181—21no—
92C22×C4×C181C2311yescharacteristic
93C4⋊C4×C181—21no—
94C4⋊C4×C181—21no—
95C4⋊C4×C181—21no—
96C4⋊C4×C181D411yescharacteristic
97C4⋊C4×C181D411yescharacteristic
98C4⋊C4×C181C2311yescharacteristic
99C4⋊C4×C181C2311yescharacteristic
100C22⋊C4×C181—21no—
101C22⋊C4×C181—21no—
102C22⋊C4×C181D411yescharacteristic
103C22⋊C4×C181D411yescharacteristic
104C42×C181—21no—
105C42×C181—21no—
106C42×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109Dic362—21no—
110Dic362—21no—
111Dic362—81no—
112D724—21no—
113D724—21no—
114C22⋊D181—81no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C2×Dic181—21no—
118C4×D181—81no—
119#13089678—21no—
120#13089678—21no—
121#13089678—21no—
122#13089678—21no—
123C23×C181—21no—
124C23×C181C2×D411yescharacteristic
125Q8×C181—21no—
126Q8×C181#4112yes—
127D4×C181—24no—
128D4×C181—21no—
129D4×C181#4112yes—
130C2×C4×C181—24no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—81no—
137C2×C4×C181—81no—
138C2×C4×C181—81no—
139C2×C4×C181C2×D411yescharacteristic
140C2×C4×C181C2×D411yescharacteristic
141C2×C4×C181C2×D411yescharacteristic
142C2×C4×C181C2×D411yescharacteristic
143C2×C4×C181C2×D411yescharacteristic
144C2×C4×C181C2411yescharacteristic
145C22×C181—21no—
146C22×C181—22no—
147C22×C181—21no—
148C22×C181—21no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181C22×D411yescharacteristic
152C2×D181—41no—
153C2×D181—41no—
154C2×D181—41no—
155C4×C181—21no—
156C4×C181—22no—
157C4×C181—21no—
158C4×C181—21no—
159C4×C181—21no—
160C4×C181—21no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181C2×#4111yescharacteristic
164C4×C181C2×#4111yescharacteristic
165Dic181—41no—
166Dic181—41no—
167Dic181—41no—
168C2×C181—41no—
169C2×C181—42no—
170C2×C181#52511yescharacteristic
171C2×C181#57711yescharacteristic
172C2×C181#57711yescharacteristic
173D181—81no—
174C181#312511yescharacteristic, complemented, Sylow
175#3125—1811nomaximal, Sylow
176#542—1811no—
177#520D18111yescharacteristic, complemented
178#483—1811no—
179#481—1811no—
180#476—1811no—
181#475—1811no—
182#464—1811no—
183#463—1811no—
184#452—1811no—
185#449—1811no—
186#442—1811no—
187#441—1811no—
188C4×SD16—1811no—
189C4×SD16—1811no—
190#433—1811no—
191C2×#41C2×D18111yescharacteristic
192C2×Q16—1811no—
193C2×SD16—1811no—
194C2×SD16—1811no—
195C2×D8—1811no—
196C4⋊Q8—1811no—
197#126—3621no—
198#124—3621no—
199#124—1811no—
200#123—3621no—
201C22⋊Q8—3621no—
202C22⋊Q8—1811no—
203#121—1811no—
204C4×Q8—1811no—
205C4×Q8C2×D18111yescharacteristic
206C4×Q8C2×D18111yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—1811no—
210C4×D4C2×D18111yescharacteristic
211C4×D4C2×D18111yescharacteristic
212#117—21no—
213#117C2×D18111yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D18111yescharacteristic
216#106—1811no—
217#106—1811no—
218#106—1811no—
219#106—1811no—
220C4⋊C8—1811no—
221C4⋊C8—1811no—
222#103—1811no—
223#103—1811no—
224#103—1811no—
225#103—1811no—
226#102—1811no—
227#102—1811no—
228#102—1811no—
229#102—1811no—
230C22⋊C8—1811no—
231C22⋊C8—1811no—
232#97—1811no—
233C4×C8—1811no—
234#41—22no—
235#41—22no—
236C2×Q8—3621no—
237C2×Q8—1811no—
238C2×Q8C22×D18111yescharacteristic
239C2×D4—21no—
240C2×D4—3621no—
241C2×D4—1811no—
242C2×D4C22×D18111yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—3621no—
248C22×C4C22×D18111yescharacteristic
249Q16—3622no—
250SD16—3622no—
251SD16—3622no—
252D8—3622no—
253C2×C8—1811no—
254C2×C8—1811no—
255C2×C8—1811no—
256C2×C8—1811no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—3621no—
261C4⋊C4—3621no—
262C4⋊C4—3621no—
263C4⋊C4—1811no—
264C4⋊C4—1811no—
265C4⋊C4C22⋊D18111yescharacteristic
266C4⋊C4C22⋊D18111yescharacteristic
267C4⋊C4C22×D18111yescharacteristic
268C4⋊C4C22×D18111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—3621no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—3621no—
275C22⋊C4—3621no—
276C22⋊C4C22⋊D18111yescharacteristic
277C22⋊C4C22⋊D18111yescharacteristic
278C42—21no—
279C42—21no—
280C42—3621no—
281C42C22×D18111yescharacteristic
282C42C22×D18111yescharacteristic
283C23—21no—
284C23—3621no—
285C23C2×C22⋊D18111yescharacteristic
286Q8—21no—
287Q8—3621no—
288Q8—3621no—
289Q8—14481no—
290Q8#1566844912yes—
291D4—24no—
292D4—21no—
293D4—3621no—
294D4—3621no—
295D4—14481no—
296D4#1566844912yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—3621no—
307C2×C4—3621no—
308C2×C4—3621no—
309C2×C4—14481no—
310C2×C4C2×C22⋊D18111yescharacteristic
311C2×C4C2×C22⋊D18111yescharacteristic
312C2×C4C2×C22⋊D18111yescharacteristic
313C2×C4C2×C22⋊D18111yescharacteristic
314C2×C4C2×C22⋊D18111yescharacteristic
315C2×C4C23×D18111yescharacteristic
316C8—3621no—
317C8—3621no—
318C8—3621no—
319C8—3621no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—7241no—
327C22—7241no—
328C22—7241no—
329C22C22×C22⋊D18111yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—7241no—
339C4—7241no—
340C4—7241no—
341C4C2×#1566844911yescharacteristic
342C4C2×#1566844911yescharacteristic
343C2—41no—
344C2—42no—
345C2—14481no—
346C2#2604179011yescharacteristic
347C2#2604208711yescharacteristic
348C2#2604209011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#520×C181C2
socleC22×C181C22×D4
prime radical#26041424C2
hypercenter#520D181
hypocenterC181#3125
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #26041900C2semidirect
2. #26041609C2semidirect
3. #26041597C2semidirect
4. #26041569C2semidirect
5. #26041564C2semidirect
6. #26041501C2semidirect
7. #26041494C2semidirect
8. #26041441C2semidirect
10. #26041389C2semidirect
11. #26041384C2semidirect
12. C4×#15668436C2semidirect
13. C4×#15668437C2semidirect
14. #26041340C2semidirect
15. #520×C181C2semidirect
174. C181#3125semidirect
177. #520D181semidirect

Maximal subgroups

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

subgroupindex
#260419002
#260416092
#260415972
#260415692
#260415642
#260415012
#260414942
#260414412
#260414242
#260413892
#260413842
C4×#156684362
C4×#156684372
#260413402
#520×C1812
#3125181