Finite Group Databasebeta

← #37543824

Subgroups — #37543824

Order 23168.

392 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
1C4×#15668449C211yesmaximal, characteristic, complemented
2#26041617C211yesmaximal, characteristic, complemented
3#26041600C211yesmaximal, characteristic, complemented
4#26041583C211yesmaximal, characteristic, complemented
5#26041576C211yesmaximal, characteristic, complemented
6#26041498C211yesmaximal, characteristic, complemented
7#26041491C211yesmaximal, characteristic, complemented
8#26041439C211yesmaximal, characteristic, complemented
9#26041422C211yesmaximal, characteristic
10#26041389C211yesmaximal, characteristic, complemented
11#26041384C211yesmaximal, characteristic, complemented
12#26041379C211yesmaximal, characteristic, complemented
13#26041377C211yesmaximal, characteristic, complemented
14#26041336C211yesmaximal, characteristic, complemented
15#529×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668437C2211yescharacteristic
19C2×#15668436C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C4×Dic362C2211yescharacteristic
22C4×Dic362C2211yescharacteristic
23C4×D724C2211yescharacteristic
24C4×D724C2211yescharacteristic
25C4×C22⋊D181—21no—
26C4×C22⋊D181—21no—
27#19153775C2211yescharacteristic
28#19153773—21no—
29C42×D181—21no—
30#19153749C2211yescharacteristic
31#19153749C2211yescharacteristic
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
47#19153727C2211yescharacteristic
48#126×C181—21no—
49#125×C181C2211yescharacteristic
50#124×C181C2211yescharacteristic
51#123×C181—21no—
52C22⋊Q8×C181C2211yescharacteristic
53#121×C181C2211yescharacteristic
54C4×Q8×C181C2211yescharacteristic
55C4×D4×C181—21no—
56C4×D4×C181C2211yescharacteristic
57#117×C181—21no—
58C2×C42×C181C2211yescharacteristic
59#15668449—22no—
60#15668449—22no—
61C2×Dic362C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C4×D181—21no—
65C2×C4×D181—21no—
66C2×C4×D181—21no—
67#15668439—22no—
68#15668437—22no—
69#15668436—22no—
70#15668434—22no—
71C2×#13089678C2311yescharacteristic
72C2×#13089678C2311yescharacteristic
73C2×#13089678C2311yescharacteristic
74C2×#13089678C2311yescharacteristic
75C4⋊Dic181C2311yescharacteristic
76C4⋊Dic181C2311yescharacteristic
77#15668428—21no—
78#15668428—21no—
79C22⋊Dic181—21no—
80#15668426—21no—
81#15668426—21no—
82C4×Dic181—21no—
83C4×Dic181—21no—
84C4×Dic181—21no—
85C2×Q8×C181C2311yescharacteristic
86C2×D4×C181—21no—
87C2×D4×C181C2311yescharacteristic
88C22×C4×C181—21no—
89C22×C4×C181D411yescharacteristic
90C22×C4×C181D411yescharacteristic
91C22×C4×C181C2311yescharacteristic
92C4⋊C4×C181—21no—
93C4⋊C4×C181—21no—
94C4⋊C4×C181—21no—
95C4⋊C4×C181—21no—
96C4⋊C4×C181C2311yescharacteristic
97C4⋊C4×C181C2311yescharacteristic
98C22⋊C4×C181—21no—
99C22⋊C4×C181—21no—
100C22⋊C4×C181—21no—
101C22⋊C4×C181—21no—
102C22⋊C4×C181—21no—
103C42×C181—21no—
104C42×C181D411yescharacteristic
105C42×C181D411yescharacteristic
106C42×C181C2311yescharacteristic
107C42×C181C2311yescharacteristic
108C22×D181—21no—
109Dic362—21no—
110Dic362#4112yes—
111D724—21no—
112D724#4112yes—
113C22⋊D181—24no—
114C2×Dic181—21no—
115C2×Dic181—21no—
116C2×Dic181—21no—
117C4×D181—24no—
118C4×D181—42no—
119C4×D181—42no—
120#13089678—21no—
121#13089678—21no—
122#13089678—21no—
123#13089678—21no—
124C23×C181—21no—
125C23×C181C2×D411yescharacteristic
126Q8×C181—21no—
127Q8×C181—21no—
128D4×C181—21no—
129D4×C181—21no—
130D4×C181—42no—
131C2×C4×C181—21no—
132C2×C4×C181—21no—
133C2×C4×C181—21no—
134C2×C4×C181—21no—
135C2×C4×C181—21no—
136C2×C4×C181—41no—
137C2×C4×C181—41no—
138C2×C4×C181—42no—
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—21no—
147C22×C181—21no—
148C22×C181—41no—
149C22×C181—41no—
150C22×C181—41no—
151C22×C181C22×D411yescharacteristic
152C2×D181—22no—
153C2×D181—41no—
154C2×D181—41no—
155C4×C181—21no—
156C4×C181—21no—
157C4×C181—21no—
158C4×C181—21no—
159C4×C181—21no—
160C4×C181—41no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181C2×#4111yescharacteristic
164C4×C181C2×#4111yescharacteristic
165Dic181—22no—
166Dic181—41no—
167Dic181—41no—
168C2×C181—41no—
169C2×C181—81no—
170C2×C181#52511yescharacteristic
171C2×C181#57511yescharacteristic
172C2×C181#57511yescharacteristic
173D181—42no—
174C181#311111yescharacteristic, complemented, Sylow
175#3111—1811nomaximal, Sylow
176#529D18111yescharacteristic, complemented
177C4×#41—1811no—
178#485—1811no—
179#482—1811no—
180#479—1811no—
181#478—1811no—
182#464—1811no—
183#463—1811no—
184#452—1811no—
185#449—1811no—
186#442—1811no—
187#441—1811no—
188#440—1811no—
189#440—1811no—
190#432—1811no—
191C2×#41—1811no—
192C2×Q16—1811no—
193C2×SD16—1811no—
194C2×SD16—1811no—
195C2×D8—1811no—
196#126—21no—
197#125C2×D18111yescharacteristic
198#124C2×D18111yescharacteristic
199#123—21no—
200C22⋊Q8C2×D18111yescharacteristic
201#121C2×D18111yescharacteristic
202C4×Q8—1811no—
203C4×Q8—1811no—
204C4×Q8C2×D18111yescharacteristic
205C4×D4—21no—
206C4×D4—3621no—
207C4×D4—3621no—
208C4×D4—1811no—
209C4×D4—1811no—
210C4×D4C2×D18111yescharacteristic
211#117—21no—
212#117—3621no—
213#117—1811no—
214C2×C42—3621no—
215C2×C42C2×D18111yescharacteristic
216#107—1811no—
217#107—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—
233#97—1811no—
234#41—3622no—
235#41—3622no—
236C2×Q8—1811no—
237C2×Q8C22×D18111yescharacteristic
238C2×D4—21no—
239C2×D4—3621no—
240C2×D4—1811no—
241C2×D4C22×D18111yescharacteristic
242C22×C4—21no—
243C22×C4—3621no—
244C22×C4—3621no—
245C22×C4—3621no—
246C22×C4C22⋊D18111yescharacteristic
247C22×C4C22⋊D18111yescharacteristic
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—21no—
261C4⋊C4—3621no—
262C4⋊C4—3621no—
263C4⋊C4—1811no—
264C4⋊C4—1811no—
265C4⋊C4C22×D18111yescharacteristic
266C4⋊C4C22×D18111yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—3621no—
273C22⋊C4—3621no—
274C22⋊C4—3621no—
275C42—21no—
276C42—3621no—
277C42—3621no—
278C42—3621no—
279C42C22⋊D18111yescharacteristic
280C42C22⋊D18111yescharacteristic
281C42C22×D18111yescharacteristic
282C42C22×D18111yescharacteristic
283C23—21no—
284C23—3621no—
285C23C2×C22⋊D18111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—3621no—
289Q8—1812no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—3624no—
294D4—3621no—
295D4—1812no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—3624no—
305C2×C4—3621no—
306C2×C4—3621no—
307C2×C4—3621no—
308C2×C4—7242no—
309C2×C4—7242no—
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—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3622no—
327C22—7241no—
328C22—7241no—
329C22C22×C22⋊D18111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—3622no—
339C4—7241no—
340C4—7241no—
341C4#41×D18111yescharacteristic
342C4#41×D18111yescharacteristic
343C2—41no—
344C2—81no—
345C2—7242no—
346C2#2604178611yescharacteristic
347C2#2604207711yescharacteristic
348C2#2604207711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#529×C181C2
socleC22×C181C22×D4
prime radical#26041422C2
hypercenter#529D181
hypocenterC181#3111
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#15668449C2semidirect
2. #26041617C2semidirect
3. #26041600C2semidirect
4. #26041583C2semidirect
5. #26041576C2semidirect
6. #26041498C2semidirect
7. #26041491C2semidirect
8. #26041439C2semidirect
10. #26041389C2semidirect
11. #26041384C2semidirect
12. #26041379C2semidirect
13. #26041377C2semidirect
14. #26041336C2semidirect
15. #529×C181C2semidirect
174. C181#3111semidirect
176. #529D181semidirect

Maximal subgroups

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

subgroupindex
C4×#156684492
#260416172
#260416002
#260415832
#260415762
#260414982
#260414912
#260414392
#260414222
#260413892
#260413842
#260413792
#260413772
#260413362
#529×C1812
#3111181