Finite Group Databasebeta

← #37545606

Subgroups — #37545606

Order 23168.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041964C211yesmaximal, characteristic, complemented
2#26041935C211yesmaximal, characteristic
3#26041632C211yesmaximal, characteristic, complemented
4#26041622C211yesmaximal, characteristic, complemented
5#26041585C211yesmaximal, characteristic, complemented
6#26041521C211yesmaximal, characteristic, complemented
7#26041506C211yesmaximal, characteristic, complemented
8#26041500C211yesmaximal, characteristic, complemented
9#26041442C211yesmaximal, characteristic, complemented
10#26041437C211yesmaximal, characteristic, complemented
11#26041373C211yesmaximal, characteristic, complemented
12#26041342C211yesmaximal, characteristic, complemented
13#26041272C211yesmaximal, characteristic, complemented
14C2×#19153739C211yesmaximal, characteristic, complemented
15#480×C181C211yesmaximal, characteristic, complemented
16C2×#15668448C2211yescharacteristic
17C22×Dic362C2211yescharacteristic
18C2×Dic724C2211yescharacteristic
19C2×Dic724C2211yescharacteristic
20C2×#15668437C2211yescharacteristic
21C22×#13089678C2211yescharacteristic
22C2×C8×D181C2211yescharacteristic
23#19153811—21no—
24#19153807C2211yescharacteristic
25#19153806—21no—
26#19153803C2211yescharacteristic
27#19153802—21no—
28#19153799—21no—
29#19153796C2211yescharacteristic
30#19153796C2211yescharacteristic
31#19153795C2211yescharacteristic
32#19153793—21no—
33#19153788—21no—
34#19153781C2211yescharacteristic
35#19153781C2211yescharacteristic
36D4×Dic181—21no—
37C4×C22⋊D181C2211yescharacteristic
38#19153775—21no—
39#19153774C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153739C2211yescharacteristic
49#19153737C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#121×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#107×C181C2211yescharacteristic
55#107×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668448—22no—
60#15668448—41no—
61C2×Dic362—22no—
62C2×Dic362—21no—
63C2×Dic362—41no—
64C2×Dic362C2311yescharacteristic
65C2×Dic362C2311yescharacteristic
66C2×Dic362C2311yescharacteristic
67C2×C22⋊D181—21no—
68C2×C22⋊D181D411yescharacteristic
69C22×Dic181—21no—
70C22×Dic181—21no—
71C2×C4×D181C2311yescharacteristic
72Dic724—22no—
73Dic724—41no—
74#15668437—41no—
75C2×#13089678—41no—
76C2×#13089678C2311yescharacteristic
77C2×#13089678C2311yescharacteristic
78C8×D181—41no—
79C4⋊Dic181—21no—
80C4⋊Dic181—21no—
81C4⋊Dic181—21no—
82C4⋊Dic181C2311yescharacteristic
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428D411yescharacteristic
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91C22⋊Dic181D411yescharacteristic
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96C4×Dic181—21no—
97C4×Dic181—21no—
98C4×Dic181—21no—
99C4×Dic181C2311yescharacteristic
100C2×D4×C181—21no—
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103C22×C4×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C4⋊C4×C181—21no—
107C4⋊C4×C181C2311yescharacteristic
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22×D181C2×D411yescharacteristic
112Dic362—21no—
113Dic362—21no—
114Dic362—21no—
115Dic362—21no—
116Dic362—21no—
117Dic362—42no—
118Dic362#4112yes—
119C22⋊D181—22no—
120C22⋊D181—42no—
121C2×Dic181—21no—
122C2×Dic181—21no—
123C2×Dic181—21no—
124C2×Dic181—21no—
125C2×Dic181—42no—
126C2×Dic181—42no—
127C2×Dic181C2×D411yescharacteristic
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C4×D181—21no—
131C4×D181—21no—
132#13089678—21no—
133#13089678—21no—
134C23×C181—21no—
135C23×C181C2×D411yescharacteristic
136D4×C181—21no—
137D4×C181—21no—
138D4×C181—42no—
139C2×C4×C181—21no—
140C2×C4×C181—21no—
141C2×C4×C181—21no—
142C2×C4×C181—21no—
143C2×C4×C181—21no—
144C2×C4×C181—42no—
145C2×C4×C181C2×D411yescharacteristic
146C2×C4×C181C2411yescharacteristic
147C8×C181—21no—
148C8×C181—21no—
149C22×C181—21no—
150C22×C181—21no—
151C22×C181—41no—
152C22×C181—41no—
153C22×C181—41no—
154C22×C181#13512yes—
155C22×C181C22×D411yescharacteristic
156C2×D181—21no—
157C2×D181—21no—
158C2×D181—21no—
159C4×C181—21no—
160C4×C181—41no—
161C4×C181—41no—
162C4×C181—41no—
163C4×C181C2×#4111yescharacteristic
164C4×C181H(5,𝔽2)11yescharacteristic
165Dic181—21no—
166Dic181—22no—
167Dic181—21no—
168Dic181—21no—
169Dic181—41no—
170Dic181—41no—
171Dic181—41no—
172C2×C181—22no—
173C2×C181—81no—
174C2×C181#54611yescharacteristic
175C2×C181C2×#13511yescharacteristic
176C2×C181#57811yescharacteristic
177D181—41no—
178C181#330011yescharacteristic, complemented, Sylow
179#3300—1811nomaximal, Sylow
180#552—1811no—
181#548—1811no—
182#488—1811no—
183#485—1811no—
184#480D18111yescharacteristic, complemented
185#479—1811no—
186#467—1811no—
187#465—1811no—
188#464—1811no—
189#452—1811no—
190#451—1811no—
191C4×Q16—1811no—
192C8×D4—1811no—
193#416—1811no—
194C2×#103—1811no—
195C2×#41—1811no—
196C22×Q8—1811no—
197C2×Q16—1811no—
198C2×Q16—1811no—
199C2×SD16—1811no—
200C22×C8—1811no—
201C22×C8—1811no—
202#126—3621no—
203#125—3621no—
204#125—1811no—
205#124—3621no—
206#124—1811no—
207#123—3621no—
208C22⋊Q8—3621no—
209C22⋊Q8—1811no—
210C22⋊Q8—1811no—
211C22⋊Q8—1811no—
212#121—3621no—
213#121C2×D18111yescharacteristic
214C4×Q8—1811no—
215C4×Q8—1811no—
216C4×D4—3621no—
217C4×D4—1811no—
218#117—3621no—
219#117—1811no—
220C2×C4⋊C4C2×D18111yescharacteristic
221#107C2×D18111yescharacteristic
222#107C2×D18111yescharacteristic
223#106—1811no—
224C4⋊C8—1811no—
225#103—1811no—
226#103—1811no—
227#103—1811no—
228#103—1811no—
229#103—1811no—
230#103—1811no—
231#103—1811no—
232#102—1811no—
233#102C2×D18111yescharacteristic
234#102C2×D18111yescharacteristic
235C22⋊C8—1811no—
236C22⋊C8C2×D18111yescharacteristic
237C4×C8—1811no—
238#41—3622no—
239#41—7241no—
240C2×Q8—3622no—
241C2×Q8—3621no—
242C2×Q8—1811no—
243C2×Q8—1811no—
244C2×Q8—1811no—
245C2×Q8—7241no—
246C2×D4—21no—
247C2×D4—3621no—
248C2×D4—1811no—
249C2×D4C22×D18111yescharacteristic
250C22×C4—21no—
251C22×C4—3621no—
252C22×C4—3621no—
253C22×C4—1811no—
254C22×C4C22×D18111yescharacteristic
255Q16—3622no—
256Q16—7241no—
257SD16—7241no—
258C2×C8—1811no—
259C2×C8—1811no—
260C2×C8—7241no—
261C2×C8—7241no—
262C2×C8C22×D18111yescharacteristic
263C2×C8C22×D18111yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—3621no—
266C4⋊C4—3621no—
267C4⋊C4—3621no—
268C4⋊C4—3621no—
269C4⋊C4—3621no—
270C4⋊C4—3621no—
271C4⋊C4—3621no—
272C4⋊C4—1811no—
273C4⋊C4—1811no—
274C4⋊C4C22×D18111yescharacteristic
275C4⋊C4C22×D18111yescharacteristic
276C4⋊C4C22×D18111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—3621no—
279C22⋊C4—3621no—
280C22⋊C4—3621no—
281C22⋊C4—3621no—
282C22⋊C4—3621no—
283C22⋊C4—3621no—
284C22⋊C4—1811no—
285C22⋊C4—1811no—
286C42—3621no—
287C42—3621no—
288C42—3621no—
289C42—1811no—
290C23—21no—
291C23—1811no—
292C23D4×D18111yescharacteristic
293Q8—3621no—
294Q8—3621no—
295Q8—3621no—
296Q8—3621no—
297Q8—3621no—
298Q8—1812no—
299Q8—7242no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—3622no—
304D4—7242no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—3621no—
312C2×C4—3621no—
313C2×C4—3621no—
314C2×C4—3621no—
315C2×C4—3621no—
316C2×C4—3621no—
317C2×C4—1811no—
318C2×C4—1811no—
319C2×C4—1811no—
320C2×C4—7242no—
321C2×C4—7242no—
322C2×C4D4×D18111yescharacteristic
323C2×C4C23×D18111yescharacteristic
324C8—21no—
325C8—21no—
326C8—3621no—
327C8—3621no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—3621no—
334C22—3621no—
335C22—3621no—
336C22#1915383512yes—
337C22C2×D4×D18111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—3621no—
343C4—3622no—
344C4—3621no—
345C4—3621no—
346C4—7241no—
347C4—7241no—
348C4—7241no—
349C4#41×D18111yescharacteristic
350C4#1915386211yescharacteristic
351C2—22no—
352C2—81no—
353C2—7241no—
354C2#2604192111yescharacteristic
355C2C2×#1915383511yescharacteristic
356C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#480×C181C2
socleC22×C181C22×D4
prime radical#26041935C2
hypercenter#480D181
hypocenterC181#3300
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #26041964C2semidirect
3. #26041632C2semidirect
4. #26041622C2semidirect
5. #26041585C2semidirect
6. #26041521C2semidirect
7. #26041506C2semidirect
8. #26041500C2semidirect
9. #26041442C2semidirect
10. #26041437C2semidirect
11. #26041373C2semidirect
12. #26041342C2semidirect
13. #26041272C2semidirect
14. C2×#19153739C2semidirect
15. #480×C181C2semidirect
178. C181#3300semidirect
184. #480D181semidirect

Maximal subgroups

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

subgroupindex
#260419642
#260419352
#260416322
#260416222
#260415852
#260415212
#260415062
#260415002
#260414422
#260414372
#260413732
#260413422
#260412722
C2×#191537392
#480×C1812
#3300181