Finite Group Databasebeta

← #37544834

Subgroups — #37544834

Order 23168.

376 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#26041902C211yesmaximal, characteristic, complemented
2#26041850C211yesmaximal, characteristic, complemented
3#26041672C211yesmaximal, characteristic, complemented
4#26041660C211yesmaximal, characteristic, complemented
5#26041637C211yesmaximal, characteristic, complemented
6#26041628C211yesmaximal, characteristic, complemented
7#26041499C211yesmaximal, characteristic, complemented
8#26041493C211yesmaximal, characteristic, complemented
9#26041487C211yesmaximal, characteristic, complemented
10#26041483C211yesmaximal, characteristic, complemented
11#26041434C211yesmaximal, characteristic, complemented
12#26041424C211yesmaximal, characteristic
13#26041420C211yesmaximal, characteristic, complemented
14#26041337C211yesmaximal, characteristic, complemented
15#452×C181C211yesmaximal, characteristic, complemented
16C22×Dic362C2211yescharacteristic
17C2×#15668439C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668438C2211yescharacteristic
20C2×#15668438C2211yescharacteristic
21C2×#15668436C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23#19153815C2211yescharacteristic
24#19153814C2211yescharacteristic
25#19153814C2211yescharacteristic
26#19153811—21no—
27#19153805C2211yescharacteristic
28#19153803C2211yescharacteristic
29#19153803C2211yescharacteristic
30#19153802—21no—
31#19153798—21no—
32#19153797—21no—
33#19153797—21no—
34#19153796—21no—
35#19153795—21no—
36#19153795—21no—
37#19153790C2211yescharacteristic
38Q8×Dic181C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153775C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153745C2211yescharacteristic
43#19153741C2211yescharacteristic
44#19153741C2211yescharacteristic
45#19153740C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153739C2211yescharacteristic
48#19153737C2211yescharacteristic
49C22⋊#13089678C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×#41×C181C2211yescharacteristic
53C2×Q16×C181C2211yescharacteristic
54C2×SD16×C181C2211yescharacteristic
55C22⋊Q8×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59C2×Dic362—21no—
60C2×Dic362—21no—
61C2×Dic362—41no—
62C2×Dic362—41no—
63C2×Dic362C2311yescharacteristic
64C2×Dic362C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C22×Dic181—21no—
68C2×C4×D181—21no—
69#15668439—41no—
70#15668439—41no—
71#15668438—41no—
72#15668438—41no—
73#15668436—41no—
74#15668434—41no—
75C2×#13089678C2311yescharacteristic
76C2×#13089678C2311yescharacteristic
77C4⋊Dic181—21no—
78C4⋊Dic181D411yescharacteristic
79C4⋊Dic181D411yescharacteristic
80C4⋊Dic181C2311yescharacteristic
81#15668428—21no—
82#15668428—21no—
83#15668428—21no—
84#15668428—21no—
85#15668428—21no—
86C22⋊Dic181—21no—
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181D411yescharacteristic
91C22⋊Dic181D411yescharacteristic
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
99#41×C181—41no—
100#41×C181—41no—
101C2×Q8×C181C2311yescharacteristic
102C2×Q8×C181C2311yescharacteristic
103C2×D4×C181—21no—
104C2×D4×C181C2311yescharacteristic
105C22×C4×C181—21no—
106C22×C4×C181C2311yescharacteristic
107Q16×C181—41no—
108SD16×C181—41no—
109C2×C8×C181C2311yescharacteristic
110C2×C8×C181C2311yescharacteristic
111C4⋊C4×C181—21no—
112C4⋊C4×C181C2311yescharacteristic
113C22⋊C4×C181—21no—
114C22×D181—21no—
115Dic362—21no—
116Dic362—21no—
117Dic362—21no—
118Dic362—21no—
119Dic362—42no—
120Dic362—81no—
121D724—21no—
122D724—21no—
123C22⋊D181—81no—
124C2×Dic181—21no—
125C2×Dic181—21no—
126C2×Dic181—21no—
127C2×Dic181—42no—
128C2×Dic181C2×D411yescharacteristic
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C4×D181—81no—
133#13089678—21no—
134#13089678—21no—
135C23×C181—21no—
136C23×C181C2×D411yescharacteristic
137Q8×C181—21no—
138Q8×C181—21no—
139Q8×C181—21no—
140Q8×C181—21no—
141D4×C181—21no—
142D4×C181—21no—
143D4×C181—42no—
144C2×C4×C181—21no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181—42no—
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2411yescharacteristic
152C8×C181—21no—
153C8×C181—21no—
154C22×C181—21no—
155C22×C181—21no—
156C22×C181—21no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181C22×D411yescharacteristic
161C2×D181—41no—
162C2×D181—41no—
163C2×D181—41no—
164C4×C181—21no—
165C4×C181—41no—
166C4×C181—41no—
167C4×C181—41no—
168C4×C181H(5,𝔽2)11yescharacteristic
169C4×C181H(5,𝔽2)11yescharacteristic
170Dic181—21no—
171Dic181—21no—
172Dic181—21no—
173Dic181—21no—
174Dic181—41no—
175Dic181—41no—
176Dic181—41no—
177C2×C181—41no—
178C2×C181—81no—
179C2×C181#53511yescharacteristic
180C2×C181#57711yescharacteristic
181C2×C181#57811yescharacteristic
182D181—81no—
183C181#322511yescharacteristic, complemented, Sylow
184#3225—1811nomaximal, Sylow
185#542—1811no—
186#536—1811no—
187#497—1811no—
188#495—1811no—
189#489—1811no—
190#487—1811no—
191#464—1811no—
192#463—1811no—
193#462—1811no—
194#461—1811no—
195#452D18111yescharacteristic, complemented
196#451—1811no—
197#449—1811no—
198#448—1811no—
199#433—1811no—
200C2×#41C2×D18111yescharacteristic
201C22×Q8—1811no—
202C2×Q16—1811no—
203C2×Q16—1811no—
204C2×Q16C2×D18111yescharacteristic
205C2×SD16—1811no—
206C2×SD16—1811no—
207C2×SD16—1811no—
208C2×SD16C2×D18111yescharacteristic
209C2×D8—1811no—
210C4⋊Q8—1811no—
211C4⋊Q8—1811no—
212C4⋊Q8—1811no—
213#126—3621no—
214#124—3621no—
215#124—1811no—
216#124—1811no—
217#124—1811no—
218#123—3621no—
219#123—3621no—
220#123—3621no—
221C22⋊Q8—3621no—
222C22⋊Q8—3621no—
223C22⋊Q8—3621no—
224C22⋊Q8C2×D18111yescharacteristic
225#121—1811no—
226C4×Q8—1811no—
227C4×D4—1811no—
228#117—1811no—
229C4⋊C8—1811no—
230C4⋊C8—1811no—
231#103—1811no—
232#103—1811no—
233#103—1811no—
234#103—1811no—
235#103—1811no—
236#103C2×D18111yescharacteristic
237#102—1811no—
238#102C2×D18111yescharacteristic
239C22⋊C8—1811no—
240C22⋊C8C2×D18111yescharacteristic
241#97—1811no—
242C4×C8—1811no—
243#41—41no—
244#41—41no—
245C2×Q8—3621no—
246C2×Q8—3621no—
247C2×Q8—1811no—
248C2×Q8—1811no—
249C2×Q8—7241no—
250C2×Q8—7241no—
251C2×Q8C22×D18111yescharacteristic
252C2×Q8C22×D18111yescharacteristic
253C2×D4—21no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4C22×D18111yescharacteristic
257C22×C4—21no—
258C22×C4—3621no—
259C22×C4—3621no—
260C22×C4C22×D18111yescharacteristic
261Q16—41no—
262Q16—7241no—
263Q16—7241no—
264SD16—41no—
265SD16—7241no—
266SD16—7241no—
267SD16—7241no—
268D8—7241no—
269C2×C8—1811no—
270C2×C8—1811no—
271C2×C8C22×D18111yescharacteristic
272C2×C8C22×D18111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—3621no—
275C4⋊C4—3621no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4—1811no—
283C4⋊C4C22×D18111yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—3621no—
286C22⋊C4—3621no—
287C22⋊C4—3621no—
288C22⋊C4—3621no—
289C22⋊C4—3621no—
290C22⋊C4—3621no—
291C22⋊C4—3621no—
292C22⋊C4—3621no—
293C22⋊C4—1811no—
294C22⋊C4—1811no—
295C42—3621no—
296C42—1811no—
297C42—1811no—
298C23—21no—
299C23—3621no—
300C23D4×D18111yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—3621no—
306Q8—3621no—
307Q8—3621no—
308Q8—3621no—
309Q8—14481no—
310Q8—7242no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—3621no—
315D4—3621no—
316D4—14481no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—3621no—
326C2×C4—14481no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—1811no—
330C2×C4—1811no—
331C2×C4—7242no—
332C2×C4D4×D18111yescharacteristic
333C2×C4C23×D18111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3621no—
337C8—3621no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—7241no—
345C22—7241no—
346C22—7241no—
347C22C2×D4×D18111yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—3621no—
353C4—3621no—
354C4—3621no—
355C4—3621no—
356C4—7241no—
357C4—7241no—
358C4—7241no—
359C4#1915386111yescharacteristic
360C4#1915386111yescharacteristic
361C2—41no—
362C2—81no—
363C2—14481no—
364C2#2604184411yescharacteristic
365C2#2604208611yescharacteristic
366C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#452×C181C2
socleC22×C181C22×D4
prime radical#26041424C2
hypercenter#452D181
hypocenterC181#3225
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #26041902C2semidirect
2. #26041850C2semidirect
3. #26041672C2semidirect
4. #26041660C2semidirect
5. #26041637C2semidirect
6. #26041628C2semidirect
7. #26041499C2semidirect
8. #26041493C2semidirect
9. #26041487C2semidirect
10. #26041483C2semidirect
11. #26041434C2semidirect
13. #26041420C2semidirect
14. #26041337C2semidirect
15. #452×C181C2semidirect
183. C181#3225semidirect
195. #452D181semidirect

Maximal subgroups

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

subgroupindex
#260419022
#260418502
#260416722
#260416602
#260416372
#260416282
#260414992
#260414932
#260414872
#260414832
#260414342
#260414242
#260414202
#260413372
#452×C1812
#3225181