Finite Group Databasebeta

← #37544833

Subgroups — #37544833

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#26041903C211yesmaximal, characteristic, complemented
2#26041854C211yesmaximal, characteristic, complemented
3#26041671C211yesmaximal, characteristic, complemented
4#26041663C211yesmaximal, characteristic, complemented
5#26041641C211yesmaximal, characteristic, complemented
6#26041504C211yesmaximal, characteristic, complemented
7#26041497C211yesmaximal, characteristic, complemented
8#26041488C211yesmaximal, characteristic, complemented
9#26041483C211yesmaximal, characteristic, complemented
10#26041444C211yesmaximal, characteristic, complemented
11#26041436C211yesmaximal, characteristic, complemented
12#26041427C211yesmaximal, characteristic
13#26041419C211yesmaximal, characteristic, complemented
14#26041338C211yesmaximal, characteristic, complemented
15#487×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×Q8×D181C2211yescharacteristic
18C2×Dic724C2211yescharacteristic
19C2×#15668439C2211yescharacteristic
20C2×#15668439C2211yescharacteristic
21C2×#15668438C2211yescharacteristic
22C2×#15668438C2211yescharacteristic
23C2×#15668436C2211yescharacteristic
24C2×#15668436C2211yescharacteristic
25C2×D1448C2211yescharacteristic
26#19153814C2211yescharacteristic
27#19153811—21no—
28#19153805—21no—
29#19153805C2211yescharacteristic
30#19153804C2211yescharacteristic
31#19153804C2211yescharacteristic
32#19153801—21no—
33#19153801—21no—
34#19153801—21no—
35#19153796C2211yescharacteristic
36#19153794—21no—
37#19153794—21no—
38#19153792—21no—
39#19153791C2211yescharacteristic
40#19153781C2211yescharacteristic
41#19153778C2211yescharacteristic
42#19153773C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153739C2211yescharacteristic
46#19153739C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51#19153727C2211yescharacteristic
52C4⋊Q8×C181C2211yescharacteristic
53C4⋊Q8×C181C2211yescharacteristic
54#103×C181C2211yescharacteristic
55#103×C181C2211yescharacteristic
56#103×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58C4×C8×C181C2211yescharacteristic
59#15668450—41no—
60#15668450—41no—
61C2×Dic362—21no—
62C2×Dic362C2311yescharacteristic
63C2×Dic362C2311yescharacteristic
64Q8×D181—41no—
65Q8×D181—41no—
66C2×D724—21no—
67C2×D724—21no—
68C2×D724C2311yescharacteristic
69C2×D724C2311yescharacteristic
70C2×C4×D181—21no—
71C2×C4×D181—21no—
72C2×C4×D181—21no—
73C2×C4×D181C2311yescharacteristic
74Dic724—41no—
75#15668439—41no—
76#15668439—41no—
77#15668438—41no—
78#15668438—41no—
79#15668436—41no—
80#15668436—41no—
81D1448—41no—
82C2×#13089678C2311yescharacteristic
83C2×#13089678C2311yescharacteristic
84C4⋊Dic181—21no—
85#15668428—21no—
86#15668428—21no—
87#15668428—21no—
88#15668428D411yescharacteristic
89#15668428D411yescharacteristic
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426—21no—
99#15668426D411yescharacteristic
100#15668426D411yescharacteristic
101C4×Dic181—21no—
102C4×Dic181C2311yescharacteristic
103C2×Q8×C181—21no—
104C2×Q8×C181C2311yescharacteristic
105C2×Q8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181—21no—
110C4⋊C4×C181—21no—
111C4⋊C4×C181C2311yescharacteristic
112C4⋊C4×C181C2311yescharacteristic
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115C22×D181—21no—
116C22×D181C2×D411yescharacteristic
117Dic362—21no—
118Dic362—21no—
119Dic362—21no—
120Dic362—21no—
121Dic362—42no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—42no—
127D724—81no—
128C2×Dic181—21no—
129C2×Dic181—21no—
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C4×D181—21no—
134C4×D181—21no—
135C4×D181—42no—
136C4×D181—42no—
137C4×D181—81no—
138#13089678—21no—
139#13089678—21no—
140Q8×C181—21no—
141Q8×C181—21no—
142Q8×C181—21no—
143Q8×C181—21no—
144Q8×C181—81no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181C2×D411yescharacteristic
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2411yescharacteristic
152C8×C181—21no—
153C8×C181—21no—
154C22×C181C22×D411yescharacteristic
155C2×D181—21no—
156C2×D181—21no—
157C2×D181—21no—
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×C181—41no—
170C4×C181H(5,𝔽2)11yescharacteristic
171C4×C181H(5,𝔽2)11yescharacteristic
172Dic181—21no—
173Dic181—21no—
174Dic181—21no—
175Dic181—41no—
176Dic181—41no—
177C2×C181#53511yescharacteristic
178C2×C181#57711yescharacteristic
179C2×C181#57811yescharacteristic
180D181—41no—
181D181—81no—
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#487D18111yescharacteristic, complemented
191#464—1811no—
192#463—1811no—
193#462—1811no—
194#461—1811no—
195#452—1811no—
196#451—1811no—
197#449—1811no—
198#448—1811no—
199#433—1811no—
200C2×#41—1811no—
201C22×Q8—1811no—
202C2×Q16—1811no—
203C2×Q16—1811no—
204C2×Q16—1811no—
205C2×SD16—1811no—
206C2×SD16—1811no—
207C2×SD16—1811no—
208C2×SD16—1811no—
209C2×D8—1811no—
210C4⋊Q8—1811no—
211C4⋊Q8C2×D18111yescharacteristic
212C4⋊Q8C2×D18111yescharacteristic
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⋊Q8—1811no—
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#103C2×D18111yescharacteristic
234#103C2×D18111yescharacteristic
235#103C2×D18111yescharacteristic
236#103C2×D18111yescharacteristic
237#102—1811no—
238#102—1811no—
239C22⋊C8—1811no—
240C22⋊C8—1811no—
241#97—1811no—
242C4×C8C2×D18111yescharacteristic
243#41—7241no—
244#41—7241no—
245C2×Q8—21no—
246C2×Q8—3621no—
247C2×Q8—1811no—
248C2×Q8—1811no—
249C2×Q8—7241no—
250C2×Q8—7241no—
251C2×Q8C22×D18111yescharacteristic
252C2×Q8C22×D18111yescharacteristic
253C2×D4—3621no—
254C2×D4—3621no—
255C2×D4—1811no—
256C2×D4—1811no—
257C22×C4—3621no—
258C22×C4—3621no—
259C22×C4—3621no—
260C22×C4—1811no—
261Q16—7241no—
262Q16—7241no—
263Q16—7241no—
264SD16—7241no—
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—21no—
275C4⋊C4—21no—
276C4⋊C4—3621no—
277C4⋊C4—3621no—
278C4⋊C4—3621no—
279C4⋊C4—3621no—
280C4⋊C4—1811no—
281C4⋊C4—1811no—
282C4⋊C4C22×D18111yescharacteristic
283C4⋊C4C22×D18111yescharacteristic
284C22⋊C4—3621no—
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—
297C42C22×D18111yescharacteristic
298C23—3621no—
299C23—3621no—
300C23—1811no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—81no—
306Q8—3621no—
307Q8—3621no—
308Q8—3621no—
309Q8—3621no—
310Q8—7242no—
311D4—3621no—
312D4—3621no—
313D4—3621no—
314D4—3621no—
315D4—14481no—
316D4—7242no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—3621no—
322C2×C4—3621no—
323C2×C4—3621no—
324C2×C4—3621no—
325C2×C4—14481no—
326C2×C4—1811no—
327C2×C4—1811no—
328C2×C4—1811no—
329C2×C4—7242no—
330C2×C4—7242no—
331C2×C4D4×D18111yescharacteristic
332C2×C4D4×D18111yescharacteristic
333C2×C4C23×D18111yescharacteristic
334C8—21no—
335C8—21no—
336C8—3621no—
337C8—3621no—
338C22—3621no—
339C22—3621no—
340C22—3621no—
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—41no—
354C4—3621no—
355C4—3621no—
356C4—3621no—
357C4—7241no—
358C4—7241no—
359C4#1915386211yescharacteristic
360C4#1915386211yescharacteristic
361C2—14481no—
362C2—14481no—
363C2—7241no—
364C2#2604184711yescharacteristic
365C2#2604208511yescharacteristic
366C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#487×C181C2
socleC22×C181C22×D4
prime radical#26041427C2
hypercenter#487D181
hypocenterC181#3225
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #26041903C2semidirect
2. #26041854C2semidirect
3. #26041671C2semidirect
4. #26041663C2semidirect
5. #26041641C2semidirect
6. #26041504C2semidirect
7. #26041497C2semidirect
8. #26041488C2semidirect
9. #26041483C2semidirect
10. #26041444C2semidirect
11. #26041436C2semidirect
13. #26041419C2semidirect
14. #26041338C2semidirect
15. #487×C181C2semidirect
183. C181#3225semidirect
190. #487D181semidirect

Maximal subgroups

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

subgroupindex
#260419032
#260418542
#260416712
#260416632
#260416412
#260415042
#260414972
#260414882
#260414832
#260414442
#260414362
#260414272
#260414192
#260413382
#487×C1812
#3225181