Finite Group Databasebeta

← #37544763

Subgroups — #37544763

Order 23168.

396 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041828C211yesmaximal, characteristic, complemented
2#26041816C211yesmaximal, characteristic, complemented
3#26041672C211yesmaximal, characteristic, complemented
4#26041665C211yesmaximal, characteristic, complemented
5#26041646C211yesmaximal, characteristic, complemented
6#26041642C211yesmaximal, characteristic, complemented
7#26041501C211yesmaximal, characteristic, complemented
8#26041495C211yesmaximal, characteristic, complemented
9#26041491C211yesmaximal, characteristic, complemented
10#26041440C211yesmaximal, characteristic, complemented
11#26041438C211yesmaximal, characteristic, complemented
12#26041427C211yesmaximal, characteristic, complemented
13#26041425C211yesmaximal, characteristic, complemented
14#26041335C211yesmaximal, characteristic, complemented
15#464×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18C2×#15668439C2211yescharacteristic
19C2×#15668438C2211yescharacteristic
20C2×#15668436C2211yescharacteristic
21C2×#15668436C2211yescharacteristic
22C2×D1448C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24#19153814C2211yescharacteristic
25#19153812C2211yescharacteristic
26#19153811—21no—
27#19153807C2211yescharacteristic
28#19153805C2211yescharacteristic
29#19153804C2211yescharacteristic
30#19153801—21no—
31#19153792C2211yescharacteristic
32#19153791C2211yescharacteristic
33#19153789—21no—
34#19153789—21no—
35C4×D724—21no—
36C4×D724C2211yescharacteristic
37#19153776—21no—
38#19153776—21no—
39#19153773—21no—
40C42×D181C2211yescharacteristic
41C4⋊#13089678C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153740C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153728C2211yescharacteristic
49#19153728C2211yescharacteristic
50#19153726C2211yescharacteristic
51#19153726C2211yescharacteristic
52C2×Q16×C181C2211yescharacteristic
53C2×SD16×C181C2211yescharacteristic
54#124×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668450—41no—
60#15668450—41no—
61#15668448—41no—
62#15668448—41no—
63C2×Dic362C2311yescharacteristic
64C2×D724—21no—
65C2×D724—21no—
66C2×D724C2311yescharacteristic
67C2×D724C2311yescharacteristic
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C22×Dic181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181D411yescharacteristic
75C2×C4×D181D411yescharacteristic
76C2×C4×D181C2311yescharacteristic
77#15668439—41no—
78#15668438—41no—
79#15668436—41no—
80#15668436—41no—
81D1448—41no—
82#15668434—41no—
83C2×#13089678C2311yescharacteristic
84C2×#13089678C2311yescharacteristic
85C4⋊Dic181—21no—
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90#15668428—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98C4×Dic181D411yescharacteristic
99C4×Dic181D411yescharacteristic
100C4×Dic181C2311yescharacteristic
101C2×Q8×C181C2311yescharacteristic
102C2×Q8×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104Q16×C181—41no—
105SD16×C181—41no—
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C22⋊C4×C181—21no—
111C22⋊C4×C181—21no—
112C42×C181—21no—
113C42×C181C2311yescharacteristic
114C22×D181—21no—
115C22×D181—21no—
116C22×D181C2×D411yescharacteristic
117Dic362—21no—
118Dic362—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122D724—21no—
123D724—42no—
124D724—42no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C22⋊D181—42no—
128C2×Dic181—21no—
129C2×Dic181—21no—
130C2×Dic181—42no—
131C2×Dic181C2×D411yescharacteristic
132C2×Dic181C2×D411yescharacteristic
133C2×Dic181C2×D411yescharacteristic
134C4×D181—21no—
135C4×D181—21no—
136C4×D181—41no—
137C4×D181—41no—
138C4×D181—42no—
139C4×D181—42no—
140#13089678—21no—
141#13089678—21no—
142C23×C181—21no—
143Q8×C181—21no—
144Q8×C181—21no—
145Q8×C181—21no—
146Q8×C181—21no—
147D4×C181—21no—
148D4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2411yescharacteristic
155C8×C181—21no—
156C8×C181—21no—
157C22×C181—41no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181C22×D411yescharacteristic
161C2×D181—21no—
162C2×D181—21no—
163C2×D181—21no—
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C4×C181—21no—
171C4×C181—21no—
172C4×C181—41no—
173C4×C181—41no—
174C4×C181—41no—
175C4×C181H(5,𝔽2)11yescharacteristic
176C4×C181H(5,𝔽2)11yescharacteristic
177Dic181—21no—
178Dic181—21no—
179Dic181—21no—
180Dic181—41no—
181Dic181—41no—
182C2×C181—81no—
183C2×C181#53511yescharacteristic
184C2×C181#57511yescharacteristic
185C2×C181#57511yescharacteristic
186D181—41no—
187D181—81no—
188D181—81no—
189C181#321911yescharacteristic, complemented, Sylow
190#3219—1811nomaximal, Sylow
191#532—1811no—
192#529—1811no—
193#497—1811no—
194#496—1811no—
195#491—1811no—
196#490—1811no—
197#464—1811no—
198#464D18111yescharacteristic, complemented
199#463—1811no—
200#463—1811no—
201#452—1811no—
202#452—1811no—
203#449—1811no—
204#449—1811no—
205#432—1811no—
206C2×#41—1811no—
207C2×#41—1811no—
208C2×Q16—1811no—
209C2×Q16C2×D18111yescharacteristic
210C2×SD16—1811no—
211C2×SD16—1811no—
212C2×SD16—1811no—
213C2×SD16C2×D18111yescharacteristic
214C2×D8—1811no—
215C2×D8—1811no—
216C4⋊Q8—1811no—
217#127—1811no—
218#126—3621no—
219#125—1811no—
220#124—1811no—
221#124—1811no—
222#124C2×D18111yescharacteristic
223#123—3621no—
224C22⋊Q8—1811no—
225#121—3621no—
226#121—3621no—
227#121—1811no—
228C4×Q8C2×D18111yescharacteristic
229C4×D4—3621no—
230C4×D4—3621no—
231C4×D4—3621no—
232C4×D4—1811no—
233#117—3621no—
234C2×C42—1811no—
235C4⋊C8—1811no—
236C4⋊C8C2×D18111yescharacteristic
237#103—1811no—
238#103—1811no—
239#103—1811no—
240#103C2×D18111yescharacteristic
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102C2×D18111yescharacteristic
245C22⋊C8—1811no—
246C22⋊C8—1811no—
247#97—1811no—
248#97—1811no—
249#41—7241no—
250#41—7241no—
251#41—7241no—
252#41—7241no—
253C2×Q8—1811no—
254C2×Q8C22×D18111yescharacteristic
255C2×Q8C22×D18111yescharacteristic
256C2×D4—3621no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—1811no—
262C2×D4—1811no—
263C2×D4C22×D18111yescharacteristic
264C22×C4—3621no—
265C22×C4—3621no—
266C22×C4—3621no—
267C22×C4—1811no—
268C22×C4—1811no—
269C22×C4—1811no—
270Q16—41no—
271Q16—7241no—
272SD16—41no—
273SD16—7241no—
274SD16—7241no—
275SD16—7241no—
276D8—7241no—
277D8—7241no—
278C2×C8—1811no—
279C2×C8—1811no—
280C2×C8C22×D18111yescharacteristic
281C2×C8C22×D18111yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—3621no—
284C4⋊C4—3621no—
285C4⋊C4—3621no—
286C4⋊C4—3621no—
287C4⋊C4—3621no—
288C4⋊C4—1811no—
289C4⋊C4C22×D18111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—3621no—
293C22⋊C4—3621no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C42—21no—
300C42—1811no—
301C42—1811no—
302C42—1811no—
303C42C22×D18111yescharacteristic
304C23—21no—
305C23—3621no—
306C23—3621no—
307C23—1811no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—3621no—
313Q8—3621no—
314D4—21no—
315D4—21no—
316D4—3621no—
317D4—3621no—
318D4—3621no—
319D4—3621no—
320D4—7242no—
321D4—7242no—
322D4—7242no—
323D4—7242no—
324D4—7242no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—3621no—
329C2×C4—3621no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—1811no—
333C2×C4—1811no—
334C2×C4—1811no—
335C2×C4—7241no—
336C2×C4—7241no—
337C2×C4—7242no—
338C2×C4—7242no—
339C2×C4—7242no—
340C2×C4D4×D18111yescharacteristic
341C2×C4D4×D18111yescharacteristic
342C2×C4C23×D18111yescharacteristic
343C8—21no—
344C8—21no—
345C8—3621no—
346C8—3621no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—3621no—
351C22—3621no—
352C22—3621no—
353C22—7241no—
354C22—7241no—
355C22—7241no—
356C22—7241no—
357C22—7241no—
358C22—7241no—
359C22C2×D4×D18111yescharacteristic
360C4—21no—
361C4—21no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—3621no—
366C4—3621no—
367C4—3621no—
368C4—7241no—
369C4—7241no—
370C4#1915386111yescharacteristic
371C4#1915386211yescharacteristic
372C2—81no—
373C2—14481no—
374C2—14481no—
375C2—7241no—
376C2#2604184511yescharacteristic
377C2#2604207611yescharacteristic
378C2#2604207811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#464×C181C2
socleC22×C181C22×D4
hypercenter#464D181
hypocenterC181#3219
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #26041828C2semidirect
2. #26041816C2semidirect
3. #26041672C2semidirect
4. #26041665C2semidirect
5. #26041646C2semidirect
6. #26041642C2semidirect
7. #26041501C2semidirect
8. #26041495C2semidirect
9. #26041491C2semidirect
10. #26041440C2semidirect
11. #26041438C2semidirect
12. #26041427C2semidirect
13. #26041425C2semidirect
14. #26041335C2semidirect
15. #464×C181C2semidirect
189. C181#3219semidirect
198. #464D181semidirect

Maximal subgroups

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

subgroupindex
#260418282
#260418162
#260416722
#260416652
#260416462
#260416422
#260415012
#260414952
#260414912
#260414402
#260414382
#260414272
#260414252
#260413352
#464×C1812
#3219181