Finite Group Databasebeta

← #37546758

Subgroups — #37546758

Order 23168.

418 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042011C211yesmaximal, characteristic, complemented
2#26041950C211yesmaximal, characteristic, complemented
3#26041669C211yesmaximal, characteristic, complemented
4#26041665C211yesmaximal, characteristic, complemented
5#26041654C211yesmaximal, characteristic, complemented
6#26041497C211yesmaximal, characteristic, complemented
7#26041477C211yesmaximal, characteristic, complemented
8#26041475C211yesmaximal, characteristic, complemented
9#26041473C211yesmaximal, characteristic, complemented
10#26041472C211yesmaximal, characteristic, complemented
11#26041408C211yesmaximal, characteristic, complemented
12#26041389C211yesmaximal, characteristic, complemented
13#26041388C211yesmaximal, characteristic, complemented
14#26041364C211yesmaximal, characteristic, complemented
15#463×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×#15668436C2211yescharacteristic
18C2×#15668436C2211yescharacteristic
19C2×D1448C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23C2×#15668434C2211yescharacteristic
24#19153813C2211yescharacteristic
25#19153812C2211yescharacteristic
26#19153812C2211yescharacteristic
27#19153812C2211yescharacteristic
28#19153805C2211yescharacteristic
29#19153802—21no—
30#19153800—21no—
31#19153798—21no—
32#19153790—21no—
33#19153789—21no—
34#19153789—21no—
35Q8×Dic181C2211yescharacteristic
36C4×Dic362C2211yescharacteristic
37C4×D724C2211yescharacteristic
38D4×Dic181C2211yescharacteristic
39#19153778C2211yescharacteristic
40#19153778C2211yescharacteristic
41#19153776—21no—
42#19153747C2211yescharacteristic
43#19153745C2211yescharacteristic
44#19153745C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic
47#19153737C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153727C2211yescharacteristic
50#19153726C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52C2×SD16×C181C2211yescharacteristic
53C2×D8×C181C2211yescharacteristic
54#124×C181C2211yescharacteristic
55C4×D4×C181C2211yescharacteristic
56C4⋊C8×C181C2211yescharacteristic
57#103×C181C2211yescharacteristic
58#102×C181C2211yescharacteristic
59#15668449—44no—
60C2×Dic362D411yescharacteristic
61C2×D724—21no—
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×D724C2311yescharacteristic
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—21no—
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C22×Dic181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76#15668436—22no—
77#15668436—41no—
78D1448—41no—
79D1448—41no—
80#15668434—22no—
81#15668434—22no—
82#15668434—41no—
83C2×#13089678C2311yescharacteristic
84C2×#13089678C2311yescharacteristic
85C4⋊Dic181—21no—
86C4⋊Dic181D411yescharacteristic
87C4⋊Dic181C2311yescharacteristic
88#15668428D411yescharacteristic
89#15668428D411yescharacteristic
90C22⋊Dic181—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C4×Dic181C2311yescharacteristic
99C2×Q8×C181C2311yescharacteristic
100C2×D4×C181C2311yescharacteristic
101C2×D4×C181C2311yescharacteristic
102C22×C4×C181—21no—
103SD16×C181—41no—
104D8×C181—41no—
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181C2311yescharacteristic
108C22⋊C4×C181—21no—
109C22⋊C4×C181—21no—
110C22⋊C4×C181—21no—
111C42×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—21no—
114C22×D181—21no—
115Dic362—22no—
116D724—21no—
117D724—21no—
118D724—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122D724—42no—
123D724—81no—
124C22⋊D181—42no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C22⋊D181—81no—
128C22⋊D181—81no—
129C22⋊D181—81no—
130C2×Dic181—21no—
131C2×Dic181—81no—
132C2×Dic181C2×D411yescharacteristic
133C2×Dic181C2×D411yescharacteristic
134C2×Dic181C2×D411yescharacteristic
135C2×Dic181C2×D411yescharacteristic
136C4×D181—42no—
137C4×D181—42no—
138C4×D181—81no—
139#13089678—21no—
140#13089678#4112yescomplemented
141C23×C181—21no—
142C23×C181—21no—
143Q8×C181—21no—
144Q8×C181—21no—
145D4×C181—21no—
146D4×C181—21no—
147D4×C181—21no—
148D4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—42no—
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×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181C22×D411yescharacteristic
164C2×D181—41no—
165C2×D181—41no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C4×C181—21no—
174C4×C181—21no—
175C4×C181—41no—
176C4×C181—41no—
177C4×C181C2×#4111yescharacteristic
178C4×C181H(5,𝔽2)11yescharacteristic
179Dic181—21no—
180Dic181—21no—
181Dic181—21no—
182Dic181—41no—
183Dic181AGL(1,ℤ/8)12yes—
184C2×C181—81no—
185C2×C181—81no—
186C2×C181#55011yescharacteristic
187C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C181#57611yescharacteristic
189D181—81no—
190D181—81no—
191D181—81no—
192C181#339911yescharacteristic, complemented, Sylow
193#3399—1811nomaximal, Sylow
194#559—1811no—
195#550—1811no—
196#496—1811no—
197#496—1811no—
198#493—1811no—
199#463—1811no—
200#463D18111yescharacteristic, complemented
201#460—1811no—
202#459—1811no—
203#459—1811no—
204#459—1811no—
205#446—1811no—
206#442—1811no—
207#442—1811no—
208C4×SD16—1811no—
209C2×#41—3621no—
210C2×SD16—1811no—
211C2×SD16—1811no—
212C2×SD16C2×D18111yescharacteristic
213C2×D8—1811no—
214C2×D8—1811no—
215C2×D8—1811no—
216C2×D8—1811no—
217C2×D8—1811no—
218C2×D8C2×D18111yescharacteristic
219#127—1811no—
220#127—1811no—
221#127—1811no—
222#127—1811no—
223#124—3621no—
224#124—1811no—
225#124C2×D18111yescharacteristic
226#123—3621no—
227#123—3621no—
228#121—3621no—
229#121—3621no—
230#121—3621no—
231C4×Q8—1811no—
232C4×Q8—1811no—
233C4×D4—3621no—
234C4×D4—1811no—
235C4×D4—1811no—
236C4×D4—1811no—
237C4×D4—1811no—
238C4×D4C2×D18111yescharacteristic
239#106—1811no—
240C4⋊C8—1811no—
241C4⋊C8—1811no—
242C4⋊C8C2×D18111yescharacteristic
243#103C2×D18111yescharacteristic
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102—1811no—
248#102C2×D18111yescharacteristic
249#97—1811no—
250#97—1811no—
251C4×C8—1811no—
252#41—7244no—
253C2×Q8—1811no—
254C2×Q8C22×D18111yescharacteristic
255C2×D4—3621no—
256C2×D4—3621no—
257C2×D4—3621no—
258C2×D4—3621no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—1811no—
264C2×D4—1811no—
265C2×D4—1811no—
266C2×D4C22×D18111yescharacteristic
267C2×D4C22×D18111yescharacteristic
268C22×C4—21no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4—3621no—
272C22×C4—3621no—
273SD16—41no—
274SD16—3622no—
275SD16—7241no—
276D8—41no—
277D8—3622no—
278D8—3622no—
279D8—7241no—
280D8—7241no—
281D8—7241no—
282C2×C8—1811no—
283C2×C8—1811no—
284C2×C8C22×D18111yescharacteristic
285C2×C8C22×D18111yescharacteristic
286C4⋊C4—3621no—
287C4⋊C4—1811no—
288C4⋊C4—1811no—
289C4⋊C4—1811no—
290C4⋊C4—1811no—
291C4⋊C4C22×D18111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C42—3621no—
302C42—1811no—
303C42—1811no—
304C42C22×D18111yescharacteristic
305C23—21no—
306C23—21no—
307C23—3621no—
308C23—3621no—
309C23—3621no—
310Q8—21no—
311Q8—21no—
312Q8—3622no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—3621no—
318D4—3621no—
319D4—3621no—
320D4—3621no—
321D4—3621no—
322D4—3621no—
323D4—14481no—
324D4—14481no—
325D4—14481no—
326D4—14481no—
327D4—7242no—
328D4—7242no—
329D4—7242no—
330D4—7242no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—3621no—
335C2×C4—14481no—
336C2×C4—14481no—
337C2×C4—1811no—
338C2×C4—1811no—
339C2×C4—1811no—
340C2×C4—1811no—
341C2×C4—7242no—
342C2×C4—7242no—
343C2×C4D4×D18111yescharacteristic
344C2×C4D4×D18111yescharacteristic
345C2×C4C23×D18111yescharacteristic
346C8—21no—
347C8—21no—
348C8—3621no—
349C8—1812no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—7241no—
357C22—7241no—
358C22—7241no—
359C22—7241no—
360C22—7241no—
361C22—7241no—
362C22—7241no—
363C22—7241no—
364C22—7241no—
365C22C2×D4×D18111yescharacteristic
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—3621no—
371C4—3621no—
372C4—3621no—
373C4—1812no—
374C4—7241no—
375C4#41×D18111yescharacteristic
376C4#1915386111yescharacteristic
377C2—81no—
378C2—81no—
379C2—14481no—
380C2—14481no—
381C2—14481no—
382C2#2604194711yescharacteristic
383C2AGL(1,ℤ/8)×D18111yescharacteristic
384C2#2604208111yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#463×C181C2
socleC22×C181C22×D4
hypercenter#463D181
hypocenterC181#3399
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #26042011C2semidirect
2. #26041950C2semidirect
3. #26041669C2semidirect
4. #26041665C2semidirect
5. #26041654C2semidirect
6. #26041497C2semidirect
7. #26041477C2semidirect
8. #26041475C2semidirect
9. #26041473C2semidirect
10. #26041472C2semidirect
11. #26041408C2semidirect
12. #26041389C2semidirect
13. #26041388C2semidirect
14. #26041364C2semidirect
15. #463×C181C2semidirect
140. #13089678#41semidirect
192. C181#3399semidirect
200. #463D181semidirect

Maximal subgroups

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

subgroupindex
#260420112
#260419502
#260416692
#260416652
#260416542
#260414972
#260414772
#260414752
#260414732
#260414722
#260414082
#260413892
#260413882
#260413642
#463×C1812
#3399181