Finite Group Databasebeta

← #37546046

Subgroups — #37546046

Order 23168.

430 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041947C211yesmaximal, characteristic, complemented
2#26041930C211yesmaximal, characteristic, complemented
3#26041624C211yesmaximal, characteristic, complemented
4#26041599C211yesmaximal, characteristic, complemented
5#26041563C211yesmaximal, characteristic, complemented
6#26041533C211yesmaximal, characteristic, complemented
7#26041530C211yesmaximal, characteristic, complemented
8#26041473C211yesmaximal, characteristic, complemented
9#26041426C211yesmaximal, characteristic, complemented
10#26041425C211yesmaximal, characteristic, complemented
11#26041366C211yesmaximal, characteristic, complemented
12#26041354C211yesmaximal, characteristic, complemented
13#26041278C211yesmaximal, characteristic, complemented
14#26041277C211yesmaximal, characteristic, complemented
15#481×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×#15668449C2211yescharacteristic
18C2×#15668448C2211yescharacteristic
19C2×#15668438C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22C2×#15668433C2211yescharacteristic
23C2×#15668432C2211yescharacteristic
24#19153815C2211yescharacteristic
25#19153812—21no—
26#19153812C2211yescharacteristic
27#19153801—21no—
28#19153799—21no—
29#19153794—21no—
30#19153791C2211yescharacteristic
31#19153791C2211yescharacteristic
32#19153790C2211yescharacteristic
33#19153789—21no—
34#19153788—21no—
35#19153781C2211yescharacteristic
36#19153778C2211yescharacteristic
37C4×C22⋊D181C2211yescharacteristic
38#19153776—21no—
39C4⋊C4×D181C2211yescharacteristic
40#19153747C2211yescharacteristic
41#19153745C2211yescharacteristic
42#19153741C2211yescharacteristic
43#19153739C2211yescharacteristic
44#19153739C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153737C2211yescharacteristic
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic
49#19153736C2211yescharacteristic
50#19153728C2211yescharacteristic
51C8×Dic181C2211yescharacteristic
52#121×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic
54#106×C181C2211yescharacteristic
55#106×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic
58C22⋊C8×C181C2211yescharacteristic
59#15668449—22no—
60#15668449—41no—
61#15668449—44no—
62#15668448—22no—
63#15668448—41no—
64C2×Dic362—21no—
65C2×Dic362C2311yescharacteristic
66C2×D724—21no—
67C2×D724—21no—
68C2×D724C2311yescharacteristic
69C2×D724C2311yescharacteristic
70C2×C22⋊D181—21no—
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181D411yescharacteristic
76C22×Dic181—21no—
77C2×C4×D181—21no—
78C2×C4×D181—21no—
79C2×C4×D181—21no—
80C2×C4×D181C2311yescharacteristic
81#15668438—22no—
82D1448—41no—
83#15668434—41no—
84#15668433—41no—
85#15668432—41no—
86C2×#13089678C2311yescharacteristic
87C2×#13089678C2311yescharacteristic
88C4⋊Dic181C2311yescharacteristic
89#15668428—21no—
90#15668428—21no—
91#15668428—21no—
92#15668428D411yescharacteristic
93C22⋊Dic181D411yescharacteristic
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426D411yescharacteristic
99C4×Dic181—21no—
100C4×Dic181C2311yescharacteristic
101C2×D4×C181—21no—
102C2×D4×C181C2311yescharacteristic
103C22×C4×C181—21no—
104C22×C4×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C4⋊C4×C181—21no—
108C4⋊C4×C181C2311yescharacteristic
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C22⋊C4×C181—21no—
112C22×D181—21no—
113C22×D181—21no—
114C22×D181C2×D411yescharacteristic
115Dic362—21no—
116Dic362—42no—
117Dic362#4112yescomplemented
118D724—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122D724—42no—
123D724—81no—
124C22⋊D181—22no—
125C22⋊D181—42no—
126C22⋊D181—42no—
127C22⋊D181—42no—
128C22⋊D181—42no—
129C22⋊D181—81no—
130C2×Dic181—21no—
131C2×Dic181—21no—
132C2×Dic181—42no—
133C2×Dic181C2×D411yescharacteristic
134C2×Dic181C2×D411yescharacteristic
135C2×Dic181C2×D411yescharacteristic
136C4×D181—21no—
137C4×D181—21no—
138C4×D181—42no—
139C4×D181—42no—
140C4×D181—42no—
141#13089678—21no—
142#13089678—21no—
143C23×C181—21no—
144C23×C181C2×D411yescharacteristic
145D4×C181—21no—
146D4×C181—21no—
147D4×C181—81no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181—21no—
153C2×C4×C181—42no—
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2411yescharacteristic
156C8×C181—21no—
157C8×C181—21no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—21no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181—41no—
164C22×C181C22×D411yescharacteristic
165C2×D181—21no—
166C2×D181—21no—
167C2×D181—21no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C4×C181—21no—
175C4×C181—41no—
176C4×C181—41no—
177C4×C181—41no—
178C4×C181C2×#4111yescharacteristic
179C4×C181H(5,𝔽2)11yescharacteristic
180Dic181—21no—
181Dic181—22no—
182Dic181—21no—
183Dic181—41no—
184Dic181AGL(1,ℤ/8)12yes—
185C2×C181—41no—
186C2×C181—81no—
187C2×C181#54611yescharacteristic
188C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C181#57711yescharacteristic
190D181—41no—
191D181—81no—
192D181—81no—
193C181#333211yescharacteristic, complemented, Sylow
194#3332—1811nomaximal, Sylow
195#550—1811no—
196#547—1811no—
197#486—1811no—
198#481—1811no—
199#481D18111yescharacteristic, complemented
200#475—1811no—
201#469—1811no—
202#469—1811no—
203#459—1811no—
204#449—1811no—
205#449—1811no—
206C4×SD16—1811no—
207#436—1811no—
208#417—1811no—
209#417—1811no—
210C2×#41—3621no—
211C2×#41—1811no—
212C2×#41—1811no—
213C2×SD16—1811no—
214C2×D8—1811no—
215C2×D8—1811no—
216C2×M16—1811no—
217C2×M16—1811no—
218C4⋊Q8—1811no—
219#127—3621no—
220#127—1811no—
221#123—3621no—
222#123—3621no—
223C22⋊Q8—3621no—
224#121—3621no—
225#121—3621no—
226#121—1811no—
227#121—1811no—
228#121—1811no—
229#121C2×D18111yescharacteristic
230C4×Q8—1811no—
231C4×D4—3621no—
232C4×D4—1811no—
233C4×D4—1811no—
234C2×C4⋊C4—1811no—
235C2×C4⋊C4C2×D18111yescharacteristic
236#106—1811no—
237#106C2×D18111yescharacteristic
238#106C2×D18111yescharacteristic
239C4⋊C8—1811no—
240#103—1811no—
241#103—1811no—
242#103—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102—1811no—
248#102C2×D18111yescharacteristic
249#102C2×D18111yescharacteristic
250C22⋊C8—1811no—
251C22⋊C8C2×D18111yescharacteristic
252C4×C8—1811no—
253#41—3622no—
254#41—3622no—
255#41—7241no—
256#41—7244no—
257#41—7241no—
258C2×Q8—3621no—
259C2×Q8—1811no—
260C2×D4—21no—
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—1811no—
269C2×D4—1811no—
270C2×D4—1811no—
271C2×D4C22×D18111yescharacteristic
272C22×C4—21no—
273C22×C4—3621no—
274C22×C4—3621no—
275C22×C4—3621no—
276C22×C4—3621no—
277C22×C4—1811no—
278C22×C4C22×D18111yescharacteristic
279SD16—3622no—
280D8—7241no—
281D8—7241no—
282M16—7241no—
283M16—7241no—
284C2×C8—1811no—
285C2×C8—1811no—
286C2×C8C22×D18111yescharacteristic
287C2×C8C22×D18111yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—3621no—
290C4⋊C4—3621no—
291C4⋊C4—3621no—
292C4⋊C4—1811no—
293C4⋊C4—1811no—
294C4⋊C4C22×D18111yescharacteristic
295C4⋊C4C22×D18111yescharacteristic
296C4⋊C4C22×D18111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—1811no—
303C22⋊C4—1811no—
304C42—3621no—
305C42—1811no—
306C23—21no—
307C23—3621no—
308C23—3621no—
309C23—1811no—
310C23D4×D18111yescharacteristic
311Q8—3621no—
312Q8—1812no—
313Q8—7242no—
314D4—21no—
315D4—21no—
316D4—81no—
317D4—3622no—
318D4—3621no—
319D4—3621no—
320D4—3621no—
321D4—3621no—
322D4—14481no—
323D4—14481no—
324D4—7242no—
325D4—7242no—
326D4—7242no—
327D4—7242no—
328D4—7242no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—3621no—
336C2×C4—3621no—
337C2×C4—3621no—
338C2×C4—3621no—
339C2×C4—1811no—
340C2×C4—1811no—
341C2×C4—1811no—
342C2×C4—7242no—
343C2×C4—7242no—
344C2×C4—7242no—
345C2×C4—7242no—
346C2×C4D4×D18111yescharacteristic
347C2×C4C23×D18111yescharacteristic
348C8—21no—
349C8—21no—
350C8—3621no—
351C8—3621no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—3621no—
359C22—3621no—
360C22—3621no—
361C22—7241no—
362C22—7241no—
363C22—7241no—
364C22—7241no—
365C22—7241no—
366C22—7241no—
367C22C2×D4×D18111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—3621no—
373C4—3622no—
374C4—3621no—
375C4—1812no—
376C4—7241no—
377C4#41×D18111yescharacteristic
378C4#1915386211yescharacteristic
379C2—41no—
380C2—81no—
381C2—14481no—
382C2—14481no—
383C2—7241no—
384C2#2604192111yescharacteristic
385C2AGL(1,ℤ/8)×D18111yescharacteristic
386C2#2604208511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#481×C181C2
socleC22×C181C22×D4
hypercenter#481D181
hypocenterC181#3332
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #26041947C2semidirect
2. #26041930C2semidirect
3. #26041624C2semidirect
4. #26041599C2semidirect
5. #26041563C2semidirect
6. #26041533C2semidirect
7. #26041530C2semidirect
8. #26041473C2semidirect
9. #26041426C2semidirect
10. #26041425C2semidirect
11. #26041366C2semidirect
12. #26041354C2semidirect
13. #26041278C2semidirect
14. #26041277C2semidirect
15. #481×C181C2semidirect
117. Dic362#41semidirect
193. C181#3332semidirect
199. #481D181semidirect

Maximal subgroups

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

subgroupindex
#260419472
#260419302
#260416242
#260415992
#260415632
#260415332
#260415302
#260414732
#260414262
#260414252
#260413662
#260413542
#260412782
#260412772
#481×C1812
#3332181