Finite Group Databasebeta

← #37545512

Subgroups — #37545512

Order 23168.

460 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042090C211yesmaximal, characteristic, complemented
2#26042087C211yesmaximal, characteristic, complemented
3#26042086C211yesmaximal, characteristic, complemented
4#26041650C211yesmaximal, characteristic, complemented
5#26041544C211yesmaximal, characteristic, complemented
6#26041542C211yesmaximal, characteristic, complemented
7#26041540C211yesmaximal, characteristic, complemented
8#26041539C211yesmaximal, characteristic, complemented
9#26041462C211yesmaximal, characteristic, complemented
10#26041460C211yesmaximal, characteristic, complemented
11#26041447C211yesmaximal, characteristic, complemented
12#26041445C211yesmaximal, characteristic, complemented
13#26041396C211yesmaximal, characteristic, complemented
14#26041394C211yesmaximal, characteristic, complemented
15#577×C181C211yesmaximal, characteristic, complemented
16#19153863C2211yescharacteristic
17#19153862C2211yescharacteristic, complemented
18#19153848—21no—
19#19153847—21no—
20#19153847C2211yescharacteristic, complemented
21#19153846—21no—
22#19153846C2211yescharacteristic, complemented
23#19153846C2211yescharacteristic, complemented
24#19153842—21no—
25#19153842C2211yescharacteristic
26#19153841—21no—
27#19153841C2211yescharacteristic
28#19153841C2211yescharacteristic
29#19153840—21no—
30#19153837—21no—
31#19153836—21no—
32#19153836—21no—
33#19153836C2211yescharacteristic
34C2×#15668438C2211yescharacteristic, complemented
35C2×#15668437—21no—
36C2×#15668437C2211yescharacteristic, complemented
37C2×#15668436—21no—
38C2×#15668436C2211yescharacteristic, complemented
39SD16×D181—21no—
40#19153823C2211yescharacteristic, complemented
41#19153823C2211yescharacteristic, complemented
42#19153822C2211yescharacteristic, complemented
43#19153814C2211yescharacteristic, complemented
44#19153812C2211yescharacteristic
45#19153752C2211yescharacteristic, complemented
46#19153751C2211yescharacteristic, complemented
47#19153743C2211yescharacteristic, complemented
48#19153743C2211yescharacteristic, complemented
49#19153743C2211yescharacteristic, complemented
50#19153742C2211yescharacteristic, complemented
51#19153735C2211yescharacteristic, complemented
52#19153734C2211yescharacteristic, complemented
53#19153733C2211yescharacteristic, complemented
54#19153732C2211yescharacteristic, complemented
55C8×Dic181C2211yescharacteristic, complemented
562−1+4×C181C2211yescharacteristic
57H(5,𝔽2)×C181C2211yescharacteristic, complemented
58#137×C181—21no—
59#137×C181C2211yescharacteristic, complemented
60AGL(1,ℤ/8)×C181—21no—
61AGL(1,ℤ/8)×C181C2211yescharacteristic
62#135×C181—21no—
63#135×C181C2211yescharacteristic
64C2×SD16×C181—21no—
65C2×SD16×C181C2211yescharacteristic, complemented
66#131×C181C2211yescharacteristic, complemented
67#15668450—21no—
68#15668449—21no—
69#15668449—21no—
70#15668449C2311yescharacteristic
71#15668448—21no—
72#15668448—41no—
73C2×Dic362—21no—
74C2×Dic362C2311yescharacteristic
75Q8×D181—21no—
76C2×D724—21no—
77C2×D724C2311yescharacteristic
78C2×C22⋊D181—41no—
79D4×D181—21no—
80D4×D181—41no—
81#15668439—21no—
82#15668439—21no—
83#15668439—21no—
84#15668439D411yescharacteristic, complemented
85#15668438—21no—
86#15668438—21no—
87#15668437—21no—
88#15668437—21no—
89#15668437—21no—
90#15668437—21no—
91#15668437—21no—
92#15668437D411yescharacteristic, complemented
93#15668436—21no—
94#15668436—21no—
95#15668436—21no—
96#15668436—21no—
97#15668436—21no—
98#15668436D411yescharacteristic, complemented
99#15668434—21no—
100#15668434—21no—
101#15668434—21no—
102#15668434D411yescharacteristic, complemented
103#15668433—21no—
104#15668433—21no—
105#15668433C2311yescharacteristic
106#15668433C2311yescharacteristic
107#15668433C2311yescharacteristic
108#15668432—21no—
109C2×#13089678—21no—
110C2×#13089678—21no—
111C2×#13089678C2311yescharacteristic
112C8×D181—21no—
113#15668428—41no—
114C4×Dic181C2311yescharacteristic
115#41×C181—21no—
116#41×C181—21no—
117#41×C181—21no—
118#41×C181—21no—
119#41×C181—41no—
120#41×C181C2311yescharacteristic
121#41×C181C2311yescharacteristic
122#41×C181C2311yescharacteristic
123C2×Q8×C181—21no—
124C2×Q8×C181—21no—
125C2×Q8×C181C2311yescharacteristic
126C2×D4×C181—21no—
127C2×D4×C181—21no—
128C2×D4×C181—41no—
129C2×D4×C181C2311yescharacteristic
130Q16×C181—21no—
131Q16×C181D411yescharacteristic, complemented
132SD16×C181—21no—
133SD16×C181—21no—
134SD16×C181—21no—
135SD16×C181—21no—
136SD16×C181D411yescharacteristic, complemented
137SD16×C181D411yescharacteristic, complemented
138D8×C181—21no—
139D8×C181D411yescharacteristic, complemented
140M16×C181—21no—
141M16×C181C2311yescharacteristic
142C2×C8×C181—21no—
143C2×C8×C181C2311yescharacteristic
144C22×D181—21no—
145C22×D181—41no—
146Dic362—21no—
147Dic362—21no—
148Dic362—41no—
149Dic362C2×D411yescharacteristic
150D724—21no—
151D724—21no—
152D724—41no—
153D724C2×D411yescharacteristic
154C22⋊D181—21no—
155C22⋊D181—41no—
156C22⋊D181—41no—
157C22⋊D181—82no—
158C2×Dic181—21no—
159C2×Dic181—21no—
160C2×Dic181—41no—
161C4×D181—21no—
162C4×D181—41no—
163C4×D181—41no—
164#13089678—21no—
165#13089678—21no—
166#13089678—21no—
167#13089678C2×D411yescharacteristic
168#13089678C2×D411yescharacteristic
169C23×C181—21no—
170C23×C181—41no—
171Q8×C181—21no—
172Q8×C181—21no—
173Q8×C181—41no—
174Q8×C181C2×D411yescharacteristic
175Q8×C181C2×D411yescharacteristic
176Q8×C181C2×D411yescharacteristic
177D4×C181—21no—
178D4×C181—21no—
179D4×C181—21no—
180D4×C181—21no—
181D4×C181—21no—
182D4×C181—41no—
183D4×C181—41no—
184D4×C181—41no—
185D4×C181C2×D411yescharacteristic
186D4×C181C2×D411yescharacteristic
187D4×C181C2×D411yescharacteristic
188C2×C4×C181—21no—
189C2×C4×C181—21no—
190C2×C4×C181—21no—
191C2×C4×C181—21no—
192C2×C4×C181—41no—
193C2×C4×C181—41no—
194C2×C4×C181—41no—
195C2×C4×C181C2411yescharacteristic
196C8×C181—21no—
197C8×C181C2×D411yescharacteristic
198C8×C181C2×D411yescharacteristic
199C22×C181—21no—
200C22×C181—21no—
201C22×C181—21no—
202C22×C181—41no—
203C22×C181—81no—
204C22×C181—161no—
205C22×C181H(5,𝔽2)11yescharacteristic
206C2×D181—21no—
207C2×D181—41no—
208C2×D181—81no—
209C2×D181—161no—
210C4×C181—21no—
211C4×C181—21no—
212C4×C181—21no—
213C4×C181—41no—
214C4×C181C22×D411yescharacteristic
215C4×C181C22×D411yescharacteristic
216Dic181—22no—
217Dic181—21no—
218Dic181—41no—
219C2×C181—21no—
220C2×C181—41no—
221C2×C181—41no—
222C2×C181—41no—
223C2×C181—81no—
224C2×C181D4211yescharacteristic
225D181—41no—
226D181—81no—
227C181#329111yescharacteristic, complemented, Sylow
228#3291—1811nomaximal, Sylow
229#577—1811no—
230#577—1811no—
231#577—1811no—
232#577D18111yescharacteristic, complemented
233#492—1811no—
234#471—1811no—
235#471—1811no—
236#471—1811no—
237#471—1811no—
238#456—1811no—
239#456—1811no—
240#453—1811no—
241#453—1811no—
242#443—1811no—
243#443—1811no—
2442−1+4—1811no—
2452−1+4C2×D18111yescharacteristic
246H(5,𝔽2)—1811no—
247H(5,𝔽2)C2×D18111yescharacteristic, complemented
248#137—21no—
249#137—3621no—
250#137—3621no—
251#137—3621no—
252#137—1811no—
253#137—1811no—
254#137—1811no—
255#137C2×D18111yescharacteristic, complemented
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—3621no—
258AGL(1,ℤ/8)—3621no—
259AGL(1,ℤ/8)—3621no—
260AGL(1,ℤ/8)—1811no—
261AGL(1,ℤ/8)—1811no—
262AGL(1,ℤ/8)—1811no—
263AGL(1,ℤ/8)C2×D18111yescharacteristic
264#135—21no—
265#135—3621no—
266#135—3621no—
267#135—3621no—
268#135—1811no—
269#135C2×D18111yescharacteristic
270C2×SD16—21no—
271C2×SD16—3621no—
272C2×SD16—3621no—
273C2×SD16—3621no—
274C2×SD16—1811no—
275C2×SD16—1811no—
276C2×SD16—1811no—
277C2×SD16C2×D18111yescharacteristic, complemented
278#131—1811no—
279#131—1811no—
280#131—1811no—
281#131C2×D18111yescharacteristic, complemented
282C4⋊Q8—1811no—
283#127—1811no—
284#108—1811no—
285#108—1811no—
286#104—1811no—
287#104—1811no—
288#104—1811no—
289#104—1811no—
290#101—1811no—
291#101—1811no—
292#100—1811no—
293#100—1811no—
294C4×C8—1811no—
295#41—21no—
296#41—21no—
297#41—21no—
298#41—21no—
299#41—41no—
300#41—3621no—
301#41—3621no—
302#41—3621no—
303#41—3621no—
304#41—1811no—
305#41—7241no—
306#41C22×D18111yescharacteristic
307#41C22×D18111yescharacteristic
308#41C22×D18111yescharacteristic
309C2×Q8—21no—
310C2×Q8—21no—
311C2×Q8—3621no—
312C2×Q8—3621no—
313C2×Q8—1811no—
314C2×Q8C22×D18111yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—3621no—
319C2×D4—3621no—
320C2×D4—1811no—
321C2×D4—7241no—
322C2×D4—7241no—
323C2×D4C22×D18111yescharacteristic
324Q16—21no—
325Q16—3621no—
326Q16—3621no—
327Q16—3621no—
328Q16—1811no—
329Q16C22⋊D18111yescharacteristic, complemented
330SD16—21no—
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—3621no—
335SD16—3621no—
336SD16—3621no—
337SD16—3621no—
338SD16—3621no—
339SD16—3621no—
340SD16—3621no—
341SD16—3621no—
342SD16—3621no—
343SD16—3621no—
344SD16—3621no—
345SD16—3621no—
346SD16—1811no—
347SD16—1811no—
348SD16C22⋊D18111yescharacteristic, complemented
349SD16C22⋊D18111yescharacteristic, complemented
350D8—21no—
351D8—3621no—
352D8—3621no—
353D8—3621no—
354D8—1811no—
355D8C22⋊D18111yescharacteristic, complemented
356M16—21no—
357M16—3621no—
358M16—3621no—
359M16—3621no—
360M16—1811no—
361M16—1811no—
362M16—1811no—
363M16C22×D18111yescharacteristic
364C2×C8—21no—
365C2×C8—3621no—
366C2×C8—3621no—
367C2×C8—3621no—
368C2×C8—1811no—
369C2×C8C22×D18111yescharacteristic
370C4⋊C4—7241no—
371C42—1811no—
372C23—21no—
373C23—41no—
374C23—3621no—
375C23—7241no—
376Q8—21no—
377Q8—21no—
378Q8—41no—
379Q8—3621no—
380Q8—3621no—
381Q8—1811no—
382Q8—7241no—
383Q8D4×D18111yescharacteristic
384Q8C2×C22⋊D18111yescharacteristic
385Q8C2×C22⋊D18111yescharacteristic
386D4—21no—
387D4—21no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—3621no—
395D4—3621no—
396D4—3621no—
397D4—14482no—
398D4—1811no—
399D4—7241no—
400D4—7241no—
401D4—7241no—
402D4D4×D18111yescharacteristic
403D4C2×C22⋊D18111yescharacteristic
404D4C2×C22⋊D18111yescharacteristic
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—3621no—
413C2×C4—3621no—
414C2×C4—3621no—
415C2×C4—7241no—
416C2×C4—7241no—
417C2×C4—7241no—
418C2×C4C23×D18111yescharacteristic
419C8—21no—
420C8—3621no—
421C8—3621no—
422C8—3621no—
423C8—1811no—
424C8—1811no—
425C8C2×C22⋊D18111yescharacteristic
426C8C2×C22⋊D18111yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—41no—
431C22—81no—
432C22—161no—
433C22—28961no—
434C22—3621no—
435C22—14481no—
436C22—7241no—
437C22#1915386111yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—41no—
442C4—3622no—
443C4—3621no—
444C4—7241no—
445C4C2×D4×D18111yescharacteristic
446C4C22×C22⋊D18111yescharacteristic
447C2—21no—
448C2—41no—
449C2—41no—
450C2—41no—
451C2—81no—
452C2—14481no—
453C2—7241no—
454C2D4×C22⋊D18111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#577×C181C2
socleC2×C181D42
hypercenter#577D181
hypocenterC181#3291
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ #577

Complements

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

NH ≅ G/Ntype
1. #26042090C2semidirect
2. #26042087C2semidirect
3. #26042086C2semidirect
4. #26041650C2semidirect
5. #26041544C2semidirect
6. #26041542C2semidirect
7. #26041540C2semidirect
8. #26041539C2semidirect
9. #26041462C2semidirect
10. #26041460C2semidirect
11. #26041447C2semidirect
12. #26041445C2semidirect
13. #26041396C2semidirect
14. #26041394C2semidirect
15. #577×C181C2semidirect
17. #19153862C22semidirect
20. #19153847C22semidirect
22. #19153846C22semidirect
23. #19153846C22semidirect
34. C2×#15668438C22semidirect
36. C2×#15668437C22semidirect
38. C2×#15668436C22semidirect
40. #19153823C22semidirect
41. #19153823C22semidirect
42. #19153822C22semidirect
43. #19153814C22semidirect
45. #19153752C22semidirect
46. #19153751C22semidirect
47. #19153743C22semidirect
48. #19153743C22semidirect
49. #19153743C22semidirect
50. #19153742C22semidirect
51. #19153735C22semidirect
52. #19153734C22semidirect
53. #19153733C22semidirect
54. #19153732C22semidirect
55. C8×Dic181C22semidirect
57. H(5,𝔽2)×C181C22semidirect
59. #137×C181C22semidirect
65. C2×SD16×C181C22semidirect
66. #131×C181C22semidirect
84. #15668439D4semidirect
92. #15668437D4semidirect
98. #15668436D4semidirect
102. #15668434D4semidirect
131. Q16×C181D4semidirect
136. SD16×C181D4semidirect
137. SD16×C181D4semidirect
139. D8×C181D4semidirect
227. C181#3291semidirect
232. #577D181semidirect
247. H(5,𝔽2)C2×D181semidirect
255. #137C2×D181semidirect
277. C2×SD16C2×D181semidirect
281. #131C2×D181semidirect
329. Q16C22⋊D181semidirect
348. SD16C22⋊D181semidirect
349. SD16C22⋊D181semidirect
355. D8C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
#260420902
#260420872
#260420862
#260416502
#260415442
#260415422
#260415402
#260415392
#260414622
#260414602
#260414472
#260414452
#260413962
#260413942
#577×C1812
#3291181