Finite Group Databasebeta

← #37545494

Subgroups — #37545494

Order 23168.

448 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042094C211yesmaximal, characteristic, complemented
2#26042093C211yesmaximal, characteristic, complemented
3#26042090C211yesmaximal, characteristic, complemented
4#26041670C211yesmaximal, characteristic, complemented
5#26041554C211yesmaximal, characteristic, complemented
6#26041552C211yesmaximal, characteristic, complemented
7#26041540C211yesmaximal, characteristic, complemented
8#26041539C211yesmaximal, characteristic, complemented
9#26041462C211yesmaximal, characteristic, complemented
10#26041460C211yesmaximal, characteristic, complemented
11#26041457C211yesmaximal, characteristic, complemented
12#26041450C211yesmaximal, characteristic, complemented
13#26041401C211yesmaximal, characteristic, complemented
14#26041399C211yesmaximal, characteristic, complemented
15#577×C181C211yesmaximal, characteristic, complemented
16#19153863C2211yescharacteristic
17#19153863C2211yescharacteristic, complemented
18#19153847—21no—
19#19153847C2211yescharacteristic, complemented
20#19153846—21no—
21#19153846—21no—
22#19153846C2211yescharacteristic
23#19153846C2211yescharacteristic
24#19153846C2211yescharacteristic
25#19153846C2211yescharacteristic, complemented
26#19153845—21no—
27#19153845—21no—
28#19153842—21no—
29#19153842C2211yescharacteristic
30#19153836—21no—
31#19153836—21no—
32#19153836C2211yescharacteristic
33#19153835—21no—
34C2×Dic724C2211yescharacteristic, complemented
35C2×#15668439—21no—
36C2×#15668439C2211yescharacteristic, complemented
37Q16×D181—21no—
38C2×#15668437—21no—
39C2×#15668437C2211yescharacteristic
40#19153823C2211yescharacteristic
41#19153823C2211yescharacteristic, complemented
42#19153822C2211yescharacteristic, complemented
43#19153814C2211yescharacteristic, complemented
44#19153803C2211yescharacteristic
45#19153752C2211yescharacteristic, complemented
46#19153751C2211yescharacteristic, complemented
47#19153743C2211yescharacteristic
48#19153743C2211yescharacteristic
49#19153743C2211yescharacteristic, complemented
50#19153742C2211yescharacteristic, complemented
51#19153735C2211yescharacteristic, complemented
52#19153734C2211yescharacteristic, complemented
53#19153734C2211yescharacteristic, complemented
54#19153733C2211yescharacteristic
55#19153726C2211yescharacteristic, complemented
562−1+4×C181C2211yescharacteristic
57H(5,𝔽2)×C181C2211yescharacteristic
58#137×C181—21no—
59#137×C181C2211yescharacteristic
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
66#131×C181C2211yescharacteristic
67#15668449—21no—
68#15668449—21no—
69#15668449C2311yescharacteristic
70#15668448—21no—
71#15668448—21no—
72#15668448—41no—
73#15668448—41no—
74C2×Dic362—21no—
75C2×Dic362—21no—
76C2×Dic362C2311yescharacteristic
77C2×Dic362C2311yescharacteristic
78Q8×D181—21no—
79Q8×D181—21no—
80Dic724—21no—
81Dic724—21no—
82#15668439—21no—
83#15668439—21no—
84#15668439—21no—
85#15668439—21no—
86#15668439—21no—
87#15668439—21no—
88#15668439—21no—
89#15668439D411yescharacteristic
90#15668437—21no—
91#15668437—21no—
92#15668437—21no—
93#15668437—21no—
94#15668437—21no—
95#15668437—21no—
96#15668437—21no—
97#15668437D411yescharacteristic
98#15668436—21no—
99#15668436D411yescharacteristic
100#15668434—21no—
101#15668434D411yescharacteristic
102#15668433—21no—
103#15668433—21no—
104#15668433C2311yescharacteristic
105#15668433C2311yescharacteristic
106#15668433C2311yescharacteristic
107#15668432—21no—
108C2×#13089678—21no—
109C2×#13089678—21no—
110C2×#13089678C2311yescharacteristic
111C8×D181—21no—
112#15668428—41no—
113C22⋊Dic181—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
132SD16×C181—21no—
133SD16×C181—21no—
134SD16×C181—21no—
135SD16×C181—21no—
136SD16×C181D411yescharacteristic
137SD16×C181D411yescharacteristic
138D8×C181—21no—
139D8×C181D411yescharacteristic
140M16×C181—21no—
141M16×C181C2311yescharacteristic
142C2×C8×C181—21no—
143C2×C8×C181C2311yescharacteristic
144Dic362—21no—
145Dic362—21no—
146Dic362—21no—
147Dic362—21no—
148Dic362—41no—
149Dic362—41no—
150Dic362C2×D411yescharacteristic
151D724C2×D411yescharacteristic
152C22⋊D181—21no—
153C22⋊D181—41no—
154C22⋊D181—41no—
155C2×Dic181—21no—
156C2×Dic181—21no—
157C2×Dic181—21no—
158C2×Dic181—41no—
159C2×Dic181—41no—
160C4×D181—21no—
161C4×D181—41no—
162C4×D181—41no—
163#13089678—21no—
164#13089678—21no—
165#13089678—21no—
166#13089678C2×D411yescharacteristic
167#13089678C2×D411yescharacteristic
168C23×C181—21no—
169C23×C181—41no—
170Q8×C181—21no—
171Q8×C181—21no—
172Q8×C181—41no—
173Q8×C181C2×D411yescharacteristic
174Q8×C181C2×D411yescharacteristic
175Q8×C181C2×D411yescharacteristic
176D4×C181—21no—
177D4×C181—21no—
178D4×C181—21no—
179D4×C181—21no—
180D4×C181—21no—
181D4×C181—41no—
182D4×C181—41no—
183D4×C181—41no—
184D4×C181C2×D411yescharacteristic
185D4×C181C2×D411yescharacteristic
186D4×C181C2×D411yescharacteristic
187C2×C4×C181—21no—
188C2×C4×C181—21no—
189C2×C4×C181—21no—
190C2×C4×C181—21no—
191C2×C4×C181—41no—
192C2×C4×C181—41no—
193C2×C4×C181—41no—
194C2×C4×C181C2411yescharacteristic
195C8×C181—21no—
196C8×C181C2×D411yescharacteristic
197C8×C181C2×D411yescharacteristic
198C22×C181—21no—
199C22×C181—21no—
200C22×C181—21no—
201C22×C181—41no—
202C22×C181—81no—
203C22×C181—161no—
204C22×C181H(5,𝔽2)11yescharacteristic
205C2×D181—21no—
206C4×C181—21no—
207C4×C181—21no—
208C4×C181—21no—
209C4×C181—41no—
210C4×C181C22×D411yescharacteristic
211C4×C181C22×D411yescharacteristic
212Dic181—21no—
213Dic181—41no—
214Dic181—41no—
215Dic181—41no—
216C2×C181—21no—
217C2×C181—41no—
218C2×C181—41no—
219C2×C181—41no—
220C2×C181—81no—
221C2×C181D4211yescharacteristic
222D181—41no—
223C181#328911yescharacteristic, complemented, Sylow
224#3289—1811nomaximal, Sylow
225#578—1811no—
226#578—1811no—
227#577—1811no—
228#577D18111yescharacteristic, complemented
229#497—1811no—
230#473—1811no—
231#473—1811no—
232#471—1811no—
233#471—1811no—
234#456—1811no—
235#456—1811no—
236#455—1811no—
237#454—1811no—
238#444—1811no—
239#444—1811no—
2402−1+4—1811no—
2412−1+4—1811no—
2422−1+4C2×D18111yescharacteristic
243H(5,𝔽2)C2×D18111yescharacteristic
244#137—21no—
245#137—3621no—
246#137—3621no—
247#137—3621no—
248#137—3621no—
249#137—3621no—
250#137—1811no—
251#137—1811no—
252#137—1811no—
253#137—1811no—
254#137—1811no—
255#137C2×D18111yescharacteristic
256AGL(1,ℤ/8)—21no—
257AGL(1,ℤ/8)—3621no—
258AGL(1,ℤ/8)—1811no—
259AGL(1,ℤ/8)C2×D18111yescharacteristic
260#135—21no—
261#135—3621no—
262#135—3621no—
263#135—3621no—
264#135—1811no—
265#135C2×D18111yescharacteristic
266C2×Q16—3621no—
267C2×Q16—3621no—
268C2×Q16—1811no—
269C2×Q16—1811no—
270C2×SD16—21no—
271C2×SD16—3621no—
272C2×SD16—1811no—
273C2×SD16C2×D18111yescharacteristic
274#131—1811no—
275#131—1811no—
276#131—1811no—
277#131C2×D18111yescharacteristic
278C4⋊Q8—1811no—
279#124—1811no—
280#108—1811no—
281#108—1811no—
282#104—1811no—
283#104—1811no—
284#104—1811no—
285#104—1811no—
286#101—1811no—
287#101—1811no—
288#101—1811no—
289#100—1811no—
290#97—1811no—
291#41—21no—
292#41—21no—
293#41—21no—
294#41—21no—
295#41—41no—
296#41—3621no—
297#41—3621no—
298#41—3621no—
299#41—3621no—
300#41—1811no—
301#41—7241no—
302#41—7241no—
303#41C22×D18111yescharacteristic
304#41C22×D18111yescharacteristic
305#41C22×D18111yescharacteristic
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—3621no—
309C2×Q8—3621no—
310C2×Q8—3621no—
311C2×Q8—3621no—
312C2×Q8—1811no—
313C2×Q8—1811no—
314C2×Q8C22×D18111yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4C22×D18111yescharacteristic
319Q16—21no—
320Q16—3621no—
321Q16—3621no—
322Q16—3621no—
323Q16—3621no—
324Q16—3621no—
325Q16—3621no—
326Q16—3621no—
327Q16—3621no—
328Q16—3621no—
329Q16—1811no—
330Q16C22⋊D18111yescharacteristic
331SD16—21no—
332SD16—21no—
333SD16—21no—
334SD16—21no—
335SD16—3621no—
336SD16—3621no—
337SD16—3621no—
338SD16—3621no—
339SD16—3621no—
340SD16—3621no—
341SD16—3621no—
342SD16—3621no—
343SD16—1811no—
344SD16—1811no—
345SD16C22⋊D18111yescharacteristic
346SD16C22⋊D18111yescharacteristic
347D8—21no—
348D8—3621no—
349D8—1811no—
350D8C22⋊D18111yescharacteristic
351M16—21no—
352M16—3621no—
353M16—3621no—
354M16—3621no—
355M16—1811no—
356M16—1811no—
357M16—1811no—
358M16C22×D18111yescharacteristic
359C2×C8—21no—
360C2×C8—3621no—
361C2×C8—3621no—
362C2×C8—3621no—
363C2×C8—1811no—
364C2×C8C22×D18111yescharacteristic
365C4⋊C4—7241no—
366C22⋊C4—7241no—
367C42—1811no—
368C23—21no—
369C23—41no—
370Q8—21no—
371Q8—21no—
372Q8—41no—
373Q8—3621no—
374Q8—3621no—
375Q8—3621no—
376Q8—3621no—
377Q8—1811no—
378Q8—7241no—
379Q8—7241no—
380Q8D4×D18111yescharacteristic
381Q8C2×C22⋊D18111yescharacteristic
382Q8C2×C22⋊D18111yescharacteristic
383D4—21no—
384D4—21no—
385D4—21no—
386D4—21no—
387D4—21no—
388D4—41no—
389D4—41no—
390D4—41no—
391D4—3621no—
392D4—1811no—
393D4—7241no—
394D4—7241no—
395D4D4×D18111yescharacteristic
396D4C2×C22⋊D18111yescharacteristic
397D4C2×C22⋊D18111yescharacteristic
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—3621no—
406C2×C4—3621no—
407C2×C4—3621no—
408C2×C4—3621no—
409C2×C4—7241no—
410C2×C4—7241no—
411C2×C4—7241no—
412C2×C4—7241no—
413C2×C4C23×D18111yescharacteristic
414C8—21no—
415C8—3621no—
416C8—3621no—
417C8—3621no—
418C8—1811no—
419C8—1811no—
420C8C2×C22⋊D18111yescharacteristic
421C8C2×C22⋊D18111yescharacteristic
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—81no—
427C22—161no—
428C22—3621no—
429C22#1915386111yescharacteristic
430C4—21no—
431C4—21no—
432C4—21no—
433C4—41no—
434C4—3621no—
435C4—7241no—
436C4—7241no—
437C4—7241no—
438C4C2×D4×D18111yescharacteristic
439C4C22×C22⋊D18111yescharacteristic
440C2—21no—
441C2—41no—
442C2—41no—
443C2—41no—
444C2—81no—
445C2—7241no—
446C2D4×C22⋊D18111yescharacteristic
subgroupG/H
centerC2D4×C22⋊D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#577×C181C2
socleC2×C181D42
hypercenter#577D181
hypocenterC181#3289
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. #26042094C2semidirect
2. #26042093C2semidirect
3. #26042090C2semidirect
4. #26041670C2semidirect
5. #26041554C2semidirect
6. #26041552C2semidirect
7. #26041540C2semidirect
8. #26041539C2semidirect
9. #26041462C2semidirect
10. #26041460C2semidirect
11. #26041457C2semidirect
12. #26041450C2semidirect
13. #26041401C2semidirect
14. #26041399C2semidirect
15. #577×C181C2semidirect
17. #19153863C22semidirect
19. #19153847C22semidirect
25. #19153846C22semidirect
34. C2×Dic724C22semidirect
36. C2×#15668439C22semidirect
41. #19153823C22semidirect
42. #19153822C22semidirect
43. #19153814C22semidirect
45. #19153752C22semidirect
46. #19153751C22semidirect
49. #19153743C22semidirect
50. #19153742C22semidirect
51. #19153735C22semidirect
52. #19153734C22semidirect
53. #19153734C22semidirect
55. #19153726C22semidirect
223. C181#3289semidirect
228. #577D181semidirect

Maximal subgroups

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

subgroupindex
#260420942
#260420932
#260420902
#260416702
#260415542
#260415522
#260415402
#260415392
#260414622
#260414602
#260414572
#260414502
#260414012
#260413992
#577×C1812
#3289181