Finite Group Databasebeta

← #37545858

Subgroups — #37545858

Order 23168.

462 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041977C211yesmaximal, characteristic, complemented
2D4×C22⋊D181C211yesmaximal, characteristic, complemented
3#26041642C211yesmaximal, characteristic, complemented
4#26041601C211yesmaximal, characteristic, complemented
5#26041597C211yesmaximal, characteristic, complemented
6#26041577C211yesmaximal, characteristic, complemented
7#26041531C211yesmaximal, characteristic, complemented
8#26041515C211yesmaximal, characteristic, complemented
9#26041473C211yesmaximal, characteristic, complemented
10#26041414C211yesmaximal, characteristic, complemented
11#26041413C211yesmaximal, characteristic, complemented
12#26041388C211yesmaximal, characteristic, complemented
13#26041350C211yesmaximal, characteristic, complemented
14#26041282C211yesmaximal, characteristic, complemented
15C2×#102×C181C211yesmaximal, characteristic, complemented
16C22×C22⋊D181—21no—
17C2×D4×D181C2211yescharacteristic
18C2×D1448C2211yescharacteristic, complemented
19C2×#15668434C2211yescharacteristic
20C2×#15668434C2211yescharacteristic, complemented
21C2×#15668432C2211yescharacteristic, complemented
22#19153812C2211yescharacteristic
23#19153811—21no—
24#19153807C2211yescharacteristic, complemented
25#19153801—21no—
26#19153791C2211yescharacteristic, complemented
27#19153790—21no—
28#19153790C2211yescharacteristic
29#19153790C2211yescharacteristic, complemented
30#19153788—21no—
31#19153787C2211yescharacteristic
32#19153785—21no—
33#19153784—21no—
34D4×Dic181C2211yescharacteristic
35#19153778C2211yescharacteristic, complemented
36C4×C22⋊D181—21no—
37C4×C22⋊D181C2211yescharacteristic
38#19153774C2211yescharacteristic, complemented
39#19153750C2211yescharacteristic, complemented
40#19153747C2211yescharacteristic, complemented
41#19153747C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic, complemented
44#19153738C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic, complemented
49C22⋊#13089678C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51#19153726C2211yescharacteristic, complemented
52C22×D4×C181C2211yescharacteristic
53C22×C8×C181C2211yescharacteristic, complemented
54C2×C4⋊C4×C181C2211yescharacteristic, complemented
55#102×C181C2211yescharacteristic
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic, complemented
58#102×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C2×D724—21no—
61C2×D724C2311yescharacteristic
62C2×D724C2311yescharacteristic
63C2×C22⋊D181—21no—
64C2×C22⋊D181—21no—
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69C2×C22⋊D181—44no—
70C2×C22⋊D181D411yescharacteristic
71D4×D181—22no—
72D4×D181—41no—
73C22×Dic181—21no—
74C2×C4×D181—21no—
75C2×C4×D181C2311yescharacteristic
76D1448—41no—
77#15668434—22no—
78#15668434—41no—
79#15668432—41no—
80C2×#13089678C2311yescharacteristic
81C2×#13089678C2311yescharacteristic
82C4⋊Dic181—21no—
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85#15668428—21no—
86#15668428D411yescharacteristic
87C22⋊Dic181—21no—
88C22⋊Dic181—21no—
89C22⋊Dic181D411yescharacteristic
90#15668426—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426D411yescharacteristic
96C4×Dic181—21no—
97C4×Dic181C2311yescharacteristic
98C24×C181—21no—
99C2×D4×C181—22no—
100C2×D4×C181—21no—
101C2×D4×C181—41no—
102C2×D4×C181C2311yescharacteristic
103C2×D4×C181C2311yescharacteristic
104C22×C4×C181—21no—
105C22×C4×C181C2311yescharacteristic
106C2×C8×C181—41no—
107C2×C8×C181C2311yescharacteristic
108C2×C8×C181C2311yescharacteristic
109C4⋊C4×C181—21no—
110C4⋊C4×C181C2311yescharacteristic
111C4⋊C4×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—21no—
114C22×D181—42no—
115C22×D181—42no—
116C22×D181—81no—
117C22×D181C2×D411yescharacteristic
118D724—21no—
119D724—21no—
120D724—21no—
121D724—21no—
122D724—81no—
123C22⋊D181—22no—
124C22⋊D181—42no—
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—81no—
139#13089678—21no—
140#13089678—21no—
141C23×C181—21no—
142C23×C181—21no—
143C23×C181—42no—
144C23×C181—42no—
145C23×C181—81no—
146C23×C181C2×D411yescharacteristic
147D4×C181—21no—
148D4×C181—21no—
149D4×C181—21no—
150D4×C181—42no—
151D4×C181#4112yes—
152C2×C4×C181—21no—
153C2×C4×C181—21no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—81no—
157C2×C4×C181C2×D411yescharacteristic
158C2×C4×C181C2411yescharacteristic
159C8×C181—21no—
160C8×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—22no—
164C22×C181—41no—
165C22×C181—41no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181—84no—
170C22×C181AGL(1,ℤ/8)12yes—
171C22×C181C22×D411yescharacteristic
172C2×D181—21no—
173C2×D181—21no—
174C2×D181—21no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—84no—
182C4×C181—21no—
183C4×C181—41no—
184C4×C181—41no—
185C4×C181C2×#4111yescharacteristic
186C4×C181H(5,𝔽2)11yescharacteristic
187Dic181—21no—
188Dic181—21no—
189Dic181—21no—
190Dic181—41no—
191Dic181—41no—
192C2×C181—22no—
193C2×C181—42no—
194C2×C181—81no—
195C2×C181#54611yescharacteristic
196C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
197C2×C181#57611yescharacteristic
198D181—41no—
199D181—81no—
200D181—81no—
201C181#331811yescharacteristic, complemented, Sylow
202#3318—1811nomaximal, Sylow
203#553—1811no—
204D42—1811no—
205#490—1811no—
206#482—1811no—
207#481—1811no—
208#478—1811no—
209#469—1811no—
210#466—1811no—
211#459—1811no—
212#447—1811no—
213#447—1811no—
214#442—1811no—
215#435—1811no—
216#418—1811no—
217C2×#102D18111yescharacteristic, complemented
218C22×D4—3621no—
219C22×D4—1811no—
220C22×D4C2×D18111yescharacteristic
221C2×D8—1811no—
222C2×D8—1811no—
223C2×D8—1811no—
224C2×M16—1811no—
225C22×C8C2×D18111yescharacteristic, complemented
226#127—1811no—
227#126—3621no—
228#125—1811no—
229#123—3621no—
230#121—3621no—
231#121—3621no—
232#121—1811no—
233#121—1811no—
234#121—1811no—
235#121—1811no—
236#120—3621no—
237#120—3621no—
238C4×D4—3621no—
239C4×D4—1811no—
240C4×D4—1811no—
241C4×D4—1811no—
242#117—1811no—
243C2×C4⋊C4C2×D18111yescharacteristic, complemented
244#107—1811no—
245#106—1811no—
246#106—1811no—
247C4⋊C8—1811no—
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102—1811no—
252#102—1811no—
253#102—1811no—
254#102C2×D18111yescharacteristic
255#102C2×D18111yescharacteristic
256#102C2×D18111yescharacteristic, complemented
257#102C2×D18111yescharacteristic, complemented
258C22⋊C8—1811no—
259C22⋊C8—1811no—
260#97—1811no—
261C24—21no—
262C24—3621no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—3621no—
267C2×D4—3622no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—3621no—
274C2×D4—1811no—
275C2×D4—1811no—
276C2×D4—1811no—
277C2×D4—7241no—
278C2×D4—7244no—
279C2×D4C22×D18111yescharacteristic
280C2×D4C22×D18111yescharacteristic
281C22×C4—21no—
282C22×C4—3621no—
283C22×C4—3621no—
284C22×C4—1811no—
285C22×C4C22×D18111yescharacteristic
286D8—3622no—
287D8—7241no—
288D8—7241no—
289M16—7241no—
290C2×C8—41no—
291C2×C8—1811no—
292C2×C8—1811no—
293C2×C8C22×D18111yescharacteristic
294C2×C8C22×D18111yescharacteristic
295C4⋊C4—21no—
296C4⋊C4—3621no—
297C4⋊C4—3621no—
298C4⋊C4—1811no—
299C4⋊C4—1811no—
300C4⋊C4—1811no—
301C4⋊C4C22×D18111yescharacteristic
302C4⋊C4C22×D18111yescharacteristic
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C22⋊C4—1811no—
311C22⋊C4—1811no—
312C42—3621no—
313C42—1811no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—42no—
318C23—81no—
319C23—3621no—
320C23—3621no—
321C23—14481no—
322C23—1811no—
323C23—7242no—
324C23—7242no—
325C23D4×D18111yescharacteristic
326D4—21no—
327D4—21no—
328D4—21no—
329D4—42no—
330D4—3622no—
331D4—3621no—
332D4—3621no—
333D4—3621no—
334D4—3621no—
335D4—14481no—
336D4—14481no—
337D4—7242no—
338D4—7242no—
339D4—7242no—
340D4—7242no—
341D4—7242no—
342D4#1566844912yes—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—81no—
348C2×C4—3621no—
349C2×C4—3621no—
350C2×C4—3621no—
351C2×C4—3621no—
352C2×C4—14481no—
353C2×C4—1811no—
354C2×C4—1811no—
355C2×C4—1811no—
356C2×C4—7242no—
357C2×C4D4×D18111yescharacteristic
358C2×C4C23×D18111yescharacteristic
359C8—21no—
360C8—21no—
361C8—3621no—
362C8—3621no—
363C22—21no—
364C22—21no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—84no—
372C22—3621no—
373C22—3621no—
374C22—3621no—
375C22—14484no—
376C22—7241no—
377C22—7241no—
378C22—7241no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22#1915384312yes—
383C22C2×D4×D18111yescharacteristic
384C4—21no—
385C4—41no—
386C4—41no—
387C4—3621no—
388C4—3621no—
389C4—3621no—
390C4—7241no—
391C4—7241no—
392C4C2×#1566844911yescharacteristic
393C4#1915386111yescharacteristic
394C2—22no—
395C2—42no—
396C2—81no—
397C2—14481no—
398C2—14481no—
399C2—7241no—
400C2#2604191911yescharacteristic
401C2C2×#1915384311yescharacteristic
402C2#2604208011yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC2×#102×C181C2
socleC22×C181C22×D4
hypercenterC2×#102D181
hypocenterC181#3318
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #26041977C2semidirect
2. D4×C22⋊D181C2semidirect
3. #26041642C2semidirect
4. #26041601C2semidirect
5. #26041597C2semidirect
6. #26041577C2semidirect
7. #26041531C2semidirect
8. #26041515C2semidirect
9. #26041473C2semidirect
10. #26041414C2semidirect
11. #26041413C2semidirect
12. #26041388C2semidirect
13. #26041350C2semidirect
14. #26041282C2semidirect
15. C2×#102×C181C2semidirect
18. C2×D1448C22semidirect
20. C2×#15668434C22semidirect
21. C2×#15668432C22semidirect
24. #19153807C22semidirect
26. #19153791C22semidirect
29. #19153790C22semidirect
35. #19153778C22semidirect
38. #19153774C22semidirect
39. #19153750C22semidirect
40. #19153747C22semidirect
41. #19153747C22semidirect
42. #19153745C22semidirect
43. #19153738C22semidirect
44. #19153738C22semidirect
46. #19153737C22semidirect
47. #19153736C22semidirect
48. #19153736C22semidirect
49. C22⋊#13089678C22semidirect
50. #19153728C22semidirect
51. #19153726C22semidirect
53. C22×C8×C181C22semidirect
54. C2×C4⋊C4×C181C22semidirect
57. #102×C181C22semidirect
58. #102×C181C22semidirect
201. C181#3318semidirect
217. C2×#102D181semidirect
225. C22×C8C2×D181semidirect
243. C2×C4⋊C4C2×D181semidirect
256. #102C2×D181semidirect
257. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419772
D4×C22⋊D1812
#260416422
#260416012
#260415972
#260415772
#260415312
#260415152
#260414732
#260414142
#260414132
#260413882
#260413502
#260412822
C2×#102×C1812
#3318181