Finite Group Databasebeta

← #37545744

Subgroups — #37545744

Order 23168.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041969C211yesmaximal, characteristic, complemented
2D4×D724C211yesmaximal, characteristic
3#26041644C211yesmaximal, characteristic, complemented
4#26041604C211yesmaximal, characteristic, complemented
5#26041593C211yesmaximal, characteristic, complemented
6#26041580C211yesmaximal, characteristic, complemented
7#26041525C211yesmaximal, characteristic, complemented
8#26041508C211yesmaximal, characteristic, complemented
9#26041480C211yesmaximal, characteristic, complemented
10#26041432C211yesmaximal, characteristic, complemented
11#26041432C211yesmaximal, characteristic, complemented
12#26041381C211yesmaximal, characteristic, complemented
13#26041285C211yesmaximal, characteristic, complemented
14C2×#19153738C211yesmaximal, characteristic, complemented
15#435×C181C211yesmaximal, characteristic, complemented
16C22×D724C2211yescharacteristic
17C22×D724C2211yescharacteristic
18C2×D4×D181—21no—
19C2×#15668438C2211yescharacteristic
20C2×#15668438C2211yescharacteristic, complemented
21C2×#15668438C2211yescharacteristic, complemented
22#19153813C2211yescharacteristic
23#19153809—21no—
24#19153808C2211yescharacteristic, complemented
25#19153806—21no—
26#19153797—21no—
27#19153795C2211yescharacteristic, complemented
28#19153795C2211yescharacteristic, complemented
29#19153791—21no—
30#19153790C2211yescharacteristic
31#19153790C2211yescharacteristic
32#19153786—21no—
33#19153786—21no—
34C4×Dic362C2211yescharacteristic, complemented
35C4×D724C2211yescharacteristic
36#19153775C2211yescharacteristic, complemented
37#19153772—21no—
38C2×C4⋊Dic181C2211yescharacteristic, complemented
39#19153750C2211yescharacteristic, complemented
40#19153750C2211yescharacteristic, complemented
41#19153748C2211yescharacteristic, complemented
42#19153741C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic
46#19153738C2211yescharacteristic, complemented
47#19153738C2211yescharacteristic, complemented
48#19153738C2211yescharacteristic, complemented
49#19153738C2211yescharacteristic, complemented
50#19153738C2211yescharacteristic, complemented
51#19153738C2211yescharacteristic, complemented
52C2×M16×C181C2211yescharacteristic, complemented
53C22×C8×C181C2211yescharacteristic, complemented
54C4×D4×C181C2211yescharacteristic
55C4⋊C8×C181C2211yescharacteristic, complemented
56C22⋊C8×C181C2211yescharacteristic, complemented
57C22⋊C8×C181C2211yescharacteristic, complemented
58#97×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C23×D181—21no—
61C2×Dic362C2311yescharacteristic
62C2×D724—22no—
63C2×D724—22no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—21no—
68C2×D724—41no—
69C2×D724—41no—
70C2×D724C2311yescharacteristic
71C2×D724C2311yescharacteristic
72C2×D724C2311yescharacteristic
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75D4×D181—44no—
76C22×Dic181—21no—
77C2×C4×D181—21no—
78#15668438—22no—
79#15668438—41no—
80#15668438—41no—
81C4⋊Dic181—21no—
82C4⋊Dic181C2311yescharacteristic
83C4⋊Dic181C2311yescharacteristic
84C4⋊Dic181C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86#15668428—21no—
87#15668428—21no—
88#15668428—21no—
89#15668428—21no—
90#15668428—21no—
91C22⋊Dic181—21no—
92C22⋊Dic181—21no—
93C22⋊Dic181—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97C4×Dic181—21no—
98C4×Dic181—21no—
99C2×D4×C181D411yescharacteristic
100C22×C4×C181C2311yescharacteristic
101C22×C4×C181C2311yescharacteristic
102M16×C181—41no—
103C2×C8×C181—41no—
104C2×C8×C181C2311yescharacteristic
105C2×C8×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181D411yescharacteristic
109C22⋊C4×C181D411yescharacteristic
110C22⋊C4×C181D411yescharacteristic
111C42×C181C2311yescharacteristic
112C22×D181—21no—
113C22×D181—21no—
114C22×D181—21no—
115C22×D181—42no—
116C22×D181—42no—
117C22×D181—42no—
118C22×D181—42no—
119C22×D181—81no—
120C22×D181—81no—
121Dic362—21no—
122Dic362—21no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—21no—
127D724—21no—
128D724—42no—
129D724—42no—
130D724—42no—
131D724—81no—
132D724#4112yes—
133C22⋊D181—42no—
134C22⋊D181—42no—
135C2×Dic181—21no—
136C2×Dic181—21no—
137C2×Dic181—21no—
138C2×Dic181—21no—
139C2×Dic181—21no—
140C2×Dic181—42no—
141C4×D181—42no—
142C23×C181C2×D411yescharacteristic
143C23×C181C2×D411yescharacteristic
144D4×C181—22no—
145C2×C4×C181—21no—
146C2×C4×C181—21no—
147C2×C4×C181—21no—
148C2×C4×C181—21no—
149C2×C4×C181C2×D411yescharacteristic
150C2×C4×C181C2×D411yescharacteristic
151C2×C4×C181C2×D411yescharacteristic
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2411yescharacteristic
154C8×C181—21no—
155C8×C181—21no—
156C8×C181—21no—
157C8×C181—21no—
158C22×C181—21no—
159C22×C181—21no—
160C22×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181AGL(1,ℤ/8)12yes—
164C22×C181C22×D411yescharacteristic
165C2×D181—22no—
166C2×D181—41no—
167C2×D181—41no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—84no—
175C2×D181—84no—
176C4×C181—21no—
177C4×C181—21no—
178C4×C181—21no—
179C4×C181—21no—
180C4×C181C2×#4111yescharacteristic
181C4×C181H(5,𝔽2)11yescharacteristic
182Dic181—41no—
183Dic181—41no—
184Dic181—41no—
185Dic181—41no—
186Dic181—41no—
187C2×C181—22no—
188C2×C181—41no—
189C2×C181#54611yescharacteristic
190C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C181#57711yescharacteristic
192D181—42no—
193D181—81no—
194D181—81no—
195C181#331011yescharacteristic, complemented, Sylow
196#3310—1811nomaximal, Sylow
197#552—1811no—
198D42—1811no—
199#490—1811no—
200#482—1811no—
201#480—1811no—
202#478—1811no—
203#468—1811no—
204#465—1811no—
205#460—1811no—
206#450—1811no—
207#450—1811no—
208#440—1811no—
209#435D18111yescharacteristic, complemented
210#418—1811no—
211C2×#102—1811no—
212C22×D4—3621no—
213C22×D4—1811no—
214C22×D4—1811no—
215C2×SD16—1811no—
216C2×SD16—1811no—
217C2×SD16—1811no—
218C2×M16C2×D18111yescharacteristic, complemented
219C22×C8C2×D18111yescharacteristic, complemented
220#127—1811no—
221#126—3621no—
222#125—3621no—
223#125—1811no—
224#123—3621no—
225C22⋊Q8—1811no—
226C22⋊Q8—1811no—
227#121—3621no—
228#121—1811no—
229#121—1811no—
230#120—3621no—
231#120—3621no—
232C4×Q8—1811no—
233C4×D4—1811no—
234C4×D4C2×D18111yescharacteristic
235#117—3621no—
236#117—1811no—
237C2×C4⋊C4—1811no—
238#107—1811no—
239#107—1811no—
240#106—1811no—
241C4⋊C8C2×D18111yescharacteristic, complemented
242#103—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102—1811no—
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102—1811no—
252C22⋊C8C2×D18111yescharacteristic, complemented
253C22⋊C8C2×D18111yescharacteristic, complemented
254#97C2×D18111yescharacteristic, complemented
255C24—3621no—
256C24—3621no—
257C2×Q8—1811no—
258C2×D4—3622no—
259C2×D4—3622no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—3621no—
264C2×D4—3621no—
265C2×D4—3621no—
266C2×D4—1811no—
267C2×D4—1811no—
268C2×D4—1811no—
269C2×D4—7241no—
270C2×D4—7241no—
271C2×D4—7244no—
272C2×D4D72411yescharacteristic
273C22×C4—3621no—
274C22×C4—3621no—
275C22×C4C22×D18111yescharacteristic
276C22×C4C22×D18111yescharacteristic
277SD16—3622no—
278SD16—7241no—
279SD16—7241no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D18111yescharacteristic
283C2×C8C22×D18111yescharacteristic
284C2×C8C22×D18111yescharacteristic
285C2×C8C22×D18111yescharacteristic
286C4⋊C4—3621no—
287C4⋊C4—3621no—
288C4⋊C4—3621no—
289C4⋊C4—3621no—
290C4⋊C4—3621no—
291C4⋊C4—3621no—
292C4⋊C4—1811no—
293C4⋊C4—1811no—
294C4⋊C4—1811no—
295C4⋊C4—1811no—
296C4⋊C4D72411yescharacteristic
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C22⋊C4—3621no—
301C22⋊C4—3621no—
302C22⋊C4—3621no—
303C22⋊C4D72411yescharacteristic
304C22⋊C4D72411yescharacteristic
305C42—3621no—
306C42—3621no—
307C42C22×D18111yescharacteristic
308C23—3621no—
309C23—3621no—
310C23—3621no—
311C23—14481no—
312C23—14481no—
313C23—7242no—
314C23—7242no—
315C23—7242no—
316C23—7242no—
317C23C2×D72411yescharacteristic
318C23C2×D72411yescharacteristic
319Q8—3621no—
320Q8—3621no—
321D4—22no—
322D4—3621no—
323D4—3621no—
324D4—3621no—
325D4—3621no—
326D4—3621no—
327D4—14481no—
328D4—1812no—
329D4—7242no—
330D4—7242no—
331D4—7242no—
332D4—7242no—
333D4—7242no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—3621no—
339C2×C4—3621no—
340C2×C4—3621no—
341C2×C4—3621no—
342C2×C4—3621no—
343C2×C4—7242no—
344C2×C4—7242no—
345C2×C4C2×D72411yescharacteristic
346C2×C4C2×D72411yescharacteristic
347C2×C4C2×D72411yescharacteristic
348C2×C4C2×D72411yescharacteristic
349C2×C4C23×D18111yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—3622no—
360C22—14484no—
361C22—14484no—
362C22—7241no—
363C22—7241no—
364C22—7241no—
365C22—7241no—
366C22—7241no—
367C22—7241no—
368C22—7241no—
369C22—7241no—
370C22#1915384412yes—
371C22C22×D72411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—7241no—
377C4—7241no—
378C4—7241no—
379C4—7241no—
380C4—7241no—
381C4#41×D18111yescharacteristic
382C4#1915386111yescharacteristic
383C2—22no—
384C2—41no—
385C2—14481no—
386C2—14481no—
387C2—7242no—
388C2#2604192411yescharacteristic
389C2C2×#1915384411yescharacteristic
390C2#2604209111yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#435×C181C2
socleC22×C181C22×D4
prime radicalD4×D724C2
hypercenter#435D181
hypocenterC181#3310
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #26041969C2semidirect
3. #26041644C2semidirect
4. #26041604C2semidirect
5. #26041593C2semidirect
6. #26041580C2semidirect
7. #26041525C2semidirect
8. #26041508C2semidirect
9. #26041480C2semidirect
10. #26041432C2semidirect
11. #26041432C2semidirect
12. #26041381C2semidirect
13. #26041285C2semidirect
14. C2×#19153738C2semidirect
15. #435×C181C2semidirect
20. C2×#15668438C22semidirect
21. C2×#15668438C22semidirect
24. #19153808C22semidirect
27. #19153795C22semidirect
28. #19153795C22semidirect
34. C4×Dic362C22semidirect
36. #19153775C22semidirect
38. C2×C4⋊Dic181C22semidirect
39. #19153750C22semidirect
40. #19153750C22semidirect
41. #19153748C22semidirect
42. #19153741C22semidirect
46. #19153738C22semidirect
47. #19153738C22semidirect
48. #19153738C22semidirect
49. #19153738C22semidirect
50. #19153738C22semidirect
51. #19153738C22semidirect
52. C2×M16×C181C22semidirect
53. C22×C8×C181C22semidirect
55. C4⋊C8×C181C22semidirect
56. C22⋊C8×C181C22semidirect
57. C22⋊C8×C181C22semidirect
58. #97×C181C22semidirect
195. C181#3310semidirect
209. #435D181semidirect
218. C2×M16C2×D181semidirect
219. C22×C8C2×D181semidirect
241. C4⋊C8C2×D181semidirect
252. C22⋊C8C2×D181semidirect
253. C22⋊C8C2×D181semidirect
254. #97C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419692
D4×D7242
#260416442
#260416042
#260415932
#260415802
#260415252
#260415082
#260414802
#260414322
#260413812
#260412852
C2×#191537382
#435×C1812
#3310181