Finite Group Databasebeta

← #37545864

Subgroups — #37545864

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#26041975C211yesmaximal, characteristic, complemented
2D4×D724C211yesmaximal, characteristic, complemented
3#26041644C211yesmaximal, characteristic, complemented
4#26041604C211yesmaximal, characteristic, complemented
5#26041598C211yesmaximal, characteristic, complemented
6#26041580C211yesmaximal, characteristic, complemented
7#26041532C211yesmaximal, characteristic, complemented
8#26041515C211yesmaximal, characteristic, complemented
9#26041475C211yesmaximal, characteristic, complemented
10#26041415C211yesmaximal, characteristic, complemented
11#26041415C211yesmaximal, characteristic, complemented
12#26041392C211yesmaximal, characteristic, complemented
13#26041285C211yesmaximal, characteristic, complemented
14C2×#19153738C211yesmaximal, characteristic, complemented
15#435×C181C211yesmaximal, characteristic, complemented
16C22×D724C2211yescharacteristic
17C22×D724C2211yescharacteristic
18C2×D4×D181—21no—
19C2×D1448C2211yescharacteristic
20C2×D1448C2211yescharacteristic, complemented
21C2×D1448C2211yescharacteristic, complemented
22#19153813C2211yescharacteristic
23#19153811—21no—
24#19153808C2211yescharacteristic, complemented
25#19153798—21no—
26#19153791—21no—
27#19153790C2211yescharacteristic
28#19153790C2211yescharacteristic
29#19153790C2211yescharacteristic, complemented
30#19153790C2211yescharacteristic, complemented
31#19153788—21no—
32#19153786—21no—
33#19153786—21no—
34C4×D724C2211yescharacteristic
35C4×D724C2211yescharacteristic, complemented
36#19153776—21no—
37#19153775C2211yescharacteristic, complemented
38C2×C4⋊Dic181C2211yescharacteristic, complemented
39#19153750C2211yescharacteristic, complemented
40#19153748C2211yescharacteristic, complemented
41#19153748C2211yescharacteristic, complemented
42#19153738C2211yescharacteristic
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic
45#19153738C2211yescharacteristic, complemented
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×D724—22no—
62C2×D724—22no—
63C2×D724—21no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—41no—
68C2×D724—41no—
69C2×D724C2311yescharacteristic
70C2×D724C2311yescharacteristic
71C2×D724C2311yescharacteristic
72C2×D724C2311yescharacteristic
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181—21no—
76C2×C22⋊D181—21no—
77D4×D181—44no—
78C22×Dic181—21no—
79C2×C4×D181—21no—
80C2×C4×D181—21no—
81D1448—22no—
82D1448—41no—
83D1448—41no—
84C4⋊Dic181—21no—
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87C4⋊Dic181C2311yescharacteristic
88C4⋊Dic181C2311yescharacteristic
89#15668428—21no—
90#15668428—21no—
91C22⋊Dic181—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95#15668426—21no—
96#15668426—21no—
97#15668426—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—21no—
116C22×D181—42no—
117C22×D181—42no—
118C22×D181—42no—
119C22×D181—42no—
120C22×D181—81no—
121C22×D181—81no—
122D724—21no—
123D724—21no—
124D724—21no—
125D724—21no—
126D724—21no—
127D724—21no—
128D724—21no—
129D724—42no—
130D724—42no—
131D724—42no—
132D724—81no—
133D724#4112yes—
134C22⋊D181—42no—
135C22⋊D181—42no—
136C22⋊D181—42no—
137C22⋊D181—81no—
138C2×Dic181—21no—
139C2×Dic181—21no—
140C2×Dic181—21no—
141C2×Dic181—21no—
142C2×Dic181—81no—
143C4×D181—42no—
144C4×D181—81no—
145C23×C181C2×D411yescharacteristic
146C23×C181C2×D411yescharacteristic
147D4×C181—22no—
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—21no—
151C2×C4×C181—21no—
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2×D411yescharacteristic
155C2×C4×C181C2×D411yescharacteristic
156C2×C4×C181C2411yescharacteristic
157C8×C181—21no—
158C8×C181—21no—
159C8×C181—21no—
160C8×C181—21no—
161C22×C181—21no—
162C22×C181—21no—
163C22×C181—21no—
164C22×C181—21no—
165C22×C181—21no—
166C22×C181AGL(1,ℤ/8)12yes—
167C22×C181C22×D411yescharacteristic
168C2×D181—22no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181—41no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—84no—
181C2×D181—84no—
182C4×C181—21no—
183C4×C181—21no—
184C4×C181—21no—
185C4×C181—21no—
186C4×C181C2×#4111yescharacteristic
187C4×C181H(5,𝔽2)11yescharacteristic
188Dic181—41no—
189Dic181—41no—
190Dic181—41no—
191Dic181—41no—
192C2×C181—22no—
193C2×C181—41no—
194C2×C181#54611yescharacteristic
195C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
196C2×C181#57611yescharacteristic
197D181—42no—
198D181—81no—
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#435D18111yescharacteristic, complemented
216#418—1811no—
217C2×#102—1811no—
218C22×D4—3621no—
219C22×D4—1811no—
220C22×D4—1811no—
221C2×D8—1811no—
222C2×D8—1811no—
223C2×D8—1811no—
224C2×M16C2×D18111yescharacteristic, complemented
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×D4C2×D18111yescharacteristic
242#117—1811no—
243C2×C4⋊C4—1811no—
244#107—1811no—
245#106—1811no—
246#106—1811no—
247C4⋊C8C2×D18111yescharacteristic, complemented
248#102—1811no—
249#102—1811no—
250#102—1811no—
251#102—1811no—
252#102—1811no—
253#102—1811no—
254#102—1811no—
255#102—1811no—
256#102—1811no—
257#102—1811no—
258C22⋊C8C2×D18111yescharacteristic, complemented
259C22⋊C8C2×D18111yescharacteristic, complemented
260#97C2×D18111yescharacteristic, complemented
261C24—3621no—
262C24—3621no—
263C2×D4—3622no—
264C2×D4—3622no—
265C2×D4—3621no—
266C2×D4—3621no—
267C2×D4—3621no—
268C2×D4—3621no—
269C2×D4—3621no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3621no—
273C2×D4—1811no—
274C2×D4—1811no—
275C2×D4—1811no—
276C2×D4—1811no—
277C2×D4—7241no—
278C2×D4—7241no—
279C2×D4—7244no—
280C2×D4D72411yescharacteristic
281C22×C4—3621no—
282C22×C4—3621no—
283C22×C4—3621no—
284C22×C4C22×D18111yescharacteristic
285C22×C4C22×D18111yescharacteristic
286D8—3622no—
287D8—7241no—
288D8—7241no—
289M16—41no—
290C2×C8—41no—
291C2×C8C22×D18111yescharacteristic
292C2×C8C22×D18111yescharacteristic
293C2×C8C22×D18111yescharacteristic
294C2×C8C22×D18111yescharacteristic
295C4⋊C4—3621no—
296C4⋊C4—3621no—
297C4⋊C4—3621no—
298C4⋊C4—1811no—
299C4⋊C4—1811no—
300C4⋊C4—1811no—
301C4⋊C4—1811no—
302C4⋊C4D72411yescharacteristic
303C22⋊C4—3621no—
304C22⋊C4—3621no—
305C22⋊C4—3621no—
306C22⋊C4—3621no—
307C22⋊C4—3621no—
308C22⋊C4—3621no—
309C22⋊C4—3621no—
310C22⋊C4D72411yescharacteristic
311C22⋊C4D72411yescharacteristic
312C42—3621no—
313C42C22×D18111yescharacteristic
314C23—3621no—
315C23—3621no—
316C23—3621no—
317C23—3621no—
318C23—14481no—
319C23—14481no—
320C23—7242no—
321C23—7242no—
322C23—7242no—
323C23—7242no—
324C23C2×D72411yescharacteristic
325C23C2×D72411yescharacteristic
326D4—22no—
327D4—3621no—
328D4—3621no—
329D4—3621no—
330D4—3621no—
331D4—3621no—
332D4—3621no—
333D4—3621no—
334D4—14481no—
335D4—14481no—
336D4—1812no—
337D4—7242no—
338D4—7242no—
339D4—7242no—
340D4—7242no—
341D4—7242no—
342D4—7242no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—3621no—
348C2×C4—3621no—
349C2×C4—3621no—
350C2×C4—3621no—
351C2×C4—14481no—
352C2×C4—14481no—
353C2×C4—7242no—
354C2×C4C2×D72411yescharacteristic
355C2×C4C2×D72411yescharacteristic
356C2×C4C2×D72411yescharacteristic
357C2×C4C2×D72411yescharacteristic
358C2×C4C23×D18111yescharacteristic
359C8—21no—
360C8—21no—
361C8—21no—
362C8—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—3622no—
369C22—14484no—
370C22—14484no—
371C22—7241no—
372C22—7241no—
373C22—7241no—
374C22—7241no—
375C22—7241no—
376C22—7241no—
377C22—7241no—
378C22—7241no—
379C22—7241no—
380C22—7241no—
381C22—7241no—
382C22#1915384412yes—
383C22C22×D72411yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—21no—
388C4—7241no—
389C4—7241no—
390C4—7241no—
391C4—7241no—
392C4#41×D18111yescharacteristic
393C4#1915386111yescharacteristic
394C2—22no—
395C2—41no—
396C2—14481no—
397C2—14481no—
398C2—14481no—
399C2—7242no—
400C2#2604192411yescharacteristic
401C2C2×#1915384411yescharacteristic
402C2#2604208411yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#435×C181C2
socleC22×C181C22×D4
hypercenter#435D181
hypocenterC181#3318
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. #26041975C2semidirect
2. D4×D724C2semidirect
3. #26041644C2semidirect
4. #26041604C2semidirect
5. #26041598C2semidirect
6. #26041580C2semidirect
7. #26041532C2semidirect
8. #26041515C2semidirect
9. #26041475C2semidirect
10. #26041415C2semidirect
11. #26041415C2semidirect
12. #26041392C2semidirect
13. #26041285C2semidirect
14. C2×#19153738C2semidirect
15. #435×C181C2semidirect
20. C2×D1448C22semidirect
21. C2×D1448C22semidirect
24. #19153808C22semidirect
29. #19153790C22semidirect
30. #19153790C22semidirect
35. C4×D724C22semidirect
37. #19153775C22semidirect
38. C2×C4⋊Dic181C22semidirect
39. #19153750C22semidirect
40. #19153748C22semidirect
41. #19153748C22semidirect
45. #19153738C22semidirect
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
201. C181#3318semidirect
215. #435D181semidirect
224. C2×M16C2×D181semidirect
225. C22×C8C2×D181semidirect
247. C4⋊C8C2×D181semidirect
258. C22⋊C8C2×D181semidirect
259. C22⋊C8C2×D181semidirect
260. #97C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419752
D4×D7242
#260416442
#260416042
#260415982
#260415802
#260415322
#260415152
#260414752
#260414152
#260413922
#260412852
C2×#191537382
#435×C1812
#3318181