Finite Group Databasebeta

← #37545532

Subgroups — #37545532

Order 23168.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041930C211yesmaximal, characteristic, complemented
2#26041913C211yesmaximal, characteristic, complemented
3#26041624C211yesmaximal, characteristic, complemented
4#26041594C211yesmaximal, characteristic, complemented
5#26041558C211yesmaximal, characteristic, complemented
6#26041516C211yesmaximal, characteristic, complemented
7#26041513C211yesmaximal, characteristic, complemented
8#26041473C211yesmaximal, characteristic, complemented
9#26041415C211yesmaximal, characteristic, complemented
10#26041414C211yesmaximal, characteristic, complemented
11#26041361C211yesmaximal, characteristic, complemented
12#26041342C211yesmaximal, characteristic, complemented
13C2×#19153736C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#480×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C22×D724C2211yescharacteristic
18C2×D4×D181—21no—
19C2×D4×D181C2211yescharacteristic
20C2×D1448C2211yescharacteristic
21C2×D1448C2211yescharacteristic, complemented
22C2×#15668434C2211yescharacteristic, complemented
23C22×#13089678C2211yescharacteristic, complemented
24C2×C8×D181C2211yescharacteristic, complemented
25#19153815C2211yescharacteristic, complemented
26#19153812C2211yescharacteristic
27#19153801—21no—
28#19153799—21no—
29#19153794—21no—
30#19153791C2211yescharacteristic
31#19153791C2211yescharacteristic, complemented
32#19153790C2211yescharacteristic, complemented
33#19153789—21no—
34#19153786—21no—
35#19153784—21no—
36#19153778C2211yescharacteristic
37#19153778C2211yescharacteristic, complemented
38C4×C22⋊D181C2211yescharacteristic
39C4⋊C4×D181C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153738C2211yescharacteristic
43#19153738C2211yescharacteristic, complemented
44#19153737C2211yescharacteristic, complemented
45#19153736C2211yescharacteristic
46#19153736C2211yescharacteristic
47#19153736C2211yescharacteristic, complemented
48#19153736C2211yescharacteristic, complemented
49#19153736C2211yescharacteristic, complemented
50#19153728C2211yescharacteristic, complemented
51C8×Dic181C2211yescharacteristic, complemented
52#121×C181C2211yescharacteristic
53C2×C4⋊C4×C181C2211yescharacteristic, complemented
54#107×C181C2211yescharacteristic, complemented
55#107×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic, complemented
57#102×C181C2211yescharacteristic, complemented
58C22⋊C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60C23×D181—21no—
61#15668449—44no—
62C2×Dic362—21no—
63C2×D724—22no—
64C2×D724—21no—
65C2×D724—21no—
66C2×D724—21no—
67C2×D724—41no—
68C2×D724C2311yescharacteristic
69C2×D724C2311yescharacteristic
70C2×D724C2311yescharacteristic
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181D411yescharacteristic
76D4×D181—22no—
77D4×D181—41no—
78D4×D181—44no—
79C2×C4×D181—21no—
80C2×C4×D181—21no—
81C2×C4×D181—21no—
82C2×C4×D181C2311yescharacteristic
83D1448—22no—
84D1448—41no—
85#15668434—41no—
86C2×#13089678—41no—
87C2×#13089678C2311yescharacteristic
88C2×#13089678C2311yescharacteristic
89C8×D181—41no—
90C4⋊Dic181C2311yescharacteristic
91#15668428—21no—
92#15668428—21no—
93#15668428D411yescharacteristic
94C22⋊Dic181D411yescharacteristic
95#15668426—21no—
96#15668426—21no—
97#15668426—21no—
98#15668426—21no—
99#15668426—21no—
100#15668426D411yescharacteristic
101C4×Dic181C2311yescharacteristic
102C2×D4×C181—21no—
103C2×D4×C181C2311yescharacteristic
104C22×C4×C181—21no—
105C22×C4×C181C2311yescharacteristic
106C2×C8×C181C2311yescharacteristic
107C2×C8×C181C2311yescharacteristic
108C4⋊C4×C181—21no—
109C4⋊C4×C181C2311yescharacteristic
110C4⋊C4×C181C2311yescharacteristic
111C4⋊C4×C181C2311yescharacteristic
112C22⋊C4×C181—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—
122C22×D181C2×D411yescharacteristic
123Dic362—42no—
124D724—21no—
125D724—21no—
126D724—21no—
127D724—21no—
128D724—21no—
129D724—42no—
130D724—42no—
131D724—42no—
132D724#4112yescomplemented
133C22⋊D181—42no—
134C22⋊D181—42no—
135C22⋊D181—42no—
136C22⋊D181—81no—
137C22⋊D181D814yescomplemented
138C2×Dic181—21no—
139C2×Dic181C2×D411yescharacteristic
140C2×Dic181C2×D411yescharacteristic
141C2×Dic181C2×D411yescharacteristic
142C4×D181—21no—
143C4×D181—21no—
144C4×D181—42no—
145C4×D181—42no—
146C4×D181—42no—
147#13089678—21no—
148#13089678—21no—
149C23×C181—21no—
150C23×C181C2×D411yescharacteristic
151D4×C181—21no—
152D4×C181—21no—
153D4×C181—42no—
154C2×C4×C181—21no—
155C2×C4×C181—21no—
156C2×C4×C181—21no—
157C2×C4×C181—21no—
158C2×C4×C181—21no—
159C2×C4×C181—42no—
160C2×C4×C181C2×D411yescharacteristic
161C2×C4×C181C2411yescharacteristic
162C8×C181—21no—
163C8×C181—21no—
164C22×C181—21no—
165C22×C181—21no—
166C22×C181—41no—
167C22×C181—41no—
168C22×C181—41no—
169C22×C181C2×D812yes—
170C22×C181C22×D411yescharacteristic
171C2×D181—21no—
172C2×D181—21no—
173C2×D181—22no—
174C2×D181—41no—
175C2×D181—41no—
176C2×D181—41no—
177C2×D181—41no—
178C2×D181—41no—
179C2×D181—41no—
180C2×D181—41no—
181C2×D181—41no—
182C2×D181—84no—
183C2×D181—84no—
184C2×D181C2×D812yes—
185C4×C181—21no—
186C4×C181—41no—
187C4×C181—41no—
188C4×C181—41no—
189C4×C181C2×#4111yescharacteristic
190C4×C181H(5,𝔽2)11yescharacteristic
191Dic181—21no—
192Dic181—21no—
193Dic181—41no—
194Dic181C2×D812yes—
195C2×C181—22no—
196C2×C181—81no—
197C2×C181#54611yescharacteristic
198C2×C181C22×D811yescharacteristic
199C2×C181#57711yescharacteristic
200D181—22no—
201D181—42no—
202D181—81no—
203D181—81no—
204C181#329411yescharacteristic, complemented, Sylow
205#3294—1811nomaximal, Sylow
206#547—1811no—
207D42—1811no—
208#486—1811no—
209#480—1811no—
210#480D18111yescharacteristic, complemented
211#474—1811no—
212#466—1811no—
213#466—1811no—
214#459—1811no—
215#447—1811no—
216#447—1811no—
217C4×D8—1811no—
218C8×D4—1811no—
219C2×#102—1811no—
220C2×#102—1811no—
221C2×#41—3621no—
222C22×D4—3621no—
223C22×D4—1811no—
224C22×D4—1811no—
225C2×D8—1811no—
226C2×D8—1811no—
227C2×D8—1811no—
228C22×C8—1811no—
229C22×C8—1811no—
230C4⋊Q8—1811no—
231#127—1811no—
232#123—3621no—
233#123—3621no—
234C22⋊Q8—3621no—
235#121—3621no—
236#121—1811no—
237#121—1811no—
238#121—1811no—
239#121C2×D18111yescharacteristic
240#120—3621no—
241#120—3621no—
242C4×D4—1811no—
243C4×D4—1811no—
244C4×D4—1811no—
245C2×C4⋊C4—1811no—
246C2×C4⋊C4C2×D18111yescharacteristic, complemented
247#107—1811no—
248#107C2×D18111yescharacteristic, complemented
249#107C2×D18111yescharacteristic, complemented
250C4⋊C8—1811no—
251#102—1811no—
252#102—1811no—
253#102—1811no—
254#102—1811no—
255#102—1811no—
256#102—1811no—
257#102—1811no—
258#102—1811no—
259#102C2×D18111yescharacteristic, complemented
260#102C2×D18111yescharacteristic, complemented
261C22⋊C8—1811no—
262C22⋊C8C2×D18111yescharacteristic, complemented
263C4×C8—1811no—
264C24—3621no—
265C24—3621no—
266#41—7244no—
267C2×Q8—3621no—
268C2×D4—21no—
269C2×D4—3622no—
270C2×D4—3621no—
271C2×D4—3621no—
272C2×D4—3622no—
273C2×D4—3621no—
274C2×D4—3621no—
275C2×D4—3621no—
276C2×D4—3621no—
277C2×D4—3621no—
278C2×D4—1811no—
279C2×D4—1811no—
280C2×D4—1811no—
281C2×D4—1811no—
282C2×D4—7241no—
283C2×D4—7241no—
284C2×D4—7244no—
285C2×D4C22×D18111yescharacteristic
286C22×C4—21no—
287C22×C4—3621no—
288C22×C4—3621no—
289C22×C4—3621no—
290C22×C4—1811no—
291C22×C4C22×D18111yescharacteristic
292D8—3622no—
293D8—7241no—
294D8—7241no—
295C2×C8—1811no—
296C2×C8—1811no—
297C2×C8—7241no—
298C2×C8—7241no—
299C2×C8C22×D18111yescharacteristic
300C2×C8C22×D18111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—3621no—
303C4⋊C4—3621no—
304C4⋊C4—1811no—
305C4⋊C4—1811no—
306C4⋊C4C22×D18111yescharacteristic
307C4⋊C4C22×D18111yescharacteristic
308C4⋊C4C22×D18111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—3621no—
311C22⋊C4—3621no—
312C22⋊C4—3621no—
313C22⋊C4—3621no—
314C22⋊C4—3621no—
315C22⋊C4—1811no—
316C22⋊C4—1811no—
317C42—1811no—
318C23—21no—
319C23—3621no—
320C23—3621no—
321C23—3621no—
322C23—14481no—
323C23—14481no—
324C23—1811no—
325C23—7242no—
326C23—7242no—
327C23—7242no—
328C23—7242no—
329C23D4×D18111yescharacteristic
330Q8—7242no—
331D4—21no—
332D4—21no—
333D4—42no—
334D4—3621no—
335D4—3621no—
336D4—3621no—
337D4—3621no—
338D4—3621no—
339D4—14481no—
340D4—1814no—
341D4—1812no—
342D4—7242no—
343D4—7242no—
344D4—7242no—
345D4—7242no—
346D4—7242no—
347D4—7242no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—3621no—
355C2×C4—3621no—
356C2×C4—3621no—
357C2×C4—1811no—
358C2×C4—1811no—
359C2×C4—1811no—
360C2×C4—7242no—
361C2×C4—7242no—
362C2×C4—7242no—
363C2×C4D4×D18111yescharacteristic
364C2×C4C23×D18111yescharacteristic
365C8—21no—
366C8—21no—
367C8—3621no—
368C8—3621no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—3621no—
375C22—3621no—
376C22—3622no—
377C22—14484no—
378C22—14484no—
379C22—1812no—
380C22—7241no—
381C22—7241no—
382C22—7241no—
383C22—7241no—
384C22—7241no—
385C22—7241no—
386C22—7241no—
387C22—7241no—
388C22D8×D18112yes—
389C22C2×D4×D18111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—3621no—
395C4—3621no—
396C4—1812no—
397C4—7241no—
398C4#41×D18111yescharacteristic
399C4#1915386211yescharacteristic
400C2—22no—
401C2—81no—
402C2—3622no—
403C2—14481no—
404C2—14481no—
405C2—7242no—
406C2#2604192111yescharacteristic
407C2C2×D8×D18111yescharacteristic
408C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#480×C181C2
socleC22×C181C22×D4
hypercenter#480D181
hypocenterC181#3294
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #26041930C2semidirect
2. #26041913C2semidirect
3. #26041624C2semidirect
4. #26041594C2semidirect
5. #26041558C2semidirect
6. #26041516C2semidirect
7. #26041513C2semidirect
8. #26041473C2semidirect
9. #26041415C2semidirect
10. #26041414C2semidirect
11. #26041361C2semidirect
12. #26041342C2semidirect
13. C2×#19153736C2semidirect
14. #102×D181C2semidirect
15. #480×C181C2semidirect
21. C2×D1448C22semidirect
22. C2×#15668434C22semidirect
23. C22×#13089678C22semidirect
24. C2×C8×D181C22semidirect
25. #19153815C22semidirect
31. #19153791C22semidirect
32. #19153790C22semidirect
37. #19153778C22semidirect
39. C4⋊C4×D181C22semidirect
40. #19153749C22semidirect
41. #19153745C22semidirect
43. #19153738C22semidirect
44. #19153737C22semidirect
47. #19153736C22semidirect
48. #19153736C22semidirect
49. #19153736C22semidirect
50. #19153728C22semidirect
51. C8×Dic181C22semidirect
53. C2×C4⋊C4×C181C22semidirect
54. #107×C181C22semidirect
55. #107×C181C22semidirect
56. #102×C181C22semidirect
57. #102×C181C22semidirect
58. C22⋊C8×C181C22semidirect
132. D724#41semidirect
137. C22⋊D181D8semidirect
204. C181#3294semidirect
210. #480D181semidirect
246. C2×C4⋊C4C2×D181semidirect
248. #107C2×D181semidirect
249. #107C2×D181semidirect
259. #102C2×D181semidirect
260. #102C2×D181semidirect
262. C22⋊C8C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260419302
#260419132
#260416242
#260415942
#260415582
#260415162
#260415132
#260414732
#260414152
#260414142
#260413612
#260413422
C2×#191537362
#102×D1812
#480×C1812
#3294181