Finite Group Databasebeta

← #37543719

Subgroups — #37543719

Order 23168.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041826C211yesmaximal, characteristic, complemented
2C4×D4×D181C211yesmaximal, characteristic, complemented
3#26041594C211yesmaximal, characteristic, complemented
4#26041591C211yesmaximal, characteristic, complemented
5#26041558C211yesmaximal, characteristic, complemented
6#26041557C211yesmaximal, characteristic, complemented
7#26041473C211yesmaximal, characteristic, complemented
8#26041472C211yesmaximal, characteristic, complemented
9#26041414C211yesmaximal, characteristic, complemented
10#26041411C211yesmaximal, characteristic, complemented
11C4×D1448C211yesmaximal, characteristic, complemented
12C4×#15668434C211yesmaximal, characteristic, complemented
13C4×#15668434C211yesmaximal, characteristic, complemented
14#26041330C211yesmaximal, characteristic, complemented
15C4×D8×C181C211yesmaximal, characteristic, complemented
16C2×#15668449—21no—
17C2×D4×D181C2211yescharacteristic
18C22×C4×D181—21no—
19C2×D1448C2211yescharacteristic
20C2×#15668434C2211yescharacteristic
21C2×#15668434C2211yescharacteristic
22#19153815C2211yescharacteristic, complemented
23#19153812C2211yescharacteristic, complemented
24#19153802—21no—
25#19153791C2211yescharacteristic
26#19153789—21no—
27#19153787C2211yescharacteristic
28C4×D724C2211yescharacteristic
29C4×D724C2211yescharacteristic, complemented
30D4×Dic181C2211yescharacteristic
31#19153778C2211yescharacteristic
32C4×C22⋊D181—21no—
33C4×C22⋊D181—21no—
34#19153776—21no—
35C4⋊C4×D181C2211yescharacteristic
36C22⋊C4×D181—21no—
37C42×D181C2211yescharacteristic
38#19153750C2211yescharacteristic, complemented
39#19153749C2211yescharacteristic, complemented
40#19153749C2211yescharacteristic, complemented
41#19153745C2211yescharacteristic, complemented
42#19153745C2211yescharacteristic, complemented
43#19153738C2211yescharacteristic
44#19153738C2211yescharacteristic, complemented
45#19153737C2211yescharacteristic
46#19153737C2211yescharacteristic, complemented
47#19153736C2211yescharacteristic
48#19153736C2211yescharacteristic, complemented
49#19153728C2211yescharacteristic
50#19153728C2211yescharacteristic
51C4×#13089678C2211yescharacteristic, complemented
52C2×D8×C181C2211yescharacteristic
53C4×D4×C181C2211yescharacteristic
54C4×D4×C181C2211yescharacteristic, complemented
55#107×C181C2211yescharacteristic, complemented
56#102×C181C2211yescharacteristic
57#102×C181C2211yescharacteristic, complemented
58C4×C8×C181C2211yescharacteristic, complemented
59C23×D181—21no—
60#15668449—44no—
61C2×Dic362—21no—
62C2×D724—21no—
63C2×D724C2311yescharacteristic
64C2×D724C2311yescharacteristic
65C2×C22⋊D181—21no—
66C2×C22⋊D181—21no—
67C2×C22⋊D181—21no—
68C2×C22⋊D181—21no—
69D4×D181—22no—
70D4×D181—22no—
71C22×Dic181—21no—
72C2×C4×D181—21no—
73C2×C4×D181—21no—
74C2×C4×D181—21no—
75C2×C4×D181—21no—
76C2×C4×D181—44no—
77C2×C4×D181D411yescharacteristic
78C2×C4×D181D411yescharacteristic
79C2×C4×D181C2311yescharacteristic
80D1448—22no—
81#15668434—22no—
82#15668434—22no—
83C2×#13089678C2311yescharacteristic
84C2×#13089678C2311yescharacteristic
85C4⋊Dic181C2311yescharacteristic
86C4⋊Dic181C2311yescharacteristic
87#15668428—21no—
88#15668428—21no—
89C22⋊Dic181—21no—
90C22⋊Dic181—21no—
91#15668426—21no—
92#15668426—21no—
93#15668426—21no—
94#15668426—21no—
95C4×Dic181D411yescharacteristic
96C4×Dic181D411yescharacteristic
97C4×Dic181C2311yescharacteristic
98C2×D4×C181C2311yescharacteristic
99C2×D4×C181C2311yescharacteristic
100C22×C4×C181—21no—
101C22×C4×C181—21no—
102D8×C181—22no—
103C2×C8×C181C2311yescharacteristic
104C2×C8×C181C2311yescharacteristic
105C4⋊C4×C181C2311yescharacteristic
106C4⋊C4×C181C2311yescharacteristic
107C22⋊C4×C181—21no—
108C22⋊C4×C181—21no—
109C42×C181C2311yescharacteristic
110C22×D181—24no—
111C22×D181—21no—
112C22×D181—21no—
113C22×D181—42no—
114C22×D181—42no—
115C22×D181C2×D411yescharacteristic
116Dic362—42no—
117D724—21no—
118D724—21no—
119D724—21no—
120D724—42no—
121D724#4112yescomplemented
122C22⋊D181—24no—
123C22⋊D181—42no—
124C22⋊D181—42no—
125C22⋊D181—42no—
126C2×Dic181—21no—
127C2×Dic181—21no—
128C2×Dic181—42no—
129C2×Dic181C2×D411yescharacteristic
130C2×Dic181C2×D411yescharacteristic
131C2×Dic181C2×D411yescharacteristic
132C4×D181—21no—
133C4×D181—21no—
134C4×D181—41no—
135C4×D181—42no—
136C4×D181—42no—
137C4×D181—42no—
138C4×D181—42no—
139C4×D181D814yescomplemented
140#13089678—21no—
141#13089678—21no—
142C23×C181—21no—
143C23×C181—21no—
144D4×C181—21no—
145D4×C181—21no—
146D4×C181—21no—
147D4×C181#4112yescomplemented
148C2×C4×C181—21no—
149C2×C4×C181—21no—
150C2×C4×C181—42no—
151C2×C4×C181—42no—
152C2×C4×C181C2×D411yescharacteristic
153C2×C4×C181C2×D411yescharacteristic
154C2×C4×C181C2411yescharacteristic
155C8×C181—21no—
156C8×C181—21no—
157C22×C181—22no—
158C22×C181—41no—
159C22×C181—41no—
160C22×C181—41no—
161C22×C181—41no—
162C22×C181—41no—
163C22×C181C22×D411yescharacteristic
164C2×D181—21no—
165C2×D181—21no—
166C2×D181—22no—
167C2×D181—48no—
168C2×D181—41no—
169C2×D181—41no—
170C2×D181—41no—
171C2×D181—41no—
172C2×D181—41no—
173C2×D181C2×D812yes—
174C4×C181—21no—
175C4×C181—41no—
176C4×C181—41no—
177C4×C181C2×D812yes—
178C4×C181C2×#4111yescharacteristic
179C4×C181C2×#4111yescharacteristic
180Dic181—21no—
181Dic181—21no—
182Dic181—41no—
183Dic181—41no—
184Dic181C2×D812yes—
185C2×C181—42no—
186C2×C181—81no—
187C2×C181#52511yescharacteristic
188C2×C181C22×D811yescharacteristic
189C2×C181#57511yescharacteristic
190D181—22no—
191D181—42no—
192D181—81no—
193C181#310011yescharacteristic, complemented, Sylow
194#3100—1811nomaximal, Sylow
195#532—1811no—
196C2×C4×D4—1811no—
197#480—1811no—
198#480—1811no—
199#474—1811no—
200#474—1811no—
201#459—1811no—
202#459—1811no—
203#447—1811no—
204#447—1811no—
205C4×D8—1811no—
206C4×D8—1811no—
207C4×D8—1811no—
208C4×D8D18111yescharacteristic, complemented
209#431—1811no—
210C2×#41—3621no—
211C22×D4—1811no—
212C23×C4—3621no—
213C2×D8—1811no—
214C2×D8—1811no—
215C2×D8—1811no—
216C2×D8C2×D18111yescharacteristic
217C4⋊Q8—1811no—
218#127—1811no—
219#124—3621no—
220#121—3621no—
221#121—1811no—
222#121—1811no—
223C4×D4—3621no—
224C4×D4—3621no—
225C4×D4—3621no—
226C4×D4—1811no—
227C4×D4—1811no—
228C4×D4—1811no—
229C4×D4—1811no—
230C4×D4C2×D18111yescharacteristic
231C4×D4C2×D18111yescharacteristic, complemented
232C2×C4⋊C4—1811no—
233C2×C22⋊C4—3621no—
234C2×C42—1811no—
235#107—1811no—
236#107—1811no—
237#107—1811no—
238#107C2×D18111yescharacteristic, complemented
239C4⋊C8—1811no—
240C4⋊C8—1811no—
241#102—1811no—
242#102—1811no—
243#102—1811no—
244#102—1811no—
245#102—1811no—
246#102—1811no—
247#102C2×D18111yescharacteristic
248#102C2×D18111yescharacteristic, complemented
249C22⋊C8—1811no—
250C22⋊C8—1811no—
251C4×C8—1811no—
252C4×C8C2×D18111yescharacteristic, complemented
253C24—3621no—
254#41—7244no—
255C2×Q8—3621no—
256C2×D4—3621no—
257C2×D4—3622no—
258C2×D4—3622no—
259C2×D4—3621no—
260C2×D4—3621no—
261C2×D4—3621no—
262C2×D4—3621no—
263C2×D4—1811no—
264C2×D4—1811no—
265C2×D4C22×D18111yescharacteristic
266C2×D4C22×D18111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3621no—
270C22×C4—3621no—
271C22×C4—3621no—
272C22×C4—3621no—
273C22×C4—3621no—
274C22×C4—1811no—
275C22×C4—1811no—
276C22×C4—1811no—
277C22×C4—7244no—
278D8—22no—
279D8—3622no—
280D8—3622no—
281D8—3622no—
282C2×C8—1811no—
283C2×C8—1811no—
284C2×C8C22×D18111yescharacteristic
285C2×C8C22×D18111yescharacteristic
286C4⋊C4—3621no—
287C4⋊C4—3621no—
288C4⋊C4—1811no—
289C4⋊C4—1811no—
290C4⋊C4C22×D18111yescharacteristic
291C4⋊C4C22×D18111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—3621no—
295C22⋊C4—3621no—
296C22⋊C4—3621no—
297C22⋊C4—3621no—
298C22⋊C4—3621no—
299C22⋊C4—3621no—
300C42—1811no—
301C42—1811no—
302C42—1811no—
303C42C22×D18111yescharacteristic
304C23—21no—
305C23—21no—
306C23—3624no—
307C23—3621no—
308C23—3621no—
309C23—1811no—
310C23—7242no—
311C23—7242no—
312Q8—7242no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—3624no—
317D4—3621no—
318D4—3621no—
319D4—3621no—
320D4—1812no—
321D4—7242no—
322D4—7242no—
323D4—7242no—
324D4—7242no—
325D4#1566844912yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—3621no—
331C2×C4—3621no—
332C2×C4—3621no—
333C2×C4—3621no—
334C2×C4—1811no—
335C2×C4—1811no—
336C2×C4—1811no—
337C2×C4—1814no—
338C2×C4—7241no—
339C2×C4—7242no—
340C2×C4—7242no—
341C2×C4—7242no—
342C2×C4—7242no—
343C2×C4—7242no—
344C2×C4D4×D18111yescharacteristic
345C2×C4D4×D18111yescharacteristic
346C2×C4C23×D18111yescharacteristic
347C8—21no—
348C8—21no—
349C8—3621no—
350C8—3621no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—3621no—
358C22—3621no—
359C22—3622no—
360C22—1812no—
361C22—7248no—
362C22—7241no—
363C22—7241no—
364C22—7241no—
365C22—7241no—
366C22—7241no—
367C22C2×D4×D18111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—3621no—
372C4—3621no—
373C4—1812no—
374C4—7241no—
375C4—7241no—
376C4D8×D18112yes—
377C4#41×D18111yescharacteristic
378C4C2×#1566844911yescharacteristic
379C2—42no—
380C2—81no—
381C2—3622no—
382C2—14481no—
383C2—7242no—
384C2#2604178811yescharacteristic
385C2C2×D8×D18111yescharacteristic
386C2#2604207611yescharacteristic
subgroupG/H
centerC2×C4D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
FittingC4×D8×C181C2
socleC22×C181C22×D4
hypercenterC4×D8D181
hypocenterC181#3100
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #26041826C2semidirect
2. C4×D4×D181C2semidirect
3. #26041594C2semidirect
4. #26041591C2semidirect
5. #26041558C2semidirect
6. #26041557C2semidirect
7. #26041473C2semidirect
8. #26041472C2semidirect
9. #26041414C2semidirect
10. #26041411C2semidirect
11. C4×D1448C2semidirect
12. C4×#15668434C2semidirect
13. C4×#15668434C2semidirect
14. #26041330C2semidirect
15. C4×D8×C181C2semidirect
22. #19153815C22semidirect
23. #19153812C22semidirect
29. C4×D724C22semidirect
38. #19153750C22semidirect
39. #19153749C22semidirect
40. #19153749C22semidirect
41. #19153745C22semidirect
42. #19153745C22semidirect
44. #19153738C22semidirect
46. #19153737C22semidirect
48. #19153736C22semidirect
51. C4×#13089678C22semidirect
54. C4×D4×C181C22semidirect
55. #107×C181C22semidirect
57. #102×C181C22semidirect
58. C4×C8×C181C22semidirect
121. D724#41semidirect
139. C4×D181D8semidirect
147. D4×C181#41semidirect
193. C181#3100semidirect
208. C4×D8D181semidirect
231. C4×D4C2×D181semidirect
238. #107C2×D181semidirect
248. #102C2×D181semidirect
252. C4×C8C2×D181semidirect
325. D4#15668449semidirect

Maximal subgroups

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

subgroupindex
#260418262
C4×D4×D1812
#260415942
#260415912
#260415582
#260415572
#260414732
#260414722
#260414142
#260414112
C4×D14482
C4×#156684342
#260413302
C4×D8×C1812
#3100181