Finite Group Databasebeta

← #37545263

Subgroups — #37545263

Order 23168.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153843C211yesmaximal, characteristic, complemented
2C2×#19153837C211yesmaximal, characteristic, complemented
3#26041951C211yesmaximal, characteristic, complemented
4#26041924C211yesmaximal, characteristic, complemented
5#26041668C211yesmaximal, characteristic, complemented
6#26041526C211yesmaximal, characteristic, complemented
7#26041516C211yesmaximal, characteristic, complemented
8#26041501C211yesmaximal, characteristic, complemented
9#26041474C211yesmaximal, characteristic, complemented
10#26041444C211yesmaximal, characteristic, complemented
11#26041427C211yesmaximal, characteristic, complemented
12#26041425C211yesmaximal, characteristic, complemented
13#26041414C211yesmaximal, characteristic, complemented
14#26041352C211yesmaximal, characteristic, complemented
15#440×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668450C2211yescharacteristic, complemented
18C2×#15668448C2211yescharacteristic
19C2×D4×D181C2211yescharacteristic
20#19153843—24no—
21#19153837—24no—
22C2×#15668439C2211yescharacteristic, complemented
23C2×#15668438C2211yescharacteristic, complemented
24C2×#15668438C2211yescharacteristic, complemented
25C2×#15668436C2211yescharacteristic
26C2×D1448C2211yescharacteristic
27C2×D1448C2211yescharacteristic
28C2×#15668434C2211yescharacteristic
29C2×#15668434C2211yescharacteristic
30C2×#15668432C2211yescharacteristic
31C2×C8×D181C2211yescharacteristic, complemented
32#19153813—21no—
33#19153813C2211yescharacteristic, complemented
34#19153804C2211yescharacteristic
35#19153800—21no—
36#19153796C2211yescharacteristic
37#19153791—21no—
38#19153791—21no—
39#19153791C2211yescharacteristic
40#19153791C2211yescharacteristic
41#19153791C2211yescharacteristic, complemented
42#19153790—21no—
43#19153786—21no—
44C4×D724—21no—
45C4×D724C2211yescharacteristic
46C2×#15668426—21no—
47C4⋊#13089678C2211yescharacteristic, complemented
48#19153739C2211yescharacteristic, complemented
49#19153736C2211yescharacteristic
50#19153736C2211yescharacteristic, complemented
51#19153736C2211yescharacteristic, complemented
52#19153728C2211yescharacteristic
53#19153728C2211yescharacteristic, complemented
54C2×SD16×C181C2211yescharacteristic
55C4×Q8×C181C2211yescharacteristic, complemented
56C4×D4×C181C2211yescharacteristic
57#107×C181C2211yescharacteristic, complemented
58#103×C181C2211yescharacteristic, complemented
59#102×C181C2211yescharacteristic
60#97×C181C2211yescharacteristic, complemented
61C23×D181—21no—
62#15668450—22no—
63#15668450—22no—
64#15668450—41no—
65#15668450—41no—
66#15668448—22no—
67#15668448—41no—
68C2×Dic362C2311yescharacteristic
69C2×D724—21no—
70C2×D724—21no—
71C2×D724—21no—
72C2×D724—21no—
73C2×D724—21no—
74C2×D724—21no—
75C2×D724—21no—
76C2×D724D411yescharacteristic
77C2×D724C2311yescharacteristic
78C2×D724C2311yescharacteristic
79C2×D724C2311yescharacteristic
80C2×C22⋊D181—21no—
81C2×C22⋊D181—21no—
82D4×D181—22no—
83D4×D181—41no—
84C22×Dic181—21no—
85C2×C4×D181—21no—
86C2×C4×D181—21no—
87C2×C4×D181C2311yescharacteristic
88C2×C4×D181C2311yescharacteristic
89#15668439—22no—
90#15668438—22no—
91#15668438—41no—
92#15668436—22no—
93D1448—22no—
94D1448—41no—
95#15668434—22no—
96#15668434—22no—
97#15668432—22no—
98C2×#13089678C2311yescharacteristic
99C2×#13089678C2311yescharacteristic
100C8×D181—22no—
101C4⋊Dic181—21no—
102C4⋊Dic181D411yescharacteristic
103#15668426—21no—
104#15668426—21no—
105#15668426—21no—
106#15668426—21no—
107#15668426—21no—
108#15668426—21no—
109#15668426D411yescharacteristic
110#15668426D411yescharacteristic
111C2×Q8×C181C2311yescharacteristic
112C2×D4×C181C2311yescharacteristic
113C22×C4×C181—21no—
114SD16×C181D414yescomplemented
115C2×C8×C181C2311yescharacteristic
116C2×C8×C181C2311yescharacteristic
117C4⋊C4×C181—21no—
118C4⋊C4×C181C2311yescharacteristic
119C4⋊C4×C181C2311yescharacteristic
120C22⋊C4×C181—21no—
121C42×C181—21no—
122C42×C181C2311yescharacteristic
123C22×D181—21no—
124C22×D181—21no—
125C22×D181—21no—
126C22×D181—42no—
127C22×D181—42no—
128C22×D181—81no—
129C22×D181C2×D411yescharacteristic
130C22×D181C2×D411yescharacteristic
131Dic362—21no—
132Dic362—21no—
133D724—21no—
134D724—21no—
135D724—21no—
136D724—21no—
137D724—21no—
138D724—21no—
139D724—41no—
140D724—42no—
141D724—42no—
142D724—42no—
143D724—81no—
144D724—81no—
145D724—81no—
146D724—81no—
147C22⋊D181—42no—
148C22⋊D181—42no—
149C2×Dic181—21no—
150C2×Dic181—42no—
151C2×Dic181C2×D411yescharacteristic
152C2×Dic181C2×D411yescharacteristic
153C4×D181—21no—
154C4×D181—21no—
155C4×D181—21no—
156C4×D181—21no—
157C4×D181—42no—
158C4×D181—42no—
159#13089678—21no—
160#13089678—21no—
161C23×C181—21no—
162Q8×C181—21no—
163Q8×C181C2×D412yes—
164D4×C181—21no—
165D4×C181C2×D412yes—
166C2×C4×C181—21no—
167C2×C4×C181—21no—
168C2×C4×C181—21no—
169C2×C4×C181—81no—
170C2×C4×C181C2×D411yescharacteristic
171C2×C4×C181C2×D411yescharacteristic
172C2×C4×C181C2411yescharacteristic
173C8×C181—21no—
174C8×C181C2×D412yes—
175C22×C181—22no—
176C22×C181—41no—
177C22×C181—41no—
178C22×C181C22×D411yescharacteristic
179C2×D181—21no—
180C2×D181—21no—
181C2×D181—21no—
182C2×D181—21no—
183C2×D181—21no—
184C2×D181—21no—
185C2×D181—41no—
186C2×D181—41no—
187C2×D181—41no—
188C2×D181—41no—
189C2×D181—41no—
190C2×D181—41no—
191C2×D181—41no—
192C2×D181—41no—
193C2×D181—41no—
194C2×D181—84no—
195C4×C181—22no—
196C4×C181—21no—
197C4×C181—21no—
198C4×C181—41no—
199C4×C181—41no—
200C4×C181C22×D411yescharacteristic
201C4×C181H(5,𝔽2)11yescharacteristic
202Dic181—21no—
203Dic181—21no—
204Dic181—41no—
205C2×C181—42no—
206C2×C181D4211yescharacteristic
207C2×C181#57511yescharacteristic
208C2×C181#57611yescharacteristic
209D181—41no—
210D181—41no—
211D181—81no—
212D181—81no—
213D181—81no—
214C181#326811yescharacteristic, complemented, Sylow
215#3268—1811nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1811no—
217C2×#135—1811no—
218#550—1811no—
219#546—1811no—
220#496—1811no—
221#468—1811no—
222#466—1811no—
223#464—1811no—
224#459—1811no—
225#452—1811no—
226#449—1811no—
227#449—1811no—
228#447—1811no—
229#440D18111yescharacteristic, complemented
230#435—1811no—
231C2×#41—1811no—
232C2×#41—1811no—
233C2×#41—1811no—
234C22×D4—1811no—
235AGL(1,ℤ/8)—3624no—
236#135—3624no—
237C2×Q16—1811no—
238C2×SD16—1811no—
239C2×SD16—1811no—
240C2×SD16—1811no—
241C2×SD16C2×D18111yescharacteristic
242C2×D8—1811no—
243C2×D8—1811no—
244C2×D8—1811no—
245C2×D8—1811no—
246C2×M16—1811no—
247C22×C8—1811no—
248#127—3621no—
249#127—1811no—
250#124—1811no—
251#123—3621no—
252C22⋊Q8—1811no—
253#121—3621no—
254#121—3621no—
255#121—3621no—
256#121—1811no—
257#121—1811no—
258#121—1811no—
259#120—3621no—
260C4×Q8C2×D18111yescharacteristic, complemented
261C4×D4—3621no—
262C4×D4—1811no—
263C4×D4C2×D18111yescharacteristic
264C2×C22⋊C4—3621no—
265#107C2×D18111yescharacteristic, complemented
266C4⋊C8—1811no—
267#103—1811no—
268#103C2×D18111yescharacteristic, complemented
269#102—1811no—
270#102—1811no—
271#102—1811no—
272#102C2×D18111yescharacteristic
273C22⋊C8—1811no—
274C22⋊C8—1811no—
275#97C2×D18111yescharacteristic, complemented
276C24—3621no—
277#41—3622no—
278#41—3622no—
279#41—3622no—
280#41—7241no—
281#41—7241no—
282#41—7241no—
283C2×Q8—1811no—
284C2×Q8C22×D18111yescharacteristic
285C2×D4—3621no—
286C2×D4—3621no—
287C2×D4—3621no—
288C2×D4—3621no—
289C2×D4—3621no—
290C2×D4—3622no—
291C2×D4—3621no—
292C2×D4—3621no—
293C2×D4—3621no—
294C2×D4—3621no—
295C2×D4—1811no—
296C2×D4—1811no—
297C2×D4—1811no—
298C2×D4—1811no—
299C2×D4—7241no—
300C2×D4C22×D18111yescharacteristic
301C22×C4—21no—
302C22×C4—3621no—
303C22×C4—3621no—
304C22×C4—3621no—
305C22×C4—1811no—
306C22×C4—1811no—
307Q16—3622no—
308SD16—3622no—
309SD16—3622no—
310SD16—7241no—
311SD16D72414yescomplemented
312D8—3622no—
313D8—3622no—
314D8—3622no—
315D8—7241no—
316M16—3622no—
317C2×C8—3622no—
318C2×C8—1811no—
319C2×C8—1811no—
320C2×C8C22×D18111yescharacteristic
321C2×C8C22×D18111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—3621no—
324C4⋊C4—1811no—
325C4⋊C4C22×D18111yescharacteristic
326C4⋊C4C22×D18111yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—3621no—
329C22⋊C4—3621no—
330C22⋊C4—3621no—
331C22⋊C4—3621no—
332C22⋊C4—3621no—
333C22⋊C4—3621no—
334C22⋊C4—1811no—
335C22⋊C4—1811no—
336C42—21no—
337C42C22×D18111yescharacteristic
338C23—21no—
339C23—3621no—
340C23—3621no—
341C23—3621no—
342C23—14481no—
343C23—1811no—
344C23—1811no—
345C23—7242no—
346C23—7242no—
347Q8—21no—
348Q8—3621no—
349Q8—3621no—
350Q8C2×D72412yes—
351D4—21no—
352D4—3621no—
353D4—3621no—
354D4—3621no—
355D4—3621no—
356D4—3621no—
357D4—3621no—
358D4—14481no—
359D4—14481no—
360D4—14481no—
361D4—14481no—
362D4—7241no—
363D4—7242no—
364D4—7242no—
365D4—7242no—
366D4—7242no—
367D4—7242no—
368D4C2×D72412yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—3621no—
374C2×C4—3621no—
375C2×C4—3621no—
376C2×C4—3621no—
377C2×C4—3621no—
378C2×C4—1811no—
379C2×C4—1811no—
380C2×C4—7242no—
381C2×C4—7242no—
382C2×C4—7242no—
383C2×C4D4×D18111yescharacteristic
384C2×C4D4×D18111yescharacteristic
385C2×C4C23×D18111yescharacteristic
386C8—21no—
387C8—3621no—
388C8—3621no—
389C8C2×D72412yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—3621no—
394C22—3621no—
395C22—3621no—
396C22—3621no—
397C22—3621no—
398C22—3621no—
399C22—14484no—
400C22—7241no—
401C22—7241no—
402C22—7241no—
403C22—7241no—
404C22—7241no—
405C22—7241no—
406C22—7241no—
407C22—7241no—
408C22—7241no—
409C22C2×D4×D18111yescharacteristic
410C4—22no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—3621no—
416C4—3621no—
417C4—7241no—
418C4C22×D72411yescharacteristic
419C4#1915386211yescharacteristic
420C2—42no—
421C2—14481no—
422C2—14481no—
423C2—14481no—
424C2—7241no—
425C2—7241no—
426C2D4×D72411yescharacteristic
427C2#2604207811yescharacteristic
428C2#2604208311yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#440×C181C2
socleC22×C181C22×D4
hypercenter#440D181
hypocenterC181#3268
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#19153843C2semidirect
2. C2×#19153837C2semidirect
3. #26041951C2semidirect
4. #26041924C2semidirect
5. #26041668C2semidirect
6. #26041526C2semidirect
7. #26041516C2semidirect
8. #26041501C2semidirect
9. #26041474C2semidirect
10. #26041444C2semidirect
11. #26041427C2semidirect
12. #26041425C2semidirect
13. #26041414C2semidirect
14. #26041352C2semidirect
15. #440×C181C2semidirect
17. C2×#15668450C22semidirect
22. C2×#15668439C22semidirect
23. C2×#15668438C22semidirect
24. C2×#15668438C22semidirect
31. C2×C8×D181C22semidirect
33. #19153813C22semidirect
41. #19153791C22semidirect
47. C4⋊#13089678C22semidirect
48. #19153739C22semidirect
50. #19153736C22semidirect
51. #19153736C22semidirect
53. #19153728C22semidirect
55. C4×Q8×C181C22semidirect
57. #107×C181C22semidirect
58. #103×C181C22semidirect
60. #97×C181C22semidirect
114. SD16×C181D4semidirect
214. C181#3268semidirect
229. #440D181semidirect
260. C4×Q8C2×D181semidirect
265. #107C2×D181semidirect
268. #103C2×D181semidirect
275. #97C2×D181semidirect
311. SD16D724semidirect

Maximal subgroups

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

subgroupindex
C2×#191538432
C2×#191538372
#260419512
#260419242
#260416682
#260415262
#260415162
#260415012
#260414742
#260414442
#260414272
#260414252
#260414142
#260413522
#440×C1812
#3268181