Finite Group Databasebeta

← #37543400

Subgroups — #37543400

Order 23168.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19153840C211yesmaximal, characteristic, complemented
2C2×#19153822C211yesmaximal, characteristic, complemented
3#26041858C211yesmaximal, characteristic, complemented
4#26041845C211yesmaximal, characteristic, complemented
5#26041530C211yesmaximal, characteristic, complemented
6#26041529C211yesmaximal, characteristic, complemented
7#26041526C211yesmaximal, characteristic, complemented
8#26041523C211yesmaximal, characteristic, complemented
9#26041514C211yesmaximal, characteristic, complemented
10#26041508C211yesmaximal, characteristic, complemented
11#26041507C211yesmaximal, characteristic, complemented
12#26041320C211yesmaximal, characteristic, complemented
13#26041272C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#466×C181C211yesmaximal, characteristic, complemented
16C2×#15668449C2211yescharacteristic
17C2×#15668448C2211yescharacteristic
18C2×D4×D181C2211yescharacteristic
19#19153840—24no—
20C2×#15668438C2211yescharacteristic
21C2×#15668437C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23#19153822—24no—
24C2×#15668433C2211yescharacteristic, complemented
25C2×#15668432C2211yescharacteristic
26C2×#15668432C2211yescharacteristic, complemented
27C2×C8×D181C2211yescharacteristic
28C2×C8×D181C2211yescharacteristic, complemented
29#19153812—21no—
30#19153802—21no—
31#19153796C2211yescharacteristic, complemented
32#19153795C2211yescharacteristic, complemented
33#19153793—21no—
34#19153791C2211yescharacteristic
35#19153790C2211yescharacteristic
36#19153789—21no—
37#19153788—21no—
38#19153787—21no—
39#19153787C2211yescharacteristic
40#19153787C2211yescharacteristic, complemented
41#19153786—21no—
42#19153784—21no—
43#19153774C2211yescharacteristic
44C4⋊C4×D181C2211yescharacteristic
45#19153749C2211yescharacteristic, complemented
46#19153748C2211yescharacteristic, complemented
47#19153747C2211yescharacteristic, complemented
48#19153741C2211yescharacteristic, complemented
49#19153739C2211yescharacteristic, complemented
50#19153738C2211yescharacteristic
51#19153737C2211yescharacteristic
52#19153737C2211yescharacteristic, complemented
53#19153736C2211yescharacteristic
54C2×D8×C181C2211yescharacteristic
55C22×C8×C181C2211yescharacteristic, complemented
56#121×C181C2211yescharacteristic
57#121×C181C2211yescharacteristic, complemented
58#107×C181C2211yescharacteristic, complemented
59#102×C181C2211yescharacteristic
60#102×C181C2211yescharacteristic, complemented
61C23×D181—21no—
62#15668449—22no—
63#15668449—22no—
64#15668448—22no—
65#15668448—22no—
66C2×Dic362D411yescharacteristic
67C2×Dic362C2311yescharacteristic
68C2×D724—21no—
69C2×D724D411yescharacteristic
70C2×D724C2311yescharacteristic
71C2×C22⋊D181—21no—
72C2×C22⋊D181—21no—
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181—21no—
76C2×C22⋊D181D411yescharacteristic
77C2×C22⋊D181D411yescharacteristic
78D4×D181—22no—
79D4×D181—22no—
80C22×Dic181—21no—
81C2×C4×D181—21no—
82C2×C4×D181C2311yescharacteristic
83C2×C4×D181C2311yescharacteristic
84#15668438—22no—
85#15668437—22no—
86#15668434—22no—
87#15668433—22no—
88#15668432—22no—
89#15668432D414yescomplemented
90C2×#13089678C2311yescharacteristic
91C2×#13089678C2311yescharacteristic
92C8×D181—22no—
93C8×D181—22no—
94C4⋊Dic181—21no—
95C4⋊Dic181C2311yescharacteristic
96C4⋊Dic181C2311yescharacteristic
97#15668428—21no—
98#15668428—21no—
99C22⋊Dic181—21no—
100C22⋊Dic181—21no—
101C22⋊Dic181—21no—
102#15668426—21no—
103#15668426—21no—
104#15668426—21no—
105#15668426—21no—
106C4×Dic181—21no—
107C2×D4×C181—21no—
108C2×D4×C181—21no—
109C2×D4×C181C2311yescharacteristic
110C2×D4×C181C2311yescharacteristic
111C22×C4×C181C2311yescharacteristic
112D8×C181—22no—
113C2×C8×C181—22no—
114C2×C8×C181C2311yescharacteristic
115C2×C8×C181C2311yescharacteristic
116C4⋊C4×C181C2311yescharacteristic
117C4⋊C4×C181C2311yescharacteristic
118C22⋊C4×C181—21no—
119C22⋊C4×C181—21no—
120C22×D181—21no—
121C22×D181—42no—
122C22×D181—81no—
123C22×D181—81no—
124C22×D181C2×D411yescharacteristic
125C22×D181C2×D411yescharacteristic
126Dic362—22no—
127Dic362—21no—
128Dic362—21no—
129D724—22no—
130D724—21no—
131D724—21no—
132D724—81no—
133C22⋊D181—22no—
134C22⋊D181—22no—
135C22⋊D181—42no—
136C22⋊D181—42no—
137C22⋊D181—81no—
138C22⋊D181—81no—
139C22⋊D181—81no—
140C2×Dic181—21no—
141C2×Dic181—21no—
142C2×Dic181—21no—
143C2×Dic181—42no—
144C2×Dic181C2×D411yescharacteristic
145C2×Dic181C2×D411yescharacteristic
146C4×D181—21no—
147C4×D181—21no—
148C4×D181—81no—
149C4×D181C2×D412yes—
150C4×D181#4112yes—
151#13089678—21no—
152#13089678C2×D412yes—
153C23×C181—21no—
154C23×C181—21no—
155C23×C181C2×D411yescharacteristic
156D4×C181—21no—
157D4×C181—21no—
158D4×C181—21no—
159D4×C181—21no—
160D4×C181—81no—
161D4×C181—81no—
162C2×C4×C181—21no—
163C2×C4×C181—21no—
164C2×C4×C181—21no—
165C2×C4×C181—21no—
166C2×C4×C181C2×D411yescharacteristic
167C2×C4×C181C2411yescharacteristic
168C8×C181—21no—
169C8×C181C2×D412yes—
170C22×C181—21no—
171C22×C181—21no—
172C22×C181—21no—
173C22×C181—41no—
174C22×C181—41no—
175C22×C181—41no—
176C22×C181—41no—
177C22×C181—41no—
178C22×C181—41no—
179C22×C181C22×D411yescharacteristic
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—84no—
189C2×D181#12112yes—
190C4×C181—21no—
191C4×C181—41no—
192C4×C181—41no—
193C4×C181C22×D411yescharacteristic
194C4×C181C2×#4111yescharacteristic
195Dic181—21no—
196Dic181—41no—
197Dic181—41no—
198Dic181—41no—
199Dic181#12112yes—
200C2×C181—41no—
201C2×C181—81no—
202C2×C181—81no—
203C2×C181C2×#12111yescharacteristic
204C2×C181#57611yescharacteristic
205C2×C181#57711yescharacteristic
206D181—22no—
207D181—41no—
208D181—81no—
209C181#306211yescharacteristic, complemented, Sylow
210#3062—1811nomaximal, Sylow
211C2×AGL(1,ℤ/8)—1811no—
212C2×#131—1811no—
213#537—1811no—
214#535—1811no—
215#469—1811no—
216#469—1811no—
217#468—1811no—
218#468—1811no—
219#466—1811no—
220#466D18111yescharacteristic, complemented
221#465—1811no—
222#465—1811no—
223#428—1811no—
224#416—1811no—
225C2×#102—1811no—
226C2×#41—1811no—
227C2×#41—1811no—
228C22×D4—1811no—
229AGL(1,ℤ/8)—3624no—
230C2×SD16—1811no—
231C2×SD16—1811no—
232C2×D8—1811no—
233C2×D8C2×D18111yescharacteristic
234#131—3624no—
235C2×M16—1811no—
236C2×M16—1811no—
237C2×M16—1811no—
238C22×C8—1811no—
239C22×C8—1811no—
240C22×C8C2×D18111yescharacteristic, complemented
241#127—3621no—
242#124—3621no—
243C22⋊Q8—3621no—
244C22⋊Q8—1811no—
245C22⋊Q8—1811no—
246#121—3621no—
247#121—3621no—
248#121—3621no—
249#121—1811no—
250#121—1811no—
251#121—1811no—
252#121—1811no—
253#121C2×D18111yescharacteristic
254#121C2×D18111yescharacteristic, complemented
255#120—3621no—
256#120—3621no—
257#117—1811no—
258C2×C4⋊C4—1811no—
259#107—1811no—
260#107C2×D18111yescharacteristic, complemented
261#106—1811no—
262#106—1811no—
263#103—1811no—
264#103—1811no—
265#102—1811no—
266#102—1811no—
267#102—1811no—
268#102—1811no—
269#102C2×D18111yescharacteristic
270#102C2×D18111yescharacteristic, complemented
271C24—3621no—
272#41—3622no—
273#41—3622no—
274#41—3622no—
275#41—3622no—
276C2×Q8—1811no—
277C2×Q8—1811no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—3621no—
281C2×D4—3621no—
282C2×D4—3621no—
283C2×D4—3621no—
284C2×D4—3621no—
285C2×D4—3622no—
286C2×D4—3622no—
287C2×D4—3621no—
288C2×D4—1811no—
289C2×D4—1811no—
290C2×D4—1811no—
291C2×D4—1811no—
292C2×D4C22×D18111yescharacteristic
293C2×D4C22×D18111yescharacteristic
294C22×C4—3621no—
295C22×C4—3621no—
296C22×C4—1811no—
297C22×C4—1811no—
298C22×C4C22×D18111yescharacteristic
299SD16—3622no—
300SD16—3622no—
301D8—22no—
302D8—3622no—
303M16—3622no—
304M16—3622no—
305M16—1814no—
306C2×C8—22no—
307C2×C8—3622no—
308C2×C8—3622no—
309C2×C8—1811no—
310C2×C8—1811no—
311C2×C8C22×D18111yescharacteristic
312C2×C8C22×D18111yescharacteristic
313C4⋊C4—3621no—
314C4⋊C4—3621no—
315C4⋊C4—3621no—
316C4⋊C4—1811no—
317C4⋊C4—1811no—
318C4⋊C4C22×D18111yescharacteristic
319C4⋊C4C22×D18111yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—3621no—
323C22⋊C4—3621no—
324C22⋊C4—3621no—
325C22⋊C4—3621no—
326C22⋊C4—3621no—
327C22⋊C4—3621no—
328C22⋊C4—3621no—
329C42—3621no—
330C23—21no—
331C23—21no—
332C23—3621no—
333C23—14481no—
334C23—14481no—
335C23—1811no—
336C23—1811no—
337C23—7242no—
338C23D4×D18111yescharacteristic
339Q8—3622no—
340Q8—3621no—
341Q8—3621no—
342D4—21no—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—81no—
347D4—81no—
348D4—3622no—
349D4—3622no—
350D4—3622no—
351D4—3621no—
352D4—3621no—
353D4—14481no—
354D4—14481no—
355D4—14481no—
356D4—14481no—
357D4—7242no—
358D4—7242no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—3621no—
364C2×C4—3621no—
365C2×C4—3621no—
366C2×C4—3621no—
367C2×C4—3621no—
368C2×C4—14481no—
369C2×C4—1811no—
370C2×C4—1811no—
371C2×C4—1812no—
372C2×C4—1812no—
373C2×C4—7242no—
374C2×C4D4×D18111yescharacteristic
375C2×C4C23×D18111yescharacteristic
376C8—21no—
377C8—3621no—
378C8—1812no—
379C8D4×D18112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—3621no—
390C22—3621no—
391C22—3621no—
392C22—3621no—
393C22—3621no—
394C22—14484no—
395C22—1812no—
396C22—7241no—
397C22—7241no—
398C22—7241no—
399C22C2×D4×D18111yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—3621no—
404C4—1812no—
405C4—7241no—
406C4—7241no—
407C4—7241no—
408C4C2×D4×D18111yescharacteristic
409C4#41×D18111yescharacteristic
410C2—41no—
411C2—81no—
412C2—81no—
413C2—3622no—
414C2—14481no—
415C2—7241no—
416C2#121×D18111yescharacteristic
417C2#2604208011yescharacteristic
418C2#2604208611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#466×C181C2
socleC22×C181C22×D4
hypercenter#466D181
hypocenterC181#3062
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#19153840C2semidirect
2. C2×#19153822C2semidirect
3. #26041858C2semidirect
4. #26041845C2semidirect
5. #26041530C2semidirect
6. #26041529C2semidirect
7. #26041526C2semidirect
8. #26041523C2semidirect
9. #26041514C2semidirect
10. #26041508C2semidirect
11. #26041507C2semidirect
12. #26041320C2semidirect
13. #26041272C2semidirect
14. #102×D181C2semidirect
15. #466×C181C2semidirect
24. C2×#15668433C22semidirect
26. C2×#15668432C22semidirect
28. C2×C8×D181C22semidirect
31. #19153796C22semidirect
32. #19153795C22semidirect
40. #19153787C22semidirect
45. #19153749C22semidirect
46. #19153748C22semidirect
47. #19153747C22semidirect
48. #19153741C22semidirect
49. #19153739C22semidirect
52. #19153737C22semidirect
55. C22×C8×C181C22semidirect
57. #121×C181C22semidirect
58. #107×C181C22semidirect
60. #102×C181C22semidirect
89. #15668432D4semidirect
209. C181#3062semidirect
220. #466D181semidirect
240. C22×C8C2×D181semidirect
254. #121C2×D181semidirect
260. #107C2×D181semidirect
270. #102C2×D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538402
C2×#191538222
#260418582
#260418452
#260415302
#260415292
#260415262
#260415232
#260415142
#260415082
#260415072
#260413202
#260412722
#102×D1812
#466×C1812
#3062181