Finite Group Databasebeta

← #37543396

Subgroups — #37543396

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×#19153843C211yesmaximal, characteristic, complemented
2C2×#19153824C211yesmaximal, characteristic, complemented
3#26041859C211yesmaximal, characteristic, complemented
4#26041845C211yesmaximal, characteristic, complemented
5#26041532C211yesmaximal, characteristic, complemented
6#26041531C211yesmaximal, characteristic, complemented
7#26041528C211yesmaximal, characteristic, complemented
8#26041516C211yesmaximal, characteristic, complemented
9#26041513C211yesmaximal, characteristic, complemented
10#26041510C211yesmaximal, characteristic, complemented
11#26041505C211yesmaximal, characteristic, complemented
12#26041320C211yesmaximal, characteristic, complemented
13#26041274C211yesmaximal, characteristic, complemented
14#102×D181C211yesmaximal, characteristic, complemented
15#468×C181C211yesmaximal, characteristic, complemented
16C2×#15668450C2211yescharacteristic
17C2×#15668449C2211yescharacteristic
18C2×D4×D181C2211yescharacteristic
19#19153843—24no—
20C2×#15668436C2211yescharacteristic
21C2×D1448C2211yescharacteristic
22C2×#15668434C2211yescharacteristic
23#19153824—24no—
24C2×#15668432C2211yescharacteristic
25C2×#15668432C2211yescharacteristic, complemented
26C22×#13089678C2211yescharacteristic, complemented
27C2×C8×D181C2211yescharacteristic
28C2×C8×D181C2211yescharacteristic, complemented
29#19153812—21no—
30#19153802—21no—
31#19153794—21no—
32#19153792C2211yescharacteristic, complemented
33#19153791—21no—
34#19153791C2211yescharacteristic
35#19153791C2211yescharacteristic, complemented
36#19153790C2211yescharacteristic
37#19153790C2211yescharacteristic, complemented
38#19153789—21no—
39#19153789—21no—
40#19153787C2211yescharacteristic
41#19153786—21no—
42#19153784—21no—
43#19153774C2211yescharacteristic
44C4⋊C4×D181C2211yescharacteristic
45#19153749C2211yescharacteristic, complemented
46#19153748C2211yescharacteristic, complemented
47#19153747C2211yescharacteristic, complemented
48#19153740C2211yescharacteristic, complemented
49#19153738C2211yescharacteristic
50#19153738C2211yescharacteristic, complemented
51#19153737C2211yescharacteristic
52#19153736C2211yescharacteristic
53#19153736C2211yescharacteristic, complemented
54C2×SD16×C181C2211yescharacteristic
55C2×M16×C181C2211yescharacteristic, complemented
56C22⋊Q8×C181C2211yescharacteristic, complemented
57#121×C181C2211yescharacteristic
58#107×C181C2211yescharacteristic, complemented
59#103×C181C2211yescharacteristic, complemented
60#102×C181C2211yescharacteristic
61C23×D181—21no—
62#15668450—22no—
63#15668450—22no—
64#15668449—22no—
65#15668449—22no—
66C2×Dic362D411yescharacteristic
67C2×D724—21no—
68C2×D724—21no—
69C2×D724—21no—
70C2×D724D411yescharacteristic
71C2×D724C2311yescharacteristic
72C2×D724C2311yescharacteristic
73C2×C22⋊D181—21no—
74C2×C22⋊D181—21no—
75C2×C22⋊D181—21no—
76C2×C22⋊D181—21no—
77C2×C22⋊D181D411yescharacteristic
78C2×C22⋊D181D411yescharacteristic
79D4×D181—22no—
80D4×D181—22no—
81C2×C4×D181—21no—
82C2×C4×D181—21no—
83C2×C4×D181C2311yescharacteristic
84C2×C4×D181C2311yescharacteristic
85#15668436—22no—
86D1448—22no—
87#15668434—22no—
88#15668432—22no—
89#15668432D414yescomplemented
90C2×#13089678—22no—
91C2×#13089678C2311yescharacteristic
92C2×#13089678C2311yescharacteristic
93C8×D181—22no—
94C8×D181—22no—
95C4⋊Dic181C2311yescharacteristic
96C4⋊Dic181C2311yescharacteristic
97#15668428—21no—
98#15668428—21no—
99C22⋊Dic181—21no—
100#15668426—21no—
101#15668426—21no—
102#15668426—21no—
103#15668426—21no—
104#15668426—21no—
105#15668426—21no—
106C4×Dic181—21no—
107C2×Q8×C181C2311yescharacteristic
108C2×D4×C181—21no—
109C2×D4×C181C2311yescharacteristic
110C22×C4×C181C2311yescharacteristic
111SD16×C181—22no—
112M16×C181—22no—
113C2×C8×C181C2311yescharacteristic
114C2×C8×C181C2311yescharacteristic
115C4⋊C4×C181—21no—
116C4⋊C4×C181C2311yescharacteristic
117C4⋊C4×C181C2311yescharacteristic
118C22⋊C4×C181—21no—
119C22⋊C4×C181—21no—
120C22×D181—21no—
121C22×D181—21no—
122C22×D181—42no—
123C22×D181—81no—
124C22×D181—81no—
125C22×D181C2×D411yescharacteristic
126C22×D181C2×D411yescharacteristic
127Dic362—22no—
128D724—22no—
129D724—21no—
130D724—21no—
131D724—21no—
132D724—21no—
133D724—42no—
134D724—81no—
135D724—81no—
136C22⋊D181—22no—
137C22⋊D181—22no—
138C22⋊D181—42no—
139C22⋊D181—81no—
140C22⋊D181—81no—
141C22⋊D181—81no—
142C2×Dic181—21no—
143C2×Dic181—21no—
144C2×Dic181C2×D411yescharacteristic
145C2×Dic181C2×D411yescharacteristic
146C4×D181—21no—
147C4×D181—21no—
148C4×D181—42no—
149C4×D181—81no—
150C4×D181C2×D412yes—
151C4×D181#4112yes—
152#13089678—21no—
153#13089678C2×D412yes—
154C23×C181—21no—
155C23×C181C2×D411yescharacteristic
156Q8×C181—21no—
157Q8×C181—21no—
158D4×C181—21no—
159D4×C181—21no—
160D4×C181—81no—
161C2×C4×C181—21no—
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×C181C22×D411yescharacteristic
177C2×D181—21no—
178C2×D181—21no—
179C2×D181—21no—
180C2×D181—21no—
181C2×D181—21no—
182C2×D181—41no—
183C2×D181—41no—
184C2×D181—41no—
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×C181—41no—
194C4×C181C22×D411yescharacteristic
195C4×C181C2×#4111yescharacteristic
196Dic181—21no—
197Dic181—41no—
198Dic181—41no—
199Dic181#12112yes—
200C2×C181—41no—
201C2×C181—81no—
202C2×C181C2×#12111yescharacteristic
203C2×C181#57611yescharacteristic
204C2×C181#57711yescharacteristic
205D181—22no—
206D181—41no—
207D181—81no—
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#468D18111yescharacteristic, complemented
219#466—1811no—
220#466—1811no—
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×SD16C2×D18111yescharacteristic
232C2×D8—1811no—
233C2×D8—1811no—
234#131—3624no—
235C2×M16—1811no—
236C2×M16—1811no—
237C2×M16C2×D18111yescharacteristic, complemented
238C22×C8—1811no—
239C22×C8—1811no—
240C22×C8—1811no—
241#127—3621no—
242#124—3621no—
243C22⋊Q8—3621no—
244C22⋊Q8—1811no—
245C22⋊Q8C2×D18111yescharacteristic, complemented
246#121—3621no—
247#121—3621no—
248#121—3621no—
249#121—1811no—
250#121—1811no—
251#121—1811no—
252#121—1811no—
253#121—1811no—
254#121C2×D18111yescharacteristic
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#103C2×D18111yescharacteristic, complemented
265#102—1811no—
266#102—1811no—
267#102—1811no—
268#102—1811no—
269#102—1811no—
270#102C2×D18111yescharacteristic
271C24—3621no—
272#41—3622no—
273#41—3622no—
274#41—3622no—
275#41—3622no—
276C2×Q8—1811no—
277C2×Q8C22×D18111yescharacteristic
278C2×D4—21no—
279C2×D4—3621no—
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×D4—1811no—
293C2×D4C22×D18111yescharacteristic
294C22×C4—3621no—
295C22×C4—3621no—
296C22×C4—1811no—
297C22×C4—1811no—
298C22×C4C22×D18111yescharacteristic
299SD16—22no—
300SD16—3622no—
301D8—3622no—
302D8—3622no—
303M16—22no—
304M16—3622no—
305M16—1814no—
306C2×C8—3622no—
307C2×C8—3622no—
308C2×C8—3622no—
309C2×C8—1811no—
310C2×C8—1811no—
311C2×C8C22×D18111yescharacteristic
312C2×C8C22×D18111yescharacteristic
313C4⋊C4—21no—
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—3621no—
332C23—3621no—
333C23—14481no—
334C23—14481no—
335C23—1811no—
336C23—1811no—
337C23—7242no—
338C23D4×D18111yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—3622no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—3622no—
346D4—3622no—
347D4—3622no—
348D4—3621no—
349D4—3621no—
350D4—3621no—
351D4—3621no—
352D4—14481no—
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—21no—
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—3621no—
387C22—3621no—
388C22—3621no—
389C22—3621no—
390C22—3621no—
391C22—14484no—
392C22—1812no—
393C22—7241no—
394C22—7241no—
395C22—7241no—
396C22—7241no—
397C22—7241no—
398C22—7241no—
399C22C2×D4×D18111yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—3621no—
405C4—1812no—
406C4—7241no—
407C4—7241no—
408C4C2×D4×D18111yescharacteristic
409C4#41×D18111yescharacteristic
410C2—41no—
411C2—81no—
412C2—3622no—
413C2—14481no—
414C2—14481no—
415C2—7241no—
416C2#121×D18111yescharacteristic
417C2#2604208311yescharacteristic
418C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#468×C181C2
socleC22×C181C22×D4
hypercenter#468D181
hypocenterC181#3062
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#19153843C2semidirect
2. C2×#19153824C2semidirect
3. #26041859C2semidirect
4. #26041845C2semidirect
5. #26041532C2semidirect
6. #26041531C2semidirect
7. #26041528C2semidirect
8. #26041516C2semidirect
9. #26041513C2semidirect
10. #26041510C2semidirect
11. #26041505C2semidirect
12. #26041320C2semidirect
13. #26041274C2semidirect
14. #102×D181C2semidirect
15. #468×C181C2semidirect
25. C2×#15668432C22semidirect
26. C22×#13089678C22semidirect
28. C2×C8×D181C22semidirect
32. #19153792C22semidirect
35. #19153791C22semidirect
37. #19153790C22semidirect
45. #19153749C22semidirect
46. #19153748C22semidirect
47. #19153747C22semidirect
48. #19153740C22semidirect
50. #19153738C22semidirect
53. #19153736C22semidirect
55. C2×M16×C181C22semidirect
56. C22⋊Q8×C181C22semidirect
58. #107×C181C22semidirect
59. #103×C181C22semidirect
89. #15668432D4semidirect
209. C181#3062semidirect
218. #468D181semidirect
237. C2×M16C2×D181semidirect
245. C22⋊Q8C2×D181semidirect
260. #107C2×D181semidirect
264. #103C2×D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538432
C2×#191538242
#260418592
#260418452
#260415322
#260415312
#260415282
#260415162
#260415132
#260415102
#260415052
#260413202
#260412742
#102×D1812
#468×C1812
#3062181