Finite Group Databasebeta

← #24919097

Subgroups — #24919097

Order 10624.

498 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581823C211yesmaximal, characteristic, complemented
2C2×#14581819C211yesmaximal, characteristic, complemented
3#19128362C211yesmaximal, characteristic, complemented
4#19128348C211yesmaximal, characteristic, complemented
5#19128082C211yesmaximal, characteristic, complemented
6#19127958C211yesmaximal, characteristic, complemented
7#19127952C211yesmaximal, characteristic, complemented
8#19127921C211yesmaximal, characteristic, complemented
9#19127919C211yesmaximal, characteristic, complemented
10#19127866C211yesmaximal, characteristic, complemented
11#19127850C211yesmaximal, characteristic, complemented
12#19127848C211yesmaximal, characteristic, complemented
13#19127786C211yesmaximal, characteristic, complemented
14#19127776C211yesmaximal, characteristic, complemented
15#448×C83C211yesmaximal, characteristic, complemented
16C2×#13050591C2211yescharacteristic
17C2×#13050590C2211yescharacteristic
18C2×D4×D83C2211yescharacteristic
19#14581823—24no—
20#14581819—24no—
21C2×#13050580C2211yescharacteristic, complemented
22C2×#13050580C2211yescharacteristic, complemented
23C2×#13050579C2211yescharacteristic, complemented
24C2×#13050577C2211yescharacteristic
25C2×#13050577C2211yescharacteristic
26C2×D664C2211yescharacteristic
27C2×#13050575C2211yescharacteristic
28C2×#13050574C2211yescharacteristic, complemented
29C2×#13050573C2211yescharacteristic
30#14581781—21no—
31#14581781C2211yescharacteristic, complemented
32#14581779C2211yescharacteristic
33#14581774—21no—
34#14581772C2211yescharacteristic
35#14581768—21no—
36#14581768C2211yescharacteristic
37#14581766—21no—
38#14581766C2211yescharacteristic, complemented
39#14581763—21no—
40#14581760—21no—
41Q8×Dic83C2211yescharacteristic, complemented
42#14581754C2211yescharacteristic
43C4×C22⋊D83—21no—
44C4×C22⋊D83C2211yescharacteristic
45C22⋊C4×D83—21no—
46#14581723C2211yescharacteristic, complemented
47Dic83⋊C8C2211yescharacteristic, complemented
48#14581717C2211yescharacteristic, complemented
49#14581714C2211yescharacteristic
50#14581713C2211yescharacteristic
51#14581712C2211yescharacteristic, complemented
52(C2×D83)⋊C8C2211yescharacteristic
53C8×Dic83C2211yescharacteristic, complemented
54C22×Q8×C83C2211yescharacteristic, complemented
55C2×SD16×C83C2211yescharacteristic
56C2×SD16×C83C2211yescharacteristic
57#121×C83C2211yescharacteristic
58#103×C83C2211yescharacteristic, complemented
59#103×C83C2211yescharacteristic, complemented
60C22⋊C8×C83C2211yescharacteristic, complemented
61C23×D83—21no—
62#13050591—22no—
63#13050591—41no—
64#13050590—22no—
65#13050590—41no—
66C2×Dic166C2311yescharacteristic
67C2×D332—21no—
68C2×D332C2311yescharacteristic
69C2×D332C2311yescharacteristic
70C2×C22⋊D83—21no—
71C2×C22⋊D83—21no—
72C2×C22⋊D83—21no—
73C2×C22⋊D83D411yescharacteristic
74D4×D83—22no—
75D4×D83—41no—
76C2×C4×D83—21no—
77C2×C4×D83—21no—
78C2×C4×D83—21no—
79C2×C4×D83C2311yescharacteristic
80#13050580—22no—
81#13050580—22no—
82#13050579—41no—
83#13050577—22no—
84#13050577D414yescomplemented
85D664—22no—
86#13050575—22no—
87#13050574—22no—
88#13050573—22no—
89C2×C83⋊C8C2311yescharacteristic
90C2×C83⋊C8C2311yescharacteristic
91C4⋊Dic83—21no—
92C4⋊Dic83—21no—
93C4⋊Dic83C2311yescharacteristic
94Dic83⋊C4—21no—
95Dic83⋊C4D411yescharacteristic
96C22⋊Dic83—21no—
97C22⋊Dic83—21no—
98C22⋊Dic83D411yescharacteristic
99(C2×D83)⋊C4—21no—
100(C2×D83)⋊C4—21no—
101(C2×D83)⋊C4—21no—
102(C2×D83)⋊C4—21no—
103(C2×D83)⋊C4—21no—
104(C2×D83)⋊C4—21no—
105(C2×D83)⋊C4D411yescharacteristic
106C4×Dic83—21no—
107C4×Dic83C2311yescharacteristic
108C2×Q8×C83—21no—
109C2×Q8×C83—22no—
110C2×Q8×C83—41no—
111C2×Q8×C83C2311yescharacteristic
112C2×Q8×C83C2311yescharacteristic
113C2×D4×C83—21no—
114C2×D4×C83C2311yescharacteristic
115C22×C4×C83—21no—
116C22×C4×C83C2311yescharacteristic
117SD16×C83—22no—
118SD16×C83—41no—
119C2×C8×C83C2311yescharacteristic
120C2×C8×C83C2311yescharacteristic
121C4⋊C4×C83C2311yescharacteristic
122C22⋊C4×C83—21no—
123C23×C83—21no—
124C23×C83C2×D411yescharacteristic
125C22×D83—21no—
126C22×D83—21no—
127C22×D83—42no—
128C22×D83—42no—
129C22×D83—81no—
130C22×D83C2×D411yescharacteristic
131Q8×C83—21no—
132Q8×C83—21no—
133Q8×C83—21no—
134Q8×C83—42no—
135Q8×C83C2×D412yes—
136D4×C83—21no—
137D4×C83—21no—
138D4×C83—81no—
139C2×C4×C83—21no—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83—21no—
144C2×C4×C83—42no—
145C2×C4×C83C2×D411yescharacteristic
146C2×C4×C83C2411yescharacteristic
147C22⋊D83—41no—
148C22⋊D83—42no—
149C22⋊D83—42no—
150C22⋊D83—42no—
151C2×Dic83—21no—
152C2×Dic83—21no—
153C2×Dic83C2×D411yescharacteristic
154C2×Dic83C2×D411yescharacteristic
155C2×Dic83C2×D411yescharacteristic
156D332—21no—
157D332—21no—
158D332—21no—
159D332—42no—
160D332C2×D412yes—
161C4×D83—21no—
162C4×D83—21no—
163C4×D83—42no—
164C4×D83—42no—
165C4×D83—81no—
166Dic166—21no—
167Dic166—21no—
168C8×C83—21no—
169C8×C83—21no—
170C83⋊C8—21no—
171C83⋊C8C2×D412yes—
172C22×C83—21no—
173C22×C83—21no—
174C22×C83—21no—
175C22×C83—41no—
176C22×C83—41no—
177C22×C83—41no—
178C22×C83C22×D411yescharacteristic
179C2×D83—21no—
180C2×D83—22no—
181C2×D83—21no—
182C2×D83—21no—
183C2×D83—41no—
184C2×D83—41no—
185C2×D83—41no—
186C2×D83—41no—
187C2×D83—41no—
188C2×D83—84no—
189C4×C83—21no—
190C4×C83—22no—
191C4×C83—41no—
192C4×C83—41no—
193C4×C83C22×D411yescharacteristic
194C4×C83H(5,𝔽2)11yescharacteristic
195Dic83—21no—
196Dic83—21no—
197Dic83—21no—
198Dic83—41no—
199Dic83—41no—
200C2×C83—41no—
201C2×C83—81no—
202C2×C83D4211yescharacteristic
203C2×C83#57511yescharacteristic
204C2×C83#57711yescharacteristic
205D83—41no—
206D83—42no—
207D83—81no—
208#3275—831nomaximal, Sylow
209C83#327511yescharacteristic, complemented, Sylow
210C2×#137—831no—
211C2×AGL(1,ℤ/8)—831no—
212#548—831no—
213#546—831no—
214#495—831no—
215#470—831no—
216#469—831no—
217#464—831no—
218#463—831no—
219#452—831no—
220#450—831no—
221#449—831no—
222#448D8311yescharacteristic, complemented
223C4×SD16—831no—
224#436—831no—
225C2×#41—831no—
226C2×#41—831no—
227C22×Q8C2×D8311yescharacteristic, complemented
228C22×D4—831no—
229#137—1664no—
230AGL(1,ℤ/8)—1664no—
231C2×Q16—831no—
232C2×Q16—831no—
233C2×SD16—831no—
234C2×SD16—831no—
235C2×SD16—831no—
236C2×SD16C2×D8311yescharacteristic
237C2×SD16C2×D8311yescharacteristic
238C2×D8—831no—
239C2×D8—831no—
240C2×M16—831no—
241C2×M16—831no—
242#124—831no—
243#124—831no—
244#124—1661no—
245#123—1661no—
246C22⋊Q8—831no—
247C22⋊Q8—831no—
248C22⋊Q8—1661no—
249#121—831no—
250#121—1661no—
251#121—1661no—
252#121C2×D8311yescharacteristic
253#120—1661no—
254C4×Q8—831no—
255C4×D4—831no—
256C4×D4—831no—
257C4×D4—1661no—
258C2×C22⋊C4—1661no—
259#106—831no—
260C4⋊C8—831no—
261#103—831no—
262#103C2×D8311yescharacteristic, complemented
263#103C2×D8311yescharacteristic, complemented
264#102—831no—
265#102—831no—
266#102—831no—
267C22⋊C8—831no—
268C22⋊C8C2×D8311yescharacteristic, complemented
269C4×C8—831no—
270C24—1661no—
271#41—3321no—
272#41—3321no—
273#41—1662no—
274#41—1662no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—831no—
279C2×Q8C22×D8311yescharacteristic
280C2×Q8C22×D8311yescharacteristic
281C2×D4—21no—
282C2×D4—3321no—
283C2×D4—831no—
284C2×D4—831no—
285C2×D4—831no—
286C2×D4—1661no—
287C2×D4—1661no—
288C2×D4—1662no—
289C2×D4—1661no—
290C2×D4—1661no—
291C2×D4C22×D8311yescharacteristic
292C22×C4—21no—
293C22×C4—831no—
294C22×C4—1661no—
295C22×C4—1661no—
296C22×C4—1661no—
297C22×C4C22×D8311yescharacteristic
298Q16—1662no—
299Q16—1662no—
300SD16—22no—
301SD16—41no—
302SD16—3321no—
303SD16—834no—
304SD16—1662no—
305D8—1662no—
306D8—1662no—
307M16—1662no—
308M16—1662no—
309C2×C8—831no—
310C2×C8—831no—
311C2×C8C22×D8311yescharacteristic
312C2×C8C22×D8311yescharacteristic
313C4⋊C4—831no—
314C4⋊C4—831no—
315C4⋊C4—1661no—
316C4⋊C4—1661no—
317C4⋊C4—1661no—
318C4⋊C4C22×D8311yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—831no—
321C22⋊C4—831no—
322C22⋊C4—1661no—
323C22⋊C4—1661no—
324C22⋊C4—1661no—
325C22⋊C4—1661no—
326C22⋊C4—1661no—
327C22⋊C4—1661no—
328C22⋊C4—1661no—
329C22⋊C4—1661no—
330C42—831no—
331C42—1661no—
332C23—21no—
333C23—3322no—
334C23—3322no—
335C23—831no—
336C23—6641no—
337C23—1661no—
338C23—1661no—
339C23D4×D8311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—42no—
344Q8—1661no—
345Q8—1661no—
346Q8D4×D8312yes—
347D4—21no—
348D4—21no—
349D4—81no—
350D4—3322no—
351D4—3322no—
352D4—3322no—
353D4—3321no—
354D4—3322no—
355D4—832no—
356D4—1661no—
357D4—1661no—
358D4—1661no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—3322no—
366C2×C4—3322no—
367C2×C4—831no—
368C2×C4—831no—
369C2×C4—831no—
370C2×C4—6641no—
371C2×C4—1661no—
372C2×C4—1661no—
373C2×C4—1661no—
374C2×C4—1661no—
375C2×C4D4×D8311yescharacteristic
376C2×C4C23×D8311yescharacteristic
377C8—21no—
378C8—21no—
379C8—832no—
380C8—1661no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—3321no—
388C22—3321no—
389C22—3321no—
390C22—3321no—
391C22—3321no—
392C22—6644no—
393C22—1662no—
394C22—1661no—
395C22—1661no—
396C22—1661no—
397C22C2×D4×D8311yescharacteristic
398C4—21no—
399C4—22no—
400C4—41no—
401C4—41no—
402C4—3321no—
403C4—3321no—
404C4—1661no—
405C4—1661no—
406C4—1661no—
407C4C2×D4×D8311yescharacteristic
408C4#1458183711yescharacteristic
409C2—41no—
410C2—81no—
411C2—3322no—
412C2—3321no—
413C2—6641no—
414C2#1912833311yescharacteristic
415C2#1912850011yescharacteristic
416C2#1912850711yescharacteristic
subgroupG/H
centerC22C2×D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting#448×C83C2
socleC22×C83C22×D4
hypercenter#448D83
hypocenterC83#3275
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#14581823C2semidirect
2. C2×#14581819C2semidirect
3. #19128362C2semidirect
4. #19128348C2semidirect
5. #19128082C2semidirect
6. #19127958C2semidirect
7. #19127952C2semidirect
8. #19127921C2semidirect
9. #19127919C2semidirect
10. #19127866C2semidirect
11. #19127850C2semidirect
12. #19127848C2semidirect
13. #19127786C2semidirect
14. #19127776C2semidirect
15. #448×C83C2semidirect
21. C2×#13050580C22semidirect
22. C2×#13050580C22semidirect
23. C2×#13050579C22semidirect
28. C2×#13050574C22semidirect
31. #14581781C22semidirect
38. #14581766C22semidirect
41. Q8×Dic83C22semidirect
46. #14581723C22semidirect
47. Dic83⋊C8C22semidirect
48. #14581717C22semidirect
51. #14581712C22semidirect
53. C8×Dic83C22semidirect
54. C22×Q8×C83C22semidirect
58. #103×C83C22semidirect
59. #103×C83C22semidirect
60. C22⋊C8×C83C22semidirect
84. #13050577D4semidirect
209. C83#3275semidirect
222. #448D83semidirect
227. C22×Q8C2×D83semidirect
262. #103C2×D83semidirect
263. #103C2×D83semidirect
268. C22⋊C8C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#145818232
C2×#145818192
#191283622
#191283482
#191280822
#191279582
#191279522
#191279212
#191279192
#191278662
#191278502
#191278482
#191277862
#191277762
#448×C832
#327583