Finite Group Databasebeta

← #24918969

Subgroups — #24918969

Order 10624.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14581822C211yesmaximal, characteristic, complemented
2C22×#13050578C211yesmaximal, characteristic, complemented
3D4×Dic166C211yesmaximal, characteristic, complemented
4#19128096C211yesmaximal, characteristic, complemented
5#19127945C211yesmaximal, characteristic, complemented
6#19127940C211yesmaximal, characteristic, complemented
7#19127920C211yesmaximal, characteristic, complemented
8#19127906C211yesmaximal, characteristic, complemented
9#19127863C211yesmaximal, characteristic, complemented
10#19127856C211yesmaximal, characteristic, complemented
11#19127852C211yesmaximal, characteristic, complemented
12#19127839C211yesmaximal, characteristic, complemented
13#19127801C211yesmaximal, characteristic, complemented
14#19127773C211yesmaximal, characteristic, complemented
15#546×C83C211yesmaximal, characteristic
16C22×Dic166C2211yescharacteristic
17C22×Dic166C2211yescharacteristic, complemented
18#14581822—24no—
19C2×#13050580C2211yescharacteristic, complemented
20C2×#13050580C2211yescharacteristic, complemented
21C2×#13050580C2211yescharacteristic, complemented
22C2×#13050578—24no—
23C2×#13050578C2211yescharacteristic
24C2×#13050578C2211yescharacteristic
25C2×#13050578C2211yescharacteristic
26C2×#13050578C2211yescharacteristic
27C2×#13050578C2211yescharacteristic
28C2×#13050578C2211yescharacteristic
29C2×#13050574C2211yescharacteristic, complemented
30C22×C83⋊C8C2211yescharacteristic
31#14581792C2211yescharacteristic, complemented
32#14581791—21no—
33#14581771C2211yescharacteristic
34#14581771C2211yescharacteristic, complemented
35#14581769—21no—
36#14581769—21no—
37C4×Dic166C2211yescharacteristic, complemented
38D4×Dic83—21no—
39#14581725C2211yescharacteristic, complemented
40C4⋊(C83⋊C8)C2211yescharacteristic, complemented
41#14581716C2211yescharacteristic, complemented
42#14581715C2211yescharacteristic, complemented
43#14581715C2211yescharacteristic, complemented
44#14581715C2211yescharacteristic, complemented
45#14581713C2211yescharacteristic
46#14581713C2211yescharacteristic
47C22⋊(C83⋊C8)C2211yescharacteristic
48C22⋊(C83⋊C8)C2211yescharacteristic, complemented
49#14581703C2211yescharacteristic, complemented
50C2×#41×C83C2211yescharacteristic
51C22×D4×C83C2211yescharacteristic
52#124×C83C2211yescharacteristic
53#123×C83—21no—
54C22⋊Q8×C83C2211yescharacteristic
55#121×C83—21no—
56#121×C83C2211yescharacteristic
57#120×C83—21no—
58C4×D4×C83C2211yescharacteristic
59C4×D4×C83C2211yescharacteristic
60C2×C22⋊C4×C83—21no—
61C2×Dic166—22no—
62C2×Dic166—22no—
63C2×Dic166—21no—
64C2×Dic166—21no—
65C2×Dic166—41no—
66C2×Dic166—41no—
67C2×Dic166C2311yescharacteristic
68C2×Dic166C2311yescharacteristic
69C2×Dic166C2311yescharacteristic
70C22×Dic83—21no—
71C22×Dic83—21no—
72#13050580—22no—
73#13050580—22no—
74#13050580—41no—
75#13050578—22no—
76#13050578—22no—
77#13050578—22no—
78#13050578—22no—
79#13050578—41no—
80#13050578D414yescomplemented
81#13050574—22no—
82C2×C83⋊C8—22no—
83C2×C83⋊C8C2311yescharacteristic
84C2×C83⋊C8C2311yescharacteristic
85C2×C83⋊C8C2311yescharacteristic
86C2×C83⋊C8C2311yescharacteristic
87C4⋊Dic83—21no—
88C4⋊Dic83—21no—
89C4⋊Dic83C2311yescharacteristic
90Dic83⋊C4—21no—
91Dic83⋊C4—21no—
92Dic83⋊C4—21no—
93C22⋊Dic83—21no—
94C22⋊Dic83—21no—
95C4×Dic83—21no—
96C24×C83—21no—
97#41×C83—22no—
98#41×C83—41no—
99C2×Q8×C83C2311yescharacteristic
100C2×D4×C83—22no—
101C2×D4×C83—21no—
102C2×D4×C83—21no—
103C2×D4×C83—21no—
104C2×D4×C83—41no—
105C2×D4×C83D411yescharacteristic
106C2×D4×C83C2311yescharacteristic
107C2×D4×C83C2311yescharacteristic
108C22×C4×C83—21no—
109C22×C4×C83—21no—
110C22×C4×C83C2311yescharacteristic
111C22×C4×C83C2311yescharacteristic
112C4⋊C4×C83—21no—
113C4⋊C4×C83D411yescharacteristic
114C4⋊C4×C83C2311yescharacteristic
115C22⋊C4×C83—21no—
116C22⋊C4×C83—21no—
117C22⋊C4×C83—21no—
118C22⋊C4×C83—21no—
119C22⋊C4×C83—21no—
120C22⋊C4×C83D411yescharacteristic
121C22⋊C4×C83D411yescharacteristic
122C42×C83C2311yescharacteristic
123C23×C83—21no—
124C23×C83—21no—
125C23×C83—42no—
126C23×C83—42no—
127C23×C83—81no—
128C23×C83C2×D411yescharacteristic
129C23×C83C2×D411yescharacteristic
130Q8×C83—21no—
131Q8×C83—21no—
132D4×C83—22no—
133D4×C83—21no—
134D4×C83—21no—
135D4×C83—21no—
136D4×C83—42no—
137D4×C83—42no—
138D4×C83—81no—
139D4×C83C2×D412yes—
140C2×C4×C83—21no—
141C2×C4×C83—21no—
142C2×C4×C83—21no—
143C2×C4×C83—21no—
144C2×C4×C83—21no—
145C2×C4×C83—21no—
146C2×C4×C83—42no—
147C2×C4×C83—81no—
148C2×C4×C83C2×D411yescharacteristic
149C2×C4×C83C2×D411yescharacteristic
150C2×C4×C83C2×D411yescharacteristic
151C2×C4×C83C2×D411yescharacteristic
152C2×C4×C83C2411yescharacteristic
153C2×Dic83—21no—
154C2×Dic83—21no—
155C2×Dic83—21no—
156C2×Dic83—21no—
157C2×Dic83—42no—
158C2×Dic83—42no—
159Dic166—21no—
160Dic166—21no—
161Dic166—21no—
162Dic166—21no—
163Dic166—21no—
164Dic166—42no—
165Dic166—42no—
166Dic166C2×D412yes—
167C83⋊C8—21no—
168C83⋊C8—21no—
169C83⋊C8—21no—
170C83⋊C8C2×D412yes—
171C22×C83—21no—
172C22×C83—21no—
173C22×C83—21no—
174C22×C83—22no—
175C22×C83—21no—
176C22×C83—21no—
177C22×C83—41no—
178C22×C83—41no—
179C22×C83—41no—
180C22×C83—41no—
181C22×C83—41no—
182C22×C83—84no—
183C22×C83#13712yescomplemented
184C22×C83C22×D411yescharacteristic
185C4×C83—21no—
186C4×C83—21no—
187C4×C83—21no—
188C4×C83—21no—
189C4×C83—41no—
190C4×C83—41no—
191C4×C83C22×D411yescharacteristic
192C4×C83H(5,𝔽2)11yescharacteristic
193Dic83—22no—
194Dic83—41no—
195Dic83—41no—
196Dic83—41no—
197C2×C83—22no—
198C2×C83—41no—
199C2×C83—42no—
200C2×C83—81no—
201C2×C83D4211yescharacteristic
202C2×C83C2×#13711yescharacteristic
203C2×C83#57711yescharacteristic
204#3266—831nomaximal, Sylow
205C83#326611yescharacteristic, complemented, Sylow
206C2×#137—831no—
207C22×SD16—831no—
208D4×Q8—831no—
209#546D8311yescharacteristic
210#497—831no—
211#468—831no—
212#467—831no—
213#464—831no—
214#461—831no—
215#452—831no—
216#451—831no—
217#450—831no—
218#448—831no—
219#440—831no—
220#435—831no—
221C2×#41C2×D8311yescharacteristic
222C22×Q8—831no—
223C22×Q8—831no—
224C22×D4C2×D8311yescharacteristic
225#137—1664no—
226C2×Q16—831no—
227C2×Q16—831no—
228C2×Q16—831no—
229C2×SD16—831no—
230C2×SD16—831no—
231C2×SD16—831no—
232C2×SD16—831no—
233C2×SD16—831no—
234C2×SD16—831no—
235C2×SD16—1664no—
236C2×M16—831no—
237C22×C8—831no—
238C4⋊Q8—831no—
239C4⋊Q8—1661no—
240#124C2×D8311yescharacteristic
241#123—21no—
242C22⋊Q8—831no—
243C22⋊Q8—831no—
244C22⋊Q8—1661no—
245C22⋊Q8—1661no—
246C22⋊Q8C2×D8311yescharacteristic
247#121—21no—
248#121C2×D8311yescharacteristic
249#120—21no—
250C4×Q8—831no—
251C4×D4—1661no—
252C4×D4C2×D8311yescharacteristic
253C4×D4C2×D8311yescharacteristic
254C2×C22⋊C4—21no—
255#107—831no—
256C4⋊C8—831no—
257#103—831no—
258#103—831no—
259#103—831no—
260#103—831no—
261#102—831no—
262#102—831no—
263C22⋊C8—831no—
264C22⋊C8—831no—
265#97—831no—
266C24—21no—
267#41—22no—
268#41—41no—
269C2×Q8—3321no—
270C2×Q8—3321no—
271C2×Q8—831no—
272C2×Q8—831no—
273C2×Q8—831no—
274C2×Q8—1662no—
275C2×Q8—1662no—
276C2×Q8—1661no—
277C2×Q8—1661no—
278C2×Q8C22×D8311yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4C22⋊D8311yescharacteristic
285C2×D4C22×D8311yescharacteristic
286C2×D4C22×D8311yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—1661no—
290C22×C4—1661no—
291C22×C4C22×D8311yescharacteristic
292C22×C4C22×D8311yescharacteristic
293Q16—3321no—
294Q16—1662no—
295Q16—1662no—
296SD16—3321no—
297SD16—834no—
298SD16—1662no—
299SD16—1662no—
300SD16—1662no—
301SD16—1662no—
302M16—1662no—
303C2×C8—831no—
304C2×C8—831no—
305C2×C8—831no—
306C2×C8—831no—
307C2×C8—1662no—
308C4⋊C4—21no—
309C4⋊C4—831no—
310C4⋊C4—1661no—
311C4⋊C4—1661no—
312C4⋊C4—1661no—
313C4⋊C4—1661no—
314C4⋊C4—1661no—
315C4⋊C4C22⋊D8311yescharacteristic
316C4⋊C4C22×D8311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1661no—
323C22⋊C4—1661no—
324C22⋊C4C22⋊D8311yescharacteristic
325C22⋊C4C22⋊D8311yescharacteristic
326C42—1661no—
327C42C22×D8311yescharacteristic
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23C2×C22⋊D8311yescharacteristic
334C23C2×C22⋊D8311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—3322no—
338Q8—3322no—
339Q8—832no—
340Q8—1661no—
341Q8—1661no—
342Q8—1661no—
343Q8—1661no—
344Q8—1661no—
345D4—22no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4D4×D8312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—3322no—
362C2×C4—3322no—
363C2×C4—1661no—
364C2×C4—1661no—
365C2×C4—1661no—
366C2×C4—1661no—
367C2×C4C2×C22⋊D8311yescharacteristic
368C2×C4C2×C22⋊D8311yescharacteristic
369C2×C4C2×C22⋊D8311yescharacteristic
370C2×C4C2×C22⋊D8311yescharacteristic
371C2×C4C23×D8311yescharacteristic
372C8—832no—
373C8—1661no—
374C8—1661no—
375C8—1661no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—21no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—84no—
388C22#1458182212yescomplemented
389C22C22×C22⋊D8311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—3321no—
397C4—3321no—
398C4—3321no—
399C4—1662no—
400C4C2×D4×D8311yescharacteristic
401C4#1458183711yescharacteristic
402C2—22no—
403C2—41no—
404C2—42no—
405C2—81no—
406C2D4×C22⋊D8311yescharacteristic
407C2C2×#1458182211yescharacteristic
408C2#1912851211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
Fitting, prime radical#546×C83C2
socleC22×C83C22×D4
hypercenter#546D83
hypocenterC83#3266
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14581822C2semidirect
2. C22×#13050578C2semidirect
3. D4×Dic166C2semidirect
4. #19128096C2semidirect
5. #19127945C2semidirect
6. #19127940C2semidirect
7. #19127920C2semidirect
8. #19127906C2semidirect
9. #19127863C2semidirect
10. #19127856C2semidirect
11. #19127852C2semidirect
12. #19127839C2semidirect
13. #19127801C2semidirect
14. #19127773C2semidirect
17. C22×Dic166C22semidirect
19. C2×#13050580C22semidirect
20. C2×#13050580C22semidirect
21. C2×#13050580C22semidirect
29. C2×#13050574C22semidirect
31. #14581792C22semidirect
34. #14581771C22semidirect
37. C4×Dic166C22semidirect
39. #14581725C22semidirect
40. C4⋊(C83⋊C8)C22semidirect
41. #14581716C22semidirect
42. #14581715C22semidirect
43. #14581715C22semidirect
44. #14581715C22semidirect
48. C22⋊(C83⋊C8)C22semidirect
49. #14581703C22semidirect
80. #13050578D4semidirect
183. C22×C83#137semidirect
205. C83#3266semidirect
388. C22#14581822semidirect

Maximal subgroups

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

subgroupindex
C2×#145818222
C22×#130505782
D4×Dic1662
#191280962
#191279452
#191279402
#191279202
#191279062
#191278632
#191278562
#191278522
#191278392
#191278012
#191277732
#546×C832
#326683