Finite Group Databasebeta

← #23772256

Subgroups — #23772256

Order 10112.

492 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D79C211yesmaximal, characteristic
2#19099039C211yesmaximal, characteristic, complemented
3#19099035C211yesmaximal, characteristic
4#19098665C211yesmaximal, characteristic, complemented
5#19098664C211yesmaximal, characteristic, complemented
6#19098662C211yesmaximal, characteristic, complemented
7#19098654C211yesmaximal, characteristic, complemented
8C4×#11929611C211yesmaximal, characteristic, complemented
9C4×#11929612C211yesmaximal, characteristic, complemented
10#19098648C211yesmaximal, characteristic, complemented
11#19098600C211yesmaximal, characteristic, complemented
12#19098570C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic
14#19098520C211yesmaximal, characteristic, complemented
15#440×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929613C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21SD16×D79C418yescomplemented
22C2×#11929607C2211yescharacteristic
23C2×C8×D79C2211yescharacteristic
24Q8×Dic79C2211yescharacteristic, complemented
25C4×Dic158—21no—
26C4×Dic158C2211yescharacteristic, complemented
27#14579126—21no—
28#14579126C2211yescharacteristic, complemented
29C4×D316C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31#14579123C2211yescharacteristic
32C4×C22⋊D79—21no—
33(C22⋊D79)⋊C4—21no—
34#14579119—21no—
35#14579119C2211yescharacteristic
36#14579119C2211yescharacteristic
37#14579118—21no—
38#14579118C2211yescharacteristic
39C2×(C2×D79)⋊C4—21no—
40C22⋊C4×D79—21no—
41#14579095C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579092C2211yescharacteristic, complemented
44#14579086C2211yescharacteristic, complemented
45#14579085C2211yescharacteristic, complemented
46#14579084C2211yescharacteristic, complemented
47#14579083C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579081C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C4×C79⋊C8C2211yescharacteristic, complemented
52C8×Dic79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59#97×C79C2211yescharacteristic, complemented
60C23×D79—21no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63Q8×D79—22no—
64Q8×D79C2×C414yescomplemented
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67D4×D79—22no—
68D4×D79C2×C414yes—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74#11929613C2×C414yescomplemented
75#11929612C2×C414yescomplemented
76#11929611C2×C414yescomplemented
77#11929607—22no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C8×D79C2×C414yescomplemented
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87Dic79⋊C4D411yescharacteristic
88C22⋊Dic79—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4D411yescharacteristic
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79—21no—
98C4×Dic79—21no—
99C4×Dic79—21no—
100C4×Dic79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79—21no—
104SD16×C79C2×C414yescomplemented
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C42×C79—21no—
112C42×C79C2311yescharacteristic
113C23×C79—21no—
114C22×D79—21no—
115C22×D79—24no—
116C22×D79—81no—
117C22×D79—81no—
118C22×D79C2×D411yescharacteristic
119Q8×C79—21no—
120Q8×C79C22×C412yes—
121D4×C79—21no—
122D4×C79C22×C412yes—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—81no—
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—24no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—81no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—21no—
139D316C22×C412yes—
140C4×D79—24no—
141C4×D79—81no—
142C4×D79—81no—
143C4×D79C22×C412yes—
144C4×D79#4112yes—
145Dic158—21no—
146Dic158—24no—
147Dic158C22×C412yes—
148C8×C79—21no—
149C8×C79C22×C412yes—
150C79⋊C8—21no—
151C79⋊C8C22×C412yes—
152C22×C79—22no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79C22×D411yescharacteristic
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—22no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—84no—
162C2×D79C4×D412yes—
163C4×C79—22no—
164C4×C79—21no—
165C4×C79—21no—
166C4×C79—41no—
167C4×C79—41no—
168C4×C79C23×C411yescharacteristic
169C4×C79C2×#4111yescharacteristic
170Dic79—22no—
171Dic79—21no—
172Dic79—21no—
173Dic79—41no—
174Dic79—41no—
175Dic79C4×D412yes—
176C2×C79—42no—
177C2×C79C2×C4×D411yescharacteristic
178C2×C79#57711yescharacteristic
179C2×C79#57711yescharacteristic
180D79—22no—
181D79—42no—
182#2949—791nomaximal, Sylow
183C79#294911yescharacteristic, complemented, Sylow
184C22×SD16—791no—
185#519—791no—
186#518—791no—
187#440—791no—
188#440—791no—
189#440—791no—
190#440D7911yescharacteristic, complemented
191C4×SD16—791no—
192C4×SD16—791no—
193C4×SD16—791no—
194C4×SD16—791no—
195#427—791no—
196#419—791no—
197#418—791no—
198#405—791no—
199C22×Q8—791no—
200C22×D4—791no—
201C2×SD16—791no—
202C2×SD16—791no—
203C2×SD16—798no—
204C2×SD16—791no—
205C2×SD16C2×D7911yescharacteristic
206C2×M16—791no—
207C22×C8—791no—
208C4×Q8—791no—
209C4×Q8—791no—
210C4×Q8—791no—
211C4×Q8—1581no—
212C4×Q8—1581no—
213C4×Q8C2×D7911yescharacteristic, complemented
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—791no—
217C4×D4—1581no—
218C4×D4—1581no—
219C4×D4C2×D7911yescharacteristic
220#117—791no—
221#117—791no—
222#117—791no—
223#117—1581no—
224#117—1581no—
225C2×C22⋊C4—1581no—
226C2×C22⋊C4—1581no—
227#107—791no—
228#107C2×D7911yescharacteristic, complemented
229#106—791no—
230#106—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103C2×D7911yescharacteristic, complemented
235#102—791no—
236#102—791no—
237#102—791no—
238#102C2×D7911yescharacteristic
239#97—791no—
240#97C2×D7911yescharacteristic, complemented
241C4×C8—791no—
242C4×C8—791no—
243C24—1581no—
244C2×Q8—794no—
245C2×Q8—791no—
246C2×Q8—1581no—
247C2×Q8—1582no—
248C2×Q8C22×D7911yescharacteristic
249C2×D4—794no—
250C2×D4—791no—
251C2×D4—1582no—
252C2×D4—1581no—
253C2×D4C22×D7911yescharacteristic
254C22×C4—21no—
255C22×C4—791no—
256C22×C4—1581no—
257C22×C4—1581no—
258C22×C4—1581no—
259C22×C4—1581no—
260SD16—794no—
261SD16—794no—
262SD16—794no—
263SD16C4×D7914yescomplemented
264M16—1582no—
265C2×C8—791no—
266C2×C8—794no—
267C2×C8—791no—
268C2×C8C22×D7911yescharacteristic
269C2×C8C22×D7911yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—791no—
272C4⋊C4—791no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4C22×D7911yescharacteristic
279C4⋊C4C22×D7911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—791no—
282C22⋊C4—791no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C42—21no—
289C42—791no—
290C42—1581no—
291C42—1581no—
292C42—1581no—
293C42—1581no—
294C42—1581no—
295C42C22×D7911yescharacteristic
296C23—21no—
297C23—791no—
298C23—6321no—
299C23—6321no—
300C23—1584no—
301C23—1581no—
302Q8—21no—
303Q8—792no—
304Q8—1584no—
305Q8—1581no—
306Q8C2×C4×D7912yes—
307D4—21no—
308D4—792no—
309D4—1584no—
310D4—1581no—
311D4C2×C4×D7912yes—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—791no—
317C2×C4—792no—
318C2×C4—792no—
319C2×C4—791no—
320C2×C4—791no—
321C2×C4—6321no—
322C2×C4—6321no—
323C2×C4—6321no—
324C2×C4—1584no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4D4×D7911yescharacteristic
329C2×C4D4×D7911yescharacteristic
330C2×C4C23×D7911yescharacteristic
331C8—21no—
332C8—792no—
333C8—1581no—
334C8C2×C4×D7912yes—
335C22—22no—
336C22—41no—
337C22—41no—
338C22—3161no—
339C22—3161no—
340C22—792no—
341C22—6324no—
342C22—1582no—
343C22—1581no—
344C22—1581no—
345C22C2×D4×D7911yescharacteristic
346C4—22no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—3161no—
352C4—3161no—
353C4—792no—
354C4—1582no—
355C4—1581no—
356C4—1581no—
357C4C22×C4×D7911yescharacteristic
358C4#41×D7911yescharacteristic
359C2—42no—
360C2—3162no—
361C2—1582no—
362C2C4×D4×D7911yescharacteristic
363C2#1909937211yescharacteristic
364C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutatorC4×C79C23×C4
FrattiniC2×C4C23×D79
Fitting#440×C79C2
socleC22×C79C22×D4
prime radicalC2×D4×D79C22
cosocleC2×C4×C79C24
hypercenter#440D79
hypocenterC79#2949
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #19099039C2semidirect
4. #19098665C2semidirect
5. #19098664C2semidirect
6. #19098662C2semidirect
7. #19098654C2semidirect
8. C4×#11929611C2semidirect
9. C4×#11929612C2semidirect
10. #19098648C2semidirect
11. #19098600C2semidirect
12. #19098570C2semidirect
14. #19098520C2semidirect
15. #440×C79C2semidirect
21. SD16×D79C4semidirect
24. Q8×Dic79C22semidirect
26. C4×Dic158C22semidirect
28. #14579126C22semidirect
41. #14579095C22semidirect
42. #14579092C22semidirect
43. #14579092C22semidirect
44. #14579086C22semidirect
45. #14579085C22semidirect
46. #14579084C22semidirect
50. #14579071C22semidirect
51. C4×C79⋊C8C22semidirect
52. C8×Dic79C22semidirect
54. C4×Q8×C79C22semidirect
56. #107×C79C22semidirect
57. #103×C79C22semidirect
59. #97×C79C22semidirect
64. Q8×D79C2×C4semidirect
74. #11929613C2×C4semidirect
75. #11929612C2×C4semidirect
76. #11929611C2×C4semidirect
80. C8×D79C2×C4semidirect
104. SD16×C79C2×C4semidirect
183. C79#2949semidirect
190. #440D79semidirect
213. C4×Q8C2×D79semidirect
228. #107C2×D79semidirect
234. #103C2×D79semidirect
240. #97C2×D79semidirect
263. SD16C4×D79semidirect