Finite Group Databasebeta

← #23773749

Subgroups — #23773749

Order 10112.

404 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099190C211yesmaximal, characteristic, complemented
2#19099126C211yesmaximal, characteristic
3#19098927C211yesmaximal, characteristic, complemented
4#19098926C211yesmaximal, characteristic, complemented
5#19098925C211yesmaximal, characteristic, complemented
6#19098921C211yesmaximal, characteristic, complemented
7#19098918C211yesmaximal, characteristic, complemented
8#19098916C211yesmaximal, characteristic, complemented
9#19098908C211yesmaximal, characteristic, complemented
10#19098566C211yesmaximal, characteristic, complemented
11#19098561C211yesmaximal, characteristic, complemented
12#19098556C211yesmaximal, characteristic, complemented
13#102×D79C211yesmaximal, characteristic, complemented
14#19098517C211yesmaximal, characteristic, complemented
15#486×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929607C2211yescharacteristic
19C2×C8×D79C2211yescharacteristic
20#14579160C2211yescharacteristic, complemented
21#14579159—21no—
22#14579157C2211yescharacteristic
23#14579153C2211yescharacteristic, complemented
24#14579152C2211yescharacteristic, complemented
25#14579151—21no—
26#14579149C2211yescharacteristic
27#14579148C2211yescharacteristic
28#14579139—21no—
29#14579137—21no—
30#14579133—21no—
31#14579133—21no—
32#14579129—21no—
33#14579129—21no—
34#14579119C2211yescharacteristic
35#14579118C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic
37#14579086C2211yescharacteristic, complemented
38#14579086C2211yescharacteristic, complemented
39#14579084C2211yescharacteristic, complemented
40#14579084C2211yescharacteristic, complemented
41#14579083C2211yescharacteristic
42#14579083C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579082C2211yescharacteristic
45#14579082C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579072C2211yescharacteristic, complemented
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C4⋊Q8×C79C2211yescharacteristic, complemented
53#127×C79C2211yescharacteristic
54#102×C79C2211yescharacteristic
55#102×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929623—22no—
61#11929623—22no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69D4×D79—22no—
70D4×D79—22no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74#11929607—22no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C8×D79—22no—
78C4⋊Dic79—21no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87Dic79⋊C4D411yescharacteristic
88C22⋊Dic79—21no—
89C22⋊Dic79—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×Dic79C2311yescharacteristic
97C2×Q8×C79—21no—
98C2×D4×C79—21no—
99C2×D4×C79—21no—
100C2×D4×C79C2311yescharacteristic
101C2×D4×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C2×C8×C79C2311yescharacteristic
104C4⋊C4×C79—21no—
105C4⋊C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C22×D79—21no—
111C22×D79—42no—
112C22×D79—81no—
113C22×D79—81no—
114C22×D79C2×D411yescharacteristic
115Q8×C79—81no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—81no—
121D4×C79—81no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—42no—
128C22⋊D79—42no—
129C22⋊D79—81no—
130C22⋊D79—81no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—42no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—21no—
139D316—21no—
140C4×D79—81no—
141C4×D79#4112yes—
142C4×D79#4112yes—
143Dic158—21no—
144Dic158—21no—
145Dic158—81no—
146C8×C79—21no—
147C8×C79—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79C22×D411yescharacteristic
157C2×D79—21no—
158C2×D79—21no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C2×D79—84no—
163C2×D79#12412yes—
164C4×C79—21no—
165C4×C79—21no—
166C4×C79—41no—
167C4×C79—41no—
168C4×C79C2×#4111yescharacteristic
169C4×C79C2×#4111yescharacteristic
170Dic79—21no—
171Dic79—21no—
172Dic79—41no—
173Dic79—41no—
174Dic79—41no—
175Dic79#12412yes—
176C2×C79—81no—
177C2×C79—81no—
178C2×C79C2×#12411yescharacteristic
179C2×C79#57611yescharacteristic
180C2×C79#57711yescharacteristic
181D79—22no—
182D79—81no—
183#3136—791nomaximal, Sylow
184C79#313611yescharacteristic, complemented, Sylow
185#544—791no—
186#535—791no—
187#490—791no—
188#490—791no—
189#489—791no—
190#489—791no—
191#488—791no—
192#488—791no—
193#486—791no—
194#486D7911yescharacteristic, complemented
195#418—791no—
196#417—791no—
197#416—791no—
198C2×#102—791no—
199#405—791no—
200C2×#41—791no—
201C22×D4—791no—
202C2×M16—791no—
203C22×C8—791no—
204C4⋊Q8—791no—
205C4⋊Q8—1581no—
206C4⋊Q8C2×D7911yescharacteristic, complemented
207#127—791no—
208#127C2×D7911yescharacteristic
209#125—791no—
210#125—791no—
211#125—1581no—
212#124—791no—
213#124—791no—
214C22⋊Q8—1581no—
215C22⋊Q8—1581no—
216#121—1581no—
217#121—1581no—
218#120—1581no—
219#120—1581no—
220#117—791no—
221#117—791no—
222C2×C4⋊C4—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102C2×D7911yescharacteristic
236#102C2×D7911yescharacteristic
237#102C2×D7911yescharacteristic, complemented
238#102C2×D7911yescharacteristic, complemented
239#97—791no—
240#97—791no—
241C4×C8—791no—
242C4×C8C2×D7911yescharacteristic, complemented
243C24—1581no—
244#41—1582no—
245#41—1582no—
246C2×Q8—21no—
247C2×Q8—791no—
248C2×Q8—1581no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—791no—
252C2×D4—1582no—
253C2×D4—1582no—
254C2×D4—1581no—
255C2×D4—1581no—
256C2×D4—1581no—
257C2×D4—1581no—
258C2×D4C22×D7911yescharacteristic
259C2×D4C22×D7911yescharacteristic
260C22×C4—791no—
261C22×C4—1581no—
262C22×C4—1581no—
263M16—1582no—
264C2×C8—791no—
265C2×C8—791no—
266C2×C8—1582no—
267C2×C8C22×D7911yescharacteristic
268C2×C8C22×D7911yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—791no—
271C4⋊C4—791no—
272C4⋊C4—791no—
273C4⋊C4—791no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4C22×D7911yescharacteristic
281C4⋊C4C22×D7911yescharacteristic
282C22⋊C4—791no—
283C22⋊C4—791no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C42—791no—
290C42—1581no—
291C42C22×D7911yescharacteristic
292C23—21no—
293C23—21no—
294C23—3162no—
295C23—791no—
296C23—6321no—
297C23—6321no—
298C23—1581no—
299Q8—81no—
300Q8—6321no—
301Q8—1581no—
302Q8—1581no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—81no—
308D4—81no—
309D4—3162no—
310D4—3162no—
311D4—6321no—
312D4—6321no—
313D4—1581no—
314D4—1581no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—3162no—
318C2×C4—791no—
319C2×C4—792no—
320C2×C4—792no—
321C2×C4—791no—
322C2×C4—791no—
323C2×C4—6321no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4D4×D7911yescharacteristic
328C2×C4D4×D7911yescharacteristic
329C2×C4C23×D7911yescharacteristic
330C8—21no—
331C8—21no—
332C8—1581no—
333C8—1581no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—3161no—
341C22—3161no—
342C22—3161no—
343C22—792no—
344C22—6324no—
345C22—1581no—
346C22—1581no—
347C22C2×D4×D7911yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—3161no—
353C4—3161no—
354C4—3161no—
355C4—792no—
356C4—1581no—
357C4—1581no—
358C4#41×D7911yescharacteristic
359C4#41×D7911yescharacteristic
360C2—81no—
361C2—81no—
362C2—6321no—
363C2—1582no—
364C2#124×D7911yescharacteristic
365C2#1909936411yescharacteristic
366C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#486×C79C2
socleC22×C79C22×D4
prime radical#19099126C2
hypercenter#486D79
hypocenterC79#3136
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #19099190C2semidirect
3. #19098927C2semidirect
4. #19098926C2semidirect
5. #19098925C2semidirect
6. #19098921C2semidirect
7. #19098918C2semidirect
8. #19098916C2semidirect
9. #19098908C2semidirect
10. #19098566C2semidirect
11. #19098561C2semidirect
12. #19098556C2semidirect
13. #102×D79C2semidirect
14. #19098517C2semidirect
15. #486×C79C2semidirect
20. #14579160C22semidirect
23. #14579153C22semidirect
24. #14579152C22semidirect
37. #14579086C22semidirect
38. #14579086C22semidirect
39. #14579084C22semidirect
40. #14579084C22semidirect
45. #14579082C22semidirect
46. #14579082C22semidirect
49. #14579072C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
52. C4⋊Q8×C79C22semidirect
56. #102×C79C22semidirect
57. #102×C79C22semidirect
58. C4×C8×C79C22semidirect
184. C79#3136semidirect
194. #486D79semidirect
206. C4⋊Q8C2×D79semidirect
237. #102C2×D79semidirect
238. #102C2×D79semidirect
242. C4×C8C2×D79semidirect