Finite Group Databasebeta

← #23775620

Subgroups — #23775620

Order 10112.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099247C211yesmaximal, characteristic, complemented
2#19099207C211yesmaximal, characteristic
3#19098916C211yesmaximal, characteristic, complemented
4#19098905C211yesmaximal, characteristic, complemented
5#19098880C211yesmaximal, characteristic, complemented
6#19098861C211yesmaximal, characteristic, complemented
7#19098819C211yesmaximal, characteristic, complemented
8#19098806C211yesmaximal, characteristic, complemented
9#19098783C211yesmaximal, characteristic, complemented
10#19098722C211yesmaximal, characteristic, complemented
11SD16×Dic79C211yesmaximal, characteristic, complemented
12#19098638C211yesmaximal, characteristic, complemented
13#19098568C211yesmaximal, characteristic, complemented
14#19098561C211yesmaximal, characteristic, complemented
15#450×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×#11929614C2211yescharacteristic, complemented
18C2×#11929608C2211yescharacteristic
19C2×#11929607C2211yescharacteristic, complemented
20#14579154—21no—
21#14579152C2211yescharacteristic, complemented
22#14579151—21no—
23#14579148C2211yescharacteristic
24#14579143—21no—
25#14579142—21no—
26#14579140C2211yescharacteristic
27#14579137C2211yescharacteristic, complemented
28#14579133—21no—
29#14579132C2211yescharacteristic
30#14579130—21no—
31Q8×Dic79C2211yescharacteristic, complemented
32D4×Dic79C2211yescharacteristic
33C4×C22⋊D79C2211yescharacteristic
34#14579120C2211yescharacteristic
35#14579119—21no—
36C4⋊C4×D79C2211yescharacteristic, complemented
37C2×C22⋊Dic79—21no—
38#14579095C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579082C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929623—22no—
60#11929623—41no—
61C2×Dic158C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C2×C22⋊D79D411yescharacteristic
65C22×Dic79—21no—
66C22×Dic79—21no—
67C2×C4×D79—21no—
68C2×C4×D79C2311yescharacteristic
69#11929614—41no—
70#11929608—41no—
71#11929607—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4D411yescharacteristic
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79D411yescharacteristic
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4D411yescharacteristic
93C4×Dic79—21no—
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96C24×C79—21no—
97C2×Q8×C79C2311yescharacteristic
98C2×D4×C79—22no—
99C2×D4×C79—21no—
100C2×D4×C79—41no—
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104SD16×C79—22no—
105SD16×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—42no—
114C23×C79—42no—
115C23×C79—81no—
116C23×C79C2×D411yescharacteristic
117C22×D79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—21no—
123D4×C79—42no—
124D4×C79#4112yes—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—41no—
132C22⋊D79—42no—
133C22⋊D79—81no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—42no—
139C2×Dic79—81no—
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—42no—
146Dic158—21no—
147Dic158—21no—
148C8×C79—21no—
149C8×C79—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—22no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—84no—
162C22×C79C22×D411yescharacteristic
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—21no—
166C4×C79—21no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79C2×#4111yescharacteristic
170C4×C79H(5,𝔽2)11yescharacteristic
171Dic79—21no—
172Dic79—21no—
173Dic79—21no—
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178C2×C79—41no—
179C2×C79—42no—
180C2×C79—81no—
181C2×C79#54611yescharacteristic
182C2×C79#57511yescharacteristic
183C2×C79#57711yescharacteristic
184D79—41no—
185#3323—791nomaximal, Sylow
186C79#332311yescharacteristic, complemented, Sylow
187#552—791no—
188#546—791no—
189#488—791no—
190#485—791no—
191#481—791no—
192#478—791no—
193#470—791no—
194#468—791no—
195#464—791no—
196#452—791no—
197#450D7911yescharacteristic, complemented
198C4×SD16—791no—
199#436—791no—
200#418—791no—
201#417—791no—
202C2×#41—791no—
203C22×D4C2×D7911yescharacteristic
204C2×Q16—791no—
205C2×SD16C2×D7911yescharacteristic
206C2×SD16C2×D7911yescharacteristic
207C2×M16—791no—
208C2×M16—791no—
209#126—1581no—
210#125—791no—
211#125—1581no—
212#124—791no—
213#123—1581no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8C2×D7911yescharacteristic
218#121—791no—
219#121—1581no—
220#120—1581no—
221C4×Q8—791no—
222C4×D4—791no—
223C4×D4—791no—
224#117—791no—
225#117—1581no—
226C2×C4⋊C4—791no—
227C2×C22⋊C4—1581no—
228#107—791no—
229#106—791no—
230#106—791no—
231C4⋊C8—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102C2×D7911yescharacteristic
241#102C2×D7911yescharacteristic
242C22⋊C8—791no—
243C22⋊C8C2×D7911yescharacteristic
244C4×C8—791no—
245C24—21no—
246#41—3161no—
247#41—1582no—
248C2×Q8—791no—
249C2×Q8C22×D7911yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—791no—
254C2×D4—1581no—
255C2×D4—1581no—
256C2×D4C22×D7911yescharacteristic
257C2×D4C22×D7911yescharacteristic
258C22×C4—791no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263Q16—3161no—
264SD16—22no—
265SD16—41no—
266M16—3161no—
267M16—3161no—
268C2×C8—791no—
269C2×C8—791no—
270C2×C8C22×D7911yescharacteristic
271C2×C8C22×D7911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—791no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4C22×D7911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—791no—
286C22⋊C4—791no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C42—791no—
295C42—1581no—
296C42—1581no—
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23—791no—
303C23D4×D7911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1581no—
307Q8—1581no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—42no—
312D4—3162no—
313D4—3161no—
314D4—6321no—
315D4#1192962312yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—3162no—
321C2×C4—3162no—
322C2×C4—791no—
323C2×C4—791no—
324C2×C4—791no—
325C2×C4—6321no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4D4×D7911yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—21no—
335C8—21no—
336C8—1581no—
337C8—1581no—
338C22—21no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—84no—
348C22—1581no—
349C22—1581no—
350C22—1581no—
351C22C2×D4×D7911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—3161no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—1581no—
360C4—1581no—
361C4—1581no—
362C4C2×#1192962311yescharacteristic
363C4#1457920611yescharacteristic
364C2—41no—
365C2—42no—
366C2—81no—
367C2—3161no—
368C2#1909920011yescharacteristic
369C2#1909935911yescharacteristic
370C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#450×C79C2
socleC22×C79C22×D4
prime radical#19099207C2
hypercenter#450D79
hypocenterC79#3323
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #19099247C2semidirect
3. #19098916C2semidirect
4. #19098905C2semidirect
5. #19098880C2semidirect
6. #19098861C2semidirect
7. #19098819C2semidirect
8. #19098806C2semidirect
9. #19098783C2semidirect
10. #19098722C2semidirect
11. SD16×Dic79C2semidirect
12. #19098638C2semidirect
13. #19098568C2semidirect
14. #19098561C2semidirect
15. #450×C79C2semidirect
17. C2×#11929614C22semidirect
19. C2×#11929607C22semidirect
21. #14579152C22semidirect
27. #14579137C22semidirect
31. Q8×Dic79C22semidirect
36. C4⋊C4×D79C22semidirect
38. #14579095C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579085C22semidirect
45. #14579084C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
186. C79#3323semidirect
197. #450D79semidirect