Finite Group Databasebeta

← #23775432

Subgroups — #23775432

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#19099281C211yesmaximal, characteristic, complemented
2#19099201C211yesmaximal, characteristic
3#19098924C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098887C211yesmaximal, characteristic, complemented
6#19098851C211yesmaximal, characteristic, complemented
7#19098820C211yesmaximal, characteristic, complemented
8#19098792C211yesmaximal, characteristic, complemented
9#19098788C211yesmaximal, characteristic, complemented
10#19098725C211yesmaximal, characteristic, complemented
11#19098715C211yesmaximal, characteristic, complemented
12#19098660C211yesmaximal, characteristic, complemented
13#19098634C211yesmaximal, characteristic, complemented
14#19098566C211yesmaximal, characteristic, complemented
15#416×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929614C2211yescharacteristic, complemented
18C2×#11929613C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929607C2211yescharacteristic
21#14579160C2211yescharacteristic, complemented
22#14579155—21no—
23#14579154—21no—
24#14579150C2211yescharacteristic
25#14579147—21no—
26#14579144—21no—
27#14579141C2211yescharacteristic
28#14579140C2211yescharacteristic, complemented
29#14579137C2211yescharacteristic
30#14579135C2211yescharacteristic
31#14579133—21no—
32#14579129—21no—
33C4×Dic158—21no—
34#14579126C2211yescharacteristic, complemented
35D4×Dic79C2211yescharacteristic
36C4×C22⋊D79C2211yescharacteristic
37#14579119C2211yescharacteristic
38C2×(C2×D79)⋊C4—21no—
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic, complemented
52C2×#41×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic, complemented
54#117×C79C2211yescharacteristic, complemented
55#103×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79D411yescharacteristic
66D4×D79—22no—
67D4×D79—41no—
68C22×Dic79—21no—
69C2×C4×D79C2311yescharacteristic
70#11929614—41no—
71#11929613—41no—
72#11929612—22no—
73#11929607—41no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
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⋊Dic79D411yescharacteristic
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—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
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97#41×C79—22no—
98#41×C79—41no—
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79—41no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C42×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—42no—
115C22×D79—42no—
116C22×D79—81no—
117C22×D79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120D4×C79—21no—
121D4×C79—42no—
122D4×C79#4112yes—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—42no—
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—81no—
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141D316—21no—
142D316—21no—
143C4×D79—21no—
144C4×D79—21no—
145Dic158—21no—
146Dic158—21no—
147Dic158—42no—
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×C79C22×D411yescharacteristic
159C2×D79—21no—
160C2×D79—21no—
161C2×D79—21no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—84no—
166C4×C79—21no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79—41no—
170C4×C79C2×#4111yescharacteristic
171C4×C79H(5,𝔽2)11yescharacteristic
172Dic79—21no—
173Dic79—21no—
174Dic79—21no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178C2×C79—42no—
179C2×C79—41no—
180C2×C79#54611yescharacteristic
181C2×C79#57511yescharacteristic
182C2×C79#57711yescharacteristic
183D79—41no—
184D79—81no—
185#3311—791nomaximal, Sylow
186C79#331111yescharacteristic, complemented, Sylow
187#556—791no—
188#546—791no—
189#489—791no—
190#485—791no—
191#482—791no—
192#476—791no—
193#470—791no—
194#465—791no—
195#464—791no—
196#452—791no—
197#450—791no—
198#440—791no—
199#435—791no—
200#418—791no—
201#416D7911yescharacteristic, complemented
202C2×#41C2×D7911yescharacteristic
203C22×D4—791no—
204C2×Q16—791no—
205C2×SD16—791no—
206C2×SD16—791no—
207C2×M16—791no—
208C22×C8C2×D7911yescharacteristic, complemented
209C4⋊Q8—791no—
210#126—1581no—
211#126—1581no—
212#124—791no—
213#124—1581no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—791no—
218#121—791no—
219#121—1581no—
220#120—1581no—
221C4×Q8—791no—
222C4×Q8—1581no—
223C4×D4—791no—
224C4×D4—791no—
225#117—791no—
226#117C2×D7911yescharacteristic, complemented
227C2×C22⋊C4—1581no—
228#107—791no—
229#106—791no—
230#106—791no—
231C4⋊C8—791no—
232#103—791no—
233#103—791no—
234#103C2×D7911yescharacteristic, complemented
235#103C2×D7911yescharacteristic, complemented
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102C2×D7911yescharacteristic
241#102C2×D7911yescharacteristic
242C22⋊C8—791no—
243C22⋊C8—791no—
244#97—791no—
245C24—1581no—
246#41—22no—
247#41—41no—
248C2×Q8—791no—
249C2×Q8—1581no—
250C2×Q8C22×D7911yescharacteristic
251C2×D4—21no—
252C2×D4—3161no—
253C2×D4—791no—
254C2×D4—791no—
255C2×D4—1581no—
256C2×D4—1582no—
257C2×D4—1581no—
258C2×D4C22×D7911yescharacteristic
259C22×C4—21no—
260C22×C4—791no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263Q16—3161no—
264SD16—3161no—
265SD16—1582no—
266M16—3161no—
267C2×C8—41no—
268C2×C8—791no—
269C2×C8—791no—
270C2×C8C22×D7911yescharacteristic
271C2×C8C22×D7911yescharacteristic
272C4⋊C4—791no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4C22×D7911yescharacteristic
281C4⋊C4C22×D7911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—791no—
284C22⋊C4—791no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C42—21no—
294C42—791no—
295C42—1581no—
296C42—1581no—
297C23—21no—
298C23—3162no—
299C23—3162no—
300C23—791no—
301C23—6321no—
302C23—1581no—
303C23D4×D7911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—3162no—
307Q8—1581no—
308Q8—1581no—
309D4—21no—
310D4—42no—
311D4—3162no—
312D4—3161no—
313D4—6321no—
314D4—1581no—
315D4—1581no—
316D4#1192962412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—791no—
324C2×C4—791no—
325C2×C4—791no—
326C2×C4—6321no—
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—3161no—
345C22—3161no—
346C22—3161no—
347C22—6324no—
348C22—1581no—
349C22—1581no—
350C22—1581no—
351C22C2×D4×D7911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—1581no—
360C4—1581no—
361C4—1581no—
362C4C2×#1192962411yescharacteristic
363C4#1457920611yescharacteristic
364C2—41no—
365C2—42no—
366C2—3161no—
367C2—6321no—
368C2#1909920311yescharacteristic
369C2#1909936011yescharacteristic
370C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#416×C79C2
socleC22×C79C22×D4
prime radical#19099201C2
hypercenter#416D79
hypocenterC79#3311
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #19099281C2semidirect
3. #19098924C2semidirect
4. #19098902C2semidirect
5. #19098887C2semidirect
6. #19098851C2semidirect
7. #19098820C2semidirect
8. #19098792C2semidirect
9. #19098788C2semidirect
10. #19098725C2semidirect
11. #19098715C2semidirect
12. #19098660C2semidirect
13. #19098634C2semidirect
14. #19098566C2semidirect
15. #416×C79C2semidirect
17. C2×#11929614C22semidirect
21. #14579160C22semidirect
28. #14579140C22semidirect
34. #14579126C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. #14579092C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579085C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
51. #14579071C22semidirect
53. C22×C8×C79C22semidirect
54. #117×C79C22semidirect
55. #103×C79C22semidirect
56. #103×C79C22semidirect
186. C79#3311semidirect
201. #416D79semidirect
208. C22×C8C2×D79semidirect
226. #117C2×D79semidirect
234. #103C2×D79semidirect
235. #103C2×D79semidirect