Finite Group Databasebeta

← #23774401

Subgroups — #23774401

Order 10112.

400 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099117C211yesmaximal, characteristic, complemented
2#124×D79C211yesmaximal, characteristic
3#19098956C211yesmaximal, characteristic, complemented
4#19098954C211yesmaximal, characteristic, complemented
5#19098924C211yesmaximal, characteristic, complemented
6#19098921C211yesmaximal, characteristic, complemented
7#19098786C211yesmaximal, characteristic, complemented
8#19098785C211yesmaximal, characteristic, complemented
9#19098782C211yesmaximal, characteristic, complemented
10#19098720C211yesmaximal, characteristic, complemented
11#19098717C211yesmaximal, characteristic, complemented
12#19098715C211yesmaximal, characteristic
13#19098712C211yesmaximal, characteristic
14#19098619C211yesmaximal, characteristic, complemented
15#464×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929614C2211yescharacteristic, complemented
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929613C2211yescharacteristic
22C2×#11929612C2211yescharacteristic
23C2×#11929611C2211yescharacteristic
24#14579160C2211yescharacteristic, complemented
25#14579159C2211yescharacteristic, complemented
26#14579151—21no—
27#14579150C2211yescharacteristic
28#14579149C2211yescharacteristic
29#14579148C2211yescharacteristic
30#14579147—21no—
31#14579147—21no—
32#14579141C2211yescharacteristic
33#14579139—21no—
34#14579137C2211yescharacteristic
35C4×Dic158—21no—
36C4×Dic158C2211yescharacteristic, complemented
37#14579118—21no—
38C22⋊C4×D79—21no—
39C22⋊C4×D79—21no—
40C42×D79C2211yescharacteristic
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579081C2211yescharacteristic
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C2×Q16×C79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54#124×C79C2211yescharacteristic
55C4×Q8×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×Dic158C2311yescharacteristic
64Q8×D79—41no—
65Q8×D79—41no—
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68D4×D79—41no—
69D4×D79—41no—
70C2×C4×D79—21no—
71C2×C4×D79D411yescharacteristic
72C2×C4×D79D411yescharacteristic
73C2×C4×D79C2311yescharacteristic
74Dic316—41no—
75#11929614—41no—
76#11929614—41no—
77#11929613—41no—
78#11929612—41no—
79#11929611—41no—
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97C4×Dic79—21no—
98C4×Dic79D411yescharacteristic
99C4×Dic79D411yescharacteristic
100C4×Dic79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104Q16×C79—41no—
105SD16×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C42×C79—21no—
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C22×D79—21no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79C2×D411yescharacteristic
120Q8×C79—21no—
121Q8×C79—21no—
122Q8×C79—21no—
123Q8×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2411yescharacteristic
132C22⋊D79—42no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139D316—21no—
140D316—21no—
141C4×D79—22no—
142C4×D79—21no—
143C4×D79—21no—
144C4×D79—41no—
145C4×D79—42no—
146Dic158—21no—
147Dic158—21no—
148Dic158—21no—
149Dic158—21no—
150Dic158—42no—
151Dic158—42no—
152C8×C79—21no—
153C8×C79—21no—
154C79⋊C8—21no—
155C79⋊C8—21no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79C22×D411yescharacteristic
160C2×D79—21no—
161C2×D79—21no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—84no—
166C2×D79#13712yes—
167C4×C79—21no—
168C4×C79—21no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79H(5,𝔽2)11yescharacteristic
173C4×C79H(5,𝔽2)11yescharacteristic
174Dic79—21no—
175Dic79—21no—
176Dic79—21no—
177Dic79—41no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—81no—
181C2×C79#53511yescharacteristic
182C2×C79C2×#13711yescharacteristic
183C2×C79#57511yescharacteristic
184D79—22no—
185D79—81no—
186#3215—791nomaximal, Sylow
187C79#321511yescharacteristic, complemented, Sylow
188#533—791no—
189C2×#124—791no—
190#497—791no—
191#497—791no—
192#489—791no—
193#489—791no—
194#464—791no—
195#464—791no—
196#464—791no—
197#464D7911yescharacteristic, complemented
198#451—791no—
199#451—791no—
200#450—791no—
201#450—791no—
202#432—791no—
203C22×Q8—791no—
204C22×D4—791no—
205C2×Q16—791no—
206C2×Q16—791no—
207C2×Q16—791no—
208C2×Q16C2×D7911yescharacteristic, complemented
209C2×SD16—791no—
210C2×SD16—791no—
211C2×SD16—791no—
212C2×SD16C2×D7911yescharacteristic
213C4⋊Q8—791no—
214C4⋊Q8—791no—
215#125—1581no—
216#124—791no—
217#124—791no—
218#124—791no—
219#124—1581no—
220#124—1581no—
221#124C2×D7911yescharacteristic
222C22⋊Q8—791no—
223C22⋊Q8—791no—
224C22⋊Q8—1581no—
225C4×Q8—791no—
226C4×Q8—1581no—
227C4×Q8C2×D7911yescharacteristic, complemented
228#117—1581no—
229C2×C22⋊C4—1581no—
230C2×C22⋊C4—1581no—
231C2×C42—791no—
232C4⋊C8—791no—
233C4⋊C8C2×D7911yescharacteristic, complemented
234#103—791no—
235#103—791no—
236#103—791no—
237#103C2×D7911yescharacteristic, complemented
238#102—791no—
239#102—791no—
240#102—791no—
241#102C2×D7911yescharacteristic
242C22⋊C8—791no—
243C22⋊C8—791no—
244#97—791no—
245#97—791no—
246C24—1581no—
247C2×Q8—3161no—
248C2×Q8—3161no—
249C2×Q8—791no—
250C2×Q8—791no—
251C2×Q8—1581no—
252C2×Q8—1581no—
253C2×Q8C22×D7911yescharacteristic
254C2×Q8C22×D7911yescharacteristic
255C2×D4—3161no—
256C2×D4—3161no—
257C2×D4—791no—
258C2×D4—1581no—
259C2×D4C22×D7911yescharacteristic
260C22×C4—791no—
261C22×C4—791no—
262C22×C4—791no—
263C22×C4—1581no—
264Q16—41no—
265Q16—3161no—
266Q16—3161no—
267Q16—3161no—
268SD16—41no—
269SD16—3161no—
270SD16—3161no—
271SD16—3161no—
272C2×C8—791no—
273C2×C8—791no—
274C2×C8C22×D7911yescharacteristic
275C2×C8C22×D7911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—791no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4—1581no—
284C4⋊C4C22×D7911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C42—21no—
296C42—791no—
297C42—791no—
298C42—791no—
299C42—1581no—
300C42C22×D7911yescharacteristic
301C23—21no—
302C23—3162no—
303C23—3162no—
304C23—3162no—
305C23—791no—
306C23—1581no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8—3162no—
312Q8—3162no—
313Q8—1581no—
314Q8—1581no—
315Q8—1581no—
316Q8—1581no—
317D4—21no—
318D4—21no—
319D4—3162no—
320D4—1581no—
321D4—1581no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—3161no—
326C2×C4—3162no—
327C2×C4—791no—
328C2×C4—791no—
329C2×C4—791no—
330C2×C4—1582no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4D4×D7911yescharacteristic
337C2×C4D4×D7911yescharacteristic
338C2×C4C23×D7911yescharacteristic
339C8—21no—
340C8—21no—
341C8—1581no—
342C8—1581no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3161no—
347C22—3161no—
348C22—3161no—
349C22—792no—
350C22—6324no—
351C22—1581no—
352C22—1581no—
353C22C2×D4×D7911yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—3161no—
360C4—3161no—
361C4—3161no—
362C4—1581no—
363C4—1581no—
364C4—1581no—
365C4#1457920611yescharacteristic
366C4#1457920711yescharacteristic
367C2—81no—
368C2—6321no—
369C2—1582no—
370C2#1909912911yescharacteristic
371C2#137×D7911yescharacteristic
372C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#464×C79C2
socleC22×C79C22×D4
prime radicalC2×D4×D79C22
hypercenter#464D79
hypocenterC79#3215
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #19099117C2semidirect
3. #19098956C2semidirect
4. #19098954C2semidirect
5. #19098924C2semidirect
6. #19098921C2semidirect
7. #19098786C2semidirect
8. #19098785C2semidirect
9. #19098782C2semidirect
10. #19098720C2semidirect
11. #19098717C2semidirect
14. #19098619C2semidirect
15. #464×C79C2semidirect
18. C2×Dic316C22semidirect
19. C2×#11929614C22semidirect
20. C2×#11929614C22semidirect
24. #14579160C22semidirect
25. #14579159C22semidirect
36. C4×Dic158C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579086C22semidirect
43. #14579085C22semidirect
44. #14579084C22semidirect
50. #14579071C22semidirect
51. #14579071C22semidirect
52. C2×Q16×C79C22semidirect
55. C4×Q8×C79C22semidirect
56. C4⋊C8×C79C22semidirect
57. #103×C79C22semidirect
187. C79#3215semidirect
197. #464D79semidirect
208. C2×Q16C2×D79semidirect
227. C4×Q8C2×D79semidirect
233. C4⋊C8C2×D79semidirect
237. #103C2×D79semidirect