Finite Group Databasebeta

← #23774360

Subgroups — #23774360

Order 10112.

410 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099092C211yesmaximal, characteristic, complemented
2#124×D79C211yesmaximal, characteristic, complemented
3#19098945C211yesmaximal, characteristic, complemented
4#19098918C211yesmaximal, characteristic, complemented
5#19098917C211yesmaximal, characteristic, complemented
6#19098787C211yesmaximal, characteristic, complemented
7#19098783C211yesmaximal, characteristic, complemented
8#19098780C211yesmaximal, characteristic, complemented
9#19098776C211yesmaximal, characteristic, complemented
10#19098717C211yesmaximal, characteristic, complemented
11#19098712C211yesmaximal, characteristic, complemented
12#19098700C211yesmaximal, characteristic, complemented
13#19098695C211yesmaximal, characteristic
14#19098614C211yesmaximal, characteristic, complemented
15#495×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929612C2211yescharacteristic, complemented
20C2×#11929611C2211yescharacteristic
21C2×#11929609C2211yescharacteristic
22#14579154—21no—
23#14579153C2211yescharacteristic, complemented
24#14579150C2211yescharacteristic
25#14579149C2211yescharacteristic
26#14579148C2211yescharacteristic
27#14579147—21no—
28#14579147—21no—
29#14579143—21no—
30#14579137C2211yescharacteristic
31#14579132C2211yescharacteristic
32Q8×Dic79C2211yescharacteristic, complemented
33D4×Dic79C2211yescharacteristic, complemented
34(C22⋊D79)⋊C4—21no—
35#14579117—21no—
36C22⋊C4×D79—21no—
37C22⋊C4×D79—21no—
38C42×D79C2211yescharacteristic
39Dic79⋊C8C2211yescharacteristic, complemented
40Dic79⋊C8C2211yescharacteristic, complemented
41#14579086C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C4×C79⋊C8C2211yescharacteristic, complemented
52C2×Q16×C79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic, complemented
55C2×D8×C79C2211yescharacteristic
56#124×C79C2211yescharacteristic
57#124×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62Q8×D79—41no—
63Q8×D79—41no—
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67D4×D79—41no—
68D4×D79—41no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79D411yescharacteristic
72C2×C4×D79D411yescharacteristic
73C2×C4×D79C2311yescharacteristic
74#11929614—41no—
75#11929612—41no—
76#11929611—41no—
77#11929609—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95C4×Dic79—21no—
96C4×Dic79D411yescharacteristic
97C4×Dic79D411yescharacteristic
98C4×Dic79C2311yescharacteristic
99C2×Q8×C79C2311yescharacteristic
100C2×Q8×C79C2311yescharacteristic
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103Q16×C79—41no—
104SD16×C79—41no—
105SD16×C79—41no—
106D8×C79—41no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C23×C79—21no—
116C22×D79—21no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79C2×D411yescharacteristic
121Q8×C79—21no—
122Q8×C79—21no—
123Q8×C79—21no—
124Q8×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—42no—
135C22⋊D79—42no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—42no—
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143D316—21no—
144D316—21no—
145C4×D79—22no—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—41no—
149C4×D79—42no—
150Dic158—21no—
151Dic158—21no—
152Dic158—42no—
153C8×C79—21no—
154C8×C79—21no—
155C79⋊C8—21no—
156C79⋊C8—21no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79C22×D411yescharacteristic
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—84no—
170C2×D79#13512yes—
171C4×C79—21no—
172C4×C79—21no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79H(5,𝔽2)11yescharacteristic
176C4×C79H(5,𝔽2)11yescharacteristic
177Dic79—21no—
178Dic79—21no—
179Dic79—21no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—81no—
184C2×C79—81no—
185C2×C79#53511yescharacteristic
186C2×C79C2×#13511yescharacteristic
187C2×C79#57511yescharacteristic
188D79—22no—
189D79—81no—
190#3211—791nomaximal, Sylow
191C79#321111yescharacteristic, complemented, Sylow
192#529—791no—
193C2×#124—791no—
194#495—791no—
195#495D7911yescharacteristic, complemented
196#488—791no—
197#488—791no—
198#464—791no—
199#464—791no—
200#463—791no—
201#463—791no—
202#451—791no—
203#450—791no—
204#448—791no—
205#447—791no—
206#431—791no—
207C22×Q8—791no—
208C22×D4—791no—
209C2×Q16—791no—
210C2×Q16C2×D7911yescharacteristic, complemented
211C2×SD16—791no—
212C2×SD16—791no—
213C2×SD16C2×D7911yescharacteristic
214C2×SD16C2×D7911yescharacteristic, complemented
215C2×D8—791no—
216C2×D8C2×D7911yescharacteristic
217#126—1581no—
218#125—791no—
219#124—791no—
220#124—791no—
221#124—791no—
222#124—1581no—
223#124—1581no—
224#124C2×D7911yescharacteristic
225#124C2×D7911yescharacteristic, complemented
226#123—1581no—
227C22⋊Q8—791no—
228#121—791no—
229C4×Q8—791no—
230C4×D4—791no—
231C4×D4—1581no—
232#117—1581no—
233C2×C22⋊C4—1581no—
234C2×C22⋊C4—1581no—
235C2×C42—791no—
236C4⋊C8—791no—
237C4⋊C8—791no—
238#103—791no—
239#103—791no—
240#103—791no—
241#103—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246C22⋊C8—791no—
247C22⋊C8—791no—
248C4×C8—791no—
249C4×C8C2×D7911yescharacteristic, complemented
250C24—1581no—
251C2×Q8—3161no—
252C2×Q8—3161no—
253C2×Q8—791no—
254C2×Q8—1581no—
255C2×Q8C22×D7911yescharacteristic
256C2×Q8C22×D7911yescharacteristic
257C2×D4—3161no—
258C2×D4—3161no—
259C2×D4—791no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4C22×D7911yescharacteristic
263C2×D4C22×D7911yescharacteristic
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—1581no—
268C22×C4—1581no—
269Q16—41no—
270Q16—3161no—
271SD16—41no—
272SD16—41no—
273SD16—3161no—
274SD16—3161no—
275D8—41no—
276D8—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C42—791no—
301C42—791no—
302C42—791no—
303C42—1581no—
304C42C22×D7911yescharacteristic
305C23—21no—
306C23—21no—
307C23—3162no—
308C23—3162no—
309C23—3162no—
310C23—791no—
311C23—1581no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—3162no—
317Q8—1581no—
318Q8—1581no—
319D4—21no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—3162no—
324D4—3162no—
325D4—1581no—
326D4—1581no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—3161no—
330C2×C4—3162no—
331C2×C4—3162no—
332C2×C4—791no—
333C2×C4—791no—
334C2×C4—791no—
335C2×C4—1582no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4D4×D7911yescharacteristic
342C2×C4D4×D7911yescharacteristic
343C2×C4C23×D7911yescharacteristic
344C8—21no—
345C8—21no—
346C8—1581no—
347C8—1581no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—792no—
358C22—6324no—
359C22—1581no—
360C22—1581no—
361C22C2×D4×D7911yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—3161no—
367C4—3161no—
368C4—3161no—
369C4—1581no—
370C4—1581no—
371C4—1581no—
372C4#1457920611yescharacteristic
373C4#1457920611yescharacteristic
374C2—81no—
375C2—81no—
376C2—6321no—
377C2—1582no—
378C2#1909912611yescharacteristic
379C2#135×D7911yescharacteristic
380C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#495×C79C2
socleC22×C79C22×D4
prime radical#19098695C2
hypercenter#495D79
hypocenterC79#3211
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #19099092C2semidirect
2. #124×D79C2semidirect
3. #19098945C2semidirect
4. #19098918C2semidirect
5. #19098917C2semidirect
6. #19098787C2semidirect
7. #19098783C2semidirect
8. #19098780C2semidirect
9. #19098776C2semidirect
10. #19098717C2semidirect
11. #19098712C2semidirect
12. #19098700C2semidirect
14. #19098614C2semidirect
15. #495×C79C2semidirect
18. C2×#11929614C22semidirect
19. C2×#11929612C22semidirect
23. #14579153C22semidirect
32. Q8×Dic79C22semidirect
33. D4×Dic79C22semidirect
39. Dic79⋊C8C22semidirect
40. Dic79⋊C8C22semidirect
41. #14579086C22semidirect
42. #14579086C22semidirect
43. #14579085C22semidirect
44. #14579085C22semidirect
51. C4×C79⋊C8C22semidirect
52. C2×Q16×C79C22semidirect
54. C2×SD16×C79C22semidirect
57. #124×C79C22semidirect
58. C4×C8×C79C22semidirect
191. C79#3211semidirect
195. #495D79semidirect
210. C2×Q16C2×D79semidirect
214. C2×SD16C2×D79semidirect
225. #124C2×D79semidirect
249. C4×C8C2×D79semidirect