Finite Group Databasebeta

← #23773861

Subgroups — #23773861

Order 10112.

572 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579193C211yesmaximal, characteristic, complemented
2C2×#14579190C211yesmaximal, characteristic, complemented
3C2×#14579188C211yesmaximal, characteristic, complemented
4C2×#14579185C211yesmaximal, characteristic, complemented
5#19099112C211yesmaximal, characteristic, complemented
6#124×D79C211yesmaximal, characteristic, complemented
7#19098956C211yesmaximal, characteristic, complemented
8#19098954C211yesmaximal, characteristic, complemented
9#19098951C211yesmaximal, characteristic, complemented
10#19098949C211yesmaximal, characteristic, complemented
11#19098947C211yesmaximal, characteristic, complemented
12#19098945C211yesmaximal, characteristic, complemented
13#19098945C211yesmaximal, characteristic, complemented
14C4×#11929607C211yesmaximal, characteristic, complemented
15#495×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929623C2211yescharacteristic
18C2×Q8×D79C2211yescharacteristic
19C2×D4×D79C2211yescharacteristic
20#14579193—24no—
21#14579190—24no—
22#14579188—24no—
23#14579185—24no—
24C2×Dic316C2211yescharacteristic, complemented
25C2×#11929614C2211yescharacteristic, complemented
26C2×#11929614C2211yescharacteristic, complemented
27C2×#11929613C2211yescharacteristic
28C2×#11929613C2211yescharacteristic, complemented
29C2×#11929612C2211yescharacteristic
30C2×#11929612C2211yescharacteristic, complemented
31C2×#11929611C2211yescharacteristic
32C2×#11929611C2211yescharacteristic, complemented
33C2×D632C2211yescharacteristic
34C2×#11929609C2211yescharacteristic
35C2×#11929609C2211yescharacteristic
36C2×#11929607C2211yescharacteristic
37C2×#11929607C2211yescharacteristic
38#14579159C2211yescharacteristic, complemented
39#14579157C2211yescharacteristic, complemented
40#14579150C2211yescharacteristic
41#14579149C2211yescharacteristic
42#14579149C2211yescharacteristic, complemented
43#14579148C2211yescharacteristic
44#14579147—22no—
45#14579134—22no—
46(C22⋊D79)⋊C4—22no—
47C22⋊C4×D79—22no—
48C42×D79C2211yescharacteristic
49#14579071C2211yescharacteristic, complemented
50#14579071C2211yescharacteristic, complemented
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—
60#11929625—22no—
61#11929625—22no—
62#11929623—22no—
63#11929623—22no—
64C2×Dic158—21no—
65C2×Dic158C2311yescharacteristic
66C2×Dic158C2311yescharacteristic
67Q8×D79—22no—
68Q8×D79—22no—
69C2×D316—21no—
70C2×D316C2311yescharacteristic
71C2×D316C2311yescharacteristic
72C2×C22⋊D79—22no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75D4×D79—22no—
76D4×D79—22no—
77C22×Dic79—21no—
78C2×C4×D79—21no—
79C2×C4×D79—21no—
80C2×C4×D79D412yes—
81C2×C4×D79C2311yescharacteristic
82Dic316—22no—
83#11929614—22no—
84#11929614—22no—
85#11929613—22no—
86#11929613—22no—
87#11929612—22no—
88#11929612—22no—
89#11929611—22no—
90#11929611—22no—
91D632—22no—
92#11929609—22no—
93#11929609—22no—
94#11929607D414yescomplemented
95#11929607D414yescomplemented
96C2×C79⋊C8C2311yescharacteristic
97C2×C79⋊C8C2311yescharacteristic
98Dic79⋊C4—22no—
99C22⋊Dic79—22no—
100(C2×D79)⋊C4—22no—
101(C2×D79)⋊C4—22no—
102(C2×D79)⋊C4—22no—
103C4×Dic79D412yes—
104C4×Dic79C2311yescharacteristic
105C2×Q8×C79C2311yescharacteristic
106C2×Q8×C79C2311yescharacteristic
107C2×D4×C79C2311yescharacteristic
108C2×D4×C79C2311yescharacteristic
109Q16×C79—22no—
110SD16×C79—22no—
111SD16×C79—22no—
112D8×C79—22no—
113C2×C8×C79C2311yescharacteristic
114C2×C8×C79C2311yescharacteristic
115C22⋊C4×C79—22no—
116C22⋊C4×C79—22no—
117C42×C79C2311yescharacteristic
118C23×C79—21no—
119C23×C79—21no—
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—44no—
123C22×D79—42no—
124C22×D79C2×D411yescharacteristic
125Q8×C79—21no—
126Q8×C79—21no—
127Q8×C79—21no—
128Q8×C79—21no—
129D4×C79—21no—
130D4×C79—21no—
131D4×C79—21no—
132D4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79C2×D412yes—
136C2×C4×C79C2411yescharacteristic
137C22⋊D79—44no—
138C22⋊D79—42no—
139C22⋊D79—42no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—42no—
143C2×Dic79C2×D412yes—
144C2×Dic79C2×D411yescharacteristic
145D316—21no—
146D316—21no—
147D316—21no—
148D316—21no—
149D316—42no—
150C4×D79—42no—
151C4×D79—42no—
152C4×D79—42no—
153C4×D79C2×D412yes—
154C4×D79C2×D412yes—
155Dic158—21no—
156Dic158—21no—
157Dic158—21no—
158Dic158—21no—
159Dic158—42no—
160C8×C79C2×D412yes—
161C8×C79C2×D412yes—
162C79⋊C8C2×D412yes—
163C79⋊C8C2×D412yes—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—42no—
167C22×C79—42no—
168C22×C79C22×D411yescharacteristic
169C2×D79—22no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—42no—
173C2×D79—42no—
174C2×D79—84no—
175C2×D79#12712yes—
176C4×C79—22no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79C22×D411yescharacteristic
180C4×C79C22×D411yescharacteristic
181Dic79—22no—
182Dic79—41no—
183Dic79—41no—
184Dic79#12712yes—
185C2×C79—81no—
186C2×C79—81no—
187C2×C79C2×#12711yescharacteristic
188C2×C79#57512yes—
189D79—22no—
190D79—81no—
191D79—81no—
192#3153—791nomaximal, Sylow
193C79#315311yescharacteristic, complemented, Sylow
194C2×#137—791no—
195C2×#137—791no—
196C2×AGL(1,ℤ/8)—791no—
197C2×AGL(1,ℤ/8)—791no—
198#532—791no—
199C2×#124—791no—
200#497—791no—
201#497—791no—
202#496—791no—
203#496—791no—
204#495—791no—
205#495—791no—
206#495—791no—
207#495D7911yescharacteristic, complemented
208C4×M16—791no—
209C2×#41—791no—
210C2×#41—791no—
211C22×Q8—791no—
212C22×D4—791no—
213#137—1584no—
214#137—1584no—
215AGL(1,ℤ/8)—1584no—
216AGL(1,ℤ/8)—1584no—
217C2×Q16—791no—
218C2×Q16—791no—
219C2×Q16—791no—
220C2×Q16C2×D7911yescharacteristic, complemented
221C2×SD16—791no—
222C2×SD16—791no—
223C2×SD16—791no—
224C2×SD16—791no—
225C2×SD16—791no—
226C2×SD16—791no—
227C2×SD16C2×D7911yescharacteristic
228C2×SD16C2×D7911yescharacteristic, complemented
229C2×D8—791no—
230C2×D8—791no—
231C2×D8—791no—
232C2×D8C2×D7911yescharacteristic
233C2×M16—791no—
234C2×M16—791no—
235C4⋊Q8—791no—
236#127—791no—
237#124—791no—
238#124—791no—
239#124—791no—
240#124—791no—
241#124—1582no—
242#124C2×D7911yescharacteristic
243#124C2×D7911yescharacteristic, complemented
244#121—1582no—
245C4×D4—1582no—
246C2×C22⋊C4—1582no—
247C2×C42—791no—
248#97—791no—
249#97—791no—
250C4×C8—791no—
251C4×C8C2×D7911yescharacteristic, complemented
252C24—1581no—
253#41—1582no—
254#41—1582no—
255#41—1582no—
256#41—1582no—
257C2×Q8—791no—
258C2×Q8—791no—
259C2×Q8—1581no—
260C2×Q8—1582no—
261C2×Q8—1582no—
262C2×Q8C22×D7911yescharacteristic
263C2×Q8C22×D7911yescharacteristic
264C2×D4—791no—
265C2×D4—791no—
266C2×D4—1581no—
267C2×D4—1582no—
268C2×D4—1582no—
269C2×D4—1582no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4C22×D7911yescharacteristic
273C2×D4C22×D7911yescharacteristic
274C22×C4—792no—
275C22×C4—791no—
276C22×C4—1581no—
277C22×C4—1581no—
278C22×C4—1581no—
279Q16—22no—
280Q16—1582no—
281Q16—1582no—
282Q16—1582no—
283SD16—22no—
284SD16—22no—
285SD16—1582no—
286SD16—1582no—
287SD16—1582no—
288SD16—1582no—
289SD16—1582no—
290SD16—1582no—
291D8—22no—
292D8—1582no—
293D8—1582no—
294D8—1582no—
295M16—794no—
296M16—794no—
297C2×C8—791no—
298C2×C8—791no—
299C2×C8C22×D7911yescharacteristic
300C2×C8C22×D7911yescharacteristic
301C4⋊C4—1582no—
302C22⋊C4—22no—
303C22⋊C4—22no—
304C22⋊C4—1582no—
305C22⋊C4—1582no—
306C22⋊C4—1582no—
307C22⋊C4—1582no—
308C42—792no—
309C42—791no—
310C42C22×D7911yescharacteristic
311C23—21no—
312C23—21no—
313C23—3162no—
314C23—3164no—
315C23—791no—
316C23—1581no—
317C23—1581no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—3162no—
323Q8—1581no—
324Q8—1581no—
325Q8—1581no—
326Q8—1581no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—3162no—
332D4—3162no—
333D4—3162no—
334D4—3164no—
335D4—1581no—
336D4—1581no—
337D4—1581no—
338D4—1581no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3162no—
342C2×C4—3162no—
343C2×C4—3162no—
344C2×C4—3162no—
345C2×C4—791no—
346C2×C4—792no—
347C2×C4—792no—
348C2×C4—792no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4D4×D7912yes—
352C2×C4C23×D7911yescharacteristic
353C8—792no—
354C8—792no—
355C8D4×D7912yes—
356C8D4×D7912yes—
357C22—41no—
358C22—41no—
359C22—42no—
360C22—42no—
361C22—3161no—
362C22—3161no—
363C22—3162no—
364C22—3162no—
365C22—792no—
366C22—6324no—
367C22—1582no—
368C22C2×D4×D7911yescharacteristic
369C4—22no—
370C4—41no—
371C4—41no—
372C4—3161no—
373C4—3161no—
374C4—792no—
375C4—1582no—
376C4C2×D4×D7911yescharacteristic
377C4C2×D4×D7911yescharacteristic
378C2—81no—
379C2—81no—
380C2—6321no—
381C2—6321no—
382C2—1582no—
383C2#127×D7911yescharacteristic
384C2#1909936012yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#495×C79C2
socleC22×C79C22×D4
hypercenter#495D79
hypocenterC79#3153
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. C2×#14579193C2semidirect
2. C2×#14579190C2semidirect
3. C2×#14579188C2semidirect
4. C2×#14579185C2semidirect
5. #19099112C2semidirect
6. #124×D79C2semidirect
7. #19098956C2semidirect
8. #19098954C2semidirect
9. #19098951C2semidirect
10. #19098949C2semidirect
11. #19098947C2semidirect
12. #19098945C2semidirect
13. #19098945C2semidirect
14. C4×#11929607C2semidirect
15. #495×C79C2semidirect
24. C2×Dic316C22semidirect
25. C2×#11929614C22semidirect
26. C2×#11929614C22semidirect
28. C2×#11929613C22semidirect
30. C2×#11929612C22semidirect
32. C2×#11929611C22semidirect
38. #14579159C22semidirect
39. #14579157C22semidirect
42. #14579149C22semidirect
49. #14579071C22semidirect
50. #14579071C22semidirect
51. C4×C79⋊C8C22semidirect
52. C2×Q16×C79C22semidirect
54. C2×SD16×C79C22semidirect
57. #124×C79C22semidirect
58. C4×C8×C79C22semidirect
94. #11929607D4semidirect
95. #11929607D4semidirect
193. C79#3153semidirect
207. #495D79semidirect
220. C2×Q16C2×D79semidirect
228. C2×SD16C2×D79semidirect
243. #124C2×D79semidirect
251. C4×C8C2×D79semidirect