Finite Group Databasebeta

← #23773869

Subgroups — #23773869

Order 10112.

564 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×#14579190C211yesmaximal, characteristic, complemented
2C2×#14579188C211yesmaximal, characteristic, complemented
3C2×#14579182C211yesmaximal, characteristic, complemented
4C2×SD16×D79C211yesmaximal, characteristic, complemented
5#19099138C211yesmaximal, characteristic, complemented
6#19099126C211yesmaximal, characteristic, complemented
7#19098955C211yesmaximal, characteristic, complemented
8#19098954C211yesmaximal, characteristic, complemented
9#19098950C211yesmaximal, characteristic, complemented
10#19098949C211yesmaximal, characteristic, complemented
11#19098947C211yesmaximal, characteristic, complemented
12#19098944C211yesmaximal, characteristic, complemented
13#19098934C211yesmaximal, characteristic, complemented
14#19098517C211yesmaximal, characteristic, complemented
15#492×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929623C2211yescharacteristic
18C2×Q8×D79C2211yescharacteristic
19C2×D4×D79C2211yescharacteristic
20#14579190—24no—
21#14579188—24no—
22#14579182—24no—
23C2×Dic316C2211yescharacteristic, complemented
24C2×#11929614C2211yescharacteristic, complemented
25C2×#11929614C2211yescharacteristic, complemented
26C2×#11929613C2211yescharacteristic
27C2×#11929613C2211yescharacteristic, complemented
28C2×#11929612C2211yescharacteristic
29C2×#11929612C2211yescharacteristic, complemented
30C2×#11929611C2211yescharacteristic
31C2×#11929611C2211yescharacteristic
32SD16×D79—24no—
33C2×D632C2211yescharacteristic
34C2×#11929609C2211yescharacteristic
35C2×#11929609C2211yescharacteristic, complemented
36C2×#11929607C2211yescharacteristic
37C2×C8×D79C2211yescharacteristic
38#14579159C2211yescharacteristic, complemented
39#14579157C2211yescharacteristic
40#14579150C2211yescharacteristic, complemented
41#14579149C2211yescharacteristic
42#14579149C2211yescharacteristic, complemented
43#14579148C2211yescharacteristic
44#14579146—22no—
45#14579139—22no—
46#14579133—22no—
47#14579129—22no—
48#14579118C2211yescharacteristic
49#14579072C2211yescharacteristic, complemented
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic, complemented
55C2×SD16×C79C2211yescharacteristic, complemented
56C4⋊Q8×C79C2211yescharacteristic, complemented
57#127×C79C2211yescharacteristic
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—21no—
73C2×C22⋊D79—21no—
74C2×C22⋊D79—22no—
75D4×D79—22no—
76D4×D79—22no—
77C22×Dic79—21no—
78C2×C4×D79—21no—
79C2×C4×D79—21no—
80C2×C4×D79C2311yescharacteristic
81Dic316—22no—
82#11929614—22no—
83#11929614—22no—
84#11929613—22no—
85#11929613—22no—
86#11929612—22no—
87#11929612—22no—
88#11929611—22no—
89#11929611—22no—
90D632—22no—
91#11929609—22no—
92#11929609—22no—
93#11929607D414yescomplemented
94C2×C79⋊C8C2311yescharacteristic
95C2×C79⋊C8C2311yescharacteristic
96C8×D79D414yescomplemented
97Dic79⋊C4—22no—
98Dic79⋊C4D412yes—
99C22⋊Dic79—22no—
100(C2×D79)⋊C4—22no—
101(C2×D79)⋊C4—22no—
102(C2×D79)⋊C4—22no—
103(C2×D79)⋊C4D412yes—
104C4×Dic79C2311yescharacteristic
105C2×Q8×C79C2311yescharacteristic
106C2×Q8×C79C2311yescharacteristic
107C2×D4×C79—22no—
108C2×D4×C79C2311yescharacteristic
109C2×D4×C79C2311yescharacteristic
110SD16×C79—22no—
111SD16×C79—22no—
112SD16×C79—22no—
113SD16×C79—22no—
114C2×C8×C79C2311yescharacteristic
115C2×C8×C79C2311yescharacteristic
116C4⋊C4×C79—22no—
117C42×C79C2311yescharacteristic
118C23×C79—21no—
119C23×C79—21no—
120C22×D79—21no—
121C22×D79—21no—
122C22×D79—42no—
123C22×D79—82no—
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—
133D4×C79—82no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79C2×D412yes—
137C2×C4×C79C2411yescharacteristic
138C22⋊D79—42no—
139C22⋊D79—42no—
140C22⋊D79—82no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—42no—
144C2×Dic79C2×D412yes—
145C2×Dic79C2×D411yescharacteristic
146D316—21no—
147D316—21no—
148D316—21no—
149D316—21no—
150D316—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#57712yes—
189D79—22no—
190D79—81no—
191D79—81no—
192#3154—791nomaximal, Sylow
193C79#315411yescharacteristic, complemented, Sylow
194C2×#137—791no—
195C2×AGL(1,ℤ/8)—791no—
196C2×#135—791no—
197C22×SD16—791no—
198#536—791no—
199#535—791no—
200#497—791no—
201#497—791no—
202#496—791no—
203#496—791no—
204#495—791no—
205#495—791no—
206#492—791no—
207#492D7911yescharacteristic, complemented
208#405—791no—
209C2×#41—791no—
210C2×#41—791no—
211C22×Q8—791no—
212C22×D4—791no—
213#137—1584no—
214AGL(1,ℤ/8)—1584no—
215#135—1584no—
216C2×Q16—791no—
217C2×Q16—791no—
218C2×Q16—791no—
219C2×SD16—791no—
220C2×SD16—791no—
221C2×SD16—791no—
222C2×SD16—791no—
223C2×SD16—791no—
224C2×SD16—791no—
225C2×SD16—1584no—
226C2×SD16C2×D7911yescharacteristic
227C2×SD16C2×D7911yescharacteristic
228C2×SD16C2×D7911yescharacteristic, complemented
229C2×SD16C2×D7911yescharacteristic, complemented
230C2×D8—791no—
231C2×D8—791no—
232C2×D8—791no—
233C2×M16—791no—
234C22×C8—791no—
235C4⋊Q8—791no—
236C4⋊Q8C2×D7911yescharacteristic, complemented
237#127—791no—
238#127C2×D7911yescharacteristic
239#124—791no—
240#124—791no—
241#124—791no—
242#124—791no—
243#123—1582no—
244C22⋊Q8—1582no—
245#121—1582no—
246#120—1582no—
247#117—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—22no—
265C2×D4—791no—
266C2×D4—791no—
267C2×D4—1581no—
268C2×D4—1582no—
269C2×D4—1582no—
270C2×D4—1581no—
271C2×D4—1582no—
272C2×D4—1581no—
273C2×D4C22×D7911yescharacteristic
274C2×D4C22×D7911yescharacteristic
275C22×C4—791no—
276C22×C4—1581no—
277C22×C4—1581no—
278C22×C4—1581no—
279Q16—1582no—
280Q16—1582no—
281Q16—1582no—
282SD16—22no—
283SD16—22no—
284SD16—22no—
285SD16—22no—
286SD16—1582no—
287SD16—1582no—
288SD16—1582no—
289SD16—1582no—
290SD16—1582no—
291SD16—1582no—
292D8—1582no—
293D8—1582no—
294D8—1582no—
295M16—794no—
296C2×C8—791no—
297C2×C8—791no—
298C2×C8—794no—
299C2×C8C22×D7911yescharacteristic
300C2×C8C22×D7911yescharacteristic
301C4⋊C4—22no—
302C4⋊C4—792no—
303C4⋊C4—1582no—
304C22⋊C4—792no—
305C22⋊C4—1582no—
306C22⋊C4—1582no—
307C22⋊C4—1582no—
308C22⋊C4—1582no—
309C42—791no—
310C42C22×D7911yescharacteristic
311C23—21no—
312C23—21no—
313C23—3162no—
314C23—791no—
315C23—6322no—
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—82no—
332D4—3162no—
333D4—3162no—
334D4—3162no—
335D4—6322no—
336D4—1581no—
337D4—1581no—
338D4—1581no—
339D4—1581no—
340C2×C4—21no—
341C2×C4—21no—
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#1909936912yes—
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#492×C79C2
socleC22×C79C22×D4
hypercenter#492D79
hypocenterC79#3154
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. C2×#14579190C2semidirect
2. C2×#14579188C2semidirect
3. C2×#14579182C2semidirect
4. C2×SD16×D79C2semidirect
5. #19099138C2semidirect
6. #19099126C2semidirect
7. #19098955C2semidirect
8. #19098954C2semidirect
9. #19098950C2semidirect
10. #19098949C2semidirect
11. #19098947C2semidirect
12. #19098944C2semidirect
13. #19098934C2semidirect
14. #19098517C2semidirect
15. #492×C79C2semidirect
23. C2×Dic316C22semidirect
24. C2×#11929614C22semidirect
25. C2×#11929614C22semidirect
27. C2×#11929613C22semidirect
29. C2×#11929612C22semidirect
35. C2×#11929609C22semidirect
38. #14579159C22semidirect
40. #14579150C22semidirect
42. #14579149C22semidirect
49. #14579072C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
54. C2×SD16×C79C22semidirect
55. C2×SD16×C79C22semidirect
56. C4⋊Q8×C79C22semidirect
58. C4×C8×C79C22semidirect
93. #11929607D4semidirect
96. C8×D79D4semidirect
193. C79#3154semidirect
207. #492D79semidirect
228. C2×SD16C2×D79semidirect
229. C2×SD16C2×D79semidirect
236. C4⋊Q8C2×D79semidirect
251. C4×C8C2×D79semidirect