Finite Group Databasebeta

← #23772889

Subgroups — #23772889

Order 10112.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579190C211yesmaximal, characteristic, complemented
2C2×#14579185C211yesmaximal, characteristic
3#124×D79C211yesmaximal, characteristic, complemented
4C4×#11929623C211yesmaximal, characteristic, complemented
5#19098788C211yesmaximal, characteristic, complemented
6#19098786C211yesmaximal, characteristic, complemented
7#19098784C211yesmaximal, characteristic, complemented
8#19098782C211yesmaximal, characteristic, complemented
9#19098780C211yesmaximal, characteristic, complemented
10#19098778C211yesmaximal, characteristic, complemented
11#19098776C211yesmaximal, characteristic, complemented
12#19098585C211yesmaximal, characteristic, complemented
13#19098570C211yesmaximal, characteristic, complemented
14#19098566C211yesmaximal, characteristic, complemented
15#463×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19#14579190—24no—
20#14579185—24no—
21C2×Dic316C2211yescharacteristic, complemented
22C2×#11929614C2211yescharacteristic, complemented
23C2×#11929613C2211yescharacteristic
24C2×#11929612C2211yescharacteristic
25C2×#11929612C2211yescharacteristic, complemented
26C2×#11929609C2211yescharacteristic
27C2×#11929607C2211yescharacteristic
28C2×#11929607C2211yescharacteristic
29#14579150C2211yescharacteristic
30#14579149C2211yescharacteristic
31#14579148C2211yescharacteristic
32#14579147—21no—
33#14579147—21no—
34C4×Dic158C2211yescharacteristic, complemented
35#14579126C2211yescharacteristic, complemented
36D4×Dic79C2211yescharacteristic, complemented
37C4×C22⋊D79—21no—
38(C22⋊D79)⋊C4—21no—
39#14579119C2211yescharacteristic
40#14579117—21no—
41C22⋊C4×D79—21no—
42C22⋊C4×D79—21no—
43C2×C4×Dic79—21no—
44C42×D79C2211yescharacteristic
45C4⋊(C79⋊C8)C2211yescharacteristic, complemented
46Dic79⋊C8C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579085C2211yescharacteristic, complemented
50#14579084C2211yescharacteristic, complemented
51#14579083C2211yescharacteristic
52#14579082C2211yescharacteristic
53#14579081C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic, complemented
55C2×D8×C79C2211yescharacteristic
56#124×C79C2211yescharacteristic
57C4×D4×C79C2211yescharacteristic, complemented
58C4⋊C8×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic
61C23×D79—21no—
62#11929623—22no—
63#11929623D414yes—
64C2×Dic158—21no—
65C2×Dic158C2311yescharacteristic
66C2×Dic158C2311yescharacteristic
67Q8×D79—22no—
68Q8×D79—22no—
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72D4×D79—22no—
73D4×D79—22no—
74C22×Dic79—21no—
75C22×Dic79—21no—
76C2×C4×D79—21no—
77C2×C4×D79D411yescharacteristic
78C2×C4×D79D411yescharacteristic
79C2×C4×D79C2311yescharacteristic
80Dic316—22no—
81#11929614—22no—
82#11929613—22no—
83#11929612—22no—
84#11929612—22no—
85#11929609—22no—
86#11929607—22no—
87#11929607—22no—
88C2×C79⋊C8C2311yescharacteristic
89C2×C79⋊C8C2311yescharacteristic
90C4⋊Dic79C2311yescharacteristic
91Dic79⋊C4—21no—
92Dic79⋊C4—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95C22⋊Dic79—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101C4×Dic79—21no—
102C4×Dic79—21no—
103C4×Dic79—21no—
104C4×Dic79D411yescharacteristic
105C4×Dic79D411yescharacteristic
106C4×Dic79C2311yescharacteristic
107C2×Q8×C79C2311yescharacteristic
108C2×D4×C79C2311yescharacteristic
109C2×D4×C79C2311yescharacteristic
110C22×C4×C79—21no—
111SD16×C79—22no—
112D8×C79—22no—
113C2×C8×C79C2311yescharacteristic
114C2×C8×C79C2311yescharacteristic
115C4⋊C4×C79C2311yescharacteristic
116C22⋊C4×C79—21no—
117C22⋊C4×C79—21no—
118C22⋊C4×C79—21no—
119C42×C79C2311yescharacteristic
120C23×C79—21no—
121C23×C79—21no—
122C22×D79—21no—
123C22×D79—42no—
124C22×D79—42no—
125C22×D79—42no—
126C22×D79C2×D411yescharacteristic
127Q8×C79—21no—
128Q8×C79—21no—
129D4×C79—21no—
130D4×C79—21no—
131D4×C79—21no—
132D4×C79C2×D412yes—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—42no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2411yescharacteristic
139C22⋊D79—24no—
140C22⋊D79—42no—
141C2×Dic79—21no—
142C2×Dic79—24no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—42no—
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148C2×Dic79C2×D411yescharacteristic
149D316—21no—
150D316—21no—
151C4×D79—41no—
152C4×D79—41no—
153C4×D79—42no—
154C4×D79C2×D412yes—
155C4×D79#4112yes—
156Dic158—21no—
157Dic158—21no—
158Dic158—21no—
159Dic158—42no—
160Dic158C2×D412yes—
161C8×C79—21no—
162C8×C79—21no—
163C79⋊C8—21no—
164C79⋊C8—21no—
165C22×C79—22no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79C22×D411yescharacteristic
172C2×D79—21no—
173C2×D79—21no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—84no—
178C2×D79#12112yes—
179C4×C79—21no—
180C4×C79—21no—
181C4×C79—41no—
182C4×C79—41no—
183C4×C79C22×D411yescharacteristic
184C4×C79C2×#4111yescharacteristic
185Dic79—22no—
186Dic79—21no—
187Dic79—21no—
188Dic79—41no—
189Dic79—41no—
190Dic79#12112yes—
191C2×C79—42no—
192C2×C79—81no—
193C2×C79C2×#12111yescharacteristic
194C2×C79#57511yescharacteristic
195C2×C79#57511yescharacteristic
196D79—22no—
197D79—81no—
198#3040—791nomaximal, Sylow
199C79#304011yescharacteristic, complemented, Sylow
200C2×#137—791no—
201C2×AGL(1,ℤ/8)—791no—
202C2×#124—791no—
203C4×#41—791no—
204#464—791no—
205#464—791no—
206#464—791no—
207#464—791no—
208#463—791no—
209#463—791no—
210#463—791no—
211#463D7911yescharacteristic, complemented
212#423—791no—
213#419—791no—
214#418—791no—
215C2×#41—791no—
216C22×Q8—791no—
217C22×D4—791no—
218#137—1584no—
219AGL(1,ℤ/8)—1584no—
220C2×Q16—791no—
221C2×Q16—791no—
222C2×SD16—791no—
223C2×SD16—791no—
224C2×SD16—791no—
225C2×SD16C2×D7911yescharacteristic, complemented
226C2×D8—791no—
227C2×D8C2×D7911yescharacteristic
228C2×M16—791no—
229C2×M16—791no—
230#124—791no—
231#124—791no—
232#124—791no—
233#124—1581no—
234#124—1581no—
235#124C2×D7911yescharacteristic
236C4×Q8—791no—
237C4×Q8—791no—
238C4×D4—791no—
239C4×D4—1581no—
240C4×D4—1581no—
241C4×D4C2×D7911yescharacteristic, complemented
242#117—791no—
243#117—1581no—
244C2×C22⋊C4—1581no—
245C2×C22⋊C4—1581no—
246C2×C42—791no—
247C2×C42—1581no—
248C4⋊C8—791no—
249C4⋊C8—791no—
250C4⋊C8—791no—
251C4⋊C8C2×D7911yescharacteristic, complemented
252#103—791no—
253#103—791no—
254#103—791no—
255#103C2×D7911yescharacteristic, complemented
256#102—791no—
257#102—791no—
258#102—791no—
259#102C2×D7911yescharacteristic
260C24—1581no—
261#41—794no—
262#41—1582no—
263C2×Q8—791no—
264C2×Q8—791no—
265C2×Q8—1581no—
266C2×Q8—1582no—
267C2×Q8—1582no—
268C2×Q8C22×D7911yescharacteristic
269C2×D4—791no—
270C2×D4—1582no—
271C2×D4—1582no—
272C2×D4—1581no—
273C2×D4—1581no—
274C2×D4C22×D7911yescharacteristic
275C2×D4C22×D7911yescharacteristic
276C22×C4—21no—
277C22×C4—791no—
278C22×C4—791no—
279C22×C4—791no—
280C22×C4—1581no—
281C22×C4—1581no—
282C22×C4—1581no—
283Q16—1582no—
284Q16—1582no—
285SD16—22no—
286SD16—1582no—
287SD16—1582no—
288SD16—1582no—
289D8—22no—
290D8—1582no—
291M16—1582no—
292M16—1582no—
293C2×C8—791no—
294C2×C8—791no—
295C2×C8C22×D7911yescharacteristic
296C2×C8C22×D7911yescharacteristic
297C4⋊C4—791no—
298C4⋊C4—1581no—
299C4⋊C4—1581no—
300C4⋊C4C22×D7911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C22⋊C4—1581no—
312C42—791no—
313C42—791no—
314C42—791no—
315C42—1581no—
316C42—1581no—
317C42—1581no—
318C42C22×D7911yescharacteristic
319C23—21no—
320C23—21no—
321C23—3162no—
322C23—3162no—
323C23—3162no—
324C23—791no—
325C23—1581no—
326Q8—21no—
327Q8—21no—
328Q8—3162no—
329Q8—792no—
330Q8—1581no—
331Q8—1581no—
332Q8—1581no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—3162no—
337D4—1584no—
338D4—1581no—
339D4—1581no—
340D4D4×D7912yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—3161no—
345C2×C4—3161no—
346C2×C4—3162no—
347C2×C4—3162no—
348C2×C4—791no—
349C2×C4—792no—
350C2×C4—792no—
351C2×C4—791no—
352C2×C4—791no—
353C2×C4—1581no—
354C2×C4—1581no—
355C2×C4—1584no—
356C2×C4—1581no—
357C2×C4D4×D7911yescharacteristic
358C2×C4D4×D7911yescharacteristic
359C2×C4C23×D7911yescharacteristic
360C8—21no—
361C8—21no—
362C8—1581no—
363C8—1581no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22—792no—
374C22—6324no—
375C22—1581no—
376C22—1581no—
377C22C2×D4×D7911yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—3161no—
383C4—3161no—
384C4—792no—
385C4—1582no—
386C4—1581no—
387C4—1581no—
388C4C2×D4×D7911yescharacteristic
389C4#41×D7911yescharacteristic
390C2—42no—
391C2—81no—
392C2—6321no—
393C2—1582no—
394C2#121×D7911yescharacteristic
395C2#1909935911yescharacteristic
396C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#463×C79C2
socleC22×C79C22×D4
prime radicalC2×#14579185C2
hypercenter#463D79
hypocenterC79#3040
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#14579190C2semidirect
3. #124×D79C2semidirect
4. C4×#11929623C2semidirect
5. #19098788C2semidirect
6. #19098786C2semidirect
7. #19098784C2semidirect
8. #19098782C2semidirect
9. #19098780C2semidirect
10. #19098778C2semidirect
11. #19098776C2semidirect
12. #19098585C2semidirect
13. #19098570C2semidirect
14. #19098566C2semidirect
15. #463×C79C2semidirect
21. C2×Dic316C22semidirect
22. C2×#11929614C22semidirect
25. C2×#11929612C22semidirect
34. C4×Dic158C22semidirect
35. #14579126C22semidirect
36. D4×Dic79C22semidirect
45. C4⋊(C79⋊C8)C22semidirect
46. Dic79⋊C8C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579086C22semidirect
49. #14579085C22semidirect
50. #14579084C22semidirect
54. C2×SD16×C79C22semidirect
57. C4×D4×C79C22semidirect
58. C4⋊C8×C79C22semidirect
59. #103×C79C22semidirect
199. C79#3040semidirect
211. #463D79semidirect
225. C2×SD16C2×D79semidirect
241. C4×D4C2×D79semidirect
251. C4⋊C8C2×D79semidirect
255. #103C2×D79semidirect