Finite Group Databasebeta

← #23772919

Subgroups — #23772919

Order 10112.

490 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×#14579193C211yesmaximal, characteristic, complemented
2C2×SD16×D79C211yesmaximal, characteristic, complemented
3#19099131C211yesmaximal, characteristic
4#19099039C211yesmaximal, characteristic, complemented
5#19098788C211yesmaximal, characteristic, complemented
6#19098787C211yesmaximal, characteristic, complemented
7#19098782C211yesmaximal, characteristic, complemented
8#19098764C211yesmaximal, characteristic, complemented
9#19098763C211yesmaximal, characteristic, complemented
10#19098762C211yesmaximal, characteristic, complemented
11#19098761C211yesmaximal, characteristic, complemented
12#19098588C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#19098558C211yesmaximal, characteristic, complemented
15#464×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C2×D4×D79C2211yescharacteristic
19#14579193—24no—
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929613C2211yescharacteristic
22C2×#11929613C2211yescharacteristic, complemented
23C2×#11929612C2211yescharacteristic
24C2×#11929611C2211yescharacteristic
25C2×#11929611C2211yescharacteristic, complemented
26SD16×D79—24no—
27C2×#11929607C2211yescharacteristic
28C2×C8×D79C2211yescharacteristic
29#14579158C2211yescharacteristic
30#14579157C2211yescharacteristic
31#14579150C2211yescharacteristic
32#14579134—21no—
33#14579134—21no—
34#14579131—21no—
35#14579131—21no—
36Q8×Dic79C2211yescharacteristic, complemented
37C4×Dic158—21no—
38C4×Dic158C2211yescharacteristic, complemented
39#14579126—21no—
40#14579126C2211yescharacteristic, complemented
41#14579119—21no—
42#14579119C2211yescharacteristic
43#14579118—21no—
44#14579118C2211yescharacteristic
45C4⋊(C79⋊C8)C2211yescharacteristic, complemented
46Dic79⋊C8C2211yescharacteristic, complemented
47Dic79⋊C8C2211yescharacteristic, complemented
48#14579085C2211yescharacteristic, complemented
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic, complemented
51#14579082C2211yescharacteristic
52#14579081C2211yescharacteristic
53#14579081C2211yescharacteristic, complemented
54C2×Q16×C79C2211yescharacteristic, complemented
55C2×SD16×C79C2211yescharacteristic
56#124×C79C2211yescharacteristic
57C4×Q8×C79C2211yescharacteristic, complemented
58C4⋊C8×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic
61C23×D79—21no—
62#11929625—22no—
63#11929625—22no—
64C2×Dic158—21no—
65C2×Dic158C2311yescharacteristic
66Q8×D79—22no—
67Q8×D79D414yescomplemented
68C2×D316—21no—
69C2×D316—21no—
70C2×D316—21no—
71C2×D316C2311yescharacteristic
72C2×D316C2311yescharacteristic
73C2×C22⋊D79—21no—
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76D4×D79—22no—
77D4×D79—22no—
78C2×C4×D79—21no—
79C2×C4×D79—21no—
80C2×C4×D79C2311yescharacteristic
81#11929614—22no—
82#11929613—22no—
83#11929613—22no—
84#11929612—22no—
85#11929611—22no—
86#11929611—22no—
87#11929607—22no—
88C2×C79⋊C8C2311yescharacteristic
89C2×C79⋊C8C2311yescharacteristic
90C8×D79—22no—
91C4⋊Dic79—21no—
92C4⋊Dic79C2311yescharacteristic
93Dic79⋊C4—21no—
94Dic79⋊C4—21no—
95Dic79⋊C4D411yescharacteristic
96Dic79⋊C4D411yescharacteristic
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4D411yescharacteristic
101(C2×D79)⋊C4D411yescharacteristic
102C4×Dic79—21no—
103C4×Dic79—21no—
104C4×Dic79—21no—
105C4×Dic79—21no—
106C4×Dic79C2311yescharacteristic
107C2×Q8×C79C2311yescharacteristic
108C2×Q8×C79C2311yescharacteristic
109C2×D4×C79C2311yescharacteristic
110Q16×C79—22no—
111SD16×C79—22no—
112C2×C8×C79C2311yescharacteristic
113C2×C8×C79C2311yescharacteristic
114C4⋊C4×C79—21no—
115C4⋊C4×C79C2311yescharacteristic
116C22⋊C4×C79—21no—
117C22⋊C4×C79—21no—
118C42×C79—21no—
119C42×C79C2311yescharacteristic
120C23×C79—21no—
121C22×D79—21no—
122C22×D79—21no—
123C22×D79—42no—
124C22×D79—81no—
125C22×D79—81no—
126C22×D79C2×D411yescharacteristic
127Q8×C79—21no—
128Q8×C79—21no—
129Q8×C79—21no—
130Q8×C79C2×D412yes—
131D4×C79—21no—
132D4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2411yescharacteristic
139C22⋊D79—42no—
140C22⋊D79—81no—
141C22⋊D79—81no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79C2×D411yescharacteristic
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147D316—21no—
148D316—21no—
149D316—21no—
150D316—21no—
151D316—42no—
152D316—81no—
153D316—81no—
154C4×D79—24no—
155C4×D79—42no—
156C4×D79C2×D412yes—
157C4×D79#4112yes—
158Dic158—21no—
159Dic158—24no—
160Dic158C2×D412yes—
161C8×C79—21no—
162C8×C79—21no—
163C79⋊C8—21no—
164C79⋊C8—21no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79C22×D411yescharacteristic
169C2×D79—21no—
170C2×D79—21no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—84no—
178C2×D79#12112yes—
179C4×C79—22no—
180C4×C79—21no—
181C4×C79—21no—
182C4×C79—41no—
183C4×C79—41no—
184C4×C79C22×D411yescharacteristic
185C4×C79C2×#4111yescharacteristic
186Dic79—22no—
187Dic79—21no—
188Dic79—21no—
189Dic79—41no—
190Dic79#12112yes—
191C2×C79—81no—
192C2×C79C2×#12111yescharacteristic
193C2×C79#57711yescharacteristic
194C2×C79#57711yescharacteristic
195D79—22no—
196D79—81no—
197D79—81no—
198#3043—791nomaximal, Sylow
199C79#304311yescharacteristic, complemented, Sylow
200C2×#137—791no—
201C22×SD16—791no—
202#535—791no—
203#519—791no—
204#464—791no—
205#464—791no—
206#464—791no—
207#464D7911yescharacteristic, complemented
208#460—791no—
209#460—791no—
210#460—791no—
211#460—791no—
212#424—791no—
213#418—791no—
214#416—791no—
215C2×#41—791no—
216C22×Q8—791no—
217C22×D4—791no—
218#137—1584no—
219C2×Q16—791no—
220C2×Q16C2×D7911yescharacteristic, complemented
221C2×SD16—791no—
222C2×SD16—791no—
223C2×SD16—791no—
224C2×SD16—791no—
225C2×SD16—791no—
226C2×SD16—1584no—
227C2×SD16C2×D7911yescharacteristic
228C2×M16—791no—
229C22×C8—791no—
230#127—791no—
231#127—791no—
232#124—791no—
233#124C2×D7911yescharacteristic
234#121—1581no—
235#121—1581no—
236#120—1581no—
237#120—1581no—
238C4×Q8—791no—
239C4×Q8—791no—
240C4×Q8—791no—
241C4×Q8—1581no—
242C4×Q8—1581no—
243C4×Q8C2×D7911yescharacteristic, complemented
244#117—791no—
245#117—791no—
246#117—1581no—
247#117—1581no—
248C4⋊C8—791no—
249C4⋊C8—791no—
250C4⋊C8—791no—
251C4⋊C8C2×D7911yescharacteristic, complemented
252#103—791no—
253#103C2×D7911yescharacteristic, complemented
254#102—791no—
255#102—791no—
256#102—791no—
257#102—791no—
258#102—791no—
259#102C2×D7911yescharacteristic
260C24—1581no—
261#41—1582no—
262#41—1582no—
263C2×Q8—794no—
264C2×Q8—791no—
265C2×Q8—1581no—
266C2×Q8—1582no—
267C2×Q8C22×D7911yescharacteristic
268C2×Q8C22×D7911yescharacteristic
269C2×D4—791no—
270C2×D4—791no—
271C2×D4—1581no—
272C2×D4—1582no—
273C2×D4—1582no—
274C2×D4—1581no—
275C2×D4—1581no—
276C2×D4—1581no—
277C2×D4—1581no—
278C2×D4—1581no—
279C2×D4C22×D7911yescharacteristic
280C22×C4—791no—
281C22×C4—1581no—
282C22×C4—1581no—
283Q16—22no—
284Q16—1582no—
285SD16—22no—
286SD16—1582no—
287SD16—1582no—
288SD16—1582no—
289SD16—1582no—
290SD16—1582no—
291M16—1582no—
292C2×C8—791no—
293C2×C8—791no—
294C2×C8—1582no—
295C2×C8C22×D7911yescharacteristic
296C2×C8C22×D7911yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—791no—
299C4⋊C4—791no—
300C4⋊C4—791no—
301C4⋊C4—1581no—
302C4⋊C4—1581no—
303C4⋊C4—1581no—
304C4⋊C4C22×D7911yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—791no—
308C22⋊C4—791no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C22⋊C4—1581no—
312C42—21no—
313C42—791no—
314C42—1581no—
315C42—1581no—
316C42—1581no—
317C42—1581no—
318C42C22×D7911yescharacteristic
319C23—21no—
320C23—3162no—
321C23—791no—
322C23—6321no—
323C23—6321no—
324C23—1581no—
325C23—1581no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—792no—
330Q8—1584no—
331Q8—1581no—
332Q8D4×D7912yes—
333D4—21no—
334D4—21no—
335D4—3162no—
336D4—3162no—
337D4—6321no—
338D4—6321no—
339D4—6321no—
340D4—6321no—
341D4—1581no—
342D4—1581no—
343D4—1581no—
344D4—1581no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—3162no—
349C2×C4—791no—
350C2×C4—792no—
351C2×C4—792no—
352C2×C4—791no—
353C2×C4—791no—
354C2×C4—1584no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4D4×D7911yescharacteristic
358C2×C4D4×D7911yescharacteristic
359C2×C4C23×D7911yescharacteristic
360C8—21no—
361C8—21no—
362C8—1581no—
363C8—1581no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—3161no—
368C22—3161no—
369C22—3161no—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22—792no—
374C22—6324no—
375C22—1581no—
376C22—1581no—
377C22C2×D4×D7911yescharacteristic
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—3161no—
384C4—792no—
385C4—1582no—
386C4—1581no—
387C4—1581no—
388C4C2×D4×D7911yescharacteristic
389C4#41×D7911yescharacteristic
390C2—81no—
391C2—6321no—
392C2—6321no—
393C2—1582no—
394C2#121×D7911yescharacteristic
395C2#1909937011yescharacteristic
396C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#464×C79C2
socleC22×C79C22×D4
prime radical#19099131C2
hypercenter#464D79
hypocenterC79#3043
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. C2×#14579193C2semidirect
2. C2×SD16×D79C2semidirect
4. #19099039C2semidirect
5. #19098788C2semidirect
6. #19098787C2semidirect
7. #19098782C2semidirect
8. #19098764C2semidirect
9. #19098763C2semidirect
10. #19098762C2semidirect
11. #19098761C2semidirect
12. #19098588C2semidirect
13. #19098566C2semidirect
14. #19098558C2semidirect
15. #464×C79C2semidirect
20. C2×#11929614C22semidirect
22. C2×#11929613C22semidirect
25. C2×#11929611C22semidirect
36. Q8×Dic79C22semidirect
38. C4×Dic158C22semidirect
40. #14579126C22semidirect
45. C4⋊(C79⋊C8)C22semidirect
46. Dic79⋊C8C22semidirect
47. Dic79⋊C8C22semidirect
48. #14579085C22semidirect
50. #14579083C22semidirect
53. #14579081C22semidirect
54. C2×Q16×C79C22semidirect
57. C4×Q8×C79C22semidirect
58. C4⋊C8×C79C22semidirect
59. #103×C79C22semidirect
67. Q8×D79D4semidirect
199. C79#3043semidirect
207. #464D79semidirect
220. C2×Q16C2×D79semidirect
243. C4×Q8C2×D79semidirect
251. C4⋊C8C2×D79semidirect
253. #103C2×D79semidirect