Finite Group Databasebeta

← #23772444

Subgroups — #23772444

Order 10112.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099072C211yesmaximal, characteristic
2#19098639C211yesmaximal, characteristic, complemented
3#19098637C211yesmaximal, characteristic, complemented
4#19098635C211yesmaximal, characteristic, complemented
5#19098633C211yesmaximal, characteristic, complemented
6#19098632C211yesmaximal, characteristic, complemented
7C8×D316C211yesmaximal, characteristic, complemented
8(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
9#19098623C211yesmaximal, characteristic, complemented
10#19098622C211yesmaximal, characteristic, complemented
11#19098531C211yesmaximal, characteristic, complemented
12#19098528C211yesmaximal, characteristic, complemented
13#19098526C211yesmaximal, characteristic, complemented
14C22⋊C8×D79C211yesmaximal, characteristic, complemented
15#436×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C2×#11929608C2211yescharacteristic
19C2×#11929607C2211yescharacteristic, complemented
20C22×C79⋊C8C2211yescharacteristic, complemented
21C2×C8×D79C2211yescharacteristic
22C2×C8×D79C2211yescharacteristic
23C2×C8×D79C2211yescharacteristic, complemented
24#14579146C411yescharacteristic
25#14579143C411yescharacteristic
26#14579139C411yescharacteristic
27#14579138C411yescharacteristic
28#14579134C411yescharacteristic
29#14579133C411yescharacteristic
30#14579131C411yescharacteristic
31#14579129C411yescharacteristic
32C4×D316C2211yescharacteristic
33C4×C22⋊D79C2211yescharacteristic
34C4×C22⋊D79C2211yescharacteristic
35#14579118C2211yescharacteristic
36C4⋊(C79⋊C8)C2211yescharacteristic, complemented
37Dic79⋊C8C2211yescharacteristic, complemented
38Dic79⋊C8C2211yescharacteristic, complemented
39C22⋊(C79⋊C8)C2211yescharacteristic
40C22⋊(C79⋊C8)C2211yescharacteristic, complemented
41(C2×D79)⋊C8C2211yescharacteristic
42(C2×D79)⋊C8C2211yescharacteristic
43(C2×D79)⋊C8C2211yescharacteristic
44(C2×D79)⋊C8C2211yescharacteristic
45(C2×D79)⋊C8C2211yescharacteristic
46(C2×D79)⋊C8C2211yescharacteristic
47(C2×D79)⋊C8C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic, complemented
49#14579072C2211yescharacteristic, complemented
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×M16×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic, complemented
54C4×D4×C79C2211yescharacteristic
55C4⋊C8×C79C2211yescharacteristic, complemented
56C22⋊C8×C79C2211yescharacteristic
57C22⋊C8×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79C2×C411yescharacteristic
60#11929624—41no—
61#11929624—41no—
62C2×Dic158C2×C411yescharacteristic
63C2×D316C2×C411yescharacteristic
64C2×D316C2×C411yescharacteristic
65C2×C22⋊D79C2×C411yescharacteristic
66C2×C22⋊D79C2×C411yescharacteristic
67C2×C22⋊D79C2×C411yescharacteristic
68C2×C22⋊D79C2×C411yescharacteristic
69C22×Dic79C2×C411yescharacteristic
70C2×C4×D79—41no—
71C2×C4×D79—41no—
72C2×C4×D79C2×C411yescharacteristic
73C2×C4×D79C2×C411yescharacteristic
74C2×C4×D79C2311yescharacteristic
75C2×C4×D79C2311yescharacteristic
76C2×C4×D79C2311yescharacteristic
77#11929608—41no—
78#11929607—41no—
79C2×C79⋊C8—41no—
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C2×C79⋊C8C2311yescharacteristic
84C8×D79—41no—
85C8×D79—41no—
86C8×D79—41no—
87C4⋊Dic79C2×C411yescharacteristic
88Dic79⋊C4C2×C411yescharacteristic
89Dic79⋊C4C2×C411yescharacteristic
90Dic79⋊C4C2×C411yescharacteristic
91Dic79⋊C4C2×C411yescharacteristic
92C22⋊Dic79C2×C411yescharacteristic
93C22⋊Dic79C2×C411yescharacteristic
94(C2×D79)⋊C4C2×C411yescharacteristic
95(C2×D79)⋊C4C2×C411yescharacteristic
96(C2×D79)⋊C4C2×C411yescharacteristic
97(C2×D79)⋊C4C2×C411yescharacteristic
98(C2×D79)⋊C4C2×C411yescharacteristic
99(C2×D79)⋊C4C2×C411yescharacteristic
100C4×Dic79C2311yescharacteristic
101C2×D4×C79C2×C411yescharacteristic
102C22×C4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104M16×C79—41no—
105M16×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C2×C8×C79C2311yescharacteristic
110C4⋊C4×C79C2×C411yescharacteristic
111C22⋊C4×C79C2×C411yescharacteristic
112C22⋊C4×C79C2×C411yescharacteristic
113C42×C79C2311yescharacteristic
114C23×C79C22×C411yescharacteristic
115C23×C79C22×C411yescharacteristic
116C22×D79—22no—
117C22×D79—41no—
118C22×D79—41no—
119C22×D79C22×C411yescharacteristic
120C22×D79C22×C411yescharacteristic
121C22×D79C22×C411yescharacteristic
122D4×C79—41no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79C22×C411yescharacteristic
128C2×C4×C79C22×C411yescharacteristic
129C2×C4×C79C22×C411yescharacteristic
130C2×C4×C79C22×C411yescharacteristic
131C2×C4×C79C2411yescharacteristic
132C22⋊D79—22no—
133C22⋊D79—41no—
134C22⋊D79—41no—
135C22⋊D79—41no—
136C2×Dic79—41no—
137C2×Dic79C22×C411yescharacteristic
138C2×Dic79C22×C411yescharacteristic
139C2×Dic79C22×C411yescharacteristic
140C2×Dic79C22×C411yescharacteristic
141C2×Dic79C22×C411yescharacteristic
142D316—22no—
143D316—41no—
144C4×D79—21no—
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—21no—
150C4×D79—41no—
151C4×D79—41no—
152Dic158—41no—
153C8×C79—21no—
154C8×C79—21no—
155C8×C79—21no—
156C8×C79—21no—
157C79⋊C8—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C79⋊C8—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79C23×C411yescharacteristic
168C2×D79—21no—
169C2×D79—21no—
170C2×D79—21no—
171C2×D79—21no—
172C2×D79—21no—
173C2×D79—21no—
174C2×D79—21no—
175C2×D79—21no—
176C2×D79—44no—
177C2×D79#13112yes—
178C4×C79—21no—
179C4×C79—21no—
180C4×C79—21no—
181C4×C79—21no—
182C4×C79H(5,𝔽2)11yescharacteristic
183C4×C79H(5,𝔽2)11yescharacteristic
184Dic79—21no—
185Dic79—21no—
186Dic79—21no—
187Dic79—21no—
188Dic79—21no—
189C2×C79—41no—
190C2×C79—41no—
191C2×C79#51811yescharacteristic
192C2×C79C2×#13111yescharacteristic
193C2×C79#56811yescharacteristic
194D79—22no—
195D79—41no—
196D79—41no—
197#2976—791nomaximal, Sylow
198C79#297611yescharacteristic, complemented, Sylow
199#525—791no—
200#436—791no—
201#436D7911yescharacteristic, complemented
202#435—791no—
203#435—791no—
204#435—791no—
205#435—791no—
206C8×D4—791no—
207C8×D4—791no—
208#433—791no—
209#433—791no—
210#408—791no—
211#408—791no—
212#407—791no—
213C2×C22⋊C8—791no—
214C2×#41—791no—
215C23×C4—791no—
216C2×M16—791no—
217C2×M16—791no—
218C2×M16C2×D7911yescharacteristic
219C2×M16C2×D7911yescharacteristic, complemented
220C22×C8—791no—
221C22×C8—791no—
222C22×C8—791no—
223C22×C8—791no—
224#123—791no—
225#123—791no—
226C22⋊Q8—791no—
227C22⋊Q8—791no—
228#121—791no—
229#121—791no—
230#120—791no—
231#120—791no—
232C4×D4—791no—
233C4×D4—791no—
234C4×D4—791no—
235C4×D4C2×D7911yescharacteristic
236#117—791no—
237C4⋊C8—791no—
238C4⋊C8—791no—
239C4⋊C8—791no—
240C4⋊C8C2×D7911yescharacteristic, complemented
241C22⋊C8—791no—
242C22⋊C8—791no—
243C22⋊C8—791no—
244C22⋊C8—791no—
245C22⋊C8—791no—
246C22⋊C8—791no—
247C22⋊C8—791no—
248C22⋊C8—791no—
249C22⋊C8—791no—
250C22⋊C8—791no—
251C22⋊C8C2×D7911yescharacteristic
252C22⋊C8C2×D7911yescharacteristic, complemented
253#97—791no—
254#97—791no—
255C4×C8—791no—
256C4×C8C2×D7911yescharacteristic, complemented
257C24—791no—
258#41—3161no—
259#41—3161no—
260C2×Q8—791no—
261C2×D4—791no—
262C2×D4—791no—
263C2×D4—791no—
264C2×D4—791no—
265C2×D4—791no—
266C2×D4—791no—
267C2×D4C4×D7911yescharacteristic
268C22×C4—3161no—
269C22×C4—3161no—
270C22×C4—791no—
271C22×C4—791no—
272C22×C4—791no—
273C22×C4—791no—
274C22×C4—791no—
275C22×C4—791no—
276C22×C4C22×D7911yescharacteristic
277C22×C4C22×D7911yescharacteristic
278M16—41no—
279M16—41no—
280M16—3161no—
281M16—3161no—
282C2×C8—3161no—
283C2×C8—3161no—
284C2×C8—3161no—
285C2×C8—3161no—
286C2×C8—791no—
287C2×C8—791no—
288C2×C8—791no—
289C2×C8—791no—
290C2×C8C22×D7911yescharacteristic
291C2×C8C22×D7911yescharacteristic
292C2×C8C22×D7911yescharacteristic
293C2×C8C22×D7911yescharacteristic
294C4⋊C4—791no—
295C4⋊C4—791no—
296C4⋊C4—791no—
297C4⋊C4—791no—
298C4⋊C4—791no—
299C4⋊C4C4×D7911yescharacteristic
300C22⋊C4—791no—
301C22⋊C4—791no—
302C22⋊C4—791no—
303C22⋊C4—791no—
304C22⋊C4—791no—
305C22⋊C4—791no—
306C22⋊C4—791no—
307C22⋊C4—791no—
308C22⋊C4C4×D7911yescharacteristic
309C22⋊C4C4×D7911yescharacteristic
310C42—791no—
311C42C22×D7911yescharacteristic
312C23—3161no—
313C23—3161no—
314C23—791no—
315C23—791no—
316C23—791no—
317C23—1582no—
318C23C2×C4×D7911yescharacteristic
319C23C2×C4×D7911yescharacteristic
320Q8—3161no—
321D4—41no—
322D4—3161no—
323D4—3161no—
324D4—3161no—
325D4—3161no—
326D4—1582no—
327D4—1582no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—3161no—
333C2×C4—3161no—
334C2×C4—3161no—
335C2×C4—791no—
336C2×C4—791no—
337C2×C4—791no—
338C2×C4—791no—
339C2×C4—791no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4C2×C4×D7911yescharacteristic
347C2×C4C2×C4×D7911yescharacteristic
348C2×C4C2×C4×D7911yescharacteristic
349C2×C4C2×C4×D7911yescharacteristic
350C2×C4C23×D7911yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—1581no—
356C8—1581no—
357C8—1581no—
358C8—1581no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—3164no—
366C22—792no—
367C22—1581no—
368C22—1581no—
369C22—1581no—
370C22—1581no—
371C22—1581no—
372C22—1581no—
373C22—1581no—
374C22—1581no—
375C22C22×C4×D7911yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—1581no—
381C4—1581no—
382C4—1581no—
383C4—1581no—
384C4—1581no—
385C4#1457920611yescharacteristic
386C4#1457920711yescharacteristic
387C2—41no—
388C2—41no—
389C2—3161no—
390C2—3161no—
391C2—1582no—
392C2#1909903511yescharacteristic
393C2#131×D7911yescharacteristic
394C2#1909932911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D79
commutator, socleC22×C79C23×C4
Fitting#436×C79C2
prime radical#19099072C2
cosocleC2×C4×C79C24
hypercenter#436D79
hypocenterC79#2976
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #19098639C2semidirect
3. #19098637C2semidirect
4. #19098635C2semidirect
5. #19098633C2semidirect
6. #19098632C2semidirect
7. C8×D316C2semidirect
8. (C22⋊D79)⋊C8C2semidirect
9. #19098623C2semidirect
10. #19098622C2semidirect
11. #19098531C2semidirect
12. #19098528C2semidirect
13. #19098526C2semidirect
14. C22⋊C8×D79C2semidirect
15. #436×C79C2semidirect
19. C2×#11929607C22semidirect
20. C22×C79⋊C8C22semidirect
23. C2×C8×D79C22semidirect
36. C4⋊(C79⋊C8)C22semidirect
37. Dic79⋊C8C22semidirect
38. Dic79⋊C8C22semidirect
40. C22⋊(C79⋊C8)C22semidirect
47. (C2×D79)⋊C8C22semidirect
48. (C2×D79)⋊C8C22semidirect
49. #14579072C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
53. C2×M16×C79C22semidirect
55. C4⋊C8×C79C22semidirect
57. C22⋊C8×C79C22semidirect
58. C4×C8×C79C22semidirect
198. C79#2976semidirect
201. #436D79semidirect
219. C2×M16C2×D79semidirect
240. C4⋊C8C2×D79semidirect
252. C22⋊C8C2×D79semidirect
256. C4×C8C2×D79semidirect