Finite Group Databasebeta

← #23774494

Subgroups — #23774494

Order 10112.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099184C211yesmaximal, characteristic, complemented
2#19098950C211yesmaximal, characteristic, complemented
3#19098945C211yesmaximal, characteristic, complemented
4#19098922C211yesmaximal, characteristic, complemented
5#19098909C211yesmaximal, characteristic, complemented
6#19098782C211yesmaximal, characteristic, complemented
7#19098775C211yesmaximal, characteristic, complemented
8#19098760C211yesmaximal, characteristic, complemented
9#19098755C211yesmaximal, characteristic, complemented
10#19098725C211yesmaximal, characteristic, complemented
11#19098714C211yesmaximal, characteristic, complemented
12#19098708C211yesmaximal, characteristic, complemented
13#19098697C211yesmaximal, characteristic, complemented
14#19098624C211yesmaximal, characteristic, complemented
15#535×C79C211yesmaximal, characteristic, complemented
16C2×#11929614C2211yescharacteristic, complemented
17C2×#11929612C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929612C2211yescharacteristic, complemented
20C2×#11929611C2211yescharacteristic, complemented
21C2×#11929609C2211yescharacteristic
22C2×#11929609C2211yescharacteristic
23C2×#11929609C2211yescharacteristic, complemented
24#14579161C2211yescharacteristic, complemented
25#14579156—21no—
26#14579149C2211yescharacteristic, complemented
27#14579147—21no—
28#14579143—21no—
29#14579140C2211yescharacteristic
30#14579139—21no—
31#14579135C2211yescharacteristic
32C4×Dic158C2211yescharacteristic, complemented
33C4×D316C2211yescharacteristic, complemented
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35C4⋊(C79⋊C8)C2211yescharacteristic, complemented
36#14579085C2211yescharacteristic, complemented
37#14579085C2211yescharacteristic, complemented
38#14579082C2211yescharacteristic
39#14579082C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579082C2211yescharacteristic, complemented
43#14579082C2211yescharacteristic, complemented
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46#14579072C2211yescharacteristic, complemented
47C4×C79⋊C8C2211yescharacteristic, complemented
48C2×#41×C79C2211yescharacteristic
49C22×D4×C79C2211yescharacteristic
50#127×C79C2211yescharacteristic
51#127×C79C2211yescharacteristic
52#124×C79C2211yescharacteristic
53#124×C79C2211yescharacteristic
54#121×C79—21no—
55#121×C79—21no—
56#120×C79—21no—
57#120×C79—21no—
58#117×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C4×D79—21no—
64#11929614—41no—
65#11929612—41no—
66#11929612—41no—
67#11929612—41no—
68#11929611—41no—
69#11929609—41no—
70#11929609—41no—
71#11929609—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81C22⋊Dic79—21no—
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86C4×Dic79—21no—
87C24×C79—21no—
88#41×C79—41no—
89#41×C79—41no—
90C2×Q8×C79C2311yescharacteristic
91C2×D4×C79—21no—
92C2×D4×C79—21no—
93C2×D4×C79—21no—
94C2×D4×C79—21no—
95C2×D4×C79—21no—
96C2×D4×C79—21no—
97C2×D4×C79—41no—
98C2×D4×C79—41no—
99C2×D4×C79C2311yescharacteristic
100C2×D4×C79C2311yescharacteristic
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104C4⋊C4×C79D411yescharacteristic
105C4⋊C4×C79D411yescharacteristic
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79—21no—
110C22⋊C4×C79D411yescharacteristic
111C22⋊C4×C79D411yescharacteristic
112C42×C79C2311yescharacteristic
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C23×C79—42no—
118C23×C79—81no—
119C23×C79—81no—
120C23×C79C2×D411yescharacteristic
121C22×D79—21no—
122Q8×C79—21no—
123Q8×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—21no—
130D4×C79—42no—
131D4×C79—42no—
132D4×C79—81no—
133D4×C79—81no—
134D4×C79—81no—
135D4×C79—81no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—42no—
140C2×C4×C79C2×D411yescharacteristic
141C2×C4×C79C2×D411yescharacteristic
142C2×C4×C79C2×D411yescharacteristic
143C2×C4×C79C2×D411yescharacteristic
144C2×C4×C79C2×D411yescharacteristic
145C2×C4×C79C2411yescharacteristic
146C22⋊D79—81no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150D316—21no—
151D316—21no—
152C4×D79—81no—
153Dic158—21no—
154Dic158—21no—
155Dic158—81no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—84no—
173C22×C79C22×D411yescharacteristic
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—21no—
180C4×C79—21no—
181C4×C79—21no—
182C4×C79—41no—
183C4×C79H(5,𝔽2)11yescharacteristic
184C4×C79H(5,𝔽2)11yescharacteristic
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188C2×C79—41no—
189C2×C79—81no—
190C2×C79—81no—
191C2×C79—81no—
192C2×C79#53511yescharacteristic
193C2×C79#57611yescharacteristic
194C2×C79#57711yescharacteristic
195D79—81no—
196#3224—791nomaximal, Sylow
197C79#322411yescharacteristic, complemented, Sylow
198#542—791no—
199#535D7911yescharacteristic, complemented
200#496—791no—
201#495—791no—
202#489—791no—
203#486—791no—
204#464—791no—
205#463—791no—
206#460—791no—
207#459—791no—
208#452—791no—
209#450—791no—
210#449—791no—
211#447—791no—
212#433—791no—
213C2×#41C2×D7911yescharacteristic
214C22×D4C2×D7911yescharacteristic
215C2×Q16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×SD16—791no—
219C2×SD16—791no—
220C2×D8—791no—
221C2×D8—791no—
222C2×D8—791no—
223C4⋊Q8—791no—
224#127C2×D7911yescharacteristic
225#127C2×D7911yescharacteristic
226#126—1581no—
227#124—791no—
228#124—1581no—
229#124C2×D7911yescharacteristic
230#124C2×D7911yescharacteristic
231#123—1581no—
232C22⋊Q8—791no—
233C22⋊Q8—1581no—
234#121—21no—
235#121—21no—
236#121—791no—
237#120—21no—
238#120—21no—
239C4×Q8—791no—
240C4×D4—791no—
241#117C2×D7911yescharacteristic
242C4⋊C8—791no—
243C4⋊C8—791no—
244#103—791no—
245#103—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252C22⋊C8—791no—
253C22⋊C8—791no—
254#97—791no—
255C4×C8—791no—
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—791no—
260C2×Q8—1581no—
261C2×Q8C22×D7911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—791no—
271C2×D4—1581no—
272C2×D4C22×D7911yescharacteristic
273C2×D4C22×D7911yescharacteristic
274C2×D4C22×D7911yescharacteristic
275C22×C4—21no—
276C22×C4—1581no—
277C22×C4C22×D7911yescharacteristic
278Q16—3161no—
279SD16—3161no—
280SD16—3161no—
281SD16—3161no—
282SD16—3161no—
283D8—3161no—
284D8—3161no—
285D8—3161no—
286C2×C8—791no—
287C2×C8—791no—
288C2×C8—791no—
289C2×C8—791no—
290C4⋊C4—791no—
291C4⋊C4—791no—
292C4⋊C4—1581no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4C22⋊D7911yescharacteristic
296C4⋊C4C22⋊D7911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4C22⋊D7911yescharacteristic
307C22⋊C4C22⋊D7911yescharacteristic
308C42—1581no—
309C42C22×D7911yescharacteristic
310C42C22×D7911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23—1581no—
318C23C2×C22⋊D7911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—6321no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4—81no—
334D4—81no—
335D4—81no—
336D4—6321no—
337D4—1581no—
338D4—1581no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—6321no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4C2×C22⋊D7911yescharacteristic
348C2×C4C2×C22⋊D7911yescharacteristic
349C2×C4C2×C22⋊D7911yescharacteristic
350C2×C4C2×C22⋊D7911yescharacteristic
351C2×C4C2×C22⋊D7911yescharacteristic
352C2×C4C23×D7911yescharacteristic
353C8—1581no—
354C8—1581no—
355C8—1581no—
356C8—1581no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—84no—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22C22×C22⋊D7911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—3161no—
381C4—3161no—
382C4—3161no—
383C4#1457920611yescharacteristic
384C4#1457920611yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—6321no—
390C2#1909913011yescharacteristic
391C2#1909936611yescharacteristic
392C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#535×C79C2
socleC22×C79C22×D4
hypercenter#535D79
hypocenterC79#3224
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #19099184C2semidirect
2. #19098950C2semidirect
3. #19098945C2semidirect
4. #19098922C2semidirect
5. #19098909C2semidirect
6. #19098782C2semidirect
7. #19098775C2semidirect
8. #19098760C2semidirect
9. #19098755C2semidirect
10. #19098725C2semidirect
11. #19098714C2semidirect
12. #19098708C2semidirect
13. #19098697C2semidirect
14. #19098624C2semidirect
15. #535×C79C2semidirect
16. C2×#11929614C22semidirect
19. C2×#11929612C22semidirect
20. C2×#11929611C22semidirect
23. C2×#11929609C22semidirect
24. #14579161C22semidirect
26. #14579149C22semidirect
32. C4×Dic158C22semidirect
33. C4×D316C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. C4⋊(C79⋊C8)C22semidirect
36. #14579085C22semidirect
37. #14579085C22semidirect
42. #14579082C22semidirect
43. #14579082C22semidirect
46. #14579072C22semidirect
47. C4×C79⋊C8C22semidirect
197. C79#3224semidirect
199. #535D79semidirect