Finite Group Databasebeta

← #23774487

Subgroups — #23774487

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#19099182C211yesmaximal, characteristic, complemented
2#19099131C211yesmaximal, characteristic, complemented
3#19098953C211yesmaximal, characteristic, complemented
4#19098922C211yesmaximal, characteristic, complemented
5#19098910C211yesmaximal, characteristic, complemented
6#19098787C211yesmaximal, characteristic, complemented
7#19098780C211yesmaximal, characteristic, complemented
8#19098761C211yesmaximal, characteristic, complemented
9#19098756C211yesmaximal, characteristic, complemented
10#19098724C211yesmaximal, characteristic, complemented
11#19098712C211yesmaximal, characteristic, complemented
12#19098707C211yesmaximal, characteristic, complemented
13#19098695C211yesmaximal, characteristic, complemented
14#19098622C211yesmaximal, characteristic, complemented
15#495×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929611C2211yescharacteristic, complemented
20C2×#11929609C2211yescharacteristic
21C2×#11929609C2211yescharacteristic, complemented
22#14579161C2211yescharacteristic, complemented
23#14579158C2211yescharacteristic
24#14579157C2211yescharacteristic
25#14579154—21no—
26#14579150C2211yescharacteristic
27#14579147—21no—
28#14579145—21no—
29#14579138—21no—
30#14579137C2211yescharacteristic
31#14579134—21no—
32#14579134—21no—
33#14579132C2211yescharacteristic
34#14579131—21no—
35#14579131—21no—
36Q8×Dic79C2211yescharacteristic, complemented
37D4×Dic79C2211yescharacteristic, complemented
38#14579118C2211yescharacteristic
39Dic79⋊C8C2211yescharacteristic, complemented
40Dic79⋊C8C2211yescharacteristic, complemented
41#14579085C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579072C2211yescharacteristic, complemented
52C2×Q16×C79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic, complemented
55C2×D8×C79C2211yescharacteristic
56#124×C79C2211yescharacteristic
57#124×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929625—41no—
61#11929625—41no—
62C2×Dic158—21no—
63C2×D316—21no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72D4×D79—41no—
73D4×D79—41no—
74C22×Dic79—21no—
75C2×C4×D79—21no—
76C2×C4×D79C2311yescharacteristic
77#11929611—41no—
78#11929611—41no—
79#11929609—41no—
80#11929609—41no—
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C4⋊Dic79—21no—
84C4⋊Dic79—21no—
85C4⋊Dic79C2311yescharacteristic
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88Dic79⋊C4D411yescharacteristic
89Dic79⋊C4D411yescharacteristic
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4D411yescharacteristic
96(C2×D79)⋊C4D411yescharacteristic
97C4×Dic79—21no—
98C4×Dic79C2311yescharacteristic
99C2×Q8×C79C2311yescharacteristic
100C2×Q8×C79C2311yescharacteristic
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103Q16×C79—41no—
104SD16×C79—41no—
105SD16×C79—41no—
106D8×C79—41no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C23×C79—21no—
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—42no—
119C22×D79—81no—
120C22×D79—81no—
121C22×D79C2×D411yescharacteristic
122Q8×C79—21no—
123Q8×C79—21no—
124Q8×C79—21no—
125Q8×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—42no—
136C22⋊D79—81no—
137C22⋊D79—81no—
138C22⋊D79—81no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—81no—
142C2×Dic79C2×D411yescharacteristic
143C2×Dic79C2×D411yescharacteristic
144C2×Dic79C2×D411yescharacteristic
145D316—21no—
146D316—21no—
147D316—21no—
148D316—21no—
149D316—42no—
150D316—81no—
151D316—81no—
152C4×D79—21no—
153C4×D79—21no—
154C4×D79—42no—
155Dic158—81no—
156C8×C79—21no—
157C8×C79—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79C22×D411yescharacteristic
167C2×D79—21no—
168C2×D79—21no—
169C2×D79—21no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—84no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79H(5,𝔽2)11yescharacteristic
182C4×C79H(5,𝔽2)11yescharacteristic
183Dic79—21no—
184Dic79—21no—
185Dic79—21no—
186Dic79—41no—
187Dic79—41no—
188C2×C79—81no—
189C2×C79—81no—
190C2×C79#53511yescharacteristic
191C2×C79#57611yescharacteristic
192C2×C79#57711yescharacteristic
193D79—41no—
194D79—81no—
195D79—81no—
196#3224—791nomaximal, Sylow
197C79#322411yescharacteristic, complemented, Sylow
198#542—791no—
199#535—791no—
200#496—791no—
201#495D7911yescharacteristic, complemented
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×#41—791no—
214C22×D4—791no—
215C2×Q16C2×D7911yescharacteristic, complemented
216C2×SD16—791no—
217C2×SD16—791no—
218C2×SD16C2×D7911yescharacteristic
219C2×SD16C2×D7911yescharacteristic, complemented
220C2×D8—791no—
221C2×D8—791no—
222C2×D8C2×D7911yescharacteristic
223C4⋊Q8—791no—
224#127—791no—
225#127—791no—
226#126—1581no—
227#124—791no—
228#124—1581no—
229#124C2×D7911yescharacteristic
230#124C2×D7911yescharacteristic, complemented
231#123—1581no—
232C22⋊Q8—791no—
233C22⋊Q8—1581no—
234#121—791no—
235#121—1581no—
236#121—1581no—
237#120—1581no—
238#120—1581no—
239C4×Q8—791no—
240C4×D4—791no—
241#117—791no—
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×C8C2×D7911yescharacteristic, complemented
256C24—1581no—
257#41—3161no—
258#41—3161no—
259C2×Q8—1581no—
260C2×Q8C22×D7911yescharacteristic
261C2×Q8C22×D7911yescharacteristic
262C2×D4—3161no—
263C2×D4—3161no—
264C2×D4—791no—
265C2×D4—791no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4—1581no—
273C2×D4C22×D7911yescharacteristic
274C2×D4C22×D7911yescharacteristic
275C22×C4—791no—
276C22×C4—1581no—
277C22×C4—1581no—
278Q16—41no—
279SD16—41no—
280SD16—41no—
281SD16—3161no—
282SD16—3161no—
283D8—41no—
284D8—3161no—
285D8—3161no—
286C2×C8—791no—
287C2×C8—791no—
288C2×C8C22×D7911yescharacteristic
289C2×C8C22×D7911yescharacteristic
290C4⋊C4—791no—
291C4⋊C4—791no—
292C4⋊C4—791no—
293C4⋊C4—791no—
294C4⋊C4—1581no—
295C4⋊C4—1581no—
296C4⋊C4—1581no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—791no—
302C22⋊C4—791no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C42—791no—
309C42—1581no—
310C42C22×D7911yescharacteristic
311C23—21no—
312C23—21no—
313C23—3162no—
314C23—791no—
315C23—6321no—
316C23—6321no—
317C23—1581no—
318C23—1581no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—6321no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—3162no—
329D4—3162no—
330D4—6321no—
331D4—6321no—
332D4—6321no—
333D4—6321no—
334D4—6321no—
335D4—1581no—
336D4—1581no—
337D4—1581no—
338D4—1581no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3162no—
342C2×C4—791no—
343C2×C4—791no—
344C2×C4—791no—
345C2×C4—6321no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4D4×D7911yescharacteristic
351C2×C4D4×D7911yescharacteristic
352C2×C4C23×D7911yescharacteristic
353C8—21no—
354C8—21no—
355C8—1581no—
356C8—1581no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22—3161no—
369C22—6324no—
370C22—1581no—
371C22—1581no—
372C22—1581no—
373C22C2×D4×D7911yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—3161no—
379C4—3161no—
380C4—1581no—
381C4—1581no—
382C4—1581no—
383C4#1457920611yescharacteristic
384C4#1457920611yescharacteristic
385C2—81no—
386C2—81no—
387C2—3161no—
388C2—6321no—
389C2—6321no—
390C2#1909912611yescharacteristic
391C2#1909936511yescharacteristic
392C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#495×C79C2
socleC22×C79C22×D4
hypercenter#495D79
hypocenterC79#3224
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #19099182C2semidirect
2. #19099131C2semidirect
3. #19098953C2semidirect
4. #19098922C2semidirect
5. #19098910C2semidirect
6. #19098787C2semidirect
7. #19098780C2semidirect
8. #19098761C2semidirect
9. #19098756C2semidirect
10. #19098724C2semidirect
11. #19098712C2semidirect
12. #19098707C2semidirect
13. #19098695C2semidirect
14. #19098622C2semidirect
15. #495×C79C2semidirect
19. C2×#11929611C22semidirect
21. C2×#11929609C22semidirect
22. #14579161C22semidirect
36. Q8×Dic79C22semidirect
37. D4×Dic79C22semidirect
39. Dic79⋊C8C22semidirect
40. Dic79⋊C8C22semidirect
41. #14579085C22semidirect
42. #14579085C22semidirect
45. #14579083C22semidirect
46. #14579083C22semidirect
51. #14579072C22semidirect
52. C2×Q16×C79C22semidirect
54. C2×SD16×C79C22semidirect
57. #124×C79C22semidirect
58. C4×C8×C79C22semidirect
197. C79#3224semidirect
201. #495D79semidirect
215. C2×Q16C2×D79semidirect
219. C2×SD16C2×D79semidirect
230. #124C2×D79semidirect
255. C4×C8C2×D79semidirect