Finite Group Databasebeta

← #23774497

Subgroups — #23774497

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#19099187C211yesmaximal, characteristic, complemented
2#19099126C211yesmaximal, characteristic, complemented
3#19098950C211yesmaximal, characteristic, complemented
4#19098947C211yesmaximal, characteristic, complemented
5#19098925C211yesmaximal, characteristic, complemented
6#19098784C211yesmaximal, characteristic, complemented
7#19098777C211yesmaximal, characteristic, complemented
8#19098762C211yesmaximal, characteristic, complemented
9#19098757C211yesmaximal, characteristic, complemented
10#19098726C211yesmaximal, characteristic, complemented
11#19098715C211yesmaximal, characteristic, complemented
12#19098709C211yesmaximal, characteristic, complemented
13#19098698C211yesmaximal, characteristic, complemented
14#19098622C211yesmaximal, characteristic, complemented
15#486×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929613C2211yescharacteristic
20C2×#11929613C2211yescharacteristic, complemented
21C2×#11929612C2211yescharacteristic
22C2×#11929612C2211yescharacteristic, complemented
23C2×D632C2211yescharacteristic
24C2×#11929609C2211yescharacteristic
25C2×#11929609C2211yescharacteristic, complemented
26#14579157C2211yescharacteristic
27#14579156—21no—
28#14579150—21no—
29#14579149C2211yescharacteristic
30#14579149C2211yescharacteristic, complemented
31#14579148C2211yescharacteristic
32#14579146—21no—
33#14579141C2211yescharacteristic
34#14579137—21no—
35#14579136C2211yescharacteristic
36#14579133—21no—
37#14579133—21no—
38#14579129—21no—
39#14579129—21no—
40#14579126C2211yescharacteristic, complemented
41#14579123C2211yescharacteristic, complemented
42#14579118C2211yescharacteristic
43Dic79⋊C8C2211yescharacteristic, complemented
44Dic79⋊C8C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579084C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579072C2211yescharacteristic, complemented
52C4⋊Q8×C79C2211yescharacteristic, complemented
53#127×C79C2211yescharacteristic
54#102×C79C2211yescharacteristic
55#102×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929623—41no—
61#11929623—41no—
62C2×Dic158C2311yescharacteristic
63C2×Dic158C2311yescharacteristic
64C2×D316—21no—
65C2×D316C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71D4×D79—41no—
72D4×D79—41no—
73C22×Dic79—21no—
74C2×C4×D79—21no—
75C2×C4×D79C2311yescharacteristic
76Dic316—41no—
77#11929613—41no—
78#11929613—41no—
79#11929612—41no—
80#11929612—41no—
81D632—41no—
82#11929609—41no—
83#11929609—41no—
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C4⋊Dic79—21no—
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)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4D411yescharacteristic
100(C2×D79)⋊C4D411yescharacteristic
101C4×Dic79—21no—
102C4×Dic79C2311yescharacteristic
103C2×Q8×C79—21no—
104C2×D4×C79—21no—
105C2×D4×C79—21no—
106C2×D4×C79C2311yescharacteristic
107C2×D4×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C2×C8×C79C2311yescharacteristic
110C4⋊C4×C79—21no—
111C4⋊C4×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
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—81no—
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—81no—
128D4×C79—81no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—42no—
135C22⋊D79—42no—
136C22⋊D79—81no—
137C22⋊D79—81no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—42no—
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143C2×Dic79C2×D411yescharacteristic
144D316—21no—
145D316—21no—
146D316—21no—
147D316—21no—
148D316—81no—
149C4×D79—21no—
150C4×D79—21no—
151C4×D79—81no—
152Dic158—21no—
153Dic158—21no—
154Dic158—21no—
155Dic158—21no—
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#495—791no—
202#489—791no—
203#486D7911yescharacteristic, complemented
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×Q16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×SD16—791no—
219C2×SD16—791no—
220C2×D8—791no—
221C2×D8—791no—
222C2×D8—791no—
223C4⋊Q8C2×D7911yescharacteristic, complemented
224#127—791no—
225#127C2×D7911yescharacteristic
226#126—1581no—
227#124—791no—
228#124—791no—
229#124—791no—
230#124—1581no—
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#102C2×D7911yescharacteristic
249#102C2×D7911yescharacteristic
250#102C2×D7911yescharacteristic, complemented
251#102C2×D7911yescharacteristic, complemented
252C22⋊C8—791no—
253C22⋊C8—791no—
254#97—791no—
255C4×C8C2×D7911yescharacteristic, complemented
256C24—1581no—
257#41—3161no—
258#41—3161no—
259C2×Q8—21no—
260C2×Q8—791no—
261C2×Q8—791no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—3161no—
265C2×D4—3161no—
266C2×D4—791no—
267C2×D4—791no—
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—3161no—
279SD16—3161no—
280SD16—3161no—
281SD16—3161no—
282SD16—3161no—
283D8—3161no—
284D8—3161no—
285D8—3161no—
286C2×C8—791no—
287C2×C8—791no—
288C2×C8C22×D7911yescharacteristic
289C2×C8C22×D7911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—791no—
292C4⋊C4—791no—
293C4⋊C4—1581no—
294C4⋊C4—1581no—
295C4⋊C4C22×D7911yescharacteristic
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—791no—
298C22⋊C4—791no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
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—81no—
320Q8—1581no—
321Q8—1581no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—81no—
330D4—3162no—
331D4—3162no—
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#1457920711yescharacteristic
384C4#1457920711yescharacteristic
385C2—81no—
386C2—81no—
387C2—3161no—
388C2—6321no—
389C2—6321no—
390C2#1909913111yescharacteristic
391C2#1909936411yescharacteristic
392C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#486×C79C2
socleC22×C79C22×D4
hypercenter#486D79
hypocenterC79#3224
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #19099187C2semidirect
2. #19099126C2semidirect
3. #19098950C2semidirect
4. #19098947C2semidirect
5. #19098925C2semidirect
6. #19098784C2semidirect
7. #19098777C2semidirect
8. #19098762C2semidirect
9. #19098757C2semidirect
10. #19098726C2semidirect
11. #19098715C2semidirect
12. #19098709C2semidirect
13. #19098698C2semidirect
14. #19098622C2semidirect
15. #486×C79C2semidirect
18. C2×Dic316C22semidirect
20. C2×#11929613C22semidirect
22. C2×#11929612C22semidirect
25. C2×#11929609C22semidirect
30. #14579149C22semidirect
40. #14579126C22semidirect
41. #14579123C22semidirect
43. Dic79⋊C8C22semidirect
44. Dic79⋊C8C22semidirect
45. #14579084C22semidirect
46. #14579084C22semidirect
51. #14579072C22semidirect
52. C4⋊Q8×C79C22semidirect
56. #102×C79C22semidirect
57. #102×C79C22semidirect
58. C4×C8×C79C22semidirect
197. C79#3224semidirect
203. #486D79semidirect
223. C4⋊Q8C2×D79semidirect
250. #102C2×D79semidirect
251. #102C2×D79semidirect
255. C4×C8C2×D79semidirect