Finite Group Databasebeta

← #23774488

Subgroups — #23774488

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#19099132C211yesmaximal, characteristic, complemented
2#19098953C211yesmaximal, characteristic, complemented
3#19098945C211yesmaximal, characteristic, complemented
4#19098925C211yesmaximal, characteristic, complemented
5#19098911C211yesmaximal, characteristic, complemented
6#19098785C211yesmaximal, characteristic, complemented
7#19098778C211yesmaximal, characteristic, complemented
8#19098763C211yesmaximal, characteristic, complemented
9#19098758C211yesmaximal, characteristic, complemented
10#19098723C211yesmaximal, characteristic, complemented
11#19098713C211yesmaximal, characteristic, complemented
12#19098706C211yesmaximal, characteristic, complemented
13#19098696C211yesmaximal, characteristic, complemented
14#19098624C211yesmaximal, characteristic, complemented
15#542×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929612C2211yescharacteristic, complemented
20C2×#11929611C2211yescharacteristic
21C2×#11929611C2211yescharacteristic
22C2×#11929611C2211yescharacteristic, complemented
23C2×#11929609C2211yescharacteristic
24C2×#11929609C2211yescharacteristic
25C2×#11929609C2211yescharacteristic, complemented
26#14579158C2211yescharacteristic
27#14579158C2211yescharacteristic
28#14579149C2211yescharacteristic
29#14579149C2211yescharacteristic
30#14579136—21no—
31#14579136—21no—
32#14579131—21no—
33#14579131—21no—
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35C4⋊(C79⋊C8)C2211yescharacteristic, complemented
36#14579084C2211yescharacteristic, complemented
37#14579084C2211yescharacteristic, complemented
38#14579081C2211yescharacteristic
39#14579081C2211yescharacteristic
40#14579081C2211yescharacteristic
41#14579081C2211yescharacteristic
42#14579081C2211yescharacteristic, complemented
43#14579081C2211yescharacteristic, complemented
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46#14579072C2211yescharacteristic, complemented
47C4×C79⋊C8C2211yescharacteristic, complemented
48C4⋊Q8×C79C2211yescharacteristic, complemented
49#126×C79—21no—
50#124×C79—21no—
51#124×C79C2211yescharacteristic, complemented
52#123×C79—21no—
53C22⋊Q8×C79—21no—
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic, complemented
57C4×D4×C79C2211yescharacteristic, complemented
58#117×C79C2211yescharacteristic
59C23×D79—21no—
60#11929624—41no—
61#11929624—41no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316—21no—
67C2×D316—21no—
68C2×D316—41no—
69C2×D316—41no—
70C2×D316C2311yescharacteristic
71C2×D316C2311yescharacteristic
72C2×D316C2311yescharacteristic
73C2×C22⋊D79—21no—
74C2×C4×D79—21no—
75#11929614—41no—
76#11929612—41no—
77#11929611—41no—
78#11929611—41no—
79#11929611—41no—
80#11929609—41no—
81#11929609—41no—
82#11929609—41no—
83C2×C79⋊C8C2311yescharacteristic
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91C2×Q8×C79—21no—
92C2×Q8×C79C2311yescharacteristic
93C2×D4×C79—21no—
94C2×D4×C79C2311yescharacteristic
95C22×C4×C79—21no—
96C22×C4×C79C2311yescharacteristic
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79—21no—
100C4⋊C4×C79D411yescharacteristic
101C4⋊C4×C79D411yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79D411yescharacteristic
110C22⋊C4×C79D411yescharacteristic
111C42×C79—21no—
112C42×C79C2311yescharacteristic
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C23×C79C2×D411yescharacteristic
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—42no—
120C22×D79—81no—
121C22×D79—81no—
122Q8×C79—21no—
123Q8×C79—21no—
124Q8×C79—81no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—81no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—81no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2411yescharacteristic
140C22⋊D79—42no—
141C2×Dic79—21no—
142D316—21no—
143D316—21no—
144D316—21no—
145D316—21no—
146D316—21no—
147D316—21no—
148D316—42no—
149D316—81no—
150D316—81no—
151D316—81no—
152D316—81no—
153C4×D79—42no—
154Dic158—21no—
155Dic158—21no—
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×C79C22×D411yescharacteristic
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
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—21no—
180C4×C79—21no—
181C4×C79—21no—
182C4×C79—41no—
183C4×C79—41no—
184C4×C79—41no—
185C4×C79H(5,𝔽2)11yescharacteristic
186C4×C79H(5,𝔽2)11yescharacteristic
187Dic79—41no—
188C2×C79—41no—
189C2×C79—81no—
190C2×C79#53511yescharacteristic
191C2×C79#57611yescharacteristic
192C2×C79#57711yescharacteristic
193D79—81no—
194D79—81no—
195D79—81no—
196#3224—791nomaximal, Sylow
197C79#322411yescharacteristic, complemented, Sylow
198#542D7911yescharacteristic, complemented
199#535—791no—
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×#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#127—791no—
226#126—21no—
227#124—21no—
228#124—791no—
229#124—791no—
230#124C2×D7911yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D7911yescharacteristic
234#121—1581no—
235#121—1581no—
236#121C2×D7911yescharacteristic
237#120—1581no—
238#120—1581no—
239C4×Q8C2×D7911yescharacteristic, complemented
240C4×D4C2×D7911yescharacteristic, complemented
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—1581no—
257#41—3161no—
258#41—3161no—
259C2×Q8—21no—
260C2×Q8—791no—
261C2×Q8C22×D7911yescharacteristic
262C2×D4—21no—
263C2×D4—3161no—
264C2×D4—3161no—
265C2×D4—791no—
266C2×D4—791no—
267C2×D4—791no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4—1581no—
273C2×D4—1581no—
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—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D7911yescharacteristic
294C4⋊C4C22⋊D7911yescharacteristic
295C4⋊C4C22×D7911yescharacteristic
296C4⋊C4C22×D7911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4C22⋊D7911yescharacteristic
307C22⋊C4C22⋊D7911yescharacteristic
308C42—21no—
309C42C22×D7911yescharacteristic
310C42C22×D7911yescharacteristic
311C23—21no—
312C23—3162no—
313C23—6321no—
314C23—6321no—
315C23—1581no—
316C23—1581no—
317C23—1581no—
318C23C2×C22⋊D7911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—3162no—
328D4—3162no—
329D4—6321no—
330D4—6321no—
331D4—6321no—
332D4—6321no—
333D4—1581no—
334D4—1581no—
335D4—1581no—
336D4—1581no—
337D4—1581no—
338D4—1581no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—3162no—
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—3161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22—3161no—
369C22—3161no—
370C22—3161no—
371C22—3161no—
372C22—6324no—
373C22C22×C22⋊D7911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—3161no—
383C4#1457920711yescharacteristic
384C4#1457920711yescharacteristic
385C2—41no—
386C2—81no—
387C2—6321no—
388C2—6321no—
389C2—6321no—
390C2#1909912711yescharacteristic
391C2#1909936611yescharacteristic
392C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#542×C79C2
socleC22×C79C22×D4
hypercenter#542D79
hypocenterC79#3224
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #19099132C2semidirect
2. #19098953C2semidirect
3. #19098945C2semidirect
4. #19098925C2semidirect
5. #19098911C2semidirect
6. #19098785C2semidirect
7. #19098778C2semidirect
8. #19098763C2semidirect
9. #19098758C2semidirect
10. #19098723C2semidirect
11. #19098713C2semidirect
12. #19098706C2semidirect
13. #19098696C2semidirect
14. #19098624C2semidirect
15. #542×C79C2semidirect
18. C2×#11929614C22semidirect
19. C2×#11929612C22semidirect
22. C2×#11929611C22semidirect
25. C2×#11929609C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. C4⋊(C79⋊C8)C22semidirect
36. #14579084C22semidirect
37. #14579084C22semidirect
42. #14579081C22semidirect
43. #14579081C22semidirect
46. #14579072C22semidirect
47. C4×C79⋊C8C22semidirect
48. C4⋊Q8×C79C22semidirect
51. #124×C79C22semidirect
56. C4×Q8×C79C22semidirect
57. C4×D4×C79C22semidirect
197. C79#3224semidirect
198. #542D79semidirect
223. C4⋊Q8C2×D79semidirect
230. #124C2×D79semidirect
239. C4×Q8C2×D79semidirect
240. C4×D4C2×D79semidirect