Finite Group Databasebeta

← #23775629

Subgroups — #23775629

Order 10112.

448 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099281C211yesmaximal, characteristic, complemented
2#19099197C211yesmaximal, characteristic
3#19098908C211yesmaximal, characteristic, complemented
4#19098889C211yesmaximal, characteristic, complemented
5#19098842C211yesmaximal, characteristic, complemented
6#19098810C211yesmaximal, characteristic, complemented
7#19098807C211yesmaximal, characteristic, complemented
8#19098762C211yesmaximal, characteristic, complemented
9#19098716C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098650C211yesmaximal, characteristic, complemented
12#19098638C211yesmaximal, characteristic, complemented
13#19098567C211yesmaximal, characteristic, complemented
14#19098566C211yesmaximal, characteristic, complemented
15#482×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C2×D4×D79—21no—
18C2×D4×D79C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×#11929613C2211yescharacteristic, complemented
21C2×#11929612C2211yescharacteristic, complemented
22C2×#11929608C2211yescharacteristic, complemented
23C2×#11929607C2211yescharacteristic, complemented
24#14579160C2211yescharacteristic, complemented
25#14579157C2211yescharacteristic
26#14579155—21no—
27#14579154—21no—
28#14579147—21no—
29#14579141C2211yescharacteristic, complemented
30#14579140C2211yescharacteristic, complemented
31#14579136C2211yescharacteristic
32#14579134—21no—
33#14579131—21no—
34#14579129—21no—
35C4×Dic158—21no—
36#14579126C2211yescharacteristic, complemented
37#14579123C2211yescharacteristic
38C4×C22⋊D79C2211yescharacteristic
39#14579119C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579084C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic, complemented
46#14579081C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52#121×C79C2211yescharacteristic
53#117×C79C2211yescharacteristic, complemented
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79—21no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
64C2×D316—22no—
65C2×D316—21no—
66C2×D316—41no—
67C2×D316C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C22⋊D79D411yescharacteristic
73D4×D79—22no—
74D4×D79—44no—
75D4×D79—41no—
76C2×C4×D79—21no—
77C2×C4×D79C2311yescharacteristic
78#11929613—22no—
79#11929613—41no—
80#11929612—41no—
81#11929608—41no—
82#11929607—41no—
83C2×C79⋊C8C2311yescharacteristic
84C2×C79⋊C8C2311yescharacteristic
85C4⋊Dic79—21no—
86C4⋊Dic79C2311yescharacteristic
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90Dic79⋊C4D411yescharacteristic
91C22⋊Dic79—21no—
92C22⋊Dic79D411yescharacteristic
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4D411yescharacteristic
98C4×Dic79—21no—
99C4×Dic79—21no—
100C4×Dic79C2311yescharacteristic
101C2×D4×C79—21no—
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C42×C79—21no—
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79—81no—
121C22×D79—81no—
122C22×D79C2×D411yescharacteristic
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—42no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2411yescharacteristic
133C22⋊D79—22no—
134C22⋊D79—42no—
135C22⋊D79—42no—
136C22⋊D79—81no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142D316—21no—
143D316—21no—
144D316—21no—
145D316—42no—
146D316—42no—
147D316#4112yes—
148C4×D79—21no—
149C4×D79—21no—
150C4×D79—42no—
151Dic158—21no—
152Dic158—21no—
153Dic158—42no—
154C8×C79—21no—
155C8×C79—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C2×D79—22no—
166C2×D79—21no—
167C2×D79—21no—
168C2×D79—21no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—84no—
175C2×D79—84no—
176C4×C79—21no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79C2×#4111yescharacteristic
181C4×C79H(5,𝔽2)11yescharacteristic
182Dic79—21no—
183Dic79—21no—
184Dic79—41no—
185Dic79—41no—
186Dic79AGL(1,ℤ/8)12yes—
187C2×C79—41no—
188C2×C79—81no—
189C2×C79#54611yescharacteristic
190C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C79#57711yescharacteristic
192D79—41no—
193D79—42no—
194D79—81no—
195#3324—791nomaximal, Sylow
196C79#332411yescharacteristic, complemented, Sylow
197#556—791no—
198D42—791no—
199#486—791no—
200#482—791no—
201#482D7911yescharacteristic, complemented
202#474—791no—
203#468—791no—
204#468—791no—
205#460—791no—
206#450—791no—
207#450—791no—
208C4×SD16—791no—
209#436—791no—
210#418—791no—
211#418—791no—
212C22×D4—791no—
213C22×D4—791no—
214C22×D4—1581no—
215C2×SD16—791no—
216C2×SD16—791no—
217C2×SD16—791no—
218C2×M16—791no—
219C2×M16—791no—
220C4⋊Q8—791no—
221#127—791no—
222#126—1581no—
223#126—1581no—
224#124—1581no—
225C22⋊Q8—791no—
226C22⋊Q8—791no—
227#121—791no—
228#121—1581no—
229#121C2×D7911yescharacteristic
230#120—1581no—
231#120—1581no—
232C4×Q8—791no—
233C4×Q8—1581no—
234C4×D4—791no—
235C4×D4—791no—
236#117—791no—
237#117C2×D7911yescharacteristic, complemented
238#107—791no—
239#107C2×D7911yescharacteristic, complemented
240#106C2×D7911yescharacteristic, complemented
241C4⋊C8—791no—
242#103—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102C2×D7911yescharacteristic, complemented
251#102C2×D7911yescharacteristic, complemented
252C22⋊C8—791no—
253C22⋊C8C2×D7911yescharacteristic, complemented
254C4×C8—791no—
255C24—1581no—
256C24—1581no—
257C2×Q8—791no—
258C2×Q8—1581no—
259C2×D4—21no—
260C2×D4—3161no—
261C2×D4—3164no—
262C2×D4—3161no—
263C2×D4—791no—
264C2×D4—791no—
265C2×D4—791no—
266C2×D4—1581no—
267C2×D4—1582no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1582no—
272C2×D4—1581no—
273C2×D4C22×D7911yescharacteristic
274C22×C4—791no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277SD16—3161no—
278SD16—3161no—
279SD16—1582no—
280M16—3161no—
281M16—3161no—
282C2×C8—791no—
283C2×C8—791no—
284C2×C8C22×D7911yescharacteristic
285C2×C8C22×D7911yescharacteristic
286C4⋊C4—791no—
287C4⋊C4—791no—
288C4⋊C4—1581no—
289C4⋊C4—1581no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4C22×D7911yescharacteristic
293C4⋊C4C22×D7911yescharacteristic
294C4⋊C4C22×D7911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—791no—
298C22⋊C4—791no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C42—21no—
305C42—791no—
306C42—1581no—
307C42—1581no—
308C23—21no—
309C23—3162no—
310C23—3162no—
311C23—3162no—
312C23—3162no—
313C23—791no—
314C23—6321no—
315C23—6321no—
316C23—1581no—
317C23—1581no—
318C23D4×D7911yescharacteristic
319Q8—3162no—
320Q8—1581no—
321Q8—1581no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—3162no—
326D4—3162no—
327D4—3162no—
328D4—3162no—
329D4—792no—
330D4—6321no—
331D4—1582no—
332D4—1581no—
333D4—1581no—
334D4—1581no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—3162no—
341C2×C4—791no—
342C2×C4—791no—
343C2×C4—791no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4D4×D7911yescharacteristic
349C2×C4C23×D7911yescharacteristic
350C8—21no—
351C8—21no—
352C8—1581no—
353C8—1581no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—3161no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—6324no—
366C22—6324no—
367C22—1581no—
368C22—1582no—
369C22—1581no—
370C22—1581no—
371C22C2×D4×D7911yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—3161no—
377C4—3161no—
378C4—792no—
379C4—1581no—
380C4—1581no—
381C4#41×D7911yescharacteristic
382C4#1457920711yescharacteristic
383C2—41no—
384C2—81no—
385C2—3162no—
386C2—3161no—
387C2—6321no—
388C2#1909920511yescharacteristic
389C2AGL(1,ℤ/8)×D7911yescharacteristic
390C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#482×C79C2
socleC22×C79C22×D4
prime radical#19099197C2
hypercenter#482D79
hypocenterC79#3324
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #19099281C2semidirect
3. #19098908C2semidirect
4. #19098889C2semidirect
5. #19098842C2semidirect
6. #19098810C2semidirect
7. #19098807C2semidirect
8. #19098762C2semidirect
9. #19098716C2semidirect
10. #19098715C2semidirect
11. #19098650C2semidirect
12. #19098638C2semidirect
13. #19098567C2semidirect
14. #19098566C2semidirect
15. #482×C79C2semidirect
20. C2×#11929613C22semidirect
21. C2×#11929612C22semidirect
22. C2×#11929608C22semidirect
23. C2×#11929607C22semidirect
24. #14579160C22semidirect
29. #14579141C22semidirect
30. #14579140C22semidirect
36. #14579126C22semidirect
39. #14579119C22semidirect
40. #14579094C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579084C22semidirect
44. #14579083C22semidirect
45. #14579082C22semidirect
48. #14579081C22semidirect
49. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
53. #117×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. #102×C79C22semidirect
57. #102×C79C22semidirect
58. C22⋊C8×C79C22semidirect
196. C79#3324semidirect
201. #482D79semidirect
237. #117C2×D79semidirect
239. #107C2×D79semidirect
240. #106C2×D79semidirect
250. #102C2×D79semidirect
251. #102C2×D79semidirect
253. C22⋊C8C2×D79semidirect