Finite Group Databasebeta

← #23773339

Subgroups — #23773339

Order 10112.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#121×D79C211yesmaximal, characteristic
2#117×D79C211yesmaximal, characteristic, complemented
3#19098888C211yesmaximal, characteristic, complemented
4#19098887C211yesmaximal, characteristic, complemented
5#19098884C211yesmaximal, characteristic, complemented
6#19098883C211yesmaximal, characteristic, complemented
7#19098880C211yesmaximal, characteristic, complemented
8#19098878C211yesmaximal, characteristic, complemented
9#19098875C211yesmaximal, characteristic, complemented
10#19098604C211yesmaximal, characteristic, complemented
11#19098602C211yesmaximal, characteristic, complemented
12#19098566C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#19098525C211yesmaximal, characteristic, complemented
15#482×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79—21no—
17C2×D4×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C2×#11929607C2211yescharacteristic
20C2×#11929607C2211yescharacteristic
21#14579136C2211yescharacteristic
22#14579135C2211yescharacteristic
23#14579134—21no—
24#14579133—21no—
25#14579132C2211yescharacteristic
26#14579120C2211yescharacteristic, complemented
27#14579119C2211yescharacteristic
28#14579119C2211yescharacteristic
29#14579118—21no—
30#14579117—21no—
31C4⋊C4×D79C2211yescharacteristic
32C4⋊C4×D79C2211yescharacteristic, complemented
33C4⋊C4×D79C2211yescharacteristic, complemented
34C22⋊C4×D79—21no—
35C22⋊C4×D79—21no—
36C42×D79—21no—
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42#14579092C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, 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×D79D411yescharacteristic
61C2×D316—21no—
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66D4×D79—22no—
67D4×D79—22no—
68D4×D79—44no—
69C22×Dic79D411yescharacteristic
70C2×C4×D79—22no—
71C2×C4×D79—22no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79D411yescharacteristic
76C2×C4×D79D411yescharacteristic
77C2×C4×D79C2311yescharacteristic
78C2×C4×D79C2311yescharacteristic
79#11929607—22no—
80#11929607—22no—
81C2×C79⋊C8C2311yescharacteristic
82C2×C79⋊C8C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79—21no—
98C2×D4×C79—21no—
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C42×C79—21no—
109C23×C79—21no—
110C23×C79C2×D411yescharacteristic
111C22×D79—22no—
112C22×D79—22no—
113C22×D79—21no—
114C22×D79—41no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79C2×D411yescharacteristic
119C22×D79C2×D411yescharacteristic
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—42no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—42no—
131C22⋊D79—42no—
132C22⋊D79—42no—
133C2×Dic79—22no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139D316—21no—
140D316—21no—
141D316—42no—
142C4×D79—22no—
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—22no—
146C4×D79—42no—
147C4×D79—42no—
148C4×D79—42no—
149C4×D79#4112yes—
150C4×D79#4112yes—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—44no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—84no—
171C2×D79#12312yes—
172C2×D79AGL(1,ℤ/8)12yes—
173C4×C79—21no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79—41no—
177C4×C79C2×#4111yescharacteristic
178C4×C79C2×#4111yescharacteristic
179Dic79—21no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183Dic79#12312yes—
184C2×C79—41no—
185C2×C79—81no—
186C2×C79C2×#12311yescharacteristic
187C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C79#57511yescharacteristic
189D79—22no—
190D79—22no—
191D79—81no—
192#3094—791nomaximal, Sylow
193C79#309411yescharacteristic, complemented, Sylow
194C2×#121—791no—
195C2×#117—791no—
196#482—791no—
197#482—791no—
198#482—791no—
199#482D7911yescharacteristic, complemented
200#481—791no—
201#481—791no—
202#480—791no—
203#480—791no—
204#428—791no—
205#428—791no—
206#418—791no—
207#418—791no—
208#407—791no—
209C22×D4—791no—
210C22×D4—1581no—
211C23×C4—791no—
212C2×M16—791no—
213C2×M16—791no—
214#121—791no—
215#121—791no—
216#121—791no—
217#121—1581no—
218#121—1581no—
219#121C2×D7911yescharacteristic
220#117—791no—
221#117—791no—
222#117—791no—
223#117—1581no—
224#117—1581no—
225#117C2×D7911yescharacteristic, complemented
226C2×C4⋊C4—791no—
227C2×C4⋊C4—791no—
228C2×C4⋊C4—791no—
229C2×C22⋊C4—1581no—
230C2×C22⋊C4—1581no—
231C2×C42—1581no—
232#107—791no—
233#107—791no—
234#107—791no—
235#107C2×D7911yescharacteristic, complemented
236#106—791no—
237#106—791no—
238#106—791no—
239#106C2×D7911yescharacteristic, complemented
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102C2×D7911yescharacteristic, complemented
247#102C2×D7911yescharacteristic, complemented
248C22⋊C8—791no—
249C22⋊C8—791no—
250C22⋊C8—791no—
251C22⋊C8C2×D7911yescharacteristic, complemented
252C24—791no—
253C24—1581no—
254C2×D4—21no—
255C2×D4—3164no—
256C2×D4—791no—
257C2×D4—1581no—
258C2×D4—1582no—
259C2×D4—1582no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4C22×D7911yescharacteristic
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—791no—
268C22×C4—791no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4—1581no—
272C22×C4—1582no—
273C22×C4—1582no—
274C22×C4C22×D7911yescharacteristic
275M16—1582no—
276M16—1582no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4C22×D7911yescharacteristic
288C4⋊C4C22×D7911yescharacteristic
289C4⋊C4C22×D7911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C42—21no—
299C42—1581no—
300C42—1581no—
301C42—1581no—
302C23—21no—
303C23—3161no—
304C23—3162no—
305C23—3162no—
306C23—3162no—
307C23—791no—
308C23—791no—
309C23—1582no—
310C23—1582no—
311C23—1581no—
312C23D4×D7911yescharacteristic
313D4—21no—
314D4—21no—
315D4—42no—
316D4—3162no—
317D4—3162no—
318D4—3162no—
319D4—3162no—
320D4—1581no—
321D4—1581no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—3162no—
328C2×C4—3162no—
329C2×C4—3162no—
330C2×C4—791no—
331C2×C4—792no—
332C2×C4—792no—
333C2×C4—791no—
334C2×C4—1582no—
335C2×C4—1582no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1582no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4D4×D7911yescharacteristic
343C2×C4C23×D7911yescharacteristic
344C8—21no—
345C8—21no—
346C8—1581no—
347C8—1581no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—3164no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—792no—
359C22—792no—
360C22—6324no—
361C22—1581no—
362C22—1581no—
363C22—1581no—
364C22—1581no—
365C22C2×D4×D7911yescharacteristic
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—3161no—
371C4—3161no—
372C4—3161no—
373C4—792no—
374C4—1581no—
375C4#41×D7911yescharacteristic
376C4#41×D7911yescharacteristic
377C2—41no—
378C2—81no—
379C2—6321no—
380C2—1582no—
381C2—1582no—
382C2#123×D7911yescharacteristic
383C2AGL(1,ℤ/8)×D7911yescharacteristic
384C2#1909936011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#482×C79C2
socleC22×C79C22×D4
prime radical#121×D79C2
hypercenter#482D79
hypocenterC79#3094
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
2. #117×D79C2semidirect
3. #19098888C2semidirect
4. #19098887C2semidirect
5. #19098884C2semidirect
6. #19098883C2semidirect
7. #19098880C2semidirect
8. #19098878C2semidirect
9. #19098875C2semidirect
10. #19098604C2semidirect
11. #19098602C2semidirect
12. #19098566C2semidirect
13. #19098566C2semidirect
14. #19098525C2semidirect
15. #482×C79C2semidirect
26. #14579120C22semidirect
32. C4⋊C4×D79C22semidirect
33. C4⋊C4×D79C22semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. #14579092C22semidirect
42. #14579092C22semidirect
43. #14579083C22semidirect
44. #14579083C22semidirect
45. #14579082C22semidirect
46. #14579082C22semidirect
47. #14579081C22semidirect
48. #14579081C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. (C2×D79)⋊C8C22semidirect
53. #117×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. #102×C79C22semidirect
57. #102×C79C22semidirect
58. C22⋊C8×C79C22semidirect
193. C79#3094semidirect
199. #482D79semidirect
225. #117C2×D79semidirect
235. #107C2×D79semidirect
239. #106C2×D79semidirect
246. #102C2×D79semidirect
247. #102C2×D79semidirect
251. C22⋊C8C2×D79semidirect