Finite Group Databasebeta

← #23775608

Subgroups — #23775608

Order 10112.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099263C211yesmaximal, characteristic, complemented
2#19099206C211yesmaximal, characteristic, complemented
3#19098917C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098875C211yesmaximal, characteristic, complemented
6#19098864C211yesmaximal, characteristic, complemented
7#19098813C211yesmaximal, characteristic, complemented
8#19098806C211yesmaximal, characteristic, complemented
9#19098707C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic, complemented
11C4×#11929609C211yesmaximal, characteristic, complemented
12#19098640C211yesmaximal, characteristic, complemented
13#19098566C211yesmaximal, characteristic, complemented
14#19098563C211yesmaximal, characteristic, complemented
15#463×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19C2×#11929607C2211yescharacteristic
20C2×#11929607C2211yescharacteristic, complemented
21#14579154—21no—
22#14579153C2211yescharacteristic, complemented
23#14579144—21no—
24#14579143—21no—
25#14579137C2211yescharacteristic
26#14579134—21no—
27#14579134—21no—
28#14579132C2211yescharacteristic
29#14579132C2211yescharacteristic
30#14579132C2211yescharacteristic, complemented
31#14579131—21no—
32C4×D316C2211yescharacteristic
33C4×D316C2211yescharacteristic
34C4×C22⋊D79—21no—
35#14579119C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic, complemented
37C22⋊C4×D79—21no—
38#14579095C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579085C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C4×C79⋊C8C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic, complemented
53C2×D8×C79C2211yescharacteristic
54#124×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60#11929625—22no—
61#11929625—41no—
62C2×D316—21no—
63C2×D316D411yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69D4×D79—22no—
70D4×D79—41no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79C2311yescharacteristic
75C2×C4×D79C2311yescharacteristic
76#11929609—22no—
77#11929607—41no—
78#11929607—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79D411yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89C22⋊Dic79—21no—
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—
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79—21no—
102SD16×C79—41no—
103D8×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79—21no—
113C22×D79—21no—
114C22×D79—42no—
115C22×D79—42no—
116C22×D79—81no—
117C22×D79C2×D411yescharacteristic
118C22×D79C2×D411yescharacteristic
119Q8×C79—21no—
120Q8×C79—21no—
121D4×C79—21no—
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—81no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—42no—
132C22⋊D79—42no—
133C22⋊D79—81no—
134C22⋊D79—81no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140D316—21no—
141D316—41no—
142D316—42no—
143D316#4112yes—
144C4×D79—21no—
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—42no—
149C4×D79—81no—
150C4×D79—81no—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—22no—
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—21no—
167C2×D79—21no—
168C2×D79—21no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—84no—
172C4×C79—21no—
173C4×C79—21no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79C2×#4111yescharacteristic
177C4×C79H(5,𝔽2)11yescharacteristic
178Dic79—21no—
179Dic79—21no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—81no—
184C2×C79—81no—
185C2×C79#54611yescharacteristic
186C2×C79#57511yescharacteristic
187C2×C79#57611yescharacteristic
188D79—41no—
189D79—41no—
190D79—42no—
191#3322—791nomaximal, Sylow
192C79#332211yescharacteristic, complemented, Sylow
193#553—791no—
194#546—791no—
195#488—791no—
196#485—791no—
197#480—791no—
198#478—791no—
199#469—791no—
200#468—791no—
201#463D7911yescharacteristic, complemented
202#449—791no—
203#447—791no—
204C4×D8—791no—
205#436—791no—
206#418—791no—
207#417—791no—
208C2×#41—791no—
209C22×D4—791no—
210C2×SD16C2×D7911yescharacteristic, complemented
211C2×D8—791no—
212C2×D8C2×D7911yescharacteristic
213C2×M16—791no—
214C2×M16—791no—
215#126—1581no—
216#125—791no—
217#124C2×D7911yescharacteristic
218#123—1581no—
219#123—1581no—
220C22⋊Q8—791no—
221#121—791no—
222#121—791no—
223#121—791no—
224#121—1581no—
225#121—1581no—
226#120—1581no—
227C4×D4—791no—
228C4×D4—791no—
229C4×D4—1581no—
230C4×D4C2×D7911yescharacteristic, complemented
231#117—791no—
232C2×C4⋊C4—791no—
233C2×C22⋊C4—1581no—
234#107—791no—
235#107—791no—
236#106—791no—
237C4⋊C8C2×D7911yescharacteristic, complemented
238#103—791no—
239#103—791no—
240#103C2×D7911yescharacteristic, complemented
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102C2×D7911yescharacteristic
248C22⋊C8—791no—
249C22⋊C8—791no—
250C4×C8—791no—
251C24—1581no—
252#41—3161no—
253#41—1582no—
254C2×Q8C22×D7911yescharacteristic
255C2×D4—3161no—
256C2×D4—791no—
257C2×D4—791no—
258C2×D4—1581no—
259C2×D4—1581no—
260C2×D4—1582no—
261C2×D4—1581no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4C22×D7911yescharacteristic
265C2×D4C22×D7911yescharacteristic
266C22×C4—21no—
267C22×C4—791no—
268C22×C4—791no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4—1581no—
272SD16—41no—
273D8—41no—
274D8—1582no—
275M16—3161no—
276M16—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—791no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4—1581no—
288C4⋊C4—1581no—
289C4⋊C4C22×D7911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—791no—
294C22⋊C4—791no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C42—1581no—
302C42C22×D7911yescharacteristic
303C23—21no—
304C23—21no—
305C23—3162no—
306C23—3162no—
307C23—791no—
308C23—791no—
309C23—6321no—
310C23—1581no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—3161no—
318D4—3162no—
319D4—3162no—
320D4—3162no—
321D4—792no—
322D4—6321no—
323D4—6321no—
324D4—1581no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—3162no—
329C2×C4—791no—
330C2×C4—791no—
331C2×C4—6321no—
332C2×C4—6321no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4D4×D7911yescharacteristic
341C2×C4D4×D7911yescharacteristic
342C2×C4C23×D7911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1581no—
346C8—1581no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3161no—
354C22—3161no—
355C22—6324no—
356C22—1582no—
357C22—1581no—
358C22—1581no—
359C22—1581no—
360C22—1581no—
361C22—1581no—
362C22—1581no—
363C22C2×D4×D7911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—3161no—
369C4—3161no—
370C4—3161no—
371C4—1581no—
372C4—1581no—
373C4#41×D7911yescharacteristic
374C4#1457920611yescharacteristic
375C2—81no—
376C2—81no—
377C2—3162no—
378C2—3161no—
379C2—3161no—
380C2#1909921011yescharacteristic
381C2#1909936011yescharacteristic
382C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#463×C79C2
socleC22×C79C22×D4
hypercenter#463D79
hypocenterC79#3322
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #19099263C2semidirect
2. #19099206C2semidirect
3. #19098917C2semidirect
4. #19098902C2semidirect
5. #19098875C2semidirect
6. #19098864C2semidirect
7. #19098813C2semidirect
8. #19098806C2semidirect
9. #19098707C2semidirect
10. #19098695C2semidirect
11. C4×#11929609C2semidirect
12. #19098640C2semidirect
13. #19098566C2semidirect
14. #19098563C2semidirect
15. #463×C79C2semidirect
20. C2×#11929607C22semidirect
22. #14579153C22semidirect
30. #14579132C22semidirect
36. C4⋊C4×D79C22semidirect
38. #14579095C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. #14579085C22semidirect
42. #14579085C22semidirect
47. #14579082C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C4×C79⋊C8C22semidirect
52. C2×SD16×C79C22semidirect
55. C4×D4×C79C22semidirect
56. C4⋊C8×C79C22semidirect
57. #103×C79C22semidirect
192. C79#3322semidirect
201. #463D79semidirect
210. C2×SD16C2×D79semidirect
230. C4×D4C2×D79semidirect
237. C4⋊C8C2×D79semidirect
240. #103C2×D79semidirect