Finite Group Databasebeta

← #23775256

Subgroups — #23775256

Order 10112.

420 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#19099265C211yesmaximal, characteristic, complemented
2#19099204C211yesmaximal, characteristic, complemented
3#19098919C211yesmaximal, characteristic, complemented
4#19098896C211yesmaximal, characteristic, complemented
5#19098889C211yesmaximal, characteristic, complemented
6#19098862C211yesmaximal, characteristic, complemented
7#19098798C211yesmaximal, characteristic, complemented
8#19098780C211yesmaximal, characteristic, complemented
9#19098707C211yesmaximal, characteristic, complemented
10#19098696C211yesmaximal, characteristic, complemented
11#19098643C211yesmaximal, characteristic, complemented
12C8×C22⋊D79C211yesmaximal, characteristic, complemented
13#19098558C211yesmaximal, characteristic, complemented
14C2×#14579083C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic, complemented
21#14579154—21no—
22#14579152C2211yescharacteristic, complemented
23#14579150C2211yescharacteristic
24#14579146—21no—
25#14579145—21no—
26#14579136—21no—
27#14579136C2211yescharacteristic
28#14579133—21no—
29#14579132C2211yescharacteristic, complemented
30#14579131—21no—
31D4×Dic79—21no—
32D4×Dic79C2211yescharacteristic, complemented
33#14579123C2211yescharacteristic
34C4×C22⋊D79C2211yescharacteristic
35#14579119C2211yescharacteristic, complemented
36C2×C4⋊Dic79C2211yescharacteristic
37C22⋊C4×D79—21no—
38#14579094C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40Dic79⋊C8C2211yescharacteristic, complemented
41#14579085C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic, complemented
53C22×C8×C79C2211yescharacteristic
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929625—22no—
61#11929625—41no—
62C2×D316—21no—
63C2×D316—21no—
64C2×D316—22no—
65C2×D316—21no—
66C2×D316—41no—
67C2×D316C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79D411yescharacteristic
71C22×Dic79—21no—
72C22×Dic79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79C2311yescharacteristic
76#11929609—22no—
77#11929609—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C8×D79—41no—
81C4⋊Dic79—21no—
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79D411yescharacteristic
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4D411yescharacteristic
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79—21no—
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102SD16×C79—41no—
103C2×C8×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118C22×D79C2×D411yescharacteristic
119Q8×C79—21no—
120Q8×C79—21no—
121D4×C79—21no—
122D4×C79—21no—
123D4×C79—42no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—22no—
132C22⋊D79—81no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—81no—
136C2×Dic79—81no—
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140D316—21no—
141D316—21no—
142D316—21no—
143D316—42no—
144D316—42no—
145D316—81no—
146D316#4112yes—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—42no—
150C4×D79—81no—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79#13512yes—
161C22×C79C22×D411yescharacteristic
162C2×D79—22no—
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—21no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—84no—
172C4×C79—21no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79C2×#4111yescharacteristic
177C4×C79H(5,𝔽2)11yescharacteristic
178Dic79—21no—
179Dic79—21no—
180Dic79—21no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—22no—
184C2×C79—81no—
185C2×C79#54611yescharacteristic
186C2×C79C2×#13511yescharacteristic
187C2×C79#57611yescharacteristic
188D79—41no—
189D79—42no—
190D79—81no—
191#3297—791nomaximal, Sylow
192C79#329711yescharacteristic, complemented, Sylow
193#553—791no—
194#546—791no—
195#488—791no—
196#484—791no—
197#482—791no—
198#478—791no—
199#466—791no—
200#465D7911yescharacteristic, complemented
201#463—791no—
202#449—791no—
203#447—791no—
204C4×D8—791no—
205C8×D4—791no—
206#416—791no—
207C2×#102—791no—
208C2×#41—791no—
209C22×D4—791no—
210C2×SD16C2×D7911yescharacteristic, complemented
211C2×D8—791no—
212C2×D8—791no—
213C22×C8—791no—
214C22×C8C2×D7911yescharacteristic
215#126—1581no—
216#125—791no—
217#124—791no—
218#123—1581no—
219#123—1581no—
220C22⋊Q8C2×D7911yescharacteristic
221#121—791no—
222#121—791no—
223#121—1581no—
224#121—1581no—
225#121C2×D7911yescharacteristic
226#120—1581no—
227C4×D4—791no—
228C4×D4—791no—
229C4×D4—791no—
230C4×D4—1581no—
231#117—791no—
232C2×C4⋊C4—791no—
233C2×C22⋊C4—1581no—
234#107—791no—
235#107—791no—
236#106C2×D7911yescharacteristic, complemented
237C4⋊C8—791no—
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, complemented
248C22⋊C8—791no—
249C22⋊C8—791no—
250C4×C8—791no—
251C24—1581no—
252#41—3161no—
253#41—1582no—
254C2×Q8C22×D7911yescharacteristic
255C2×D4—21no—
256C2×D4—3161no—
257C2×D4—791no—
258C2×D4—791no—
259C2×D4—791no—
260C2×D4—1581no—
261C2×D4—1582no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22×D7911yescharacteristic
266C22×C4—791no—
267C22×C4—1581no—
268C22×C4—1581no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4C22×D7911yescharacteristic
272SD16—41no—
273D8—3161no—
274D8—1582no—
275C2×C8—41no—
276C2×C8—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—791no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4—1581no—
288C4⋊C4C22×D7911yescharacteristic
289C4⋊C4C22×D7911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—791no—
293C22⋊C4—791no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C42—791no—
302C42—1581no—
303C23—21no—
304C23—3162no—
305C23—3162no—
306C23—791no—
307C23—6321no—
308C23—1581no—
309C23—1581no—
310C23D4×D7911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—3162no—
317D4—3162no—
318D4—792no—
319D4—6321no—
320D4—6321no—
321D4—1582no—
322D4—1581no—
323D4—1581no—
324D4—1581no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—3162no—
331C2×C4—791no—
332C2×C4—791no—
333C2×C4—791no—
334C2×C4—6321no—
335C2×C4—6321no—
336C2×C4—6321no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4D4×D7911yescharacteristic
342C2×C4C23×D7911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1581no—
346C8—1581no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—3161no—
353C22—3161no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—6324no—
358C22—1582no—
359C22—1581no—
360C22—1581no—
361C22—1581no—
362C22#1457918212yes—
363C22C2×D4×D7911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3161no—
369C4—3161no—
370C4—1581no—
371C4—1581no—
372C4—1581no—
373C4#41×D7911yescharacteristic
374C4#1457920611yescharacteristic
375C2—22no—
376C2—81no—
377C2—3162no—
378C2—3161no—
379C2—6321no—
380C2#1909920211yescharacteristic
381C2C2×#1457918211yescharacteristic
382C2#1909936511yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
hypercenter#465D79
hypocenterC79#3297
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #19099265C2semidirect
2. #19099204C2semidirect
3. #19098919C2semidirect
4. #19098896C2semidirect
5. #19098889C2semidirect
6. #19098862C2semidirect
7. #19098798C2semidirect
8. #19098780C2semidirect
9. #19098707C2semidirect
10. #19098696C2semidirect
11. #19098643C2semidirect
12. C8×C22⋊D79C2semidirect
13. #19098558C2semidirect
14. C2×#14579083C2semidirect
15. #465×C79C2semidirect
20. C2×C8×D79C22semidirect
22. #14579152C22semidirect
29. #14579132C22semidirect
32. D4×Dic79C22semidirect
35. #14579119C22semidirect
38. #14579094C22semidirect
39. #14579094C22semidirect
40. Dic79⋊C8C22semidirect
41. #14579085C22semidirect
42. #14579085C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
52. C2×SD16×C79C22semidirect
56. #106×C79C22semidirect
57. #103×C79C22semidirect
58. #102×C79C22semidirect
192. C79#3297semidirect
200. #465D79semidirect
210. C2×SD16C2×D79semidirect
236. #106C2×D79semidirect
240. #103C2×D79semidirect
247. #102C2×D79semidirect