Finite Group Databasebeta

← #23775255

Subgroups — #23775255

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#19099263C211yesmaximal, characteristic, complemented
2#19099208C211yesmaximal, characteristic, complemented
3#19098918C211yesmaximal, characteristic, complemented
4#19098900C211yesmaximal, characteristic, complemented
5#19098890C211yesmaximal, characteristic, complemented
6#19098863C211yesmaximal, characteristic, complemented
7#19098798C211yesmaximal, characteristic, complemented
8#19098791C211yesmaximal, characteristic, complemented
9#19098778C211yesmaximal, characteristic, complemented
10#19098705C211yesmaximal, characteristic, complemented
11#19098695C211yesmaximal, characteristic, complemented
12C8×D316C211yesmaximal, characteristic, complemented
13#19098556C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15C4×D8×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929612C2211yescharacteristic, complemented
19C2×#11929609C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic
21C2×C8×D79C2211yescharacteristic, complemented
22#14579154—21no—
23#14579153C2211yescharacteristic, complemented
24#14579149C2211yescharacteristic
25#14579145—21no—
26#14579144—21no—
27#14579141C2211yescharacteristic
28#14579136C2211yescharacteristic
29#14579135—21no—
30#14579134—21no—
31#14579132C2211yescharacteristic
32#14579132C2211yescharacteristic, complemented
33#14579131—21no—
34C4×D316C2211yescharacteristic
35C4×C22⋊D79—21no—
36#14579119C2211yescharacteristic, complemented
37C4⋊C4×D79C2211yescharacteristic
38C2×(C2×D79)⋊C4—21no—
39#14579094C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic
53C4×D4×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic, complemented
55#107×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58C4×C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929623—22no—
61#11929623—41no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
64C2×D316D411yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70D4×D79—22no—
71D4×D79—41no—
72C22×Dic79—21no—
73C2×C4×D79—21no—
74C2×C4×D79C2311yescharacteristic
75C2×C4×D79C2311yescharacteristic
76#11929612—41no—
77#11929609—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C8×D79—41no—
81C8×D79—41no—
82C4⋊Dic79—21no—
83C4⋊Dic79D411yescharacteristic
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—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4D411yescharacteristic
97(C2×D79)⋊C4D411yescharacteristic
98C4×Dic79—21no—
99C2×D4×C79C2311yescharacteristic
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79—21no—
102C22×C4×C79—21no—
103D8×C79—22no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
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
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79#4112yes—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—81no—
126C2×C4×C79—81no—
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—42no—
131C22⋊D79—42no—
132C22⋊D79—42no—
133C22⋊D79—81no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—42no—
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140D316—22no—
141D316—21no—
142D316—21no—
143D316—81no—
144C4×D79—21no—
145C4×D79—21no—
146C4×D79—21no—
147C4×D79—21no—
148C4×D79—81no—
149Dic158—21no—
150Dic158—21no—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—22no—
156C22×C79—41no—
157C22×C79—41no—
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—21no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—84no—
171C2×D79#13512yes—
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—42no—
184C2×C79—81no—
185C2×C79#54611yescharacteristic
186C2×C79C2×#13511yescharacteristic
187C2×C79#57611yescharacteristic
188D79—22no—
189D79—41no—
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#465—791no—
201#463—791no—
202#449—791no—
203#447—791no—
204C4×D8D7911yescharacteristic, complemented
205C8×D4—791no—
206#416—791no—
207C2×#102—791no—
208C2×#41—791no—
209C22×D4—791no—
210C2×SD16—791no—
211C2×D8—791no—
212C2×D8C2×D7911yescharacteristic
213C22×C8—791no—
214C22×C8—791no—
215#126—1581no—
216#125—791no—
217#124—791no—
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—1581no—
229C4×D4C2×D7911yescharacteristic
230C4×D4C2×D7911yescharacteristic, complemented
231#117—791no—
232C2×C4⋊C4—791no—
233C2×C22⋊C4—1581no—
234#107—791no—
235#107C2×D7911yescharacteristic, complemented
236#106—791no—
237C4⋊C8—791no—
238#103—791no—
239#103—791no—
240#103—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102C2×D7911yescharacteristic
247#102C2×D7911yescharacteristic, complemented
248C22⋊C8—791no—
249C22⋊C8—791no—
250C4×C8C2×D7911yescharacteristic, complemented
251C24—1581no—
252#41—3161no—
253#41—1582no—
254C2×Q8—791no—
255C2×D4—3161no—
256C2×D4—791no—
257C2×D4—791no—
258C2×D4—1581no—
259C2×D4—1581no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1582no—
263C2×D4—1581no—
264C2×D4C22×D7911yescharacteristic
265C2×D4C22×D7911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—791no—
269C22×C4—791no—
270C22×C4—1581no—
271C22×C4—1581no—
272SD16—3161no—
273D8—22no—
274D8—3161no—
275C2×C8—3161no—
276C2×C8—3161no—
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⋊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—1581no—
302C42C22×D7911yescharacteristic
303C23—21no—
304C23—21no—
305C23—3162no—
306C23—3162no—
307C23—791no—
308C23—791no—
309C23—6321no—
310C23—1581no—
311Q8—1581no—
312Q8—1581no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—3162no—
317D4—3162no—
318D4—3162no—
319D4—6321no—
320D4—6321no—
321D4—1582no—
322D4—1581no—
323D4—1581no—
324D4#1192962412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—3162no—
330C2×C4—791no—
331C2×C4—791no—
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—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—3161no—
354C22—3161no—
355C22—3161no—
356C22—792no—
357C22—6324no—
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—
373C4C2×#1192962411yescharacteristic
374C4#1457920711yescharacteristic
375C2—42no—
376C2—81no—
377C2—3161no—
378C2—6321no—
379C2—1582no—
380C2#1909920911yescharacteristic
381C2#135×D7911yescharacteristic
382C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×D8×C79C2
socleC22×C79C22×D4
hypercenterC4×D8D79
hypocenterC79#3297
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #19099263C2semidirect
2. #19099208C2semidirect
3. #19098918C2semidirect
4. #19098900C2semidirect
5. #19098890C2semidirect
6. #19098863C2semidirect
7. #19098798C2semidirect
8. #19098791C2semidirect
9. #19098778C2semidirect
10. #19098705C2semidirect
11. #19098695C2semidirect
12. C8×D316C2semidirect
13. #19098556C2semidirect
14. #102×D79C2semidirect
15. C4×D8×C79C2semidirect
18. C2×#11929612C22semidirect
21. C2×C8×D79C22semidirect
23. #14579153C22semidirect
32. #14579132C22semidirect
36. #14579119C22semidirect
39. #14579094C22semidirect
40. #14579092C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579086C22semidirect
43. #14579086C22semidirect
44. #14579084C22semidirect
51. (C2×D79)⋊C8C22semidirect
54. C4×D4×C79C22semidirect
55. #107×C79C22semidirect
57. #102×C79C22semidirect
58. C4×C8×C79C22semidirect
192. C79#3297semidirect
204. C4×D8D79semidirect
230. C4×D4C2×D79semidirect
235. #107C2×D79semidirect
247. #102C2×D79semidirect
250. C4×C8C2×D79semidirect