Finite Group Databasebeta

← #23773641

Subgroups — #23773641

Order 10112.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099167C211yesmaximal, characteristic, complemented
2#19099035C211yesmaximal, characteristic, complemented
3#19098886C211yesmaximal, characteristic, complemented
4#19098885C211yesmaximal, characteristic, complemented
5#19098864C211yesmaximal, characteristic, complemented
6#19098863C211yesmaximal, characteristic, complemented
7#19098755C211yesmaximal, characteristic, complemented
8#19098695C211yesmaximal, characteristic, complemented
9#19098695C211yesmaximal, characteristic, complemented
10#19098675C211yesmaximal, characteristic, complemented
11#19098672C211yesmaximal, characteristic, complemented
12D8×Dic79C211yesmaximal, characteristic, complemented
13#19098643C211yesmaximal, characteristic, complemented
14#19098623C211yesmaximal, characteristic, complemented
15#459×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929609C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19#14579153C2211yescharacteristic, complemented
20#14579142—21no—
21#14579142—21no—
22#14579133—21no—
23#14579133—21no—
24#14579132C2211yescharacteristic
25#14579132C2211yescharacteristic
26C4×D316C2211yescharacteristic
27D4×Dic79C2211yescharacteristic
28D4×Dic79C2211yescharacteristic, complemented
29D4×Dic79C2211yescharacteristic, complemented
30#14579123C2211yescharacteristic
31C4×C22⋊D79—21no—
32(C22⋊D79)⋊C4—21no—
33#14579119C2211yescharacteristic
34#14579118C2211yescharacteristic
35C2×(C2×D79)⋊C4—21no—
36C22⋊C4×D79—21no—
37#14579095C2211yescharacteristic, complemented
38#14579094C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579083C2211yescharacteristic
43#14579083C2211yescharacteristic
44#14579082C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic
54#127×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56C4⋊C8×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×D316C2311yescharacteristic
61C2×C22⋊D79—21no—
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64D4×D79—22no—
65D4×D79—22no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C22×Dic79—21no—
69C2×C4×D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79C2311yescharacteristic
72#11929609—22no—
73#11929609—22no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4D411yescharacteristic
82Dic79⋊C4D411yescharacteristic
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4D411yescharacteristic
92(C2×D79)⋊C4D411yescharacteristic
93C4×Dic79—21no—
94C4×Dic79C2311yescharacteristic
95C2×D4×C79—21no—
96C2×D4×C79—21no—
97C2×D4×C79C2311yescharacteristic
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79—21no—
101D8×C79—22no—
102D8×C79—22no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C22×D79—21no—
112C22×D79—24no—
113C22×D79—81no—
114C22×D79—81no—
115C22×D79C2×D411yescharacteristic
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—81no—
122D4×C79—81no—
123D4×C79#4112yes—
124C2×C4×C79—21no—
125C2×C4×C79—81no—
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2411yescharacteristic
129C22⋊D79—24no—
130C22⋊D79—81no—
131C22⋊D79—81no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—81no—
136C2×Dic79—81no—
137C2×Dic79—81no—
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141D316—21no—
142D316#4112yes—
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—81no—
146C4×D79—81no—
147C8×C79—21no—
148C8×C79—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—22no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79C22×D411yescharacteristic
161C2×D79—22no—
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—21no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—84no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—41no—
171C4×C79C2×#4111yescharacteristic
172C4×C79C2×#4111yescharacteristic
173Dic79—21no—
174Dic79—21no—
175Dic79—21no—
176Dic79—41no—
177Dic79—41no—
178Dic79—41no—
179C2×C79—42no—
180C2×C79—81no—
181C2×C79—81no—
182C2×C79#52511yescharacteristic
183C2×C79#57611yescharacteristic
184C2×C79#57611yescharacteristic
185D79—41no—
186D79—42no—
187#3122—791nomaximal, Sylow
188C79#312211yescharacteristic, complemented, Sylow
189#540—791no—
190#518—791no—
191#482—791no—
192#482—791no—
193#478—791no—
194#478—791no—
195#459—791no—
196#459D7911yescharacteristic, complemented
197#447—791no—
198#447—791no—
199#442—791no—
200#442—791no—
201C4×D8—791no—
202C4×D8—791no—
203#433—791no—
204C22×D4—791no—
205C2×D8—791no—
206C2×D8—791no—
207C2×D8C2×D7911yescharacteristic
208C2×D8C2×D7911yescharacteristic
209#127C2×D7911yescharacteristic, complemented
210#125—791no—
211#123—1581no—
212#123—1581no—
213#121—791no—
214#121—791no—
215#121—1581no—
216#121—1581no—
217C4×D4—791no—
218C4×D4—791no—
219C4×D4—791no—
220C4×D4—791no—
221C4×D4—791no—
222C4×D4—1581no—
223C4×D4—1581no—
224C4×D4C2×D7911yescharacteristic
225#117—791no—
226#117—791no—
227C2×C22⋊C4—1581no—
228C2×C22⋊C4—1581no—
229#107—791no—
230#107—791no—
231#106—791no—
232#106—791no—
233C4⋊C8—791no—
234C4⋊C8C2×D7911yescharacteristic, complemented
235#102—791no—
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102C2×D7911yescharacteristic, complemented
242#102C2×D7911yescharacteristic, complemented
243C22⋊C8—791no—
244C22⋊C8—791no—
245#97—791no—
246C4×C8—791no—
247C24—1581no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—791no—
251C2×D4—1581no—
252C2×D4—1582no—
253C2×D4—1581no—
254C2×D4—1581no—
255C2×D4—1582no—
256C2×D4C22×D7911yescharacteristic
257C2×D4C22×D7911yescharacteristic
258C2×D4C22×D7911yescharacteristic
259C22×C4—21no—
260C22×C4—791no—
261C22×C4—1581no—
262C22×C4—1581no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266D8—22no—
267D8—22no—
268D8—1582no—
269D8—1582no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8C22×D7911yescharacteristic
273C2×C8C22×D7911yescharacteristic
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—791no—
277C4⋊C4—791no—
278C4⋊C4—791no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4C22×D7911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—791no—
284C22⋊C4—791no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C42—791no—
294C42—1581no—
295C42C22×D7911yescharacteristic
296C23—21no—
297C23—21no—
298C23—21no—
299C23—791no—
300C23—6321no—
301C23—6321no—
302C23—1584no—
303C23—1581no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—792no—
312D4—6321no—
313D4—6321no—
314D4—1584no—
315D4—1581no—
316D4#1192962312yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—791no—
320C2×C4—791no—
321C2×C4—791no—
322C2×C4—6321no—
323C2×C4—6321no—
324C2×C4—6321no—
325C2×C4—6321no—
326C2×C4—6321no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4D4×D7911yescharacteristic
333C2×C4D4×D7911yescharacteristic
334C2×C4C23×D7911yescharacteristic
335C8—21no—
336C8—21no—
337C8—1581no—
338C8—1581no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—3161no—
349C22—3161no—
350C22—6324no—
351C22—1581no—
352C22—1582no—
353C22—1581no—
354C22—1581no—
355C22C2×D4×D7911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—3161no—
360C4—3161no—
361C4—3161no—
362C4—1581no—
363C4—1581no—
364C4—1581no—
365C4#41×D7911yescharacteristic
366C4C2×#1192962311yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—3162no—
371C2—3161no—
372C2#1909907311yescharacteristic
373C2#1909936411yescharacteristic
374C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#459×C79C2
socleC22×C79C22×D4
hypercenter#459D79
hypocenterC79#3122
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #19099167C2semidirect
2. #19099035C2semidirect
3. #19098886C2semidirect
4. #19098885C2semidirect
5. #19098864C2semidirect
6. #19098863C2semidirect
7. #19098755C2semidirect
8. #19098695C2semidirect
9. #19098695C2semidirect
10. #19098675C2semidirect
11. #19098672C2semidirect
12. D8×Dic79C2semidirect
13. #19098643C2semidirect
14. #19098623C2semidirect
15. #459×C79C2semidirect
19. #14579153C22semidirect
28. D4×Dic79C22semidirect
29. D4×Dic79C22semidirect
37. #14579095C22semidirect
38. #14579094C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
46. #14579082C22semidirect
47. #14579082C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
54. #127×C79C22semidirect
56. C4⋊C8×C79C22semidirect
57. #102×C79C22semidirect
58. #102×C79C22semidirect
188. C79#3122semidirect
196. #459D79semidirect
209. #127C2×D79semidirect
234. C4⋊C8C2×D79semidirect
241. #102C2×D79semidirect
242. #102C2×D79semidirect