Finite Group Databasebeta

← #23773645

Subgroups — #23773645

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#19099169C211yesmaximal, characteristic, complemented
2#19099035C211yesmaximal, characteristic, complemented
3#19098890C211yesmaximal, characteristic, complemented
4#19098889C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, characteristic, complemented
6#19098759C211yesmaximal, characteristic, complemented
7#19098758C211yesmaximal, characteristic, complemented
8#19098698C211yesmaximal, characteristic, complemented
9#19098698C211yesmaximal, characteristic, complemented
10#19098674C211yesmaximal, characteristic, complemented
11#19098672C211yesmaximal, characteristic, complemented
12#19098645C211yesmaximal, characteristic, complemented
13#19098643C211yesmaximal, characteristic, complemented
14#19098623C211yesmaximal, characteristic, complemented
15#478×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×D632C2211yescharacteristic
18C2×D632C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21#14579158C2211yescharacteristic, complemented
22#14579146—21no—
23#14579146—21no—
24#14579136—21no—
25#14579136—21no—
26#14579136C2211yescharacteristic
27#14579136C2211yescharacteristic
28C4×D316C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30#14579123C2211yescharacteristic
31#14579123C2211yescharacteristic, complemented
32#14579123C2211yescharacteristic, complemented
33C4×C22⋊D79—21no—
34(C22⋊D79)⋊C4—21no—
35#14579119C2211yescharacteristic
36#14579118C2211yescharacteristic
37C2×(C2×D79)⋊C4—21no—
38C22⋊C4×D79—21no—
39#14579094C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41C4⋊(C79⋊C8)C2211yescharacteristic, complemented
42#14579083C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic, complemented
44#14579081C2211yescharacteristic
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52#125×C79C2211yescharacteristic, complemented
53C4×D4×C79C2211yescharacteristic
54#107×C79C2211yescharacteristic, complemented
55#106×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60C2×D316—21no—
61C2×D316—21no—
62C2×D316—21no—
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68D4×D79—22no—
69D4×D79—22no—
70C22×Dic79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79C2311yescharacteristic
76D632—22no—
77D632—22no—
78#11929609—22no—
79#11929609—22no—
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4D411yescharacteristic
84Dic79⋊C4D411yescharacteristic
85C22⋊Dic79—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4D411yescharacteristic
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C4⋊C4×C79—21no—
102C4⋊C4×C79—21no—
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C22×D79—21no—
110C22×D79—24no—
111C22×D79—21no—
112C22×D79—21no—
113C22×D79—81no—
114C22×D79—81no—
115C22×D79C2×D411yescharacteristic
116D4×C79—21no—
117D4×C79#4112yes—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—81no—
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2411yescharacteristic
125C22⋊D79—24no—
126C2×Dic79—21no—
127C2×Dic79—81no—
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131D316—21no—
132D316—21no—
133D316—21no—
134D316—21no—
135D316—21no—
136D316—81no—
137D316—81no—
138D316—81no—
139D316—81no—
140D316#4112yes—
141C4×D79—21no—
142C4×D79—21no—
143C4×D79—81no—
144C4×D79—81no—
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×C79C22×D411yescharacteristic
155C2×D79—22no—
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—21no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—84no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79—41no—
173C4×C79C2×#4111yescharacteristic
174C4×C79C2×#4111yescharacteristic
175Dic79—21no—
176Dic79—21no—
177Dic79—21no—
178Dic79—41no—
179C2×C79—42no—
180C2×C79#52511yescharacteristic
181C2×C79#57611yescharacteristic
182C2×C79#57611yescharacteristic
183D79—41no—
184D79—42no—
185D79—81no—
186D79—81no—
187#3122—791nomaximal, Sylow
188C79#312211yescharacteristic, complemented, Sylow
189#540—791no—
190#518—791no—
191#482—791no—
192#482—791no—
193#478—791no—
194#478D7911yescharacteristic, complemented
195#459—791no—
196#459—791no—
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×D8—791no—
208C2×D8—791no—
209#127—791no—
210#125C2×D7911yescharacteristic, complemented
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#107C2×D7911yescharacteristic, complemented
231#106—791no—
232#106C2×D7911yescharacteristic, complemented
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
242#102C2×D7911yescharacteristic
243C22⋊C8—791no—
244C22⋊C8—791no—
245#97—791no—
246C4×C8—791no—
247C24—1581no—
248C2×D4—791no—
249C2×D4—791no—
250C2×D4—791no—
251C2×D4—1581no—
252C2×D4—1581no—
253C2×D4—1581no—
254C2×D4—1582no—
255C2×D4—1582no—
256C2×D4—1581no—
257C2×D4—1581no—
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—1582no—
267D8—1582no—
268D8—1582no—
269D8—1582no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8C22×D7911yescharacteristic
273C2×C8C22×D7911yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—791no—
277C4⋊C4—791no—
278C4⋊C4—791no—
279C4⋊C4C22×D7911yescharacteristic
280C4⋊C4C22×D7911yescharacteristic
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—791no—
298C23—6321no—
299C23—6321no—
300C23—1584no—
301C23—1581no—
302C23—1581no—
303C23—1581no—
304D4—21no—
305D4—792no—
306D4—6321no—
307D4—6321no—
308D4—6321no—
309D4—6321no—
310D4—1584no—
311D4—1581no—
312D4—1581no—
313D4—1581no—
314D4—1581no—
315D4—1581no—
316D4#1192962512yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—791no—
322C2×C4—791no—
323C2×C4—791no—
324C2×C4—6321no—
325C2×C4—6321no—
326C2×C4—6321no—
327C2×C4—6321no—
328C2×C4—6321no—
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—3161no—
343C22—3161no—
344C22—3161no—
345C22—3161no—
346C22—3161no—
347C22—3161no—
348C22—3161no—
349C22—3161no—
350C22—6324no—
351C22—1581no—
352C22—1582no—
353C22—1581no—
354C22—1581no—
355C22C2×D4×D7911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—3161no—
362C4—1581no—
363C4—1581no—
364C4—1581no—
365C4#41×D7911yescharacteristic
366C4C2×#1192962511yescharacteristic
367C2—42no—
368C2—3162no—
369C2—3161no—
370C2—6321no—
371C2—6321no—
372C2#1909907611yescharacteristic
373C2#1909936511yescharacteristic
374C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#478×C79C2
socleC22×C79C22×D4
hypercenter#478D79
hypocenterC79#3122
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #19099169C2semidirect
2. #19099035C2semidirect
3. #19098890C2semidirect
4. #19098889C2semidirect
5. #19098860C2semidirect
6. #19098759C2semidirect
7. #19098758C2semidirect
8. #19098698C2semidirect
9. #19098698C2semidirect
10. #19098674C2semidirect
11. #19098672C2semidirect
12. #19098645C2semidirect
13. #19098643C2semidirect
14. #19098623C2semidirect
15. #478×C79C2semidirect
21. #14579158C22semidirect
31. #14579123C22semidirect
32. #14579123C22semidirect
39. #14579094C22semidirect
40. #14579092C22semidirect
41. C4⋊(C79⋊C8)C22semidirect
42. #14579083C22semidirect
43. #14579083C22semidirect
46. #14579081C22semidirect
47. #14579081C22semidirect
50. #14579071C22semidirect
51. C8×Dic79C22semidirect
52. #125×C79C22semidirect
54. #107×C79C22semidirect
55. #106×C79C22semidirect
56. C4⋊C8×C79C22semidirect
188. C79#3122semidirect
194. #478D79semidirect
210. #125C2×D79semidirect
230. #107C2×D79semidirect
232. #106C2×D79semidirect
234. C4⋊C8C2×D79semidirect