Finite Group Databasebeta

← #23773640

Subgroups — #23773640

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#19099164C211yesmaximal, characteristic, complemented
2#19099035C211yesmaximal, characteristic, complemented
3#19098890C211yesmaximal, characteristic, complemented
4#19098885C211yesmaximal, characteristic, complemented
5#19098866C211yesmaximal, characteristic, complemented
6#19098861C211yesmaximal, characteristic, complemented
7#19098757C211yesmaximal, characteristic, complemented
8#19098756C211yesmaximal, characteristic, complemented
9#19098698C211yesmaximal, characteristic, complemented
10#19098695C211yesmaximal, characteristic, complemented
11#19098673C211yesmaximal, characteristic, complemented
12#19098673C211yesmaximal, characteristic, complemented
13C4×D632C211yesmaximal, characteristic, complemented
14#19098622C211yesmaximal, characteristic, complemented
15C4×D8×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×D632C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20#14579157C2211yescharacteristic, complemented
21#14579152C2211yescharacteristic, complemented
22#14579144—21no—
23#14579143—21no—
24#14579136C2211yescharacteristic
25#14579135—21no—
26#14579134—21no—
27#14579132C2211yescharacteristic
28C4×D316C2211yescharacteristic
29C4×D316C2211yescharacteristic, complemented
30D4×Dic79C2211yescharacteristic
31#14579123C2211yescharacteristic
32C4×C22⋊D79—21no—
33(C22⋊D79)⋊C4—21no—
34#14579119C2211yescharacteristic
35#14579118C2211yescharacteristic
36C2×(C2×D79)⋊C4—21no—
37C22⋊C4×D79—21no—
38#14579095C2211yescharacteristic, complemented
39#14579092C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic, complemented
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579072C2211yescharacteristic, 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—
60C2×D316—21no—
61C2×D316C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67D4×D79—22no—
68D4×D79—22no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74D632—22no—
75#11929609—22no—
76#11929609—22no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C4⋊Dic79—21no—
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4D411yescharacteristic
84Dic79⋊C4D411yescharacteristic
85C22⋊Dic79—21no—
86C22⋊Dic79—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)⋊C4D411yescharacteristic
93(C2×D79)⋊C4D411yescharacteristic
94C4×Dic79—21no—
95C4×Dic79C2311yescharacteristic
96C2×D4×C79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C22×C4×C79—21no—
100D8×C79—22no—
101C2×C8×C79C2311yescharacteristic
102C2×C8×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C22×D79—21no—
111C22×D79—24no—
112C22×D79—21no—
113C22×D79—81no—
114C22×D79—81no—
115C22×D79C2×D411yescharacteristic
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79#4112yes—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—81no—
123C2×C4×C79—81no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—24no—
128C22⋊D79—81no—
129C22⋊D79—81no—
130C22⋊D79—81no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—81no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—21no—
138D316—21no—
139D316—21no—
140D316—81no—
141D316#4112yes—
142C4×D79—21no—
143C4×D79—21no—
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×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79C22×D411yescharacteristic
158C2×D79—22no—
159C2×D79—21no—
160C2×D79—21no—
161C2×D79—21no—
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×C79C2×#4111yescharacteristic
173C4×C79C2×#4111yescharacteristic
174Dic79—21no—
175Dic79—21no—
176Dic79—21no—
177Dic79—41no—
178Dic79—41no—
179C2×C79—42no—
180C2×C79—81no—
181C2×C79#52511yescharacteristic
182C2×C79#57611yescharacteristic
183C2×C79#57611yescharacteristic
184D79—41no—
185D79—42no—
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#478—791no—
195#459—791no—
196#459—791no—
197#447—791no—
198#447—791no—
199#442—791no—
200#442—791no—
201C4×D8—791no—
202C4×D8D7911yescharacteristic, complemented
203#433—791no—
204C22×D4—791no—
205C2×D8—791no—
206C2×D8—791no—
207C2×D8—791no—
208C2×D8C2×D7911yescharacteristic
209#127—791no—
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—1581no—
222C4×D4—1581no—
223C4×D4C2×D7911yescharacteristic
224C4×D4C2×D7911yescharacteristic, complemented
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#106—791no—
233C4⋊C8—791no—
234C4⋊C8—791no—
235#102—791no—
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102C2×D7911yescharacteristic
242#102C2×D7911yescharacteristic, complemented
243C22⋊C8—791no—
244C22⋊C8—791no—
245#97—791no—
246C4×C8C2×D7911yescharacteristic, complemented
247C24—1581no—
248C2×D4—791no—
249C2×D4—791no—
250C2×D4—1581no—
251C2×D4—1581no—
252C2×D4—1581no—
253C2×D4—1581no—
254C2×D4—1582no—
255C2×D4—1581no—
256C2×D4—1582no—
257C2×D4C22×D7911yescharacteristic
258C2×D4C22×D7911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—791no—
262C22×C4—1581no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266D8—22no—
267D8—1582no—
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—1581no—
279C4⋊C4—1581no—
280C4⋊C4C22×D7911yescharacteristic
281C4⋊C4C22×D7911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—791no—
285C22⋊C4—791no—
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—791no—
299C23—6321no—
300C23—6321no—
301C23—1584no—
302C23—1581no—
303C23—1581no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—792no—
308D4—6321no—
309D4—6321no—
310D4—6321no—
311D4—6321no—
312D4—1584no—
313D4—1581no—
314D4—1581no—
315D4—1581no—
316D4#1192962412yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
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—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—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—3161no—
361C4—3161no—
362C4—1581no—
363C4—1581no—
364C4—1581no—
365C4#41×D7911yescharacteristic
366C4C2×#1192962411yescharacteristic
367C2—42no—
368C2—81no—
369C2—3162no—
370C2—3161no—
371C2—6321no—
372C2#1909907211yescharacteristic
373C2#1909936411yescharacteristic
374C2#1909936511yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×D8×C79C2
socleC22×C79C22×D4
hypercenterC4×D8D79
hypocenterC79#3122
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. #19099164C2semidirect
2. #19099035C2semidirect
3. #19098890C2semidirect
4. #19098885C2semidirect
5. #19098866C2semidirect
6. #19098861C2semidirect
7. #19098757C2semidirect
8. #19098756C2semidirect
9. #19098698C2semidirect
10. #19098695C2semidirect
11. #19098673C2semidirect
12. #19098673C2semidirect
13. C4×D632C2semidirect
14. #19098622C2semidirect
15. C4×D8×C79C2semidirect
20. #14579157C22semidirect
21. #14579152C22semidirect
29. C4×D316C22semidirect
38. #14579095C22semidirect
39. #14579092C22semidirect
40. #14579092C22semidirect
41. Dic79⋊C8C22semidirect
42. Dic79⋊C8C22semidirect
44. #14579083C22semidirect
46. #14579082C22semidirect
48. #14579081C22semidirect
51. #14579072C22semidirect
54. C4×D4×C79C22semidirect
55. #107×C79C22semidirect
57. #102×C79C22semidirect
58. C4×C8×C79C22semidirect
188. C79#3122semidirect
202. C4×D8D79semidirect
224. C4×D4C2×D79semidirect
230. #107C2×D79semidirect
242. #102C2×D79semidirect
246. C4×C8C2×D79semidirect