Finite Group Databasebeta

← #23775488

Subgroups — #23775488

Order 10112.

410 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#19099273C211yesmaximal, characteristic, complemented
2#19099206C211yesmaximal, characteristic
3#19098922C211yesmaximal, characteristic, complemented
4#19098897C211yesmaximal, characteristic, complemented
5#19098875C211yesmaximal, characteristic, complemented
6#19098844C211yesmaximal, characteristic, complemented
7#19098806C211yesmaximal, characteristic, complemented
8#19098801C211yesmaximal, characteristic, complemented
9#19098724C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11#19098661C211yesmaximal, characteristic, complemented
12#19098633C211yesmaximal, characteristic, complemented
13#19098563C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#464×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929607C2211yescharacteristic, complemented
20C2×C8×D79C2211yescharacteristic
21#14579161C2211yescharacteristic, complemented
22#14579153—21no—
23#14579143—21no—
24#14579139—21no—
25#14579139—21no—
26#14579137C2211yescharacteristic
27#14579137C2211yescharacteristic
28#14579137C2211yescharacteristic, complemented
29#14579134—21no—
30#14579132C2211yescharacteristic
31#14579131—21no—
32C4×D316—21no—
33C4×D316C2211yescharacteristic
34C4×D316C2211yescharacteristic
35C4⋊C4×D79C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic, complemented
37C22⋊C4×D79—21no—
38#14579095C2211yescharacteristic, complemented
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579085C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579072C2211yescharacteristic, complemented
52C2×Q16×C79C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54#124×C79C2211yescharacteristic
55C4×Q8×C79C2211yescharacteristic, complemented
56C4⋊C8×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60#11929625—22no—
61#11929625—41no—
62C2×Dic158—21no—
63C2×D316—21no—
64C2×D316D411yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68D4×D79—22no—
69D4×D79—41no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79C2311yescharacteristic
75C2×C4×D79C2311yescharacteristic
76#11929611—22no—
77#11929607—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C8×D79—41no—
81C4⋊Dic79—21no—
82C4⋊Dic79D411yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91C22⋊Dic79—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
98C2×Q8×C79C2311yescharacteristic
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79C2311yescharacteristic
101Q16×C79—41no—
102SD16×C79—41no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79—21no—
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C22×D79—21no—
113C22×D79—42no—
114C22×D79—42no—
115C22×D79—81no—
116C22×D79C2×D411yescharacteristic
117C22×D79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120Q8×C79—21no—
121Q8×C79—21no—
122D4×C79—21no—
123D4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—42no—
131C22⋊D79—81no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—22no—
138D316—21no—
139D316—42no—
140D316#4112yes—
141C4×D79—21no—
142C4×D79—21no—
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—42no—
146C4×D79—81no—
147C4×D79—81no—
148C4×D79—81no—
149Dic158—81no—
150C8×C79—21no—
151C8×C79—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79C22×D411yescharacteristic
158C2×D79—21no—
159C2×D79—21no—
160C2×D79—22no—
161C2×D79—21no—
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—84no—
167C2×D79#13712yes—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79—41no—
173C4×C79C2×#4111yescharacteristic
174C4×C79H(5,𝔽2)11yescharacteristic
175Dic79—21no—
176Dic79—21no—
177Dic79—41no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—81no—
181C2×C79#54611yescharacteristic
182C2×C79C2×#13711yescharacteristic
183C2×C79#57611yescharacteristic
184D79—22no—
185D79—41no—
186D79—42no—
187#3314—791nomaximal, Sylow
188C79#331411yescharacteristic, complemented, Sylow
189#554—791no—
190#546—791no—
191#489—791no—
192#484—791no—
193#480—791no—
194#474—791no—
195#468—791no—
196#467—791no—
197#464D7911yescharacteristic, complemented
198#452—791no—
199#450—791no—
200#440—791no—
201#435—791no—
202#417—791no—
203C2×#102—791no—
204C2×#41—791no—
205C22×D4—791no—
206C2×Q16C2×D7911yescharacteristic, complemented
207C2×SD16—791no—
208C2×SD16C2×D7911yescharacteristic
209C2×M16—791no—
210C22×C8—791no—
211C4⋊Q8—791no—
212#125—1581no—
213#124C2×D7911yescharacteristic
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—791no—
218C22⋊Q8—1581no—
219C22⋊Q8—1581no—
220#121—791no—
221#121—1581no—
222#120—1581no—
223C4×Q8C2×D7911yescharacteristic, complemented
224C4×D4—791no—
225C4×D4—791no—
226C4×D4—1581no—
227C2×C4⋊C4—791no—
228C2×C4⋊C4—791no—
229C2×C22⋊C4—1581no—
230#107—791no—
231#107—791no—
232#107—791no—
233C4⋊C8C2×D7911yescharacteristic, complemented
234#103—791no—
235#103—791no—
236#103—791no—
237#103C2×D7911yescharacteristic, complemented
238#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102C2×D7911yescharacteristic
244C22⋊C8—791no—
245C22⋊C8—791no—
246#97—791no—
247C24—1581no—
248#41—3161no—
249#41—1582no—
250C2×Q8—1581no—
251C2×Q8C22×D7911yescharacteristic
252C2×Q8C22×D7911yescharacteristic
253C2×D4—3161no—
254C2×D4—791no—
255C2×D4—791no—
256C2×D4—1581no—
257C2×D4—1581no—
258C2×D4—1582no—
259C2×D4—1581no—
260C2×D4C22×D7911yescharacteristic
261C22×C4—791no—
262C22×C4—791no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266C22×C4—1581no—
267Q16—41no—
268SD16—41no—
269SD16—1582no—
270M16—3161no—
271C2×C8—3161no—
272C2×C8—791no—
273C2×C8—791no—
274C2×C8C22×D7911yescharacteristic
275C2×C8C22×D7911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—791no—
278C4⋊C4—791no—
279C4⋊C4—791no—
280C4⋊C4—791no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—791no—
291C22⋊C4—791no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C42—21no—
298C42C22×D7911yescharacteristic
299C23—21no—
300C23—3162no—
301C23—3162no—
302C23—791no—
303C23—791no—
304C23—6321no—
305C23—1581no—
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—6321no—
311D4—21no—
312D4—21no—
313D4—3162no—
314D4—3162no—
315D4—792no—
316D4—6321no—
317D4—1582no—
318D4—1581no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—3162no—
323C2×C4—791no—
324C2×C4—791no—
325C2×C4—6321no—
326C2×C4—6321no—
327C2×C4—6321no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4D4×D7911yescharacteristic
336C2×C4D4×D7911yescharacteristic
337C2×C4C23×D7911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1581no—
341C8—1581no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—3161no—
346C22—3161no—
347C22—792no—
348C22—6324no—
349C22—1582no—
350C22—1581no—
351C22—1581no—
352C22—1581no—
353C22—1581no—
354C22—1581no—
355C22C2×D4×D7911yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—3161no—
362C4—3161no—
363C4—3161no—
364C4—1581no—
365C4—1581no—
366C4#41×D7911yescharacteristic
367C4#1457920611yescharacteristic
368C2—81no—
369C2—3162no—
370C2—3161no—
371C2—1582no—
372C2#1909921011yescharacteristic
373C2#137×D7911yescharacteristic
374C2#1909936511yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#464×C79C2
socleC22×C79C22×D4
prime radical#19099206C2
hypercenter#464D79
hypocenterC79#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #19099273C2semidirect
3. #19098922C2semidirect
4. #19098897C2semidirect
5. #19098875C2semidirect
6. #19098844C2semidirect
7. #19098806C2semidirect
8. #19098801C2semidirect
9. #19098724C2semidirect
10. #19098712C2semidirect
11. #19098661C2semidirect
12. #19098633C2semidirect
13. #19098563C2semidirect
14. #102×D79C2semidirect
15. #464×C79C2semidirect
19. C2×#11929607C22semidirect
21. #14579161C22semidirect
28. #14579137C22semidirect
36. C4⋊C4×D79C22semidirect
38. #14579095C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579085C22semidirect
42. #14579085C22semidirect
43. #14579085C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579072C22semidirect
52. C2×Q16×C79C22semidirect
55. C4×Q8×C79C22semidirect
56. C4⋊C8×C79C22semidirect
57. #103×C79C22semidirect
188. C79#3314semidirect
197. #464D79semidirect
206. C2×Q16C2×D79semidirect
223. C4×Q8C2×D79semidirect
233. C4⋊C8C2×D79semidirect
237. #103C2×D79semidirect