Finite Group Databasebeta

← #23775476

Subgroups — #23775476

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#19099271C211yesmaximal, characteristic, complemented
2#19099210C211yesmaximal, characteristic
3#19098921C211yesmaximal, characteristic, complemented
4#19098900C211yesmaximal, characteristic, complemented
5#19098874C211yesmaximal, characteristic, complemented
6#19098842C211yesmaximal, characteristic, complemented
7#19098803C211yesmaximal, characteristic, complemented
8#19098783C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11#19098666C211yesmaximal, characteristic, complemented
12#19098632C211yesmaximal, characteristic, complemented
13#19098565C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×#11929614C2211yescharacteristic, complemented
19C2×#11929611C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic
21#14579160C2211yescharacteristic, complemented
22#14579151—21no—
23#14579148C2211yescharacteristic
24#14579143—21no—
25#14579141—21no—
26#14579141C2211yescharacteristic
27#14579138—21no—
28#14579137C2211yescharacteristic
29#14579132—21no—
30#14579129—21no—
31Q8×Dic79C2211yescharacteristic, complemented
32#14579123C2211yescharacteristic
33C4×C22⋊D79C2211yescharacteristic
34(C22⋊D79)⋊C4—21no—
35C2×C4⋊Dic79C2211yescharacteristic, complemented
36C4⋊C4×D79C2211yescharacteristic
37C22⋊C4×D79—21no—
38#14579094C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40Dic79⋊C8C2211yescharacteristic, complemented
41#14579086C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic, complemented
54C22⋊Q8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79D411yescharacteristic
68D4×D79—22no—
69D4×D79—41no—
70C22×Dic79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79C2311yescharacteristic
75#11929614—41no—
76#11929611—22no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C8×D79—41no—
80C4⋊Dic79—21no—
81C4⋊Dic79—21no—
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4D411yescharacteristic
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79D411yescharacteristic
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4D411yescharacteristic
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79—21no—
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102SD16×C79—41no—
103M16×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—42no—
115C22×D79—42no—
116C22×D79—81no—
117C22×D79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—81no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—22no—
131C22⋊D79—42no—
132C22⋊D79—42no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—81no—
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140D316—21no—
141D316#4112yes—
142C4×D79—21no—
143C4×D79—21no—
144C4×D79—42no—
145C4×D79—81no—
146C4×D79—81no—
147Dic158—21no—
148Dic158—21no—
149Dic158—81no—
150C8×C79—21no—
151C8×C79—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79C22×D411yescharacteristic
161C2×D79—21no—
162C2×D79—21no—
163C2×D79—22no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—84no—
167C2×D79#13712yes—
168C4×C79—21no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79C2×#4111yescharacteristic
173C4×C79H(5,𝔽2)11yescharacteristic
174Dic79—21no—
175Dic79—21no—
176Dic79—21no—
177Dic79—41no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—41no—
181C2×C79—81no—
182C2×C79#54611yescharacteristic
183C2×C79C2×#13711yescharacteristic
184C2×C79#57611yescharacteristic
185D79—22no—
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#468D7911yescharacteristic, complemented
196#467—791no—
197#464—791no—
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×Q16—791no—
207C2×SD16—791no—
208C2×SD16C2×D7911yescharacteristic
209C2×M16C2×D7911yescharacteristic, complemented
210C22×C8—791no—
211C4⋊Q8—791no—
212#125—1581no—
213#124—791no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—1581no—
218C22⋊Q8—1581no—
219C22⋊Q8C2×D7911yescharacteristic, complemented
220#121—1581no—
221#121C2×D7911yescharacteristic
222#120—1581no—
223C4×Q8—791no—
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#107C2×D7911yescharacteristic, complemented
233C4⋊C8—791no—
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—791no—
251C2×Q8—1581no—
252C2×Q8C22×D7911yescharacteristic
253C2×D4—21no—
254C2×D4—3161no—
255C2×D4—791no—
256C2×D4—791no—
257C2×D4—1581no—
258C2×D4—1582no—
259C2×D4—1581no—
260C2×D4C22×D7911yescharacteristic
261C22×C4—791no—
262C22×C4—1581no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266C22×C4C22×D7911yescharacteristic
267Q16—3161no—
268SD16—41no—
269SD16—1582no—
270M16—41no—
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—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4C22×D7911yescharacteristic
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—791no—
298C42—1581no—
299C23—21no—
300C23—3162no—
301C23—3162no—
302C23—791no—
303C23—6321no—
304C23—1581no—
305C23D4×D7911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—6321no—
309Q8—1581no—
310Q8—1581no—
311D4—21no—
312D4—21no—
313D4—81no—
314D4—3162no—
315D4—3162no—
316D4—792no—
317D4—1582no—
318D4—1581no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—3162no—
325C2×C4—791no—
326C2×C4—791no—
327C2×C4—791no—
328C2×C4—6321no—
329C2×C4—6321no—
330C2×C4—6321no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4D4×D7911yescharacteristic
337C2×C4C23×D7911yescharacteristic
338C8—21no—
339C8—21no—
340C8—1581no—
341C8—1581no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—3161no—
349C22—3161no—
350C22—792no—
351C22—6324no—
352C22—1582no—
353C22—1581no—
354C22—1581no—
355C22C2×D4×D7911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—3161no—
361C4—3161no—
362C4—3161no—
363C4—1581no—
364C4—1581no—
365C4—1581no—
366C4#41×D7911yescharacteristic
367C4#1457920611yescharacteristic
368C2—41no—
369C2—81no—
370C2—3162no—
371C2—1582no—
372C2#1909920211yescharacteristic
373C2#137×D7911yescharacteristic
374C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
prime radical#19099210C2
hypercenter#468D79
hypocenterC79#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #19099271C2semidirect
3. #19098921C2semidirect
4. #19098900C2semidirect
5. #19098874C2semidirect
6. #19098842C2semidirect
7. #19098803C2semidirect
8. #19098783C2semidirect
9. #19098723C2semidirect
10. #19098712C2semidirect
11. #19098666C2semidirect
12. #19098632C2semidirect
13. #19098565C2semidirect
14. #102×D79C2semidirect
15. #468×C79C2semidirect
18. C2×#11929614C22semidirect
21. #14579160C22semidirect
31. Q8×Dic79C22semidirect
35. C2×C4⋊Dic79C22semidirect
38. #14579094C22semidirect
39. #14579094C22semidirect
40. Dic79⋊C8C22semidirect
41. #14579086C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
51. #14579071C22semidirect
53. C2×M16×C79C22semidirect
54. C22⋊Q8×C79C22semidirect
56. #107×C79C22semidirect
57. #103×C79C22semidirect
188. C79#3314semidirect
195. #468D79semidirect
209. C2×M16C2×D79semidirect
219. C22⋊Q8C2×D79semidirect
232. #107C2×D79semidirect
237. #103C2×D79semidirect