Finite Group Databasebeta

← #23775484

Subgroups — #23775484

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#19099268C211yesmaximal, characteristic, complemented
2#19099210C211yesmaximal, characteristic
3#19098921C211yesmaximal, characteristic, complemented
4#19098900C211yesmaximal, characteristic, complemented
5#19098842C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098805C211yesmaximal, characteristic, complemented
8#19098784C211yesmaximal, characteristic, complemented
9#19098727C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098662C211yesmaximal, characteristic, complemented
12#19098637C211yesmaximal, characteristic, complemented
13#19098562C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#480×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C2×Dic316C2211yescharacteristic, complemented
19C2×#11929613C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×#11929608C2211yescharacteristic, complemented
22C2×C8×D79C2211yescharacteristic
23#14579160C2211yescharacteristic, complemented
24#14579151—21no—
25#14579148C2211yescharacteristic
26#14579143—21no—
27#14579141C2211yescharacteristic
28#14579141C2211yescharacteristic
29#14579140—21no—
30#14579140C2211yescharacteristic, complemented
31#14579139—21no—
32#14579132—21no—
33#14579129—21no—
34#14579126C2211yescharacteristic, complemented
35#14579123C2211yescharacteristic
36C4×C22⋊D79—21no—
37C4×C22⋊D79C2211yescharacteristic
38C4⋊C4×D79C2211yescharacteristic
39C22⋊C4×D79—21no—
40#14579094C2211yescharacteristic, complemented
41Dic79⋊C8C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579084C2211yescharacteristic, complemented
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic, complemented
52#121×C79C2211yescharacteristic
53C2×C4⋊C4×C79C2211yescharacteristic, complemented
54#107×C79C2211yescharacteristic, complemented
55#107×C79C2211yescharacteristic, complemented
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79D411yescharacteristic
69D4×D79—22no—
70D4×D79—41no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79C2311yescharacteristic
75Dic316—41no—
76#11929613—22no—
77#11929612—41no—
78#11929608—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C8×D79—41no—
82C4⋊Dic79—21no—
83C4⋊Dic79—21no—
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4D411yescharacteristic
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79D411yescharacteristic
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4D411yescharacteristic
98C4×Dic79—21no—
99C4×Dic79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
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
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—81no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—81no—
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2411yescharacteristic
129C22⋊D79—22no—
130C22⋊D79—42no—
131C22⋊D79—42no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—21no—
139D316#4112yes—
140C4×D79—21no—
141C4×D79—21no—
142C4×D79—42no—
143C4×D79—81no—
144C4×D79—81no—
145Dic158—21no—
146Dic158—21no—
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#480D7911yescharacteristic, complemented
194#474—791no—
195#468—791no—
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×SD16—791no—
209C2×M16—791no—
210C22×C8—791no—
211C4⋊Q8—791no—
212#125—1581no—
213#124—791no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—791no—
218C22⋊Q8—1581no—
219C22⋊Q8—1581no—
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⋊C4C2×D7911yescharacteristic, complemented
229C2×C22⋊C4—1581no—
230#107—791no—
231#107C2×D7911yescharacteristic, complemented
232#107C2×D7911yescharacteristic, complemented
233C4⋊C8—791no—
234#103—791no—
235#103—791no—
236#103—791no—
237#103—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242#102C2×D7911yescharacteristic
243#102C2×D7911yescharacteristic
244C22⋊C8—791no—
245C22⋊C8C2×D7911yescharacteristic, complemented
246#97—791no—
247C24—1581no—
248#41—3161no—
249#41—1582no—
250C2×Q8—791no—
251C2×Q8—791no—
252C2×Q8—1581no—
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—21no—
262C22×C4—791no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266C22×C4C22×D7911yescharacteristic
267Q16—3161no—
268SD16—3161no—
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—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4C22×D7911yescharacteristic
286C4⋊C4C22×D7911yescharacteristic
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—791no—
290C22⋊C4—791no—
291C22⋊C4—1581no—
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—6321no—
307Q8—1581no—
308Q8—1581no—
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—81no—
325C2×C4—3162no—
326C2×C4—791no—
327C2×C4—791no—
328C2×C4—791no—
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#1457920711yescharacteristic
368C2—41no—
369C2—81no—
370C2—3162no—
371C2—1582no—
372C2#1909920511yescharacteristic
373C2#137×D7911yescharacteristic
374C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#480×C79C2
socleC22×C79C22×D4
prime radical#19099210C2
hypercenter#480D79
hypocenterC79#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #19099268C2semidirect
3. #19098921C2semidirect
4. #19098900C2semidirect
5. #19098842C2semidirect
6. #19098807C2semidirect
7. #19098805C2semidirect
8. #19098784C2semidirect
9. #19098727C2semidirect
10. #19098715C2semidirect
11. #19098662C2semidirect
12. #19098637C2semidirect
13. #19098562C2semidirect
14. #102×D79C2semidirect
15. #480×C79C2semidirect
18. C2×Dic316C22semidirect
21. C2×#11929608C22semidirect
23. #14579160C22semidirect
30. #14579140C22semidirect
34. #14579126C22semidirect
40. #14579094C22semidirect
41. Dic79⋊C8C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
44. #14579084C22semidirect
45. #14579084C22semidirect
51. #14579071C22semidirect
53. C2×C4⋊C4×C79C22semidirect
54. #107×C79C22semidirect
55. #107×C79C22semidirect
58. C22⋊C8×C79C22semidirect
188. C79#3314semidirect
193. #480D79semidirect
228. C2×C4⋊C4C2×D79semidirect
231. #107C2×D79semidirect
232. #107C2×D79semidirect
245. C22⋊C8C2×D79semidirect