Finite Group Databasebeta

← #23775487

Subgroups — #23775487

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#19099204C211yesmaximal, characteristic
3#19098924C211yesmaximal, characteristic, complemented
4#19098896C211yesmaximal, characteristic, complemented
5#19098878C211yesmaximal, characteristic, complemented
6#19098842C211yesmaximal, characteristic, complemented
7#19098812C211yesmaximal, characteristic, complemented
8#19098787C211yesmaximal, characteristic, complemented
9#19098724C211yesmaximal, characteristic, complemented
10#19098713C211yesmaximal, characteristic, complemented
11#19098666C211yesmaximal, characteristic, complemented
12#19098634C211yesmaximal, characteristic, complemented
13#19098563C211yesmaximal, characteristic, complemented
14C2×#14579083C211yesmaximal, characteristic, complemented
15#467×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929607C2211yescharacteristic, complemented
21#14579160C2211yescharacteristic, complemented
22#14579151—21no—
23#14579150C2211yescharacteristic
24#14579146—21no—
25#14579141—21no—
26#14579138—21no—
27#14579137C2211yescharacteristic, complemented
28#14579136—21no—
29#14579136C2211yescharacteristic
30#14579131—21no—
31Q8×Dic79C2211yescharacteristic, complemented
32#14579123C2211yescharacteristic
33C4×C22⋊D79C2211yescharacteristic
34(C22⋊D79)⋊C4—21no—
35C2×C4⋊Dic79C2211yescharacteristic
36C4⋊C4×D79C2211yescharacteristic, complemented
37C22⋊C4×D79—21no—
38#14579094C2211yescharacteristic, complemented
39#14579094C2211yescharacteristic, complemented
40Dic79⋊C8C2211yescharacteristic, complemented
41#14579085C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C2×Q16×C79C2211yescharacteristic, complemented
53C22×C8×C79C2211yescharacteristic
54C22⋊Q8×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#103×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929625—22no—
61#11929625—41no—
62C2×Dic158—21no—
63C2×D316—21no—
64C2×D316—21no—
65C2×D316—22no—
66C2×D316—21no—
67C2×D316—41no—
68C2×D316C2311yescharacteristic
69C2×D316C2311yescharacteristic
70C2×C22⋊D79D411yescharacteristic
71C22×Dic79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79C2311yescharacteristic
76#11929611—22no—
77#11929611—41no—
78#11929607—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79—21no—
82C4⋊Dic79—21no—
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4D411yescharacteristic
89C22⋊Dic79D411yescharacteristic
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
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×Q8×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101Q16×C79—41no—
102C2×C8×C79—41no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79—21no—
106C4⋊C4×C79—21no—
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C23×C79C2×D411yescharacteristic
112C22×D79—21no—
113C22×D79—21no—
114C22×D79—42no—
115C22×D79—42no—
116C22×D79—81no—
117C22×D79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120Q8×C79—21no—
121Q8×C79—21no—
122C2×C4×C79—21no—
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—
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—42no—
141D316—42no—
142D316—81no—
143D316#4112yes—
144C4×D79—21no—
145C4×D79—21no—
146C4×D79—42no—
147C4×D79—81no—
148C4×D79—81no—
149Dic158—81no—
150C8×C79—21no—
151C8×C79—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79#13712yes—
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—41no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79—41no—
173C4×C79C2×#4111yescharacteristic
174C4×C79H(5,𝔽2)11yescharacteristic
175Dic79—21no—
176Dic79—21no—
177Dic79—21no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—22no—
181C2×C79#54611yescharacteristic
182C2×C79C2×#13711yescharacteristic
183C2×C79#57611yescharacteristic
184D79—41no—
185D79—42no—
186D79—81no—
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#467D7911yescharacteristic, complemented
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×Q16C2×D7911yescharacteristic, complemented
207C2×SD16—791no—
208C2×SD16—791no—
209C2×M16—791no—
210C22×C8C2×D7911yescharacteristic
211C4⋊Q8—791no—
212#125—1581no—
213#124—791no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—1581no—
217C22⋊Q8—1581no—
218C22⋊Q8C2×D7911yescharacteristic
219C22⋊Q8C2×D7911yescharacteristic
220#121—791no—
221#121—1581no—
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#103C2×D7911yescharacteristic, complemented
237#103C2×D7911yescharacteristic, complemented
238#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
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—791no—
257C2×D4—1581no—
258C2×D4—1582no—
259C2×D4—1581no—
260C2×D4—1581no—
261C22×C4—791no—
262C22×C4—1581no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4—1581no—
266C22×C4C22×D7911yescharacteristic
267Q16—41no—
268SD16—3161no—
269SD16—1582no—
270M16—3161no—
271C2×C8—41no—
272C2×C8—791no—
273C2×C8—791no—
274C2×C8C22×D7911yescharacteristic
275C2×C8C22×D7911yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
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⋊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—3162no—
300C23—3162no—
301C23—791no—
302C23—6321no—
303C23—1581no—
304C23—1581no—
305C23D4×D7911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—6321no—
311D4—3162no—
312D4—3162no—
313D4—792no—
314D4—6321no—
315D4—1582no—
316D4—1581no—
317D4—1581no—
318D4—1581no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—3162no—
326C2×C4—791no—
327C2×C4—791no—
328C2×C4—791no—
329C2×C4—6321no—
330C2×C4—6321no—
331C2×C4—6321no—
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—3161no—
345C22—3161no—
346C22—3161no—
347C22—3161no—
348C22—3161no—
349C22—6324no—
350C22—1582no—
351C22—1581no—
352C22—1581no—
353C22—1581no—
354C22#1457919312yes—
355C22C2×D4×D7911yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—3161no—
362C4—3161no—
363C4—1581no—
364C4—1581no—
365C4—1581no—
366C4#41×D7911yescharacteristic
367C4#1457920611yescharacteristic
368C2—22no—
369C2—3162no—
370C2—3161no—
371C2—6321no—
372C2#1909920211yescharacteristic
373C2C2×#1457919311yescharacteristic
374C2#1909936511yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#467×C79C2
socleC22×C79C22×D4
prime radical#19099204C2
hypercenter#467D79
hypocenterC79#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #19099271C2semidirect
3. #19098924C2semidirect
4. #19098896C2semidirect
5. #19098878C2semidirect
6. #19098842C2semidirect
7. #19098812C2semidirect
8. #19098787C2semidirect
9. #19098724C2semidirect
10. #19098713C2semidirect
11. #19098666C2semidirect
12. #19098634C2semidirect
13. #19098563C2semidirect
14. C2×#14579083C2semidirect
15. #467×C79C2semidirect
20. C2×#11929607C22semidirect
21. #14579160C22semidirect
27. #14579137C22semidirect
31. Q8×Dic79C22semidirect
36. C4⋊C4×D79C22semidirect
38. #14579094C22semidirect
39. #14579094C22semidirect
40. Dic79⋊C8C22semidirect
41. #14579085C22semidirect
42. #14579085C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. #14579071C22semidirect
52. C2×Q16×C79C22semidirect
56. #107×C79C22semidirect
57. #103×C79C22semidirect
58. #103×C79C22semidirect
188. C79#3314semidirect
196. #467D79semidirect
206. C2×Q16C2×D79semidirect
232. #107C2×D79semidirect
236. #103C2×D79semidirect
237. #103C2×D79semidirect