Finite Group Databasebeta

← #23775251

Subgroups — #23775251

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099257C211yesmaximal, characteristic, complemented
2#19099201C211yesmaximal, characteristic, complemented
3#19098919C211yesmaximal, characteristic, complemented
4#19098897C211yesmaximal, characteristic, complemented
5#19098887C211yesmaximal, characteristic, complemented
6#19098861C211yesmaximal, characteristic, complemented
7#19098799C211yesmaximal, characteristic, complemented
8#19098795C211yesmaximal, characteristic, complemented
9#19098781C211yesmaximal, characteristic, complemented
10#19098708C211yesmaximal, characteristic, complemented
11#19098698C211yesmaximal, characteristic, complemented
12#19098643C211yesmaximal, characteristic, complemented
13C8×C22⋊D79C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15#416×C79C211yesmaximal, characteristic, complemented
16C2×D4×D79C2211yescharacteristic
17C2×#11929611C2211yescharacteristic, complemented
18C2×D632C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic
21#14579155—21no—
22#14579152C2211yescharacteristic, complemented
23#14579150C2211yescharacteristic
24#14579144—21no—
25#14579143—21no—
26#14579137C2211yescharacteristic
27#14579136C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579135C2211yescharacteristic, complemented
30#14579134—21no—
31#14579133—21no—
32#14579129—21no—
33C4×D316—21no—
34D4×Dic79C2211yescharacteristic
35#14579123C2211yescharacteristic, complemented
36C4×C22⋊D79C2211yescharacteristic
37C4⋊C4×D79C2211yescharacteristic
38C2×(C2×D79)⋊C4—21no—
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic, complemented
52C2×#41×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic, complemented
54#117×C79C2211yescharacteristic, complemented
55#103×C79C2211yescharacteristic, complemented
56#103×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59C23×D79—21no—
60C2×D316—21no—
61C2×D316C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79D411yescharacteristic
67D4×D79—22no—
68D4×D79—41no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79C2311yescharacteristic
73#11929611—41no—
74D632—41no—
75#11929609—22no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C8×D79—41no—
79C4⋊Dic79—21no—
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4D411yescharacteristic
86C22⋊Dic79—21no—
87C22⋊Dic79D411yescharacteristic
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
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×Dic79C2311yescharacteristic
97#41×C79—22no—
98#41×C79—41no—
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104C2×C8×C79—41no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C42×C79—21no—
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114C22×D79—21no—
115C22×D79—42no—
116C22×D79—42no—
117C22×D79—81no—
118C22×D79C2×D411yescharacteristic
119Q8×C79—21no—
120Q8×C79—21no—
121D4×C79—21no—
122D4×C79—42no—
123D4×C79#4112yes—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—42no—
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2411yescharacteristic
132C22⋊D79—22no—
133C22⋊D79—42no—
134C22⋊D79—81no—
135C22⋊D79—81no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—81no—
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142D316—21no—
143D316—21no—
144D316—21no—
145D316—21no—
146D316—42no—
147C4×D79—21no—
148C4×D79—21no—
149C4×D79—81no—
150C4×D79—81no—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—22no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—84no—
171C2×D79#13512yes—
172C4×C79—21no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79C2×#4111yescharacteristic
177C4×C79H(5,𝔽2)11yescharacteristic
178Dic79—21no—
179Dic79—21no—
180Dic79—21no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—42no—
184C2×C79—41no—
185C2×C79#54611yescharacteristic
186C2×C79C2×#13511yescharacteristic
187C2×C79#57611yescharacteristic
188D79—22no—
189D79—81no—
190D79—81no—
191#3297—791nomaximal, Sylow
192C79#329711yescharacteristic, complemented, Sylow
193#553—791no—
194#546—791no—
195#488—791no—
196#484—791no—
197#482—791no—
198#478—791no—
199#466—791no—
200#465—791no—
201#463—791no—
202#449—791no—
203#447—791no—
204C4×D8—791no—
205C8×D4—791no—
206#416D7911yescharacteristic, complemented
207C2×#102—791no—
208C2×#41C2×D7911yescharacteristic
209C22×D4—791no—
210C2×SD16—791no—
211C2×D8—791no—
212C2×D8—791no—
213C22×C8—791no—
214C22×C8C2×D7911yescharacteristic, complemented
215#126—1581no—
216#125—791no—
217#124—791no—
218#123—1581no—
219#123—1581no—
220C22⋊Q8—791no—
221#121—791no—
222#121—791no—
223#121—791no—
224#121—1581no—
225#121—1581no—
226#120—1581no—
227C4×D4—791no—
228C4×D4—791no—
229C4×D4—791no—
230C4×D4—1581no—
231#117C2×D7911yescharacteristic, complemented
232C2×C4⋊C4—791no—
233C2×C22⋊C4—1581no—
234#107—791no—
235#107—791no—
236#106—791no—
237C4⋊C8—791no—
238#103—791no—
239#103C2×D7911yescharacteristic, complemented
240#103C2×D7911yescharacteristic, complemented
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102C2×D7911yescharacteristic
247#102C2×D7911yescharacteristic
248C22⋊C8—791no—
249C22⋊C8—791no—
250C4×C8—791no—
251C24—1581no—
252#41—22no—
253#41—41no—
254C2×Q8C22×D7911yescharacteristic
255C2×D4—21no—
256C2×D4—3161no—
257C2×D4—791no—
258C2×D4—791no—
259C2×D4—791no—
260C2×D4—1581no—
261C2×D4—1581no—
262C2×D4—1582no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22×D7911yescharacteristic
266C22×C4—21no—
267C22×C4—791no—
268C22×C4—1581no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4C22×D7911yescharacteristic
272SD16—3161no—
273D8—3161no—
274D8—1582no—
275C2×C8—41no—
276C2×C8—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8C22×D7911yescharacteristic
280C2×C8C22×D7911yescharacteristic
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4—1581no—
288C4⋊C4C22×D7911yescharacteristic
289C4⋊C4C22×D7911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—791no—
292C22⋊C4—791no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C42—21no—
302C42—791no—
303C23—21no—
304C23—3162no—
305C23—3162no—
306C23—791no—
307C23—6321no—
308C23—1581no—
309C23—1581no—
310C23D4×D7911yescharacteristic
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—42no—
315D4—3162no—
316D4—3162no—
317D4—6321no—
318D4—6321no—
319D4—1582no—
320D4—1581no—
321D4—1581no—
322D4—1581no—
323D4—1581no—
324D4#1192962412yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—42no—
331C2×C4—791no—
332C2×C4—791no—
333C2×C4—791no—
334C2×C4—6321no—
335C2×C4—6321no—
336C2×C4—6321no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4D4×D7911yescharacteristic
342C2×C4C23×D7911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1581no—
346C8—1581no—
347C22—21no—
348C22—22no—
349C22—21no—
350C22—21no—
351C22—41no—
352C22—41no—
353C22—3161no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—792no—
360C22—6324no—
361C22—1581no—
362C22—1581no—
363C22C2×D4×D7911yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—3161no—
369C4—3161no—
370C4—1581no—
371C4—1581no—
372C4—1581no—
373C4C2×#1192962411yescharacteristic
374C4#1457920611yescharacteristic
375C2—41no—
376C2—42no—
377C2—6321no—
378C2—6321no—
379C2—1582no—
380C2#1909920311yescharacteristic
381C2#135×D7911yescharacteristic
382C2#1909936511yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#416×C79C2
socleC22×C79C22×D4
hypercenter#416D79
hypocenterC79#3297
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #19099257C2semidirect
2. #19099201C2semidirect
3. #19098919C2semidirect
4. #19098897C2semidirect
5. #19098887C2semidirect
6. #19098861C2semidirect
7. #19098799C2semidirect
8. #19098795C2semidirect
9. #19098781C2semidirect
10. #19098708C2semidirect
11. #19098698C2semidirect
12. #19098643C2semidirect
13. C8×C22⋊D79C2semidirect
14. #102×D79C2semidirect
15. #416×C79C2semidirect
17. C2×#11929611C22semidirect
22. #14579152C22semidirect
29. #14579135C22semidirect
35. #14579123C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579092C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579085C22semidirect
45. #14579083C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
51. C8×Dic79C22semidirect
53. C22×C8×C79C22semidirect
54. #117×C79C22semidirect
55. #103×C79C22semidirect
56. #103×C79C22semidirect
192. C79#3297semidirect
206. #416D79semidirect
214. C22×C8C2×D79semidirect
231. #117C2×D79semidirect
239. #103C2×D79semidirect
240. #103C2×D79semidirect