Finite Group Databasebeta

← #23774160

Subgroups — #23774160

Order 10112.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099073C211yesmaximal, characteristic, complemented
2#121×D79C211yesmaximal, characteristic, complemented
3#19098900C211yesmaximal, characteristic, complemented
4#19098890C211yesmaximal, characteristic, complemented
5#19098886C211yesmaximal, characteristic, complemented
6#19098880C211yesmaximal, characteristic, complemented
7#19098797C211yesmaximal, characteristic, complemented
8#19098792C211yesmaximal, characteristic, complemented
9#19098790C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098709C211yesmaximal, characteristic, complemented
12#19098705C211yesmaximal, characteristic, complemented
13#19098695C211yesmaximal, characteristic, complemented
14C2×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
15#466×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic, complemented
17C2×D4×D79—21no—
18C2×D4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C2×#11929613C2211yescharacteristic, complemented
21C2×#11929612C2211yescharacteristic, complemented
22C2×#11929609C2211yescharacteristic, complemented
23C22×C79⋊C8C2211yescharacteristic, complemented
24#14579143—21no—
25#14579141C2211yescharacteristic
26#14579140C2211yescharacteristic, complemented
27#14579136C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579134—21no—
30#14579133—21no—
31#14579132C2211yescharacteristic
32#14579132C2211yescharacteristic
33#14579129—21no—
34D4×Dic79—21no—
35(C22⋊D79)⋊C4—21no—
36#14579119C2211yescharacteristic, complemented
37C4⋊C4×D79C2211yescharacteristic
38C22⋊C4×D79—21no—
39#14579094C2211yescharacteristic, complemented
40#14579093C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42#14579086C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic, complemented
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C2×D8×C79C2211yescharacteristic, complemented
53C22×C8×C79C2211yescharacteristic, complemented
54#121×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic, complemented
56#107×C79C2211yescharacteristic, complemented
57#102×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79D411yescharacteristic
61#11929623—41no—
62#11929623—41no—
63C2×Dic158C2311yescharacteristic
64C2×D316—21no—
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71D4×D79—41no—
72D4×D79—41no—
73D4×D79—44no—
74C22×Dic79—21no—
75C22×Dic79D411yescharacteristic
76C2×C4×D79—21no—
77C2×C4×D79—41no—
78C2×C4×D79—41no—
79C2×C4×D79D411yescharacteristic
80C2×C4×D79D411yescharacteristic
81C2×C4×D79C2311yescharacteristic
82C2×C4×D79C2311yescharacteristic
83#11929613—41no—
84#11929612—41no—
85#11929609—41no—
86C2×C79⋊C8—41no—
87C2×C79⋊C8C2311yescharacteristic
88C2×C79⋊C8C2311yescharacteristic
89C4⋊Dic79—21no—
90C4⋊Dic79C2311yescharacteristic
91C4⋊Dic79C2311yescharacteristic
92Dic79⋊C4—21no—
93Dic79⋊C4—21no—
94C22⋊Dic79—21no—
95C22⋊Dic79—21no—
96C22⋊Dic79—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4—21no—
100(C2×D79)⋊C4—21no—
101C4×Dic79—21no—
102C2×D4×C79—21no—
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C2×D4×C79C2311yescharacteristic
106C22×C4×C79C2311yescharacteristic
107D8×C79—41no—
108C2×C8×C79—41no—
109C2×C8×C79C2311yescharacteristic
110C2×C8×C79C2311yescharacteristic
111C4⋊C4×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C22⋊C4×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C23×C79C2×D411yescharacteristic
118C22×D79—22no—
119C22×D79—22no—
120C22×D79—21no—
121C22×D79—41no—
122C22×D79—42no—
123C22×D79—42no—
124C22×D79—42no—
125C22×D79C2×D411yescharacteristic
126C22×D79C2×D411yescharacteristic
127D4×C79—21no—
128D4×C79—21no—
129D4×C79—21no—
130D4×C79—21no—
131D4×C79—42no—
132D4×C79—42no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2411yescharacteristic
139C22⋊D79—42no—
140C22⋊D79—42no—
141C22⋊D79—42no—
142C22⋊D79—42no—
143C22⋊D79—42no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—41no—
148C2×Dic79—42no—
149C2×Dic79C2×D411yescharacteristic
150C2×Dic79C2×D411yescharacteristic
151D316—21no—
152D316—21no—
153D316—42no—
154C4×D79—21no—
155C4×D79—21no—
156C4×D79—21no—
157C4×D79—21no—
158C4×D79—41no—
159C4×D79—41no—
160C4×D79—42no—
161Dic158—21no—
162Dic158—21no—
163C8×C79—21no—
164C8×C79—21no—
165C79⋊C8—21no—
166C79⋊C8—21no—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79AGL(1,ℤ/8)12yes—
176C22×C79C22×D411yescharacteristic
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—21no—
180C2×D79—21no—
181C2×D79—21no—
182C2×D79—44no—
183C2×D79—41no—
184C2×D79—41no—
185C2×D79—41no—
186C2×D79—84no—
187C2×D79#13512yes—
188C4×C79—21no—
189C4×C79—41no—
190C4×C79—41no—
191C4×C79H(5,𝔽2)11yescharacteristic
192C4×C79H(5,𝔽2)11yescharacteristic
193Dic79—21no—
194Dic79—21no—
195Dic79—41no—
196Dic79—41no—
197Dic79—41no—
198C2×C79—22no—
199C2×C79—81no—
200C2×C79—81no—
201C2×C79#53411yescharacteristic
202C2×C79C2×#13511yescharacteristic
203C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
204D79—22no—
205D79—41no—
206D79—81no—
207#3188—791nomaximal, Sylow
208C79#318811yescharacteristic, complemented, Sylow
209#525—791no—
210C2×#121—791no—
211#484—791no—
212#482—791no—
213#482—791no—
214#481—791no—
215#466—791no—
216#466D7911yescharacteristic, complemented
217#465—791no—
218#465—791no—
219#450—791no—
220#449—791no—
221#449—791no—
222#447—791no—
223C2×C22⋊C8—791no—
224C2×#41—791no—
225C22×D4—791no—
226C22×D4—1581no—
227C23×C4—791no—
228C2×SD16—791no—
229C2×SD16—791no—
230C2×D8—791no—
231C2×D8C2×D7911yescharacteristic, complemented
232C22×C8—791no—
233C22×C8C2×D7911yescharacteristic, complemented
234#123—1581no—
235C22⋊Q8—791no—
236C22⋊Q8—791no—
237#121—791no—
238#121—791no—
239#121—791no—
240#121—791no—
241#121—1581no—
242#121—1581no—
243#121C2×D7911yescharacteristic
244#121C2×D7911yescharacteristic, complemented
245#120—1581no—
246C4×D4—1581no—
247C4×D4—1581no—
248#117—791no—
249C2×C4⋊C4—791no—
250C2×C22⋊C4—1581no—
251#107—791no—
252#107C2×D7911yescharacteristic, complemented
253#106—791no—
254#106—791no—
255#103—791no—
256#103—791no—
257#102—791no—
258#102—791no—
259#102—791no—
260#102—791no—
261#102C2×D7911yescharacteristic, complemented
262#102C2×D7911yescharacteristic, complemented
263C22⋊C8—791no—
264C22⋊C8—791no—
265C22⋊C8—791no—
266C22⋊C8—791no—
267C24—791no—
268C24—1581no—
269#41—3161no—
270#41—3161no—
271C2×Q8—791no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—3164no—
275C2×D4—3161no—
276C2×D4—3161no—
277C2×D4—791no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4—1581no—
282C2×D4—1581no—
283C2×D4—1581no—
284C2×D4C22×D7911yescharacteristic
285C2×D4C22×D7911yescharacteristic
286C22×C4—3161no—
287C22×C4—3161no—
288C22×C4—791no—
289C22×C4—791no—
290C22×C4—791no—
291C22×C4—791no—
292C22×C4—791no—
293C22×C4—1581no—
294C22×C4—1581no—
295C22×C4C22×D7911yescharacteristic
296SD16—3161no—
297SD16—3161no—
298D8—41no—
299D8—3161no—
300C2×C8—41no—
301C2×C8—3161no—
302C2×C8—791no—
303C2×C8—791no—
304C2×C8C22×D7911yescharacteristic
305C2×C8C22×D7911yescharacteristic
306C4⋊C4—791no—
307C4⋊C4—791no—
308C4⋊C4—1581no—
309C4⋊C4—1581no—
310C4⋊C4—1581no—
311C4⋊C4C22×D7911yescharacteristic
312C4⋊C4C22×D7911yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C22⋊C4—1581no—
318C22⋊C4—1581no—
319C22⋊C4—1581no—
320C22⋊C4—1581no—
321C22⋊C4—1581no—
322C42—1581no—
323C23—21no—
324C23—21no—
325C23—3161no—
326C23—3162no—
327C23—3162no—
328C23—3162no—
329C23—791no—
330C23—791no—
331C23—1582no—
332C23—1581no—
333C23—1582no—
334C23D4×D7911yescharacteristic
335Q8—1581no—
336Q8—1581no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—3162no—
344D4—3162no—
345D4—3162no—
346D4—3162no—
347D4—3162no—
348D4—3162no—
349D4—1581no—
350D4—1581no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3161no—
356C2×C4—3161no—
357C2×C4—3162no—
358C2×C4—3162no—
359C2×C4—3161no—
360C2×C4—791no—
361C2×C4—791no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4—1581no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4—1581no—
368C2×C4—1581no—
369C2×C4D4×D7911yescharacteristic
370C2×C4C23×D7911yescharacteristic
371C8—21no—
372C8—21no—
373C8—1581no—
374C8—1581no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—3164no—
384C22—3161no—
385C22—3161no—
386C22—3161no—
387C22—792no—
388C22—6324no—
389C22—1581no—
390C22—1581no—
391C22—1581no—
392C22—1581no—
393C22—1581no—
394C22#1457918512yes—
395C22C2×D4×D7911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—3161no—
400C4—3161no—
401C4—3161no—
402C4—1581no—
403C4—1581no—
404C4#1457920611yescharacteristic
405C4#1457920711yescharacteristic
406C2—22no—
407C2—81no—
408C2—81no—
409C2—3161no—
410C2—6321no—
411C2—1582no—
412C2#1909912111yescharacteristic
413C2#135×D7911yescharacteristic
414C2C2×#1457918511yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#466×C79C2
socleC22×C79C22×D4
hypercenter#466D79
hypocenterC79#3188
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #19099073C2semidirect
2. #121×D79C2semidirect
3. #19098900C2semidirect
4. #19098890C2semidirect
5. #19098886C2semidirect
6. #19098880C2semidirect
7. #19098797C2semidirect
8. #19098792C2semidirect
9. #19098790C2semidirect
10. #19098715C2semidirect
11. #19098709C2semidirect
12. #19098705C2semidirect
13. #19098695C2semidirect
14. C2×(C2×D79)⋊C8C2semidirect
15. #466×C79C2semidirect
16. C2×#11929623C22semidirect
20. C2×#11929613C22semidirect
21. C2×#11929612C22semidirect
22. C2×#11929609C22semidirect
23. C22×C79⋊C8C22semidirect
26. #14579140C22semidirect
36. #14579119C22semidirect
39. #14579094C22semidirect
40. #14579093C22semidirect
41. #14579092C22semidirect
42. #14579086C22semidirect
43. #14579084C22semidirect
44. #14579083C22semidirect
45. #14579082C22semidirect
46. #14579082C22semidirect
47. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. (C2×D79)⋊C8C22semidirect
52. C2×D8×C79C22semidirect
53. C22×C8×C79C22semidirect
55. #121×C79C22semidirect
56. #107×C79C22semidirect
57. #102×C79C22semidirect
58. #102×C79C22semidirect
208. C79#3188semidirect
216. #466D79semidirect
231. C2×D8C2×D79semidirect
233. C22×C8C2×D79semidirect
244. #121C2×D79semidirect
252. #107C2×D79semidirect
261. #102C2×D79semidirect
262. #102C2×D79semidirect