Finite Group Databasebeta

← #23774166

Subgroups — #23774166

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#19099076C211yesmaximal, characteristic, complemented
2#121×D79C211yesmaximal, characteristic, complemented
3#19098897C211yesmaximal, characteristic, complemented
4#19098889C211yesmaximal, characteristic, complemented
5#19098885C211yesmaximal, characteristic, complemented
6#19098883C211yesmaximal, characteristic, complemented
7#19098799C211yesmaximal, characteristic, complemented
8#19098797C211yesmaximal, characteristic, complemented
9#19098794C211yesmaximal, characteristic, complemented
10#19098712C211yesmaximal, characteristic, complemented
11#19098711C211yesmaximal, characteristic, complemented
12#19098707C211yesmaximal, characteristic, complemented
13#19098698C211yesmaximal, characteristic, complemented
14C2×(C2×D79)⋊C8C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic, complemented
17C2×D4×D79—21no—
18C2×D4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C2×#11929611C2211yescharacteristic, complemented
21C2×D632C2211yescharacteristic, complemented
22C2×#11929609C2211yescharacteristic, complemented
23C22×C79⋊C8C2211yescharacteristic, complemented
24#14579146—21no—
25#14579137C2211yescharacteristic
26#14579136C2211yescharacteristic
27#14579136C2211yescharacteristic
28#14579135C2211yescharacteristic
29#14579135C2211yescharacteristic, complemented
30#14579134—21no—
31#14579133—21no—
32#14579132C2211yescharacteristic
33#14579131—21no—
34#14579123—21no—
35(C22⋊D79)⋊C4—21no—
36#14579119C2211yescharacteristic, complemented
37C4⋊C4×D79C2211yescharacteristic
38C22⋊C4×D79—21no—
39#14579095C2211yescharacteristic, complemented
40#14579094C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579083C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic, complemented
46#14579081C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51(C2×D79)⋊C8C2211yescharacteristic, complemented
52C2×SD16×C79C2211yescharacteristic, complemented
53C22×C8×C79C2211yescharacteristic, complemented
54C22⋊Q8×C79C2211yescharacteristic, complemented
55#121×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C23×D79D411yescharacteristic
61#11929625—41no—
62#11929625—41no—
63C2×D316—21no—
64C2×D316—21no—
65C2×D316—21no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72D4×D79—41no—
73D4×D79—41no—
74D4×D79—44no—
75C22×Dic79D411yescharacteristic
76C2×C4×D79—21no—
77C2×C4×D79—21no—
78C2×C4×D79—41no—
79C2×C4×D79—41no—
80C2×C4×D79D411yescharacteristic
81C2×C4×D79D411yescharacteristic
82C2×C4×D79C2311yescharacteristic
83C2×C4×D79C2311yescharacteristic
84#11929611—41no—
85D632—41no—
86#11929609—41no—
87C2×C79⋊C8—41no—
88C2×C79⋊C8C2311yescharacteristic
89C2×C79⋊C8C2311yescharacteristic
90C4⋊Dic79C2311yescharacteristic
91C4⋊Dic79C2311yescharacteristic
92Dic79⋊C4—21no—
93Dic79⋊C4—21no—
94C22⋊Dic79—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—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×Q8×C79C2311yescharacteristic
103C2×D4×C79—21no—
104C2×D4×C79C2311yescharacteristic
105C22×C4×C79C2311yescharacteristic
106SD16×C79—41no—
107C2×C8×C79—41no—
108C2×C8×C79C2311yescharacteristic
109C2×C8×C79C2311yescharacteristic
110C4⋊C4×C79—21no—
111C4⋊C4×C79C2311yescharacteristic
112C4⋊C4×C79C2311yescharacteristic
113C22⋊C4×C79—21no—
114C22⋊C4×C79—21no—
115C23×C79—21no—
116C23×C79C2×D411yescharacteristic
117C22×D79—22no—
118C22×D79—22no—
119C22×D79—21no—
120C22×D79—21no—
121C22×D79—41no—
122C22×D79—42no—
123C22×D79—42no—
124C22×D79—42no—
125C22×D79C2×D411yescharacteristic
126C22×D79C2×D411yescharacteristic
127Q8×C79—21no—
128Q8×C79—21no—
129D4×C79—21no—
130D4×C79—21no—
131D4×C79—42no—
132C2×C4×C79—21no—
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—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—41no—
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148D316—21no—
149D316—21no—
150D316—21no—
151D316—21no—
152D316—42no—
153D316—42no—
154D316—42no—
155C4×D79—21no—
156C4×D79—21no—
157C4×D79—21no—
158C4×D79—21no—
159C4×D79—41no—
160C4×D79—41no—
161C4×D79—42no—
162C4×D79—42no—
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×C79AGL(1,ℤ/8)12yes—
173C22×C79C22×D411yescharacteristic
174C2×D79—21no—
175C2×D79—21no—
176C2×D79—21no—
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—44no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—41no—
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×C79—41no—
192C4×C79H(5,𝔽2)11yescharacteristic
193C4×C79H(5,𝔽2)11yescharacteristic
194Dic79—21no—
195Dic79—21no—
196Dic79—41no—
197Dic79—41no—
198C2×C79—22no—
199C2×C79—81no—
200C2×C79#53411yescharacteristic
201C2×C79C2×#13511yescharacteristic
202C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
203D79—22no—
204D79—41no—
205D79—81no—
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#466—791no—
217#465—791no—
218#465D7911yescharacteristic, complemented
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×SD16C2×D7911yescharacteristic, complemented
230C2×D8—791no—
231C2×D8—791no—
232C22×C8—791no—
233C22×C8C2×D7911yescharacteristic, complemented
234#123—1581no—
235C22⋊Q8—791no—
236C22⋊Q8C2×D7911yescharacteristic, complemented
237#121—791no—
238#121—791no—
239#121—791no—
240#121—791no—
241#121—791no—
242#121—1581no—
243#121—1581no—
244#121C2×D7911yescharacteristic
245#120—1581no—
246C4×D4—1581no—
247C4×D4—1581no—
248#117—791no—
249C2×C4⋊C4—791no—
250C2×C22⋊C4—1581no—
251#107—791no—
252#107—791no—
253#106—791no—
254#106C2×D7911yescharacteristic, complemented
255#103—791no—
256#103C2×D7911yescharacteristic, complemented
257#102—791no—
258#102—791no—
259#102—791no—
260#102—791no—
261#102—791no—
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×Q8C22×D7911yescharacteristic
272C2×D4—21no—
273C2×D4—3164no—
274C2×D4—3161no—
275C2×D4—3161no—
276C2×D4—791no—
277C2×D4—791no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4—1581no—
282C2×D4—1581no—
283C2×D4—1581no—
284C2×D4—1581no—
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—41no—
297SD16—3161no—
298D8—3161no—
299D8—3161no—
300C2×C8—41no—
301C2×C8—3161no—
302C2×C8—791no—
303C2×C8—791no—
304C2×C8C22×D7911yescharacteristic
305C2×C8C22×D7911yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—791no—
308C4⋊C4—791no—
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—3161no—
325C23—3162no—
326C23—3162no—
327C23—3162no—
328C23—791no—
329C23—791no—
330C23—1582no—
331C23—1581no—
332C23—1581no—
333C23—1582no—
334C23D4×D7911yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—3162no—
341D4—3162no—
342D4—3162no—
343D4—3162no—
344D4—3162no—
345D4—3162no—
346D4—3162no—
347D4—1581no—
348D4—1581no—
349D4—1581no—
350D4—1581no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—3161no—
357C2×C4—3161no—
358C2×C4—3162no—
359C2×C4—3162no—
360C2×C4—3161no—
361C2×C4—791no—
362C2×C4—791no—
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—3164no—
381C22—3161no—
382C22—3161no—
383C22—3161no—
384C22—3161no—
385C22—3161no—
386C22—3161no—
387C22—792no—
388C22—6324no—
389C22—1581no—
390C22—1581no—
391C22—1581no—
392C22—1581no—
393C22—1581no—
394C22#1457918812yes—
395C22C2×D4×D7911yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—3161no—
401C4—3161no—
402C4—1581no—
403C4—1581no—
404C4#1457920611yescharacteristic
405C4#1457920711yescharacteristic
406C2—22no—
407C2—81no—
408C2—3161no—
409C2—6321no—
410C2—6321no—
411C2—1582no—
412C2#1909912111yescharacteristic
413C2#135×D7911yescharacteristic
414C2C2×#1457918811yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
hypercenter#465D79
hypocenterC79#3188
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #19099076C2semidirect
2. #121×D79C2semidirect
3. #19098897C2semidirect
4. #19098889C2semidirect
5. #19098885C2semidirect
6. #19098883C2semidirect
7. #19098799C2semidirect
8. #19098797C2semidirect
9. #19098794C2semidirect
10. #19098712C2semidirect
11. #19098711C2semidirect
12. #19098707C2semidirect
13. #19098698C2semidirect
14. C2×(C2×D79)⋊C8C2semidirect
15. #465×C79C2semidirect
16. C2×#11929625C22semidirect
20. C2×#11929611C22semidirect
21. C2×D632C22semidirect
22. C2×#11929609C22semidirect
23. C22×C79⋊C8C22semidirect
29. #14579135C22semidirect
36. #14579119C22semidirect
39. #14579095C22semidirect
40. #14579094C22semidirect
41. #14579092C22semidirect
42. #14579085C22semidirect
43. #14579083C22semidirect
44. #14579083C22semidirect
45. #14579082C22semidirect
46. #14579081C22semidirect
47. #14579081C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. (C2×D79)⋊C8C22semidirect
52. C2×SD16×C79C22semidirect
53. C22×C8×C79C22semidirect
54. C22⋊Q8×C79C22semidirect
56. #106×C79C22semidirect
57. #103×C79C22semidirect
58. #102×C79C22semidirect
208. C79#3188semidirect
218. #465D79semidirect
229. C2×SD16C2×D79semidirect
233. C22×C8C2×D79semidirect
236. C22⋊Q8C2×D79semidirect
254. #106C2×D79semidirect
256. #103C2×D79semidirect
262. #102C2×D79semidirect