Finite Group Databasebeta

← #23775220

Subgroups — #23775220

Order 10112.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099268C211yesmaximal, characteristic, complemented
2D4×C22⋊D79C211yesmaximal, characteristic
3#19098908C211yesmaximal, characteristic, complemented
4#19098881C211yesmaximal, characteristic, complemented
5#19098880C211yesmaximal, characteristic, complemented
6#19098851C211yesmaximal, characteristic, complemented
7#19098792C211yesmaximal, characteristic, complemented
8#19098791C211yesmaximal, characteristic, complemented
9#19098762C211yesmaximal, characteristic, complemented
10#19098715C211yesmaximal, characteristic, complemented
11#19098714C211yesmaximal, characteristic, complemented
12#19098654C211yesmaximal, characteristic, complemented
13C8×C22⋊D79C211yesmaximal, characteristic, complemented
14#102×D79C211yesmaximal, characteristic, complemented
15C2×#102×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79—21no—
17C2×D4×D79C2211yescharacteristic
18C2×#11929613C2211yescharacteristic, complemented
19C2×#11929612C2211yescharacteristic
20C2×#11929612C2211yescharacteristic, complemented
21C2×C8×D79C2211yescharacteristic, complemented
22#14579160C2211yescharacteristic, complemented
23#14579157C2211yescharacteristic
24#14579151—21no—
25#14579141C2211yescharacteristic, complemented
26#14579140—21no—
27#14579140C2211yescharacteristic, complemented
28#14579139—21no—
29#14579135C2211yescharacteristic
30#14579133—21no—
31#14579132C2211yescharacteristic
32#14579130—21no—
33#14579129—21no—
34#14579126C2211yescharacteristic, complemented
35D4×Dic79C2211yescharacteristic
36C4×C22⋊D79—21no—
37C4×C22⋊D79C2211yescharacteristic
38C4⋊C4×D79C2211yescharacteristic, complemented
39#14579093C2211yescharacteristic, complemented
40#14579092C2211yescharacteristic, complemented
41#14579092C2211yescharacteristic, complemented
42Dic79⋊C8C2211yescharacteristic, complemented
43#14579086C2211yescharacteristic, complemented
44#14579083C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic, complemented
47#14579081C2211yescharacteristic, complemented
48#14579081C2211yescharacteristic, complemented
49C22⋊(C79⋊C8)C2211yescharacteristic, complemented
50(C2×D79)⋊C8C2211yescharacteristic, complemented
51C8×Dic79C2211yescharacteristic, complemented
52C22×D4×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic, complemented
54C2×C4⋊C4×C79C2211yescharacteristic, complemented
55#102×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—44no—
69C2×C22⋊D79D411yescharacteristic
70D4×D79—22no—
71D4×D79—41no—
72C22×Dic79—21no—
73C2×C4×D79—21no—
74C2×C4×D79C2311yescharacteristic
75#11929613—41no—
76#11929612—22no—
77#11929612—41no—
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C8×D79—41no—
81C4⋊Dic79—21no—
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4D411yescharacteristic
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79D411yescharacteristic
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4D411yescharacteristic
96C4×Dic79—21no—
97C4×Dic79C2311yescharacteristic
98C24×C79—21no—
99C2×D4×C79—22no—
100C2×D4×C79—21no—
101C2×D4×C79—41no—
102C2×D4×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79—21no—
105C22×C4×C79C2311yescharacteristic
106C2×C8×C79—41no—
107C2×C8×C79C2311yescharacteristic
108C2×C8×C79C2311yescharacteristic
109C4⋊C4×C79—21no—
110C4⋊C4×C79C2311yescharacteristic
111C4⋊C4×C79C2311yescharacteristic
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—42no—
115C23×C79—42no—
116C23×C79—81no—
117C23×C79C2×D411yescharacteristic
118C22×D79—21no—
119C22×D79—42no—
120C22×D79—42no—
121C22×D79—81no—
122C22×D79C2×D411yescharacteristic
123D4×C79—21no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—42no—
127D4×C79#4112yes—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—81no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2411yescharacteristic
135C22⋊D79—42no—
136C22⋊D79—42no—
137C22⋊D79—42no—
138C22⋊D79—42no—
139C22⋊D79—81no—
140C22⋊D79SD1614yescomplemented
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—42no—
145C2×Dic79C2×D411yescharacteristic
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148D316—21no—
149D316—21no—
150C4×D79—21no—
151C4×D79—21no—
152C4×D79—81no—
153Dic158—21no—
154Dic158—21no—
155Dic158—81no—
156C8×C79—21no—
157C8×C79—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—22no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—84no—
169C22×C79C2×SD1612yes—
170C22×C79C22×D411yescharacteristic
171C2×D79—21no—
172C2×D79—21no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—84no—
177C2×D79C2×SD1612yes—
178C4×C79—21no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79C2×#4111yescharacteristic
182C4×C79H(5,𝔽2)11yescharacteristic
183Dic79—21no—
184Dic79—21no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188Dic79C2×SD1612yes—
189C2×C79—22no—
190C2×C79—42no—
191C2×C79—81no—
192C2×C79#54611yescharacteristic
193C2×C79C22×SD1611yescharacteristic
194C2×C79#57611yescharacteristic
195D79—22no—
196D79—81no—
197#3295—791nomaximal, Sylow
198C79#329511yescharacteristic, complemented, Sylow
199#554—791no—
200D42—791no—
201#486—791no—
202#481—791no—
203#481—791no—
204#476—791no—
205#465—791no—
206#465—791no—
207#460—791no—
208#450—791no—
209#450—791no—
210C4×SD16—791no—
211C8×D4—791no—
212C2×#102—791no—
213C2×#102D7911yescharacteristic, complemented
214C22×D4—791no—
215C22×D4—1581no—
216C22×D4C2×D7911yescharacteristic
217C2×SD16—791no—
218C2×SD16—791no—
219C2×SD16—791no—
220C22×C8—791no—
221C22×C8C2×D7911yescharacteristic, complemented
222C4⋊Q8—791no—
223#127—791no—
224#125—1581no—
225C22⋊Q8—791no—
226C22⋊Q8—791no—
227C22⋊Q8—1581no—
228C22⋊Q8—1581no—
229#121—791no—
230#121—791no—
231#121—1581no—
232#120—1581no—
233#120—1581no—
234C4×Q8—791no—
235C4×D4—791no—
236C4×D4—791no—
237C4×D4—1581no—
238C2×C4⋊C4—791no—
239C2×C4⋊C4C2×D7911yescharacteristic, complemented
240#106—791no—
241#106—791no—
242#106—791no—
243C4⋊C8—791no—
244#103—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102C2×D7911yescharacteristic
251#102C2×D7911yescharacteristic
252#102C2×D7911yescharacteristic, complemented
253#102C2×D7911yescharacteristic, complemented
254C22⋊C8—791no—
255C22⋊C8—791no—
256C4×C8—791no—
257C24—21no—
258C24—1581no—
259C2×Q8—791no—
260C2×Q8—1581no—
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—3164no—
265C2×D4—3161no—
266C2×D4—791no—
267C2×D4—791no—
268C2×D4—1581no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4—1581no—
273C2×D4—1582no—
274C2×D4C22×D7911yescharacteristic
275C2×D4C22×D7911yescharacteristic
276C22×C4—21no—
277C22×C4—791no—
278C22×C4—1581no—
279C22×C4—1581no—
280C22×C4C22×D7911yescharacteristic
281SD16—3161no—
282SD16—3161no—
283SD16—1582no—
284C2×C8—41no—
285C2×C8—3161no—
286C2×C8—791no—
287C2×C8—791no—
288C2×C8C22×D7911yescharacteristic
289C2×C8C22×D7911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—791no—
292C4⋊C4—791no—
293C4⋊C4—791no—
294C4⋊C4—1581no—
295C4⋊C4—1581no—
296C4⋊C4—1581no—
297C4⋊C4—1581no—
298C4⋊C4—1581no—
299C4⋊C4C22×D7911yescharacteristic
300C4⋊C4C22×D7911yescharacteristic
301C22⋊C4—791no—
302C22⋊C4—791no—
303C22⋊C4—1581no—
304C22⋊C4—1581no—
305C22⋊C4—1581no—
306C22⋊C4—1581no—
307C22⋊C4—1581no—
308C42—791no—
309C42—1581no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—3162no—
316C23—3162no—
317C23—791no—
318C23—6321no—
319C23—1581no—
320C23D4×D7911yescharacteristic
321Q8—6321no—
322Q8—1581no—
323Q8—1581no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—3162no—
329D4—3162no—
330D4—3162no—
331D4—3162no—
332D4—794no—
333D4—6321no—
334D4—1581no—
335D4—1581no—
336D4#1192962412yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—3162no—
343C2×C4—791no—
344C2×C4—791no—
345C2×C4—791no—
346C2×C4—6321no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4D4×D7911yescharacteristic
353C2×C4C23×D7911yescharacteristic
354C8—21no—
355C8—21no—
356C8—1581no—
357C8—1581no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—3161no—
368C22—3161no—
369C22—3161no—
370C22—792no—
371C22—6324no—
372C22—1581no—
373C22—1581no—
374C22SD16×D7912yes—
375C22C2×D4×D7911yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—3161no—
380C4—3161no—
381C4—3161no—
382C4—792no—
383C4—1581no—
384C4—1581no—
385C4C2×#1192962411yescharacteristic
386C4#1457920611yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—6321no—
391C2—1582no—
392C2#1909920311yescharacteristic
393C2C2×SD16×D7911yescharacteristic
394C2#1909936411yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#102×C79C2
socleC22×C79C22×D4
prime radicalD4×C22⋊D79C2
hypercenterC2×#102D79
hypocenterC79#3295
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #19099268C2semidirect
3. #19098908C2semidirect
4. #19098881C2semidirect
5. #19098880C2semidirect
6. #19098851C2semidirect
7. #19098792C2semidirect
8. #19098791C2semidirect
9. #19098762C2semidirect
10. #19098715C2semidirect
11. #19098714C2semidirect
12. #19098654C2semidirect
13. C8×C22⋊D79C2semidirect
14. #102×D79C2semidirect
15. C2×#102×C79C2semidirect
18. C2×#11929613C22semidirect
20. C2×#11929612C22semidirect
21. C2×C8×D79C22semidirect
22. #14579160C22semidirect
25. #14579141C22semidirect
27. #14579140C22semidirect
34. #14579126C22semidirect
38. C4⋊C4×D79C22semidirect
39. #14579093C22semidirect
40. #14579092C22semidirect
41. #14579092C22semidirect
42. Dic79⋊C8C22semidirect
43. #14579086C22semidirect
44. #14579083C22semidirect
46. #14579082C22semidirect
47. #14579081C22semidirect
48. #14579081C22semidirect
49. C22⋊(C79⋊C8)C22semidirect
50. (C2×D79)⋊C8C22semidirect
51. C8×Dic79C22semidirect
53. C22×C8×C79C22semidirect
54. C2×C4⋊C4×C79C22semidirect
57. #102×C79C22semidirect
58. #102×C79C22semidirect
140. C22⋊D79SD16semidirect
198. C79#3295semidirect
213. C2×#102D79semidirect
221. C22×C8C2×D79semidirect
239. C2×C4⋊C4C2×D79semidirect
252. #102C2×D79semidirect
253. #102C2×D79semidirect