Finite Group Databasebeta

← #541×D79 #23776762

Subgroups — #541×D79 #23776762

Order 10112.

1004 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099176C211yesmaximal, characteristic, complemented
2#19099175C211yesmaximal, characteristic, complemented
3#19099174C211yesmaximal, characteristic, complemented
4#19099173C212yesmaximal, complemented
5#19099172C214yesmaximal, complemented
6#19099171C212yesmaximal, complemented
7#19099170C214yesmaximal, complemented
8C4⋊Q8×D79C211yesmaximal, characteristic, complemented
9#126×D79C214yesmaximal
10#125×D79C214yesmaximal, complemented
11#125×D79C211yesmaximal, characteristic, complemented
12C22⋊Q8×D79C212yesmaximal
13C4×Q8×D79C212yesmaximal, complemented
14#117×D79C211yesmaximal, characteristic
15#541×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2212yes—
17C22×C4×D79C2211yescharacteristic
18#14579161C2211yescharacteristic, complemented
19#14579160C2214yescomplemented
20#14579159C2212yescomplemented
21#14579156C2214yes—
22#14579156C2214yes—
23#14579156C2214yes—
24#14579155C2214yes—
25#14579154C2214yes—
26#14579154C2214yes—
27#14579154C2214yes—
28#14579153C2214yescomplemented
29#14579153C2211yescharacteristic, complemented
30#14579152C2214yescomplemented
31#14579152C2212yescomplemented
32#14579152C2214yescomplemented
33#14579151C2214yescomplemented
34#14579151C2214yescomplemented
35#14579151C2214yescomplemented
36#14579151C2214yescomplemented
37#14579151C2214yescomplemented
38#14579141C2212yes—
39#14579140C2212yes—
40#14579139C2214yes—
41#14579138C2214yes—
42#14579137C2212yes—
43Q8×Dic79C2212yescomplemented
44C4×Dic158C2214yescomplemented
45C4×Dic158C2212yescomplemented
46#14579126C2214yescomplemented
47#14579126C2212yescomplemented
48#14579120C2211yescharacteristic
49#14579119C2212yes—
50#14579118C2211yescharacteristic
51#14579118C2211yescharacteristic
52#14579117C2212yes—
53C4⋊C4×D79C2212yes—
54C4⋊C4×D79C2212yes—
55C4⋊C4×D79C2214yes—
56C4⋊C4×D79C2214yes—
57C4⋊C4×D79C2214yes—
58C4⋊C4×D79C2214yes—
59C22⋊C4×D79C2212yes—
60C22⋊C4×D79C2214yes—
61C42×D79C2211yescharacteristic
62C42×D79C2211yescharacteristic
63C42×D79C2214yes—
64C4⋊Q8×C79C2211yescharacteristic, complemented
65#126×C79C2214yes—
66#125×C79C2214yescomplemented
67#125×C79C2211yescharacteristic, complemented
68C22⋊Q8×C79C2212yes—
69C4×Q8×C79C2212yescomplemented
70#117×C79C2211yescharacteristic
71C23×D79C2311yescharacteristic
72C2×Dic158C2314yes—
73C2×Dic158C2312yes—
74Q8×D79—28no—
75C22×Dic79C2311yescharacteristic
76C2×C4×D79—24no—
77C2×C4×D79C2314yes—
78C2×C4×D79C2312yes—
79C2×C4×D79C2312yes—
80C2×C4×D79C2314yes—
81C2×C4×D79C2311yescharacteristic
82C2×C4×D79C2311yescharacteristic
83C2×C4×D79C2311yescharacteristic
84C2×C4×D79C2311yescharacteristic
85C4⋊Dic79C2312yes—
86C4⋊Dic79C2312yes—
87C4⋊Dic79C2314yes—
88C4⋊Dic79C2314yes—
89C4⋊Dic79C2314yes—
90C4⋊Dic79C2314yes—
91Dic79⋊C4C2312yes—
92Dic79⋊C4C2312yes—
93Dic79⋊C4C2314yes—
94Dic79⋊C4C2314yes—
95Dic79⋊C4C2314yes—
96Dic79⋊C4C2314yes—
97Dic79⋊C4C2314yes—
98Dic79⋊C4C2314yes—
99Dic79⋊C4C2314yes—
100Dic79⋊C4C2314yes—
101Dic79⋊C4C2314yes—
102C22⋊Dic79C2312yes—
103C22⋊Dic79C2314yes—
104(C2×D79)⋊C4C2312yes—
105(C2×D79)⋊C4C2312yes—
106(C2×D79)⋊C4C2314yes—
107(C2×D79)⋊C4C2314yes—
108C4×Dic79C2312yes—
109C4×Dic79C2312yes—
110C4×Dic79C2311yescharacteristic
111C4×Dic79C2311yescharacteristic
112C4×Dic79C2314yes—
113C4×Dic79C2314yes—
114C4×Dic79C2314yes—
115C2×Q8×C79C2312yes—
116C22×C4×C79C2311yescharacteristic
117C4⋊C4×C79C2312yes—
118C4⋊C4×C79C2312yes—
119C4⋊C4×C79C2314yes—
120C4⋊C4×C79C2314yes—
121C4⋊C4×C79C2314yes—
122C4⋊C4×C79C2314yes—
123C22⋊C4×C79C2312yes—
124C22⋊C4×C79C2314yes—
125C42×C79C2311yescharacteristic
126C42×C79C2311yescharacteristic
127C42×C79C2314yes—
128C23×C79C2411yescharacteristic
129C22×D79—22no—
130C22×D79—24no—
131C22×D79C2411yescharacteristic
132C22×D79C2411yescharacteristic
133Q8×C79—24no—
134C2×C4×C79—22no—
135C2×C4×C79C2412yes—
136C2×C4×C79C2412yes—
137C2×C4×C79C2414yes—
138C2×C4×C79C2414yes—
139C2×C4×C79C2411yescharacteristic
140C2×C4×C79C2411yescharacteristic
141C2×Dic79—22no—
142C2×Dic79C2412yes—
143C2×Dic79C2412yes—
144C2×Dic79C2414yes—
145C2×Dic79C2414yes—
146C2×Dic79C2411yescharacteristic
147C2×Dic79C2411yescharacteristic
148C4×D79—22no—
149C4×D79—28no—
150C4×D79—24no—
151C4×D79—24no—
152C4×D79—28no—
153C4×D79—22no—
154C4×D79—22no—
155C4×D79#4114yes—
156Dic158—24no—
157Dic158—28no—
158C22×C79—21no—
159C22×C79—22no—
160C22×C79C2511yescharacteristic
161C2×D79—21no—
162C2×D79—22no—
163C2×D79—44no—
164C2×D79C2×#4112yes—
165C2×D792−1+414yes—
166C4×C79—21no—
167C4×C79—24no—
168C4×C79—22no—
169C4×C79—22no—
170C4×C79—24no—
171C4×C79C2×#4112yes—
172Dic79—24no—
173Dic79—21no—
174Dic79—22no—
175Dic79—22no—
176Dic79—24no—
177Dic79C2×#4112yes—
178C2×C79—41no—
179C2×C79C22×#4111yescharacteristic
180C2×C79C2×2−1+412yes—
181D79—41no—
182D79#54114yesdirect product factor
183C2×#541—791nomaximal, Sylow
184C79C2×#54111yescharacteristic, complemented, Sylow
185#541—791no—
186#541—794no—
187#541—794no—
188#541—791no—
189#541—792no—
190#541—792no—
191#541—791no—
192#541D7911yescharacteristic, direct product factor
193C2×C4⋊Q8—791no—
194C2×#126—794no—
195C2×#125—791no—
196C2×#125—794no—
197C2×C22⋊Q8—792no—
198C2×C4×Q8—792no—
199C2×#117—791no—
200C22×Q8—792no—
201C23×C4—791no—
202C4⋊Q8—792no—
203C4⋊Q8—794no—
204C4⋊Q8—791no—
205C4⋊Q8C2×D7911yescharacteristic, complemented
206#126—794no—
207#126—794no—
208#126—794no—
209#126—794no—
210#126—794no—
211#126—794no—
212#126—794no—
213#126C2×D7914yes—
214#125—794no—
215#125—794no—
216#125—794no—
217#125—794no—
218#125—794no—
219#125—792no—
220#125—794no—
221#125—794no—
222#125—791no—
223#125—794no—
224#125C2×D7911yescharacteristic, complemented
225#125C2×D7914yescomplemented
226C22⋊Q8—792no—
227C22⋊Q8—792no—
228C22⋊Q8—794no—
229C22⋊Q8—792no—
230C22⋊Q8—794no—
231C22⋊Q8C2×D7912yes—
232C4×Q8—792no—
233C4×Q8—794no—
234C4×Q8—792no—
235C4×Q8—794no—
236C4×Q8—792no—
237C4×Q8C2×D7912yescomplemented
238#117—791no—
239#117—792no—
240#117—792no—
241#117—791no—
242#117—791no—
243#117C2×D7911yescharacteristic
244C2×C4⋊C4—792no—
245C2×C4⋊C4—792no—
246C2×C4⋊C4—794no—
247C2×C4⋊C4—794no—
248C2×C4⋊C4—794no—
249C2×C4⋊C4—794no—
250C2×C22⋊C4—792no—
251C2×C22⋊C4—794no—
252C2×C42—791no—
253C2×C42—791no—
254C2×C42—794no—
255C24—791no—
256C2×Q8—794no—
257C2×Q8—792no—
258C2×Q8—1588no—
259C2×Q8C22×D7912yes—
260C22×C4—791no—
261C22×C4—791no—
262C22×C4—792no—
263C22×C4—792no—
264C22×C4—794no—
265C22×C4—794no—
266C22×C4—791no—
267C22×C4—791no—
268C22×C4—791no—
269C22×C4—1584no—
270C22×C4C22×D7911yescharacteristic
271C4⋊C4—792no—
272C4⋊C4—792no—
273C4⋊C4—794no—
274C4⋊C4—794no—
275C4⋊C4—794no—
276C4⋊C4—794no—
277C4⋊C4—794no—
278C4⋊C4—794no—
279C4⋊C4—794no—
280C4⋊C4—794no—
281C4⋊C4—794no—
282C4⋊C4—792no—
283C4⋊C4—792no—
284C4⋊C4—794no—
285C4⋊C4—794no—
286C4⋊C4—794no—
287C4⋊C4—794no—
288C4⋊C4C22×D7912yes—
289C4⋊C4C22×D7912yes—
290C4⋊C4C22×D7914yes—
291C4⋊C4C22×D7914yes—
292C4⋊C4C22×D7914yes—
293C4⋊C4C22×D7914yes—
294C22⋊C4—792no—
295C22⋊C4—794no—
296C22⋊C4—792no—
297C22⋊C4—792no—
298C22⋊C4—794no—
299C22⋊C4—794no—
300C22⋊C4C22×D7912yes—
301C22⋊C4C22×D7914yes—
302C42—792no—
303C42—791no—
304C42—792no—
305C42—791no—
306C42—794no—
307C42—794no—
308C42—794no—
309C42C22×D7911yescharacteristic
310C42C22×D7911yescharacteristic
311C42C22×D7914yes—
312C23—791no—
313C23—791no—
314C23—1582no—
315C23—1584no—
316C23C23×D7911yescharacteristic
317Q8—24no—
318Q8—1588no—
319Q8—1584no—
320C2×C4—22no—
321C2×C4—791no—
322C2×C4—794no—
323C2×C4—792no—
324C2×C4—792no—
325C2×C4—794no—
326C2×C4—794no—
327C2×C4—791no—
328C2×C4—1582no—
329C2×C4—1582no—
330C2×C4—1588no—
331C2×C4—1584no—
332C2×C4—1584no—
333C2×C4—1588no—
334C2×C4—1582no—
335C2×C4—1582no—
336C2×C4C23×D7912yes—
337C2×C4C23×D7912yes—
338C2×C4C23×D7914yes—
339C2×C4C23×D7914yes—
340C2×C4C23×D7911yescharacteristic
341C2×C4C23×D7911yescharacteristic
342C22—22no—
343C22—21no—
344C22—3164no—
345C22—794no—
346C22—792no—
347C22—1582no—
348C22—1581no—
349C22C24×D7911yescharacteristic
350C4—22no—
351C4—22no—
352C4—24no—
353C4—21no—
354C4—24no—
355C4—792no—
356C4—1582no—
357C4—1582no—
358C4—1584no—
359C4—1581no—
360C4—1584no—
361C4#41×D7912yes—
362C2—41no—
363C2—3161no—
364C2—794no—
365C2C2×#41×D7911yescharacteristic
366C22−1+4×D7912yes—
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
Fitting#541×C79C2
prime radicalC23×D79C23
hypercenter#541D79
hypocenterC79C2×#541
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #541

Complements

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

NH ≅ G/Ntype
1. #19099176C2semidirect
2. #19099175C2semidirect
3. #19099174C2semidirect
4. #19099173C2semidirect
5. #19099172C2semidirect
6. #19099171C2semidirect
7. #19099170C2semidirect
8. C4⋊Q8×D79C2semidirect
10. #125×D79C2semidirect
11. #125×D79C2semidirect
13. C4×Q8×D79C2semidirect
15. #541×C79C2semidirect
18. #14579161C22semidirect
19. #14579160C22semidirect
20. #14579159C22semidirect
28. #14579153C22semidirect
29. #14579153C22semidirect
30. #14579152C22semidirect
31. #14579152C22semidirect
32. #14579152C22semidirect
33. #14579151C22semidirect
34. #14579151C22semidirect
35. #14579151C22semidirect
36. #14579151C22semidirect
37. #14579151C22semidirect
43. Q8×Dic79C22semidirect
44. C4×Dic158C22semidirect
45. C4×Dic158C22semidirect
46. #14579126C22semidirect
47. #14579126C22semidirect
64. C4⋊Q8×C79C22semidirect
66. #125×C79C22semidirect
67. #125×C79C22semidirect
69. C4×Q8×C79C22semidirect
182. D79#541direct (N × H)
184. C79C2×#541semidirect
192. #541D79direct (N × H)
205. C4⋊Q8C2×D79semidirect
224. #125C2×D79semidirect
225. #125C2×D79semidirect
237. C4×Q8C2×D79semidirect