Finite Group Databasebeta

← #23775752

Subgroups — #23775752

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099271C211yesmaximal, characteristic, complemented
2#19099213C211yesmaximal, characteristic
3#19098960C211yesmaximal, characteristic, complemented
4#19098892C211yesmaximal, characteristic, complemented
5#19098891C211yesmaximal, characteristic, complemented
6#19098880C211yesmaximal, characteristic, complemented
7#19098879C211yesmaximal, characteristic, complemented
8#19098851C211yesmaximal, characteristic, complemented
9#19098846C211yesmaximal, characteristic, complemented
10#19098789C211yesmaximal, characteristic, complemented
11SD16×Dic79C211yesmaximal, characteristic, complemented
12C8×C22⋊D79C211yesmaximal, characteristic, complemented
13C2×#14579093C211yesmaximal, characteristic, complemented
14#106×D79C211yesmaximal, characteristic, complemented
15#465×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×C8×D79C2211yescharacteristic
18#14579160C2211yescharacteristic
19#14579160C2211yescharacteristic
20#14579151—21no—
21#14579143—21no—
22#14579142—21no—
23#14579141—21no—
24#14579138—21no—
25#14579138—21no—
26#14579137C2211yescharacteristic
27#14579132C2211yescharacteristic
28Q8×Dic79C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30C4×C22⋊D79C2211yescharacteristic
31(C22⋊D79)⋊C4—21no—
32C2×C4⋊Dic79C2211yescharacteristic
33C2×C4⋊Dic79C2211yescharacteristic
34C4⋊C4×D79C2211yescharacteristic
35C4⋊C4×D79C2211yescharacteristic
36#14579093C2211yescharacteristic
37#14579093C2211yescharacteristic
38#14579093C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41#14579092C2211yescharacteristic
42#14579092C2211yescharacteristic
43#14579092C2211yescharacteristic
44Dic79⋊C8C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×SD16×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—44no—
60C2×Dic158—21no—
61C2×Dic158—21no—
62C2×C22⋊D79—21no—
63C2×C22⋊D79D411yescharacteristic
64C22×Dic79—21no—
65C22×Dic79—21no—
66C22×Dic79—21no—
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C8×D79—22no—
73C4⋊Dic79—21no—
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4D411yescharacteristic
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79D411yescharacteristic
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4D411yescharacteristic
91C4×Dic79—21no—
92C4×Dic79C2311yescharacteristic
93C2×Q8×C79C2311yescharacteristic
94C2×D4×C79—21no—
95C2×D4×C79C2311yescharacteristic
96C22×C4×C79C2311yescharacteristic
97SD16×C79—22no—
98C2×C8×C79—22no—
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C4⋊C4×C79—21no—
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C23×C79—21no—
107C23×C79C2×D411yescharacteristic
108C22×D79C2×D411yescharacteristic
109Q8×C79—21no—
110Q8×C79—21no—
111D4×C79—21no—
112D4×C79—21no—
113D4×C79—42no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79C2411yescharacteristic
121C22⋊D79—42no—
122C22⋊D79SD1614yescomplemented
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—42no—
128C2×Dic79—42no—
129C2×Dic79—81no—
130C2×Dic79C2×D411yescharacteristic
131C2×Dic79C2×D411yescharacteristic
132C2×Dic79C2×D411yescharacteristic
133C4×D79—21no—
134C4×D79—21no—
135C4×D79—42no—
136C4×D79—81no—
137Dic158—42no—
138Dic158—81no—
139C8×C79—21no—
140C8×C79#4112yescomplemented
141C79⋊C8—21no—
142C79⋊C8—21no—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79—41no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79C2×SD1612yes—
149C22×C79C22×D411yescharacteristic
150C2×D79—21no—
151C2×D79—21no—
152C2×D79C2×SD1612yes—
153C4×C79—21no—
154C4×C79—41no—
155C4×C79—41no—
156C4×C79—41no—
157C4×C79C2×#4111yescharacteristic
158C4×C792−1+411yescharacteristic
159Dic79—21no—
160Dic79—21no—
161Dic79—41no—
162Dic79—41no—
163Dic79—41no—
164Dic79—41no—
165Dic79C2×SD1612yes—
166C2×C79—22no—
167C2×C79—81no—
168C2×C79#54711yescharacteristic
169C2×C79C22×SD1611yescharacteristic
170C2×C79#57711yescharacteristic
171D79—22no—
172#3335—791nomaximal, Sylow
173C79#333511yescharacteristic, complemented, Sylow
174#554—791no—
175#547—791no—
176#498—791no—
177#483—791no—
178#483—791no—
179#481—791no—
180#481—791no—
181#476—791no—
182#475—791no—
183#465—791no—
184#465D7911yescharacteristic, complemented
185C4×SD16—791no—
186C8×D4—791no—
187C2×#106—791no—
188C2×#106—791no—
189C2×#41—1581no—
190C2×SD16C2×D7911yescharacteristic
191C22×C8—791no—
192C22×C8C2×D7911yescharacteristic
193C4⋊Q8—791no—
194C4⋊Q8—791no—
195#125—1581no—
196#123—1581no—
197#123—1581no—
198C22⋊Q8—791no—
199C22⋊Q8—1581no—
200C22⋊Q8—1581no—
201C22⋊Q8—1581no—
202C22⋊Q8C2×D7911yescharacteristic
203#121—791no—
204#121C2×D7911yescharacteristic
205C4×Q8—791no—
206C4×D4—791no—
207C4×D4—791no—
208C4×D4—1581no—
209C2×C4⋊C4—791no—
210C2×C4⋊C4—791no—
211C2×C4⋊C4—791no—
212C2×C4⋊C4—791no—
213#106—791no—
214#106—791no—
215#106—791no—
216#106—791no—
217#106—791no—
218#106—791no—
219#106—791no—
220#106—791no—
221#106C2×D7911yescharacteristic
222C4⋊C8—791no—
223#103—791no—
224#103—791no—
225#103C2×D7911yescharacteristic
226#102—791no—
227#102—791no—
228#102C2×D7911yescharacteristic
229C22⋊C8—791no—
230C22⋊C8—791no—
231C4×C8—791no—
232#41—3164no—
233C2×Q8—1581no—
234C2×Q8—1581no—
235C2×Q8C22×D7911yescharacteristic
236C2×D4—21no—
237C2×D4—791no—
238C2×D4—1581no—
239C2×D4C22×D7911yescharacteristic
240C22×C4—791no—
241C22×C4—1581no—
242C22×C4—1581no—
243C22×C4—1581no—
244C22×C4—1581no—
245C22×C4—1581no—
246C22×C4C22×D7911yescharacteristic
247SD16—22no—
248C2×C8—22no—
249C2×C8—791no—
250C2×C8—791no—
251C2×C8—1582no—
252C2×C8C22×D7911yescharacteristic
253C2×C8C22×D7911yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—791no—
256C4⋊C4—791no—
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—1581no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4C22×D7911yescharacteristic
269C4⋊C4C22×D7911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—791no—
273C22⋊C4—791no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C42—791no—
278C42—1581no—
279C23—21no—
280C23—791no—
281C23D4×D7911yescharacteristic
282Q8—21no—
283Q8—21no—
284Q8—3162no—
285Q8—6321no—
286D4—21no—
287D4—21no—
288D4—42no—
289D4—3162no—
290D4—794no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—3162no—
297C2×C4—3162no—
298C2×C4—3162no—
299C2×C4—791no—
300C2×C4—791no—
301C2×C4—791no—
302C2×C4—6321no—
303C2×C4—6321no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4D4×D7911yescharacteristic
311C2×C4C23×D7911yescharacteristic
312C8—21no—
313C8—1581no—
314C8—1581no—
315C8#1192962312yescomplemented
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—792no—
322C22—1581no—
323C22—1581no—
324C22SD16×D7912yes—
325C22C2×D4×D7911yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3161no—
331C4—3161no—
332C4—3161no—
333C4—3161no—
334C4—792no—
335C4—1581no—
336C4—1581no—
337C4C2×#1192962311yescharacteristic
338C4#1457920811yescharacteristic
339C2—22no—
340C2—81no—
341C2—1582no—
342C2#1909921311yescharacteristic
343C2C2×SD16×D7911yescharacteristic
344C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#465×C79C2
socleC22×C79C22×D4
prime radical#19099213C2
hypercenter#465D79
hypocenterC79#3335
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. #19099271C2semidirect
3. #19098960C2semidirect
4. #19098892C2semidirect
5. #19098891C2semidirect
6. #19098880C2semidirect
7. #19098879C2semidirect
8. #19098851C2semidirect
9. #19098846C2semidirect
10. #19098789C2semidirect
11. SD16×Dic79C2semidirect
12. C8×C22⋊D79C2semidirect
13. C2×#14579093C2semidirect
14. #106×D79C2semidirect
15. #465×C79C2semidirect
122. C22⋊D79SD16semidirect
140. C8×C79#41semidirect
173. C79#3335semidirect
184. #465D79semidirect
315. C8#11929623semidirect