Finite Group Databasebeta

← #23776193

Subgroups — #23776193

Order 10112.

384 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099296C211yesmaximal, characteristic, complemented
2D4×Dic158C211yesmaximal, characteristic, complemented
3#19098923C211yesmaximal, characteristic, complemented
4#19098921C211yesmaximal, characteristic, complemented
5#19098908C211yesmaximal, characteristic, complemented
6#19098853C211yesmaximal, characteristic, complemented
7#19098852C211yesmaximal, characteristic, complemented
8#19098847C211yesmaximal, characteristic, complemented
9#19098778C211yesmaximal, characteristic, complemented
10#19098776C211yesmaximal, characteristic, complemented
11#19098756C211yesmaximal, characteristic
12#19098691C211yesmaximal, characteristic, complemented
13#19098672C211yesmaximal, characteristic, complemented
14#19098654C211yesmaximal, characteristic, complemented
15#442×C79C211yesmaximal, characteristic, complemented
16C22×Dic158—21no—
17C2×#11929612C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19#14579161C2211yescharacteristic
20#14579160C2211yescharacteristic
21#14579160C2211yescharacteristic
22#14579157C2211yescharacteristic
23#14579149C2211yescharacteristic
24#14579148C2211yescharacteristic
25#14579147—21no—
26#14579144—21no—
27#14579143—21no—
28#14579140—21no—
29#14579138—21no—
30#14579138—21no—
31C4×Dic158C2211yescharacteristic
32#14579126C2211yescharacteristic
33D4×Dic79C2211yescharacteristic
34D4×Dic79C2211yescharacteristic
35#14579123C2211yescharacteristic
36C4×C22⋊D79—21no—
37#14579092C2211yescharacteristic
38#14579092C2211yescharacteristic
39C4⋊(C79⋊C8)C2211yescharacteristic
40Dic79⋊C8C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579084C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579081C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×D8×C79C2211yescharacteristic
53C4×D4×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55#106×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#97×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158—21no—
61C2×Dic158—21no—
62C2×Dic158—44no—
63C2×Dic158D411yescharacteristic
64C2×Dic158C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C22×Dic79—21no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71#11929612—22no—
72#11929609—22no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C4⋊Dic79—21no—
76C4⋊Dic79D411yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4D411yescharacteristic
83Dic79⋊C4D411yescharacteristic
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91C4×Dic79—21no—
92C4×Dic79C2311yescharacteristic
93C4×Dic79C2311yescharacteristic
94C2×D4×C79C2311yescharacteristic
95C2×D4×C79C2311yescharacteristic
96C22×C4×C79—21no—
97C22×C4×C79—21no—
98D8×C79—22no—
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C42×C79C2311yescharacteristic
106C23×C79—21no—
107C23×C79—21no—
108C22×D79—21no—
109D4×C79—21no—
110D4×C79—21no—
111D4×C79—21no—
112D4×C79#4112yes—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—42no—
116C2×C4×C79—81no—
117C2×C4×C79C2×D411yescharacteristic
118C2×C4×C79C2×D411yescharacteristic
119C2×C4×C79C2411yescharacteristic
120C22⋊D79—42no—
121C22⋊D79—81no—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—42no—
126C2×Dic79—42no—
127C2×Dic79C2×D411yescharacteristic
128C2×Dic79C2×D411yescharacteristic
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131D316—21no—
132D316—21no—
133C4×D79—81no—
134Dic158—22no—
135Dic158—21no—
136Dic158—21no—
137Dic158—42no—
138Dic158—42no—
139Dic158—42no—
140C8×C79—21no—
141C8×C79—21no—
142C79⋊C8—21no—
143C79⋊C8—21no—
144C22×C79—22no—
145C22×C79—41no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79C22×D411yescharacteristic
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C4×C79—21no—
155C4×C79—21no—
156C4×C79—41no—
157C4×C79—41no—
158C4×C79C2×#4111yescharacteristic
159C4×C792−1+411yescharacteristic
160Dic79—21no—
161Dic79—21no—
162Dic79—21no—
163Dic79—41no—
164Dic79—41no—
165Dic79—41no—
166Dic79AGL(1,ℤ/8)12yes—
167C2×C79—42no—
168C2×C79—81no—
169C2×C79#54811yescharacteristic
170C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C79#57711yescharacteristic
172D79—81no—
173#3373—791nomaximal, Sylow
174C79#337311yescharacteristic, complemented, Sylow
175#559—791no—
176D4×Q8—791no—
177#489—791no—
178#489—791no—
179#486—791no—
180#476—791no—
181#476—791no—
182#475—791no—
183#463—791no—
184#463—791no—
185#459—791no—
186#446—791no—
187#442—791no—
188#442D7911yescharacteristic, complemented
189C4×SD16—791no—
190C22×Q8—1581no—
191C2×SD16—791no—
192C2×D8—791no—
193C2×D8C2×D7911yescharacteristic
194C4⋊Q8—791no—
195C4⋊Q8—791no—
196C4⋊Q8—791no—
197#127—791no—
198#124—791no—
199#124—791no—
200#124—1581no—
201#123—1581no—
202#123—1581no—
203C22⋊Q8—1581no—
204C22⋊Q8—1581no—
205C22⋊Q8—1581no—
206C4×Q8—791no—
207C4×Q8—791no—
208C4×D4—791no—
209C4×D4—791no—
210C4×D4—791no—
211C4×D4—1581no—
212C4×D4C2×D7911yescharacteristic
213C4×D4C2×D7911yescharacteristic
214#106—791no—
215#106—791no—
216#106C2×D7911yescharacteristic
217C4⋊C8—791no—
218C4⋊C8—791no—
219C4⋊C8—791no—
220#103—791no—
221#103—791no—
222#103—791no—
223#102—791no—
224#102—791no—
225#102—791no—
226#102—791no—
227#102—791no—
228#102C2×D7911yescharacteristic
229#102C2×D7911yescharacteristic
230#97—791no—
231#97C2×D7911yescharacteristic
232C4×C8—791no—
233C2×Q8—3164no—
234C2×Q8—791no—
235C2×Q8—791no—
236C2×Q8—1581no—
237C2×Q8—1581no—
238C2×Q8—1581no—
239C2×D4—791no—
240C2×D4—1581no—
241C2×D4—1581no—
242C2×D4C22×D7911yescharacteristic
243C2×D4C22×D7911yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4—1581no—
249SD16—1582no—
250D8—22no—
251D8—1582no—
252C2×C8—791no—
253C2×C8—791no—
254C2×C8C22×D7911yescharacteristic
255C2×C8C22×D7911yescharacteristic
256C4⋊C4—791no—
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4C22×D7911yescharacteristic
266C4⋊C4C22×D7911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—1581no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C42—791no—
277C42—791no—
278C42—1581no—
279C42C22×D7911yescharacteristic
280C23—21no—
281C23—21no—
282C23—1581no—
283Q8—3162no—
284Q8—3162no—
285Q8—3162no—
286Q8—1582no—
287Q8—1581no—
288Q8—1581no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—3162no—
293D4—6321no—
294D4—1581no—
295D4—1581no—
296D4#1192962412yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—42no—
300C2×C4—81no—
301C2×C4—3162no—
302C2×C4—3162no—
303C2×C4—791no—
304C2×C4—791no—
305C2×C4—791no—
306C2×C4—791no—
307C2×C4—6321no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4D4×D7911yescharacteristic
312C2×C4D4×D7911yescharacteristic
313C2×C4C23×D7911yescharacteristic
314C8—21no—
315C8—21no—
316C8—1581no—
317C8—1581no—
318C22—22no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22C2×D4×D7911yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—3161no—
333C4—3161no—
334C4—3161no—
335C4—792no—
336C4—1581no—
337C4—1581no—
338C4—1581no—
339C4C2×#1192962411yescharacteristic
340C4#1457920811yescharacteristic
341C2—42no—
342C2—81no—
343C2—6321no—
344C2#1909922211yescharacteristic
345C2AGL(1,ℤ/8)×D7911yescharacteristic
346C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#442×C79C2
socleC22×C79C22×D4
prime radical#19098756C2
hypercenter#442D79
hypocenterC79#3373
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #19099296C2semidirect
2. D4×Dic158C2semidirect
3. #19098923C2semidirect
4. #19098921C2semidirect
5. #19098908C2semidirect
6. #19098853C2semidirect
7. #19098852C2semidirect
8. #19098847C2semidirect
9. #19098778C2semidirect
10. #19098776C2semidirect
12. #19098691C2semidirect
13. #19098672C2semidirect
14. #19098654C2semidirect
15. #442×C79C2semidirect
174. C79#3373semidirect
188. #442D79semidirect