Finite Group Databasebeta

← #23775876

Subgroups — #23775876

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099265C211yesmaximal, characteristic, complemented
2#19099213C211yesmaximal, characteristic, complemented
3#19098971C211yesmaximal, characteristic, complemented
4#19098886C211yesmaximal, characteristic, complemented
5#19098880C211yesmaximal, characteristic, complemented
6#19098879C211yesmaximal, characteristic, complemented
7#19098874C211yesmaximal, characteristic, complemented
8#19098865C211yesmaximal, characteristic, complemented
9#19098851C211yesmaximal, characteristic, complemented
10#19098813C211yesmaximal, characteristic, complemented
11#19098675C211yesmaximal, characteristic, complemented
12#19098634C211yesmaximal, characteristic, complemented
13#19098604C211yesmaximal, characteristic, complemented
14C2×#14579093C211yesmaximal, characteristic, complemented
15#466×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×#11929607C2211yescharacteristic
18#14579160C2211yescharacteristic
19#14579154—21no—
20#14579152C2211yescharacteristic
21#14579145—21no—
22#14579143—21no—
23#14579142—21no—
24#14579138—21no—
25#14579133—21no—
26#14579132C2211yescharacteristic
27#14579132C2211yescharacteristic
28D4×Dic79—21no—
29D4×Dic79C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31C4×C22⋊D79C2211yescharacteristic
32#14579119C2211yescharacteristic
33C2×C4⋊Dic79C2211yescharacteristic
34C2×C4⋊Dic79C2211yescharacteristic
35C4⋊C4×D79C2211yescharacteristic
36#14579094C2211yescharacteristic
37#14579094C2211yescharacteristic
38#14579093C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579093C2211yescharacteristic
41#14579093C2211yescharacteristic
42#14579092C2211yescharacteristic
43#14579092C2211yescharacteristic
44Dic79⋊C8C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic
52C2×D8×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54#121×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#107×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—44no—
60C2×Dic158—21no—
61C2×C22⋊D79—21no—
62C2×C22⋊D79—21no—
63C2×C22⋊D79D411yescharacteristic
64C22×Dic79—21no—
65C22×Dic79—21no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C2×C4×D79—21no—
69C2×C4×D79C2311yescharacteristic
70#11929607—22no—
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
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⋊C4D411yescharacteristic
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79D411yescharacteristic
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4D411yescharacteristic
91C4×Dic79—21no—
92C4×Dic79C2311yescharacteristic
93C2×D4×C79—21no—
94C2×D4×C79—21no—
95C2×D4×C79C2311yescharacteristic
96C2×D4×C79C2311yescharacteristic
97C22×C4×C79C2311yescharacteristic
98D8×C79—22no—
99C2×C8×C79—22no—
100C2×C8×C79C2311yescharacteristic
101C2×C8×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C23×C79—21no—
107C23×C79—21no—
108C23×C79C2×D411yescharacteristic
109C22×D79C2×D411yescharacteristic
110D4×C79—21no—
111D4×C79—21no—
112D4×C79—21no—
113D4×C79—21no—
114D4×C79—42no—
115D4×C79—42no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2411yescharacteristic
122C22⋊D79—22no—
123C22⋊D79—42no—
124C22⋊D79—81no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—42no—
130C2×Dic79—42no—
131C2×Dic79—81no—
132C2×Dic79—81no—
133C2×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C4×D79—21no—
137C4×D79—21no—
138C4×D79—42no—
139Dic158—42no—
140C8×C79—21no—
141C8×C79#4112yescomplemented
142C79⋊C8—21no—
143C79⋊C8—21no—
144C22×C79—21no—
145C22×C79—21no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79AGL(1,ℤ/8)12yes—
153C22×C79C22×D411yescharacteristic
154C2×D79—21no—
155C2×D79—21no—
156C2×D79—21no—
157C4×C79—21no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79C2×#4111yescharacteristic
161C4×C792−1+411yescharacteristic
162Dic79—21no—
163Dic79—21no—
164Dic79—21no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—22no—
170C2×C79—81no—
171C2×C79—81no—
172C2×C79#54711yescharacteristic
173C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C79#57711yescharacteristic
175D79—41no—
176#3345—791nomaximal, Sylow
177C79#334511yescharacteristic, complemented, Sylow
178#553—791no—
179#547—791no—
180#501—791no—
181#482—791no—
182#481—791no—
183#481—791no—
184#480—791no—
185#478—791no—
186#476—791no—
187#469—791no—
188#466D7911yescharacteristic, complemented
189#442—791no—
190#435—791no—
191#428—791no—
192C2×#106—791no—
193C2×#41—1581no—
194C2×D8C2×D7911yescharacteristic
195C2×M16—791no—
196C22×C8C2×D7911yescharacteristic
197C4⋊Q8—791no—
198#126—1581no—
199#125—791no—
200#123—1581no—
201#123—1581no—
202#123—1581no—
203C22⋊Q8—1581no—
204#121—791no—
205#121—791no—
206#121—1581no—
207#121C2×D7911yescharacteristic
208#121C2×D7911yescharacteristic
209C4×D4—791no—
210C4×D4—791no—
211C4×D4—791no—
212C4×D4—1581no—
213#117—791no—
214C2×C4⋊C4—791no—
215C2×C4⋊C4—791no—
216C2×C4⋊C4—791no—
217#107—791no—
218#107—791no—
219#107C2×D7911yescharacteristic
220#106—791no—
221#106—791no—
222#106—791no—
223#106—791no—
224#106—791no—
225#106—791no—
226C4⋊C8—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231#102C2×D7911yescharacteristic
232#102C2×D7911yescharacteristic
233C22⋊C8—791no—
234C22⋊C8—791no—
235#97—791no—
236#41—3164no—
237C2×Q8—1581no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—791no—
241C2×D4—1581no—
242C2×D4—1581no—
243C2×D4C22×D7911yescharacteristic
244C2×D4C22×D7911yescharacteristic
245C22×C4—791no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4—1581no—
249C22×C4—1581no—
250C22×C4—1581no—
251C22×C4C22×D7911yescharacteristic
252D8—22no—
253M16—1582no—
254C2×C8—22no—
255C2×C8—791no—
256C2×C8—791no—
257C2×C8C22×D7911yescharacteristic
258C2×C8C22×D7911yescharacteristic
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—791no—
263C4⋊C4—791no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4C22×D7911yescharacteristic
271C4⋊C4C22×D7911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—791no—
275C22⋊C4—791no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C42—791no—
282C42—1581no—
283C23—21no—
284C23—21no—
285C23—791no—
286C23D4×D7911yescharacteristic
287Q8—3162no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—42no—
294D4—3162no—
295D4—6321no—
296D4—1582no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—3162no—
302C2×C4—3162no—
303C2×C4—3162no—
304C2×C4—791no—
305C2×C4—791no—
306C2×C4—791no—
307C2×C4—6321no—
308C2×C4—6321no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4D4×D7911yescharacteristic
316C2×C4C23×D7911yescharacteristic
317C8—21no—
318C8—1581no—
319C8—1581no—
320C8#1192962312yescomplemented
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—1581no—
330C22—1581no—
331C22—1581no—
332C22#1457918512yes—
333C22C2×D4×D7911yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—3161no—
338C4—3161no—
339C4—3161no—
340C4—3161no—
341C4—1581no—
342C4—1581no—
343C4—1581no—
344C4C2×#1192962311yescharacteristic
345C4#1457920811yescharacteristic
346C2—22no—
347C2—81no—
348C2—81no—
349C2—3161no—
350C2#1909921311yescharacteristic
351C2C2×#1457918511yescharacteristic
352C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#466×C79C2
socleC22×C79C22×D4
hypercenter#466D79
hypocenterC79#3345
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #19099265C2semidirect
2. #19099213C2semidirect
3. #19098971C2semidirect
4. #19098886C2semidirect
5. #19098880C2semidirect
6. #19098879C2semidirect
7. #19098874C2semidirect
8. #19098865C2semidirect
9. #19098851C2semidirect
10. #19098813C2semidirect
11. #19098675C2semidirect
12. #19098634C2semidirect
13. #19098604C2semidirect
14. C2×#14579093C2semidirect
15. #466×C79C2semidirect
141. C8×C79#41semidirect
177. C79#3345semidirect
188. #466D79semidirect
320. C8#11929623semidirect