Finite Group Databasebeta

← #23766514

Subgroups — #23766514

Order 10112.

496 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579156C211yesmaximal, characteristic
2#19098461C211yesmaximal, characteristic, complemented
3#19098455C211yesmaximal, characteristic
4#19098454C211yesmaximal, characteristic
5#19098454C211yesmaximal, characteristic
6#19098449C211yesmaximal, characteristic, complemented
7#19098446C211yesmaximal, characteristic, complemented
8#19098444C211yesmaximal, characteristic, complemented
9#19098434C211yesmaximal, characteristic
10C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
11C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
12C4×(C2×D79)⋊C4C211yesmaximal, characteristic
13#19098410C211yesmaximal, characteristic
14#19098408C211yesmaximal, characteristic, complemented
15C4×C4⋊C4×C79C211yesmaximal, characteristic, complemented
16C22×C4×D79C2211yescharacteristic
17#14579156C418yescomplemented
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2211yescharacteristic
27C2×(C2×D79)⋊C4C2211yescharacteristic
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×C4×Dic79C2211yescharacteristic
31C2×C4×Dic79C2211yescharacteristic
32C2×C4×Dic79C2211yescharacteristic
33C2×C4×Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C2×C4⋊C4×C79C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C42×C79C2211yescharacteristic
48C2×C42×C79C2211yescharacteristic
49C2×C42×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52C23×D79C2311yescharacteristic
53C22×Dic79C2311yescharacteristic
54C22×Dic79C2311yescharacteristic
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C2×C4×D79—22no—
61C2×C4×D79—22no—
62C2×C4×D79—41no—
63C4⋊Dic79—41no—
64C4⋊Dic79C2×C414yescomplemented
65Dic79⋊C4—22no—
66Dic79⋊C4—22no—
67Dic79⋊C4—22no—
68Dic79⋊C4C2×C414yescomplemented
69(C2×D79)⋊C4—22no—
70(C2×D79)⋊C4—22no—
71(C2×D79)⋊C4—41no—
72(C2×D79)⋊C4C2×C414yes—
73(C2×D79)⋊C4C2×C414yes—
74(C2×D79)⋊C4C2×C414yes—
75C4×Dic79—22no—
76C4×Dic79—22no—
77C4×Dic79—22no—
78C4×Dic79—41no—
79C4×Dic79C2×C414yescomplemented
80C22×C4×C79C2311yescharacteristic
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C4⋊C4×C79—22no—
88C4⋊C4×C79C2×C414yescomplemented
89C42×C79—22no—
90C42×C79—41no—
91C42×C79—41no—
92C23×C79C2411yescharacteristic
93C22×D79—21no—
94C22×D79—21no—
95C22×D79—21no—
96C22×D79—21no—
97C22×D79—21no—
98C22×D79—21no—
99C22×D79C22×C412yes—
100C2×C4×C79—21no—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—21no—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79C22×C412yes—
116C2×C4×C79C22×C412yes—
117C2×C4×C79C22×C412yes—
118C2×C4×C79#4112yes—
119C2×C4×C79#4112yes—
120C2×C4×C79#4112yes—
121C2×Dic79—21no—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79C22×C412yes—
139C2×Dic79C22×C412yes—
140C2×Dic79C22×C412yes—
141C2×Dic79#4112yes—
142C4×D79—44no—
143C22×C79C23×C411yescharacteristic
144C22×C79C2×#4111yescharacteristic
145C22×C79C2×#4111yescharacteristic
146C22×C79C2×#4111yescharacteristic
147C22×C79C2×#4111yescharacteristic
148C22×C79H(5,𝔽2)11yescharacteristic
149C22×C792−1+411yescharacteristic
150C2×D79—22no—
151C2×D79—22no—
152C2×D79—22no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C4×C79—22no—
158C4×C79—22no—
159C4×C79—22no—
160C4×C79—22no—
161C4×C79—22no—
162C4×C79—22no—
163C4×C79—41no—
164Dic79—22no—
165Dic79—22no—
166Dic79—22no—
167Dic79—22no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171C2×C79C4×#4111yescharacteristic
172C2×C79C4×#4111yescharacteristic
173C2×C79#52011yescharacteristic
174C2×C79#55111yescharacteristic
175C2×C79#55211yescharacteristic
176C2×C79#55311yescharacteristic
177C2×C79#55611yescharacteristic
178D79—42no—
179#2373—791nomaximal, Sylow
180C79#237311yescharacteristic, complemented, Sylow
181C2×#126—791no—
182#389—791no—
183#388—791no—
184#388—791no—
185#388—791no—
186#387—791no—
187#387—791no—
188#387—791no—
189#385—791no—
190C4×C4⋊C4—791no—
191C4×C4⋊C4—791no—
192C4×C4⋊C4D7911yescharacteristic, complemented
193C4×C22⋊C4—791no—
194C4×C22⋊C4—791no—
195#376—791no—
196C23×C4—791no—
197#126—798no—
198C2×C4⋊C4—791no—
199C2×C4⋊C4—791no—
200C2×C4⋊C4—791no—
201C2×C4⋊C4—791no—
202C2×C4⋊C4—791no—
203C2×C4⋊C4—791no—
204C2×C4⋊C4C2×D7911yescharacteristic
205C2×C4⋊C4C2×D7911yescharacteristic
206C2×C22⋊C4—791no—
207C2×C22⋊C4—791no—
208C2×C22⋊C4—791no—
209C2×C22⋊C4—791no—
210C2×C22⋊C4—791no—
211C2×C22⋊C4—791no—
212C2×C42—791no—
213C2×C42—791no—
214C2×C42—791no—
215C2×C42—791no—
216C2×C42—791no—
217C2×C42C2×D7911yescharacteristic
218C2×C42C2×D7911yescharacteristic
219C2×C42C2×D7911yescharacteristic
220#95—791no—
221#95—791no—
222#95—791no—
223#95—791no—
224#95—791no—
225#95—791no—
226#95—791no—
227#95—791no—
228#95—791no—
229#95—791no—
230#95C2×D7911yescharacteristic
231#95C2×D7911yescharacteristic
232C24—791no—
233C22×C4—3161no—
234C22×C4—791no—
235C22×C4—791no—
236C22×C4—791no—
237C22×C4—791no—
238C22×C4—791no—
239C22×C4—791no—
240C22×C4—791no—
241C22×C4—1582no—
242C22×C4—1582no—
243C22×C4C22×D7911yescharacteristic
244C22×C4C22×D7911yescharacteristic
245C22×C4C22×D7911yescharacteristic
246C22×C4C22×D7911yescharacteristic
247C22×C4C22×D7911yescharacteristic
248C22×C4C22×D7911yescharacteristic
249C22×C4C22×D7911yescharacteristic
250C4⋊C4—22no—
251C4⋊C4—3161no—
252C4⋊C4—794no—
253C4⋊C4—794no—
254C4⋊C4—1582no—
255C4⋊C4—1582no—
256C4⋊C4—1582no—
257C4⋊C4C4×D7914yescomplemented
258C22⋊C4—3161no—
259C22⋊C4—794no—
260C22⋊C4—794no—
261C22⋊C4—794no—
262C22⋊C4—1582no—
263C22⋊C4—1582no—
264C42—22no—
265C42—41no—
266C42—41no—
267C42—3161no—
268C42—794no—
269C42—1582no—
270C42—1582no—
271C42—1582no—
272C23—792no—
273C23—1581no—
274C23—1581no—
275C23—1581no—
276C23—1581no—
277C23—1581no—
278C23—1581no—
279C23C23×D7911yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—3164no—
296C2×C4—792no—
297C2×C4—792no—
298C2×C4—792no—
299C2×C4—792no—
300C2×C4—1581no—
301C2×C4—1581no—
302C2×C4—1581no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4C2×C4×D7912yes—
318C2×C4C2×C4×D7912yes—
319C2×C4C2×C4×D7912yes—
320C2×C4#1192962412yes—
321C2×C4#1192962412yes—
322C2×C4#1192962512yes—
323C22—3161no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22—1582no—
328C22—1582no—
329C22—1582no—
330C22C22×C4×D7911yescharacteristic
331C22#41×D7911yescharacteristic
332C22C2×#1192962411yescharacteristic
333C22C2×#1192962411yescharacteristic
334C22C2×#1192962511yescharacteristic
335C22#1457920611yescharacteristic
336C22#1457920811yescharacteristic
337C4—22no—
338C4—22no—
339C4—22no—
340C4—22no—
341C4—22no—
342C4—22no—
343C4—41no—
344C4—3161no—
345C4—3161no—
346C4—3161no—
347C4—1582no—
348C4—1582no—
349C4—1582no—
350C4—1582no—
351C2—3162no—
352C2C4×#1192962411yescharacteristic
353C2C4×#1192962511yescharacteristic
354C2#1909904211yescharacteristic
355C2#1909924211yescharacteristic
356C2#1909924611yescharacteristic
357C2#1909926111yescharacteristic
358C2#1909928611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
FittingC4×C4⋊C4×C79C2
socle, cosocleC23×C79C24
prime radicalC23×D79C23
hypercenterC4×C4⋊C4D79
hypocenterC79#2373
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #19098461C2semidirect
6. #19098449C2semidirect
7. #19098446C2semidirect
8. #19098444C2semidirect
10. C4×Dic79⋊C4C2semidirect
11. C4×Dic79⋊C4C2semidirect
14. #19098408C2semidirect
15. C4×C4⋊C4×C79C2semidirect
17. #14579156C4semidirect
64. C4⋊Dic79C2×C4semidirect
68. Dic79⋊C4C2×C4semidirect
79. C4×Dic79C2×C4semidirect
88. C4⋊C4×C79C2×C4semidirect
180. C79#2373semidirect
192. C4×C4⋊C4D79semidirect
257. C4⋊C4C4×D79semidirect