Finite Group Databasebeta

← #23775391

Subgroups — #23775391

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099217C211yesmaximal, characteristic, complemented
2#19098922C211yesmaximal, characteristic, complemented
3#19098896C211yesmaximal, characteristic, complemented
4#19098874C211yesmaximal, characteristic, complemented
5#19098858C211yesmaximal, characteristic, complemented
6#19098811C211yesmaximal, characteristic, complemented
7#19098797C211yesmaximal, characteristic, complemented
8#19098775C211yesmaximal, characteristic, complemented
9#19098708C211yesmaximal, characteristic, complemented
10#19098702C211yesmaximal, characteristic, complemented
11#19098661C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14C2×#14579085C211yesmaximal, characteristic, complemented
15#548×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×#11929611C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929608C2211yescharacteristic
21C22×C79⋊C8C2211yescharacteristic
22#14579161C2211yescharacteristic
23#14579145—21no—
24#14579145—21no—
25#14579141—21no—
26#14579135C2211yescharacteristic
27#14579135C2211yescharacteristic
28C4×D316C2211yescharacteristic
29C2×C4⋊Dic79C2211yescharacteristic
30C2×C4⋊Dic79C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579094C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579085C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C22×Q8×C79C2211yescharacteristic
50#124×C79—21no—
51#124×C79C2211yescharacteristic
52C22⋊Q8×C79—21no—
53C22⋊Q8×C79C2211yescharacteristic
54#121×C79—21no—
55#121×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79—21no—
58C4×D4×C79C2211yescharacteristic
59#11929623—44no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C2×C4×D79—21no—
67#11929611—22no—
68#11929611—41no—
69#11929609—41no—
70#11929608—41no—
71C2×C79⋊C8—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79—21no—
78C4⋊Dic79—21no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84(C2×D79)⋊C4—21no—
85#41×C79—22no—
86#41×C79—41no—
87C2×Q8×C79—21no—
88C2×Q8×C79—22no—
89C2×Q8×C79—41no—
90C2×Q8×C79C2311yescharacteristic
91C2×Q8×C79C2311yescharacteristic
92C2×D4×C79—21no—
93C2×D4×C79—21no—
94C2×D4×C79D411yescharacteristic
95C2×D4×C79C2311yescharacteristic
96C22×C4×C79—21no—
97C22×C4×C79—21no—
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C4⋊C4×C79—21no—
101C4⋊C4×C79—21no—
102C4⋊C4×C79D411yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C42×C79—21no—
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C23×C79C2×D411yescharacteristic
115C22×D79—21no—
116Q8×C79—21no—
117Q8×C79—21no—
118Q8×C79—21no—
119Q8×C79—42no—
120Q8×C79#4112yescomplemented
121D4×C79—22no—
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—42no—
125D4×C79—42no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—42no—
134C2×C4×C79—42no—
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2411yescharacteristic
140C22⋊D79—42no—
141C22⋊D79—42no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—42no—
146C2×Dic79—42no—
147D316—21no—
148D316—21no—
149C4×D79—42no—
150Dic158—42no—
151C79⋊C8—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79AGL(1,ℤ/8)12yes—
164C22×C79C22×D411yescharacteristic
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—41no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—22no—
171C4×C79—21no—
172C4×C79—21no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79C2×#4111yescharacteristic
176C4×C79H(5,𝔽2)11yescharacteristic
177Dic79—41no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—22no—
181C2×C79—41no—
182C2×C79—81no—
183C2×C79#54611yescharacteristic
184C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C79#57811yescharacteristic
186D79—81no—
187#3308—791nomaximal, Sylow
188C79#330811yescharacteristic, complemented, Sylow
189#548D7911yescharacteristic, complemented
190#547—791no—
191#489—791no—
192#484—791no—
193#480—791no—
194#477—791no—
195#468—791no—
196#466—791no—
197#463—791no—
198#449—791no—
199#448—791no—
200#440—791no—
201#435—791no—
202#417—791no—
203C2×#103—791no—
204C2×#41—1581no—
205C2×#41C2×D7911yescharacteristic
206C22×Q8C2×D7911yescharacteristic
207C2×SD16—791no—
208C2×SD16—791no—
209C2×D8—791no—
210C2×M16—791no—
211C22×C8—791no—
212C4⋊Q8—791no—
213#124—21no—
214#124C2×D7911yescharacteristic
215#123—1581no—
216#123—1581no—
217C22⋊Q8—21no—
218C22⋊Q8—1581no—
219C22⋊Q8C2×D7911yescharacteristic
220#121—21no—
221#121—791no—
222#121—791no—
223#121C2×D7911yescharacteristic
224C4×Q8C2×D7911yescharacteristic
225C4×D4—21no—
226C4×D4—791no—
227C4×D4C2×D7911yescharacteristic
228C2×C4⋊C4—791no—
229C2×C4⋊C4—791no—
230#107—791no—
231#107—791no—
232#107—791no—
233C4⋊C8—791no—
234#103—791no—
235#103—791no—
236#103—791no—
237#103—791no—
238#103—791no—
239#103—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244C22⋊C8—791no—
245C22⋊C8—791no—
246#97—791no—
247#41—22no—
248#41—41no—
249#41—3164no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—1581no—
254C2×Q8C22×D7911yescharacteristic
255C2×Q8C22×D7911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—791no—
259C2×D4—1581no—
260C2×D4—1581no—
261C2×D4C22⋊D7911yescharacteristic
262C2×D4C22×D7911yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—1581no—
266C22×C4—1581no—
267C22×C4—1581no—
268C22×C4C22×D7911yescharacteristic
269C22×C4C22×D7911yescharacteristic
270SD16—3161no—
271SD16—1582no—
272D8—3161no—
273M16—3161no—
274C2×C8—3161no—
275C2×C8—791no—
276C2×C8—791no—
277C2×C8—791no—
278C2×C8—791no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—791no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4C22⋊D7911yescharacteristic
288C4⋊C4C22×D7911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4C22⋊D7911yescharacteristic
297C22⋊C4C22⋊D7911yescharacteristic
298C42—21no—
299C42C22×D7911yescharacteristic
300C23—21no—
301C23—1581no—
302C23C2×C22⋊D7911yescharacteristic
303C23C2×C22⋊D7911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—3162no—
309Q8#1192962312yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—3162no—
316D4—3162no—
317D4—1581no—
318D4—1581no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—3162no—
329C2×C4—3162no—
330C2×C4—3162no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4C2×C22⋊D7911yescharacteristic
335C2×C4C2×C22⋊D7911yescharacteristic
336C2×C4C2×C22⋊D7911yescharacteristic
337C2×C4C2×C22⋊D7911yescharacteristic
338C2×C4C23×D7911yescharacteristic
339C8—1581no—
340C8—1581no—
341C8—1581no—
342C8—1581no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—3161no—
352C22—3161no—
353C22—3161no—
354C22#1457918612yes—
355C22C22×C22⋊D7911yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—3161no—
364C4—3161no—
365C4—3161no—
366C4C2×#1192962311yescharacteristic
367C4#1457920611yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—6321no—
372C2#1909920711yescharacteristic
373C2C2×#1457918611yescharacteristic
374C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#548×C79C2
socleC22×C79C22×D4
hypercenter#548D79
hypocenterC79#3308
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #19099217C2semidirect
2. #19098922C2semidirect
3. #19098896C2semidirect
4. #19098874C2semidirect
5. #19098858C2semidirect
6. #19098811C2semidirect
7. #19098797C2semidirect
8. #19098775C2semidirect
9. #19098708C2semidirect
10. #19098702C2semidirect
11. #19098661C2semidirect
12. #19098635C2semidirect
13. #19098564C2semidirect
14. C2×#14579085C2semidirect
15. #548×C79C2semidirect
120. Q8×C79#41semidirect
188. C79#3308semidirect
189. #548D79semidirect
309. Q8#11929623semidirect