Finite Group Databasebeta

← #23775481

Subgroups — #23775481

Order 10112.

410 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#19099270C211yesmaximal, characteristic, complemented
2#19098922C211yesmaximal, characteristic, complemented
3#19098896C211yesmaximal, characteristic, complemented
4#19098874C211yesmaximal, characteristic, complemented
5#19098843C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098802C211yesmaximal, characteristic, complemented
8#19098782C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098714C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14C2×#14579082C211yesmaximal, characteristic, complemented
15#546×C79C211yesmaximal, characteristic
16C2×#11929614C2211yescharacteristic, complemented
17C2×#11929612C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929608C2211yescharacteristic, complemented
20C22×C79⋊C8C2211yescharacteristic
21#14579161C2211yescharacteristic, complemented
22#14579152—21no—
23#14579140C2211yescharacteristic
24#14579140C2211yescharacteristic, complemented
25#14579138—21no—
26#14579138—21no—
27C4×Dic158C2211yescharacteristic, complemented
28D4×Dic79—21no—
29C2×C4⋊Dic79C2211yescharacteristic
30C2×C4⋊Dic79C2211yescharacteristic, complemented
31#14579094C2211yescharacteristic, complemented
32#14579094C2211yescharacteristic, complemented
33#14579094C2211yescharacteristic, complemented
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35#14579085C2211yescharacteristic, complemented
36#14579085C2211yescharacteristic, complemented
37#14579085C2211yescharacteristic, complemented
38#14579084C2211yescharacteristic, complemented
39#14579082C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579082C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47#14579072C2211yescharacteristic, complemented
48C2×#41×C79C2211yescharacteristic
49C22×D4×C79C2211yescharacteristic
50#124×C79C2211yescharacteristic
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53#121×C79—21no—
54#121×C79C2211yescharacteristic
55#120×C79—21no—
56C4×D4×C79C2211yescharacteristic
57C4×D4×C79C2211yescharacteristic
58C2×C22⋊C4×C79—21no—
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C22×Dic79—21no—
62C22×Dic79—21no—
63#11929614—41no—
64#11929612—22no—
65#11929612—41no—
66#11929608—41no—
67C2×C79⋊C8—41no—
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C4⋊Dic79—21no—
73C4⋊Dic79—21no—
74C4⋊Dic79—21no—
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79—21no—
83C4×Dic79—21no—
84C24×C79—21no—
85#41×C79—22no—
86#41×C79—41no—
87C2×Q8×C79C2311yescharacteristic
88C2×D4×C79—22no—
89C2×D4×C79—21no—
90C2×D4×C79—21no—
91C2×D4×C79—21no—
92C2×D4×C79—41no—
93C2×D4×C79D411yescharacteristic
94C2×D4×C79C2311yescharacteristic
95C2×D4×C79C2311yescharacteristic
96C22×C4×C79—21no—
97C22×C4×C79—21no—
98C22×C4×C79C2311yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C4⋊C4×C79—21no—
101C4⋊C4×C79D411yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—42no—
114C23×C79—42no—
115C23×C79—81no—
116C23×C79C2×D411yescharacteristic
117C23×C79C2×D411yescharacteristic
118Q8×C79—21no—
119Q8×C79—21no—
120D4×C79—22no—
121D4×C79—21no—
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—42no—
125D4×C79—42no—
126D4×C79—81no—
127D4×C79#4112yes—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—42no—
135C2×C4×C79—81no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2×D411yescharacteristic
140C2×C4×C79C2411yescharacteristic
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—81no—
146C2×Dic79—81no—
147Dic158—21no—
148Dic158—21no—
149Dic158—81no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—22no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—84no—
166C22×C79#13712yes—
167C22×C79C22×D411yescharacteristic
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—21no—
171C4×C79—21no—
172C4×C79—41no—
173C4×C79—41no—
174C4×C79C2×#4111yescharacteristic
175C4×C79H(5,𝔽2)11yescharacteristic
176Dic79—41no—
177Dic79—41no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—22no—
181C2×C79—41no—
182C2×C79—42no—
183C2×C79—81no—
184C2×C79#54611yescharacteristic
185C2×C79C2×#13711yescharacteristic
186C2×C79#57611yescharacteristic
187#3314—791nomaximal, Sylow
188C79#331411yescharacteristic, complemented, Sylow
189#554—791no—
190#546D7911yescharacteristic
191#489—791no—
192#484—791no—
193#480—791no—
194#474—791no—
195#468—791no—
196#467—791no—
197#464—791no—
198#452—791no—
199#450—791no—
200#440—791no—
201#435—791no—
202#417—791no—
203C2×#102—791no—
204C2×#41C2×D7911yescharacteristic
205C22×D4C2×D7911yescharacteristic
206C2×Q16—791no—
207C2×SD16—791no—
208C2×SD16—791no—
209C2×M16—791no—
210C22×C8—791no—
211C4⋊Q8—791no—
212#125—1581no—
213#124C2×D7911yescharacteristic
214#123—21no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8—1581no—
218C22⋊Q8—1581no—
219C22⋊Q8C2×D7911yescharacteristic
220#121—21no—
221#121C2×D7911yescharacteristic
222#120—21no—
223C4×Q8—791no—
224C4×D4—1581no—
225C4×D4C2×D7911yescharacteristic
226C4×D4C2×D7911yescharacteristic
227C2×C4⋊C4—791no—
228C2×C4⋊C4—791no—
229C2×C22⋊C4—21no—
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#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244C22⋊C8—791no—
245C22⋊C8—791no—
246#97—791no—
247C24—21no—
248#41—22no—
249#41—41no—
250C2×Q8—791no—
251C2×Q8—1581no—
252C2×Q8C22×D7911yescharacteristic
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—41no—
258C2×D4C22⋊D7911yescharacteristic
259C2×D4C22×D7911yescharacteristic
260C2×D4C22×D7911yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—1581no—
264C22×C4—1581no—
265C22×C4C22×D7911yescharacteristic
266C22×C4C22×D7911yescharacteristic
267Q16—3161no—
268SD16—3161no—
269SD16—1582no—
270M16—3161no—
271C2×C8—3161no—
272C2×C8—791no—
273C2×C8—791no—
274C2×C8—791no—
275C2×C8—791no—
276C4⋊C4—21no—
277C4⋊C4—791no—
278C4⋊C4—791no—
279C4⋊C4—791no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4C22⋊D7911yescharacteristic
287C4⋊C4C22×D7911yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4C22⋊D7911yescharacteristic
296C22⋊C4C22⋊D7911yescharacteristic
297C42—1581no—
298C42C22×D7911yescharacteristic
299C23—21no—
300C23—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23C2×C22⋊D7911yescharacteristic
305C23C2×C22⋊D7911yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—6321no—
309Q8—1581no—
310Q8—1581no—
311D4—22no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—81no—
318D4#1192962312yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—6321no—
328C2×C4—6321no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4C2×C22⋊D7911yescharacteristic
334C2×C4C2×C22⋊D7911yescharacteristic
335C2×C4C2×C22⋊D7911yescharacteristic
336C2×C4C2×C22⋊D7911yescharacteristic
337C2×C4C23×D7911yescharacteristic
338C8—1581no—
339C8—1581no—
340C8—1581no—
341C8—1581no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—84no—
354C22#1457919112yes—
355C22C22×C22⋊D7911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—3161no—
363C4—3161no—
364C4—3161no—
365C4—3161no—
366C4C2×#1192962311yescharacteristic
367C4#1457920611yescharacteristic
368C2—22no—
369C2—41no—
370C2—42no—
371C2—81no—
372C2#1909920711yescharacteristic
373C2C2×#1457919111yescharacteristic
374C2#1909936611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#546×C79C2
socleC22×C79C22×D4
hypercenter#546D79
hypocenterC79#3314
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #19099270C2semidirect
2. #19098922C2semidirect
3. #19098896C2semidirect
4. #19098874C2semidirect
5. #19098843C2semidirect
6. #19098807C2semidirect
7. #19098802C2semidirect
8. #19098782C2semidirect
9. #19098725C2semidirect
10. #19098714C2semidirect
11. #19098663C2semidirect
12. #19098635C2semidirect
13. #19098564C2semidirect
14. C2×#14579082C2semidirect
16. C2×#11929614C22semidirect
19. C2×#11929608C22semidirect
21. #14579161C22semidirect
24. #14579140C22semidirect
27. C4×Dic158C22semidirect
30. C2×C4⋊Dic79C22semidirect
31. #14579094C22semidirect
32. #14579094C22semidirect
33. #14579094C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579085C22semidirect
36. #14579085C22semidirect
37. #14579085C22semidirect
38. #14579084C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. #14579072C22semidirect
188. C79#3314semidirect