Finite Group Databasebeta

← #23775616

Subgroups — #23775616

Order 10112.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099253C211yesmaximal, characteristic, complemented
2#19098917C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098879C211yesmaximal, characteristic, complemented
5#19098863C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098807C211yesmaximal, characteristic, complemented
8#19098782C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098714C211yesmaximal, characteristic, complemented
11C4×#11929612C211yesmaximal, characteristic, complemented
12#19098641C211yesmaximal, characteristic, complemented
13#19098568C211yesmaximal, characteristic, complemented
14#19098564C211yesmaximal, characteristic, complemented
15#546×C79C211yesmaximal, characteristic
16C2×#11929614C2211yescharacteristic, complemented
17C2×#11929612C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929608C2211yescharacteristic
20C2×#11929608C2211yescharacteristic, complemented
21#14579154—21no—
22#14579153C2211yescharacteristic, complemented
23#14579151—21no—
24#14579142—21no—
25#14579140C2211yescharacteristic
26#14579140C2211yescharacteristic, complemented
27C4×Dic158C2211yescharacteristic, complemented
28#14579120C2211yescharacteristic
29#14579117—21no—
30C2×C4⋊Dic79C2211yescharacteristic, complemented
31#14579094C2211yescharacteristic, complemented
32#14579092C2211yescharacteristic, complemented
33#14579092C2211yescharacteristic, 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
47C4×C79⋊C8C2211yescharacteristic, 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×Dic158C2311yescharacteristic
60C22×Dic79—21no—
61#11929614—41no—
62#11929612—22no—
63#11929612—41no—
64#11929608—41no—
65#11929608—41no—
66C2×C79⋊C8C2311yescharacteristic
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C4⋊Dic79—21no—
71C4⋊Dic79C2311yescharacteristic
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74Dic79⋊C4—21no—
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C4×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—21no—
121D4×C79—21no—
122D4×C79—21no—
123D4×C79—41no—
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—42no—
146Dic158—21no—
147Dic158—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—22no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—84no—
165C22×C79C22×D411yescharacteristic
166C4×C79—21no—
167C4×C79—21no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79C2×#4111yescharacteristic
173C4×C79H(5,𝔽2)11yescharacteristic
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177Dic79—41no—
178C2×C79—41no—
179C2×C79—41no—
180C2×C79—42no—
181C2×C79—81no—
182C2×C79#54611yescharacteristic
183C2×C79#57511yescharacteristic
184C2×C79#57711yescharacteristic
185#3323—791nomaximal, Sylow
186C79#332311yescharacteristic, complemented, Sylow
187#552—791no—
188#546D7911yescharacteristic
189#488—791no—
190#485—791no—
191#481—791no—
192#478—791no—
193#470—791no—
194#468—791no—
195#464—791no—
196#452—791no—
197#450—791no—
198C4×SD16—791no—
199#436—791no—
200#418—791no—
201#417—791no—
202C2×#41C2×D7911yescharacteristic
203C22×D4C2×D7911yescharacteristic
204C2×Q16—791no—
205C2×SD16—791no—
206C2×SD16—791no—
207C2×M16—791no—
208C2×M16—791no—
209#126—1581no—
210#125—791no—
211#125—1581no—
212#124C2×D7911yescharacteristic
213#123—21no—
214#123—1581no—
215C22⋊Q8—791no—
216C22⋊Q8—791no—
217C22⋊Q8C2×D7911yescharacteristic
218#121—21no—
219#121C2×D7911yescharacteristic
220#120—21no—
221C4×Q8—791no—
222C4×D4C2×D7911yescharacteristic
223C4×D4C2×D7911yescharacteristic
224#117—791no—
225#117—1581no—
226C2×C4⋊C4—791no—
227C2×C22⋊C4—21no—
228#107—791no—
229#106—791no—
230#106—791no—
231C4⋊C8—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241#102—791no—
242C22⋊C8—791no—
243C22⋊C8—791no—
244C4×C8—791no—
245C24—21no—
246#41—22no—
247#41—41no—
248C2×Q8—791no—
249C2×Q8C22×D7911yescharacteristic
250C2×D4—22no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C22⋊D7911yescharacteristic
256C2×D4C22×D7911yescharacteristic
257C2×D4C22×D7911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—1581no—
261C22×C4C22×D7911yescharacteristic
262C22×C4C22×D7911yescharacteristic
263Q16—3161no—
264SD16—3161no—
265SD16—1582no—
266M16—3161no—
267M16—3161no—
268C2×C8—791no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8—791no—
272C4⋊C4—21no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4C22⋊D7911yescharacteristic
283C4⋊C4C22×D7911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4C22⋊D7911yescharacteristic
293C22⋊C4C22⋊D7911yescharacteristic
294C42—1581no—
295C42—1581no—
296C42C22×D7911yescharacteristic
297C23—21no—
298C23—21no—
299C23—42no—
300C23—42no—
301C23—81no—
302C23C2×C22⋊D7911yescharacteristic
303C23C2×C22⋊D7911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—1581no—
307Q8—1581no—
308D4—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—42no—
314D4—81no—
315D4#1192962312yes—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—3162no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4C2×C22⋊D7911yescharacteristic
330C2×C4C2×C22⋊D7911yescharacteristic
331C2×C4C2×C22⋊D7911yescharacteristic
332C2×C4C2×C22⋊D7911yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—1581no—
335C8—1581no—
336C8—1581no—
337C8—1581no—
338C22—21no—
339C22—21no—
340C22—22no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22C22×C22⋊D7911yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—3161no—
359C4—3161no—
360C4—3161no—
361C4—3161no—
362C4C2×#1192962311yescharacteristic
363C4#1457920611yescharacteristic
364C2—41no—
365C2—41no—
366C2—42no—
367C2—81no—
368C2#1909920711yescharacteristic
369C2#1909936111yescharacteristic
370C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#546×C79C2
socleC22×C79C22×D4
hypercenter#546D79
hypocenterC79#3323
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. #19099253C2semidirect
2. #19098917C2semidirect
3. #19098901C2semidirect
4. #19098879C2semidirect
5. #19098863C2semidirect
6. #19098819C2semidirect
7. #19098807C2semidirect
8. #19098782C2semidirect
9. #19098725C2semidirect
10. #19098714C2semidirect
11. C4×#11929612C2semidirect
12. #19098641C2semidirect
13. #19098568C2semidirect
14. #19098564C2semidirect
16. C2×#11929614C22semidirect
20. C2×#11929608C22semidirect
22. #14579153C22semidirect
26. #14579140C22semidirect
27. C4×Dic158C22semidirect
30. C2×C4⋊Dic79C22semidirect
31. #14579094C22semidirect
32. #14579092C22semidirect
33. #14579092C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579085C22semidirect
36. #14579085C22semidirect
37. #14579085C22semidirect
38. #14579084C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. C4×C79⋊C8C22semidirect
186. C79#3323semidirect