Finite Group Databasebeta

← #23775550

Subgroups — #23775550

Order 10112.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099209C211yesmaximal, characteristic, complemented
2#19098925C211yesmaximal, characteristic, complemented
3#19098904C211yesmaximal, characteristic, complemented
4#19098887C211yesmaximal, characteristic, complemented
5#19098840C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098797C211yesmaximal, characteristic, complemented
8#19098778C211yesmaximal, characteristic, complemented
9#19098706C211yesmaximal, characteristic, complemented
10#19098696C211yesmaximal, characteristic, complemented
11#19098673C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098567C211yesmaximal, characteristic, complemented
14#19098557C211yesmaximal, characteristic, complemented
15#555×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×#11929612C2211yescharacteristic, complemented
19C2×#11929609C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic, complemented
23#14579149C2211yescharacteristic
24#14579146—21no—
25#14579140C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579134—21no—
28#14579129—21no—
29C4×D316C2211yescharacteristic
30C22⋊C4×D79—21no—
31#14579094C2211yescharacteristic, complemented
32#14579094C2211yescharacteristic, complemented
33#14579092C2211yescharacteristic, complemented
34C4⋊(C79⋊C8)C2211yescharacteristic, complemented
35#14579084C2211yescharacteristic, complemented
36#14579084C2211yescharacteristic, complemented
37#14579084C2211yescharacteristic, complemented
38#14579082C2211yescharacteristic, complemented
39#14579081C2211yescharacteristic
40#14579081C2211yescharacteristic
41#14579081C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47#14579072C2211yescharacteristic, complemented
48C4⋊Q8×C79C2211yescharacteristic, complemented
49#124×C79—21no—
50#124×C79—21no—
51#121×C79—21no—
52#121×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic, complemented
54C4×D4×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic, complemented
56#117×C79—21no—
57#117×C79C2211yescharacteristic
58#117×C79C2211yescharacteristic, complemented
59C23×D79—21no—
60#11929624—22no—
61#11929624—41no—
62C2×Dic158C2311yescharacteristic
63C2×D316—22no—
64C2×D316—21no—
65C2×D316—41no—
66C2×D316C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72#11929612—41no—
73#11929609—22no—
74#11929609—41no—
75#11929608—41no—
76C2×C79⋊C8—41no—
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87(C2×D79)⋊C4—21no—
88C2×Q8×C79—21no—
89C2×D4×C79—21no—
90C2×D4×C79—21no—
91C2×D4×C79D411yescharacteristic
92C2×D4×C79C2311yescharacteristic
93C22×C4×C79—21no—
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C4⋊C4×C79—21no—
97C4⋊C4×C79D411yescharacteristic
98C4⋊C4×C79C2311yescharacteristic
99C4⋊C4×C79C2311yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79D411yescharacteristic
107C22⋊C4×C79D411yescharacteristic
108C42×C79—21no—
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—42no—
117C22×D79—42no—
118C22×D79—81no—
119Q8×C79—81no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—41no—
123D4×C79—81no—
124D4×C79—81no—
125C2×C4×C79—21no—
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—42no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2411yescharacteristic
138C22⋊D79—42no—
139C22⋊D79—81no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142D316—21no—
143D316—21no—
144D316—21no—
145D316—42no—
146D316#4112yes—
147C4×D79—42no—
148C4×D79—81no—
149Dic158—21no—
150Dic158—21no—
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—21no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C2×D79—22no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—84no—
172C4×C79—21no—
173C4×C79—21no—
174C4×C79—21no—
175C4×C79—21no—
176C4×C79—41no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79C2×#4111yescharacteristic
180C4×C79H(5,𝔽2)11yescharacteristic
181Dic79—41no—
182Dic79—41no—
183C2×C79—41no—
184C2×C79—41no—
185C2×C79—81no—
186C2×C79#54611yescharacteristic
187C2×C79#57511yescharacteristic
188C2×C79#57611yescharacteristic
189D79—42no—
190D79—81no—
191#3319—791nomaximal, Sylow
192C79#331911yescharacteristic, complemented, Sylow
193#555D7911yescharacteristic, complemented
194#546—791no—
195#489—791no—
196#485—791no—
197#482—791no—
198#474—791no—
199#468—791no—
200#466—791no—
201#463—791no—
202#449—791no—
203#447—791no—
204#442—791no—
205#435—791no—
206#418—791no—
207#416—791no—
208C2×#41—791no—
209C22×D4—791no—
210C2×SD16—791no—
211C2×D8—791no—
212C2×D8—791no—
213C2×M16—791no—
214C22×C8—791no—
215C4⋊Q8C2×D7911yescharacteristic, complemented
216#124—21no—
217#124—21no—
218#124—791no—
219#123—1581no—
220C22⋊Q8—791no—
221#121—21no—
222#121—791no—
223#121—1581no—
224#121C2×D7911yescharacteristic
225#121C2×D7911yescharacteristic, complemented
226#120—1581no—
227C4×D4—791no—
228C4×D4C2×D7911yescharacteristic
229C4×D4C2×D7911yescharacteristic, complemented
230#117—21no—
231#117C2×D7911yescharacteristic
232#117C2×D7911yescharacteristic, complemented
233C2×C22⋊C4—1581no—
234#107—791no—
235#107—791no—
236#106—791no—
237C4⋊C8—791no—
238#103—791no—
239#103—791no—
240#103—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248C22⋊C8—791no—
249C22⋊C8—791no—
250#97—791no—
251C24—1581no—
252#41—3161no—
253#41—1582no—
254C2×Q8—21no—
255C2×Q8—791no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—3161no—
259C2×D4—791no—
260C2×D4—791no—
261C2×D4—1582no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22⋊D7911yescharacteristic
266C2×D4C22×D7911yescharacteristic
267C22×C4—21no—
268C22×C4—1581no—
269C22×C4—1581no—
270C22×C4C22×D7911yescharacteristic
271C22×C4C22×D7911yescharacteristic
272SD16—3161no—
273D8—3161no—
274D8—1582no—
275M16—3161no—
276C2×C8—3161no—
277C2×C8—791no—
278C2×C8—791no—
279C2×C8—791no—
280C2×C8—791no—
281C4⋊C4—21no—
282C4⋊C4—791no—
283C4⋊C4—1581no—
284C4⋊C4C22⋊D7911yescharacteristic
285C4⋊C4C22×D7911yescharacteristic
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⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4C22⋊D7911yescharacteristic
299C22⋊C4C22⋊D7911yescharacteristic
300C42—21no—
301C42—21no—
302C42C22×D7911yescharacteristic
303C23—21no—
304C23—3162no—
305C23—3162no—
306C23—6321no—
307C23—1581no—
308C23—1581no—
309C23C2×C22⋊D7911yescharacteristic
310C23C2×C22⋊D7911yescharacteristic
311Q8—81no—
312Q8—1581no—
313Q8—1581no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4—3162no—
320D4—3162no—
321D4—792no—
322D4—6321no—
323D4—1581no—
324D4—1581no—
325D4—1581no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—3162no—
335C2×C4—6321no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4C2×C22⋊D7911yescharacteristic
339C2×C4C2×C22⋊D7911yescharacteristic
340C2×C4C2×C22⋊D7911yescharacteristic
341C2×C4C2×C22⋊D7911yescharacteristic
342C2×C4C23×D7911yescharacteristic
343C8—1581no—
344C8—1581no—
345C8—1581no—
346C8—1581no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22—6324no—
362C22—1582no—
363C22C22×C22⋊D7911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—3161no—
372C4—3161no—
373C4#41×D7911yescharacteristic
374C4#1457920711yescharacteristic
375C2—41no—
376C2—41no—
377C2—81no—
378C2—3162no—
379C2—6321no—
380C2#1909920111yescharacteristic
381C2#1909936111yescharacteristic
382C2#1909936611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#555×C79C2
socleC22×C79C22×D4
hypercenter#555D79
hypocenterC79#3319
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #19099209C2semidirect
2. #19098925C2semidirect
3. #19098904C2semidirect
4. #19098887C2semidirect
5. #19098840C2semidirect
6. #19098807C2semidirect
7. #19098797C2semidirect
8. #19098778C2semidirect
9. #19098706C2semidirect
10. #19098696C2semidirect
11. #19098673C2semidirect
12. #19098635C2semidirect
13. #19098567C2semidirect
14. #19098557C2semidirect
15. #555×C79C2semidirect
18. C2×#11929612C22semidirect
22. C22×C79⋊C8C22semidirect
31. #14579094C22semidirect
32. #14579094C22semidirect
33. #14579092C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579084C22semidirect
36. #14579084C22semidirect
37. #14579084C22semidirect
38. #14579082C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. #14579072C22semidirect
48. C4⋊Q8×C79C22semidirect
53. #121×C79C22semidirect
55. C4×D4×C79C22semidirect
58. #117×C79C22semidirect
192. C79#3319semidirect
193. #555D79semidirect
215. C4⋊Q8C2×D79semidirect
225. #121C2×D79semidirect
229. C4×D4C2×D79semidirect
232. #117C2×D79semidirect