Finite Group Databasebeta

← #23775355

Subgroups — #23775355

Order 10112.

442 conjugacy classes of subgroups.

The subgroup lattice has 390 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#19098893C211yesmaximal, characteristic, complemented
4#19098881C211yesmaximal, characteristic, complemented
5#19098850C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098778C211yesmaximal, characteristic, complemented
9#19098706C211yesmaximal, characteristic, complemented
10#19098696C211yesmaximal, characteristic, complemented
11#19098673C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098562C211yesmaximal, characteristic, complemented
14C2×#14579081C211yesmaximal, characteristic, complemented
15#547×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C2×#11929612C2211yescharacteristic, complemented
19C2×#11929609C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic, complemented
22C22×C79⋊C8C2211yescharacteristic
23#14579149C2211yescharacteristic
24#14579146—21no—
25#14579140C2211yescharacteristic
26#14579135C2211yescharacteristic
27#14579134—21no—
28#14579129—21no—
29C4×D316C2211yescharacteristic
30C22⋊C4×D79—21no—
31#14579092C2211yescharacteristic, complemented
32#14579092C2211yescharacteristic, 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
48C2×#41×C79—21no—
49C4⋊Q8×C79C2211yescharacteristic, complemented
50#123×C79—21no—
51#123×C79—21no—
52C22⋊Q8×C79—21no—
53#121×C79C2211yescharacteristic
54#121×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56C4×D4×C79C2211yescharacteristic, complemented
57C2×C4⋊C4×C79C2211yescharacteristic
58C2×C4⋊C4×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—
88#41×C79—44no—
89C2×Q8×C79—21no—
90C2×D4×C79—21no—
91C2×D4×C79—21no—
92C2×D4×C79D411yescharacteristic
93C2×D4×C79C2311yescharacteristic
94C22×C4×C79—21no—
95C22×C4×C79—21no—
96C22×C4×C79—21no—
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C4⋊C4×C79—21no—
100C4⋊C4×C79—21no—
101C4⋊C4×C79—21no—
102C4⋊C4×C79D411yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79D411yescharacteristic
110C22⋊C4×C79D411yescharacteristic
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C23×C79C2×D411yescharacteristic
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—42no—
118C22×D79—42no—
119C22×D79—81no—
120Q8×C79—42no—
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×C79—42no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2×D411yescharacteristic
140C2×C4×C79C2411yescharacteristic
141C22⋊D79—42no—
142C22⋊D79—81no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145D316—21no—
146D316—21no—
147D316—21no—
148D316—42no—
149D316#4112yescomplemented
150C4×D79—42no—
151C4×D79—81no—
152Dic158—21no—
153Dic158—21no—
154C79⋊C8—21no—
155C79⋊C8—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79AGL(1,ℤ/8)12yes—
167C22×C79C22×D411yescharacteristic
168C2×D79—22no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—84no—
175C4×C79—21no—
176C4×C79—21no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79—41no—
182C4×C79C2×#4111yescharacteristic
183C4×C79H(5,𝔽2)11yescharacteristic
184Dic79—41no—
185Dic79—41no—
186C2×C79—22no—
187C2×C79—41no—
188C2×C79—81no—
189C2×C79#54611yescharacteristic
190C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
191C2×C79#57711yescharacteristic
192D79—42no—
193D79—81no—
194#3306—791nomaximal, Sylow
195C79#330611yescharacteristic, complemented, Sylow
196#547D7911yescharacteristic, complemented
197#546—791no—
198#489—791no—
199#483—791no—
200#481—791no—
201#476—791no—
202#469—791no—
203#465—791no—
204#463—791no—
205#449—791no—
206#447—791no—
207#442—791no—
208#435—791no—
209#417—791no—
210C2×#102—791no—
211C2×#41—21no—
212C2×#41—791no—
213C22×D4—791no—
214C2×SD16—791no—
215C2×D8—791no—
216C2×D8—791no—
217C2×M16—791no—
218C22×C8—791no—
219C4⋊Q8C2×D7911yescharacteristic, complemented
220#124—791no—
221#123—21no—
222#123—21no—
223#123—1581no—
224C22⋊Q8—21no—
225C22⋊Q8—791no—
226#121—791no—
227#121—1581no—
228#121C2×D7911yescharacteristic
229#121C2×D7911yescharacteristic, complemented
230#120—1581no—
231C4×D4—791no—
232C4×D4C2×D7911yescharacteristic
233C4×D4C2×D7911yescharacteristic, complemented
234C2×C4⋊C4C2×D7911yescharacteristic
235C2×C4⋊C4C2×D7911yescharacteristic, complemented
236C2×C22⋊C4—1581no—
237#106—791no—
238#106—791no—
239#106—791no—
240C4⋊C8—791no—
241#103—791no—
242#103—791no—
243#103—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251C22⋊C8—791no—
252C22⋊C8—791no—
253#97—791no—
254C24—1581no—
255#41—44no—
256#41—3161no—
257#41—1582no—
258C2×Q8—21no—
259C2×Q8—791no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—3161no—
263C2×D4—791no—
264C2×D4—791no—
265C2×D4—1582no—
266C2×D4—1581no—
267C2×D4—1581no—
268C2×D4—1581no—
269C2×D4C22⋊D7911yescharacteristic
270C2×D4C22×D7911yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—1581no—
275C22×C4—1581no—
276C22×C4C22×D7911yescharacteristic
277C22×C4C22×D7911yescharacteristic
278SD16—3161no—
279D8—3161no—
280D8—1582no—
281M16—3161no—
282C2×C8—3161no—
283C2×C8—791no—
284C2×C8—791no—
285C2×C8—791no—
286C2×C8—791no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—791no—
291C4⋊C4—1581no—
292C4⋊C4C22⋊D7911yescharacteristic
293C4⋊C4C22×D7911yescharacteristic
294C4⋊C4C22×D7911yescharacteristic
295C4⋊C4C22×D7911yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—1581no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C22⋊C4C22⋊D7911yescharacteristic
305C22⋊C4C22⋊D7911yescharacteristic
306C42C22×D7911yescharacteristic
307C23—21no—
308C23—3162no—
309C23—3162no—
310C23—6321no—
311C23—1581no—
312C23—1581no—
313C23C2×C22⋊D7911yescharacteristic
314C23C2×C22⋊D7911yescharacteristic
315Q8—42no—
316Q8—1581no—
317Q8—1581no—
318D4—22no—
319D4—21no—
320D4—21no—
321D4—42no—
322D4—42no—
323D4—3162no—
324D4—3162no—
325D4—792no—
326D4—6321no—
327D4—1581no—
328D4—1581no—
329D4—1581no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—3162no—
341C2×C4—6321no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4C2×C22⋊D7911yescharacteristic
345C2×C4C2×C22⋊D7911yescharacteristic
346C2×C4C2×C22⋊D7911yescharacteristic
347C2×C4C2×C22⋊D7911yescharacteristic
348C2×C4C23×D7911yescharacteristic
349C8—1581no—
350C8—1581no—
351C8—1581no—
352C8—1581no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—6324no—
367C22—1582no—
368C22#1457918712yes—
369C22C22×C22⋊D7911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—3161no—
378C4—3161no—
379C4#41×D7911yescharacteristic
380C4#1457920711yescharacteristic
381C2—22no—
382C2—41no—
383C2—81no—
384C2—3162no—
385C2—6321no—
386C2#1909920111yescharacteristic
387C2C2×#1457918711yescharacteristic
388C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#547×C79C2
socleC22×C79C22×D4
hypercenter#547D79
hypocenterC79#3306
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #19099209C2semidirect
2. #19098925C2semidirect
3. #19098893C2semidirect
4. #19098881C2semidirect
5. #19098850C2semidirect
6. #19098814C2semidirect
7. #19098790C2semidirect
8. #19098778C2semidirect
9. #19098706C2semidirect
10. #19098696C2semidirect
11. #19098673C2semidirect
12. #19098635C2semidirect
13. #19098562C2semidirect
14. C2×#14579081C2semidirect
15. #547×C79C2semidirect
18. C2×#11929612C22semidirect
21. C2×#11929608C22semidirect
31. #14579092C22semidirect
32. #14579092C22semidirect
33. #14579092C22semidirect
34. C4⋊(C79⋊C8)C22semidirect
35. #14579084C22semidirect
36. #14579084C22semidirect
37. #14579084C22semidirect
38. #14579082C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. #14579072C22semidirect
49. C4⋊Q8×C79C22semidirect
54. #121×C79C22semidirect
56. C4×D4×C79C22semidirect
58. C2×C4⋊C4×C79C22semidirect
149. D316#41semidirect
195. C79#3306semidirect
196. #547D79semidirect
219. C4⋊Q8C2×D79semidirect
229. #121C2×D79semidirect
233. C4×D4C2×D79semidirect
235. C2×C4⋊C4C2×D79semidirect