Finite Group Databasebeta

← #23774252

Subgroups — #23774252

Order 10112.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099141C211yesmaximal, characteristic, complemented
2#19098904C211yesmaximal, characteristic, complemented
3#19098887C211yesmaximal, characteristic, complemented
4#19098879C211yesmaximal, characteristic, complemented
5#19098874C211yesmaximal, characteristic, complemented
6#19098814C211yesmaximal, characteristic, complemented
7#19098807C211yesmaximal, characteristic, complemented
8#19098797C211yesmaximal, characteristic, complemented
9#19098790C211yesmaximal, characteristic, complemented
10#19098714C211yesmaximal, characteristic, complemented
11#19098706C211yesmaximal, characteristic, complemented
12#19098706C211yesmaximal, characteristic, complemented
13#19098697C211yesmaximal, characteristic, complemented
14#19098530C211yesmaximal, characteristic, complemented
15#535×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic, complemented
17C2×#11929612C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic, complemented
22C22×C79⋊C8C2211yescharacteristic, complemented
23#14579140C2211yescharacteristic
24#14579140C2211yescharacteristic, complemented
25#14579137—21no—
26#14579135C2211yescharacteristic
27#14579135C2211yescharacteristic, complemented
28#14579133—21no—
29#14579133—21no—
30#14579132—21no—
31C2×C4⋊Dic79C2211yescharacteristic, complemented
32#14579094C2211yescharacteristic, complemented
33#14579094C2211yescharacteristic, complemented
34#14579092C2211yescharacteristic, complemented
35#14579092C2211yescharacteristic, complemented
36#14579084C2211yescharacteristic, complemented
37#14579084C2211yescharacteristic, complemented
38#14579082C2211yescharacteristic
39#14579082C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic, complemented
43#14579081C2211yescharacteristic, complemented
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic, complemented
47C22⋊(C79⋊C8)C2211yescharacteristic, complemented
48C2×#41×C79C2211yescharacteristic
49C22×D4×C79C2211yescharacteristic
50#127×C79—21no—
51#124×C79—21no—
52#121×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic
54#121×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#120×C79—21no—
57#120×C79—21no—
58#117×C79C2211yescharacteristic
59#11929624—41no—
60#11929624—41no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C22×Dic79—21no—
67C2×C4×D79—21no—
68#11929612—41no—
69#11929612—41no—
70#11929609—41no—
71#11929609—41no—
72#11929608—41no—
73C2×C79⋊C8—41no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C4⋊Dic79—21no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87C24×C79—21no—
88#41×C79—41no—
89#41×C79—41no—
90C2×Q8×C79D411yescharacteristic
91C2×D4×C79—21no—
92C2×D4×C79—21no—
93C2×D4×C79—21no—
94C2×D4×C79—21no—
95C2×D4×C79—21no—
96C2×D4×C79—41no—
97C2×D4×C79—41no—
98C2×D4×C79D411yescharacteristic
99C2×D4×C79D411yescharacteristic
100C2×D4×C79D411yescharacteristic
101C2×D4×C79C2311yescharacteristic
102C2×D4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105C22×C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C22⋊C4×C79—21no—
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C42×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—42no—
117C23×C79—81no—
118C23×C79—81no—
119C23×C79C2×D411yescharacteristic
120C23×C79C2×D411yescharacteristic
121C23×C79C2×D411yescharacteristic
122C22×D79—21no—
123Q8×C79—41no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—21no—
127D4×C79—21no—
128D4×C79—41no—
129D4×C79—41no—
130D4×C79—41no—
131D4×C79—42no—
132D4×C79—81no—
133D4×C79—81no—
134D4×C79—81no—
135D4×C79—81no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79C2×D411yescharacteristic
145C2×C4×C79C2×D411yescharacteristic
146C2×C4×C79C2×D411yescharacteristic
147C2×C4×C79C2411yescharacteristic
148C22⋊D79—42no—
149C22⋊D79—81no—
150C22⋊D79—81no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—81no—
155D316—21no—
156D316—21no—
157C4×D79—42no—
158Dic158—21no—
159Dic158—21no—
160C79⋊C8—21no—
161C79⋊C8—21no—
162C79⋊C8—21no—
163C79⋊C8—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79—21no—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79—84no—
180C22×C79C22×D411yescharacteristic
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—41no—
184C4×C79—21no—
185C4×C79—21no—
186C4×C79—21no—
187C4×C79—41no—
188C4×C79—41no—
189C4×C79H(5,𝔽2)11yescharacteristic
190C4×C79H(5,𝔽2)11yescharacteristic
191Dic79—41no—
192Dic79—41no—
193Dic79—41no—
194C2×C79—41no—
195C2×C79—41no—
196C2×C79—41no—
197C2×C79—81no—
198C2×C79—81no—
199C2×C79#53411yescharacteristic
200C2×C79#57611yescharacteristic
201C2×C79#57711yescharacteristic
202D79—81no—
203#3198—791nomaximal, Sylow
204C79#319811yescharacteristic, complemented, Sylow
205#537—791no—
206#535D7911yescharacteristic, complemented
207#485—791no—
208#482—791no—
209#481—791no—
210#480—791no—
211#469—791no—
212#468—791no—
213#466—791no—
214#465—791no—
215#450—791no—
216#449—791no—
217#449—791no—
218#447—791no—
219#408—791no—
220C2×#41—791no—
221C2×#41C2×D7911yescharacteristic
222C22×D4C2×D7911yescharacteristic
223C2×SD16—791no—
224C2×SD16—791no—
225C2×D8—791no—
226C2×D8—791no—
227C2×M16—791no—
228C22×C8—791no—
229#127—21no—
230#124—21no—
231C22⋊Q8—791no—
232C22⋊Q8—791no—
233C22⋊Q8—1581no—
234#121—791no—
235#121—791no—
236#121—1581no—
237#121—1581no—
238#121—1581no—
239#121C2×D7911yescharacteristic
240#121C2×D7911yescharacteristic
241#121C2×D7911yescharacteristic
242#121C2×D7911yescharacteristic
243#120—21no—
244#120—21no—
245#117C2×D7911yescharacteristic
246C2×C4⋊C4—791no—
247#107—791no—
248#107—791no—
249#106—791no—
250#106—791no—
251#103—791no—
252#103—791no—
253#102—791no—
254#102—791no—
255#102—791no—
256#102—791no—
257#102—791no—
258#102—791no—
259C22⋊C8—791no—
260C22⋊C8—791no—
261C22⋊C8—791no—
262C22⋊C8—791no—
263C24—21no—
264#41—41no—
265#41—41no—
266#41—3161no—
267#41—3161no—
268C2×Q8—791no—
269C2×Q8C22⋊D7911yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—791no—
278C2×D4—1581no—
279C2×D4—1581no—
280C2×D4—1581no—
281C2×D4C22⋊D7911yescharacteristic
282C2×D4C22⋊D7911yescharacteristic
283C2×D4C22⋊D7911yescharacteristic
284C2×D4C22×D7911yescharacteristic
285C2×D4C22×D7911yescharacteristic
286C22×C4—1581no—
287C22×C4—1581no—
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7911yescharacteristic
290C22×C4C22×D7911yescharacteristic
291SD16—3161no—
292SD16—3161no—
293D8—3161no—
294D8—3161no—
295M16—3161no—
296C2×C8—3161no—
297C2×C8—791no—
298C2×C8—791no—
299C2×C8—791no—
300C2×C8—791no—
301C4⋊C4—791no—
302C4⋊C4—791no—
303C4⋊C4—1581no—
304C4⋊C4—1581no—
305C4⋊C4—1581no—
306C4⋊C4C22×D7911yescharacteristic
307C4⋊C4C22×D7911yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—1581no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C42—21no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—81no—
322C23—81no—
323C23—1581no—
324C23C2×C22⋊D7911yescharacteristic
325C23C2×C22⋊D7911yescharacteristic
326C23C2×C22⋊D7911yescharacteristic
327Q8—41no—
328Q8—1581no—
329Q8—1581no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—81no—
342D4—3162no—
343D4—6321no—
344D4—6321no—
345D4—1581no—
346D4—1581no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—3162no—
356C2×C4—6321no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4—1581no—
360C2×C4C2×C22⋊D7911yescharacteristic
361C2×C4C2×C22⋊D7911yescharacteristic
362C2×C4C2×C22⋊D7911yescharacteristic
363C2×C4C23×D7911yescharacteristic
364C8—1581no—
365C8—1581no—
366C8—1581no—
367C8—1581no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—84no—
384C22—3161no—
385C22—3161no—
386C22—3161no—
387C22C22×C22⋊D7911yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—3161no—
394C4—3161no—
395C4—3161no—
396C4#1457920611yescharacteristic
397C4#1457920611yescharacteristic
398C2—41no—
399C2—41no—
400C2—41no—
401C2—81no—
402C2—81no—
403C2—6321no—
404C2#1909912211yescharacteristic
405C2#1909936611yescharacteristic
406C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#535×C79C2
socleC22×C79C22×D4
hypercenter#535D79
hypocenterC79#3198
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#41 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #19099141C2semidirect
2. #19098904C2semidirect
3. #19098887C2semidirect
4. #19098879C2semidirect
5. #19098874C2semidirect
6. #19098814C2semidirect
7. #19098807C2semidirect
8. #19098797C2semidirect
9. #19098790C2semidirect
10. #19098714C2semidirect
11. #19098706C2semidirect
12. #19098706C2semidirect
13. #19098697C2semidirect
14. #19098530C2semidirect
15. #535×C79C2semidirect
16. C2×#11929624C22semidirect
21. C2×#11929608C22semidirect
22. C22×C79⋊C8C22semidirect
24. #14579140C22semidirect
27. #14579135C22semidirect
31. C2×C4⋊Dic79C22semidirect
32. #14579094C22semidirect
33. #14579094C22semidirect
34. #14579092C22semidirect
35. #14579092C22semidirect
36. #14579084C22semidirect
37. #14579084C22semidirect
42. #14579081C22semidirect
43. #14579081C22semidirect
46. C22⋊(C79⋊C8)C22semidirect
47. C22⋊(C79⋊C8)C22semidirect
204. C79#3198semidirect
206. #535D79semidirect